Foldable substrate

Abstract

The foldable substrate includes a first portion, a second portion, and a central portion therebetween. The first portion includes a substrate thickness and a first depth of compression. The central portion includes a fold region between the first transition region and the second transition region. The folding region is between the first folding surface region and the second folding surface region and does not include any teeth, and the local thickness of the folding region increases as the distance from the midline of the folding region decreases. In aspects, the folding region includes a plurality of teeth extending from the first folding surface area. In aspects, the local thickness of the fold region can be proportional to a cubic root of a sine of a fractional location as a function of a location along the fold width of the fold region that is scaled to vary over the fold width within a range of 0 to pi radians.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority under 35 U.S.C. §119 to U.S. Provisional Application No. 63 / 607,208, filed on December 7, 2023, and U.S. Provisional Application No. 63 / 436,965, filed on January 4, 2023, the contents of each of which are the basis of this application and are incorporated herein by reference in their entirety. Technical Field

[0003] The present disclosure relates generally to foldable substrates, and more particularly, to foldable substrates including portions having different thicknesses. Background Art

[0004] Glass substrates are generally used in, for example, display devices such as liquid crystal displays (LCDs), electrophoretic displays (EPDs), organic light emitting diode displays (OLEDs), plasma display panels (PDPs), and the like.

[0005] There is a desire to develop foldable versions of displays and foldable protective covers mounted on foldable displays. Foldable displays and covers should have good impact and puncture resistance. At the same time, the foldable displays and covers should have a small minimum bending radius (e.g., about 10 millimeters (mm) or less). However, plastic displays and covers with a small minimum bending radius often have poor impact and / or puncture resistance. In addition, conventional wisdom holds that ultra-thin glass sheets with a small minimum bending radius (e.g., about 75 microns (μm or micrometers) or thinner) often have poor impact and / or puncture resistance. In addition, thicker glass sheets with good impact and / or puncture resistance (e.g., greater than 125 microns) often have relatively large minimum bending radius (e.g., about 30 mm or more). Therefore, it is necessary to develop foldable devices with a small minimum bending radius and good impact and puncture resistance. Summary of the Invention

[0006] The present invention describes a foldable device comprising a foldable substrate, a foldable substrate, and a method of manufacturing a foldable device and a foldable substrate comprising a foldable substrate, wherein the foldable substrate comprises a first portion, a second portion, and a central portion located therebetween. The substrate and / or portions may comprise glass and / or ceramic portions that may provide good dimensional stability, a reduced incidence of mechanical instability, good impact resistance, and / or good puncture resistance. These portions may comprise glass and / or ceramic portions that include one or more compressive stress zones that may further improve impact resistance and / or puncture resistance. By providing a substrate comprising a glass and / or ceramic substrate, such a substrate may also improve impact resistance and / or puncture resistance while promoting good folding performance. In various aspects, the substrate thickness may be sufficiently large (e.g., from about 50 microns (micrometers or μm) to about 2 mm) to further enhance impact resistance and puncture resistance. Providing a foldable substrate including a central portion having a central thickness that is less than the thickness of the substrate (e.g., the first thickness of the first portion and / or the second thickness of the second portion) (e.g., less than about 10 μm or more) can achieve a smaller parallel plate spacing (e.g., about 10 millimeters (mm) or less, about 5 mm or less, or about 3 mm or less) based on the reduced thickness of the central portion, thereby achieving foldability and / or rollability of the foldable substrate and / or foldable device.

[0007] The inventors of the present application have determined that the local thickness profile of the folding zone described herein can unexpectedly enable a foldable substrate to fold into a substantially circular folded configuration (e.g., a folded length of approximately 1.6 times the corresponding parallel plate spacing). This is in contrast to the elliptical folding configuration of a substrate having a uniform thickness in the folding zone (e.g., a folded length of approximately 2.2 times the corresponding parallel plate spacing). Additionally, a substrate having a uniform thickness has a non-uniform stress distribution in the folded configuration, which may increase the incidence of device damage and / or destruction compared to the stress distribution of a foldable substrate having the thickness profile described herein when folded. Unexpectedly, the local increased thickness profile of the present disclosure can achieve a circular folding profile, thereby reducing the length of the folding zone and reducing stress concentration along the bend. For example, in various aspects, a smoothly varying surface can be provided in the folding zone to promote folding into a substantially circular folding configuration. Alternatively, in various aspects, a plurality of teeth (e.g., comprising substantially the thickness of the substrate) can increase the puncture resistance of the folding zone, while the folding zone (not comprising teeth) can include the local increased thickness profile discussed above, which can promote folding into a substantially circular folding configuration.

[0008] In various aspects, a foldable device and / or a foldable substrate may include one or more recesses, for example, a first central surface region recessed a first distance from a first major surface and / or a second central surface region recessed a second distance from a second major surface. Providing opposing first and second recesses can provide a central thickness that is less than the thickness of the substrate. Furthermore, providing opposing first and second recesses can reduce the maximum bending-induced strain of the foldable device, for example, between the central portion and the first and / or second portions, because the central portion including the central thickness can be closer to the mid-axis of the foldable device and / or foldable substrate than if only a single recess were provided. Furthermore, making the first distance substantially equal to the second distance can reduce the incidence of mechanical instability in the central portion, for example, because the foldable substrate is symmetrical about a plane including the midpoint of the substrate thickness and the central thickness. Furthermore, providing opposing first and second recesses can reduce the bending-induced strain of material positioned within the first and / or second recesses, compared to a single recess whose surface is recessed the sum of the first and second distances. Reducing the bending-induced strain of material positioned within the first and / or second recesses can enable a wider range of usable materials due to reduced strain requirements. For example, a harder and / or more rigid material can be positioned in the first groove, which can improve the impact resistance, puncture resistance, abrasion resistance, and / or scratch resistance of the foldable device. Additionally, controlling the properties of the first material positioned in the first groove and the second material positioned in the second groove can control the position of the intermediate axis of the foldable device and / or the foldable substrate, which can reduce (e.g., mitigate, eliminate) the occurrence of mechanical instability, device fatigue, and / or device damage.

[0009] In various aspects, a foldable device and / or a foldable substrate may include a first transition region attaching the central portion to the first portion and / or a second transition region attaching the central portion to the second portion. Providing a transition region with a smooth and / or monotonically decreasing (e.g., continuously decreasing) thickness can reduce stress concentrations in the transition region and / or avoid optical distortion. Providing a transition region of sufficient length (e.g., about 0.15 mm or longer, or about 0.3 mm or longer) can avoid optical distortion that can be generated by a sharp change in the thickness of the foldable substrate.

[0010] Some example aspects of the present disclosure are described below, and it should be understood that any features of the various aspects can be used alone or in combination with each other.

[0011] Aspect 1. A foldable substrate comprising:

[0012] a substrate thickness defined between a first major surface and a second major surface opposite the first major surface;

[0013] a first portion comprising the substrate thickness, a first compressive stress region extending from the first major surface to a first compressive depth, and a second compressive stress region extending from the second major surface to a second compressive depth;

[0014] a second portion comprising the substrate thickness, a third compressive stress region extending from the first major surface to a third compressive depth, and a fourth compressive stress region extending from the second major surface to a fourth compressive depth; and

[0015] a central portion located between the first portion and the second portion, the central portion including a folding region located between a first transition region and a second transition region, the first transition region and the second transition region including a central thickness less than a thickness of the substrate, the folding region including a first folding surface area and a second folding surface area opposite the first folding surface area, a first folding compressive stress region extending from the first folding surface area to a first folding compression depth, a second folding compressive stress region extending from the second folding surface area to a second folding compression depth, a folding width of the folding region defined between the first transition region and the second transition region, and a local thickness of the folding region in a direction of the substrate thickness between the first folding surface area and the second folding surface area increasing as a distance from a centerline of the folding region decreases,

[0016] The foldable substrate comprises a glass material or a ceramic material.

[0017] Aspect 2. A foldable substrate according to aspect 1, wherein the local thickness of the folding region varies between the center thickness and the substrate thickness, wherein the local thickness at the midline of the folding region is substantially equal to the substrate thickness.

[0018] Aspect 3. A foldable substrate according to any one of Aspects 1 to 2, wherein the local thickness of the fold zone is proportional to the cube root of the sine of the fractional position as a function of the position along the fold width of the fold zone, and the fractional position is scaled to vary in the range of 0 to π radians over the fold width of the fold zone.

[0019] Aspect 4. The foldable substrate according to any one of aspects 1 to 3, wherein the thickness of the first transition region decreases smoothly from the substrate thickness to the center thickness as the distance from the first portion increases.

[0020] Aspect 5. The foldable substrate according to any one of aspects 1 to 4, wherein the foldable substrate is symmetrical about a plane equidistant from the first major surface and the second major surface.

[0021] Aspect 6. A foldable substrate comprising:

[0022] a substrate thickness defined between a first major surface and a second major surface opposite the first major surface;

[0023] a first portion comprising the substrate thickness, a first compressive stress region extending from the first major surface to a first compressive depth, and a second compressive stress region extending from the second major surface to a second compressive depth;

[0024] a second portion comprising the substrate thickness, a third compressive stress region extending from the first major surface to a third compressive depth, and a fourth compressive stress region extending from the second major surface to a fourth compressive depth; and

[0025] a central portion located between the first portion and the second portion, the central portion including a fold zone located between a first transition region and a second transition region, the first transition region and the second transition region including a central thickness that is less than a thickness of the substrate, the fold zone including a plurality of teeth extending from a first fold surface region, the first fold surface region opposing a second fold surface region, a fold width of the fold zone defined between the first transition region and the second transition region, and a local thickness of the fold zone between the first fold surface region and the second fold surface region that does not include the plurality of teeth that increases as the distance from a centerline of the fold zone decreases,

[0026] The foldable substrate comprises a glass material or a ceramic material.

[0027] Aspect 7. The foldable substrate of aspect 6, wherein a tooth thickness of the teeth of the plurality of teeth is substantially equal to a thickness of the substrate.

[0028] Aspect 8. The foldable substrate of aspect 6, wherein the centerline of the folding region does not include a tooth of the plurality of teeth.

[0029] Aspect 9. A foldable substrate according to any one of Aspects 6 to 8, wherein a first width of a first tooth of the plurality of teeth is greater than a second width of a second tooth of the plurality of teeth, and the first tooth is closer to the center line of the folding zone than the second tooth is to the center line.

[0030] Aspect 10. A foldable substrate according to any one of Aspects 6 to 8, wherein a first width of a first tooth of the plurality of teeth is smaller than a second width of a second tooth of the plurality of teeth, and the first tooth is closer to the centerline of the folding zone than the second tooth is to the centerline.

[0031] Aspect 11. A foldable substrate according to any one of Aspects 6 to 10, wherein a first distance between a first pair of adjacent teeth in the plurality of teeth is less than a second distance between a second pair of adjacent teeth in the plurality of teeth, and the first pair of adjacent teeth is closer to the center line of the folding zone than the second pair of adjacent teeth is to the center line.

[0032] Aspect 12. A foldable substrate according to any one of Aspects 6 to 10, wherein a first distance between a first pair of adjacent teeth in the plurality of teeth is less than a second distance between a second pair of adjacent teeth in the plurality of teeth, and the first pair of adjacent teeth is closer to the center line of the folding zone than the second pair of adjacent teeth is to the center line.

[0033] Aspect 13. A foldable substrate according to any one of Aspects 6 to 12, wherein the local thickness of the fold zone is proportional to the cube root of the sine of the fractional position as a function of the position along the fold width of the fold zone, and the fractional position is scaled to vary in the range of 0 to π radians over the fold width of the fold zone.

[0034] Aspect 14. A foldable substrate according to any one of aspects 6 to 13, wherein the thickness of the first transition region not including the plurality of teeth decreases smoothly from the substrate thickness to the center thickness as the distance from the first portion increases.

[0035] Aspect 15. The foldable substrate of any one of aspects 1 to 14, wherein the folding region is symmetrical about a plane extending through the midline of the folding region and equidistant from the first portion and the second portion.

[0036] Aspect 16. The foldable substrate according to any one of aspects 1 to 15, wherein a folded configuration of the foldable substrate folded about the midline of the folding region in a parallel plate test is substantially circular.

[0037] Aspect 17. The foldable substrate of any one of aspects 1 to 15, wherein the fold width of the fold region is substantially equal to a minimum parallel plate spacing of the foldable substrate in a parallel plate test.

[0038] Aspect 18. The foldable substrate according to any one of aspects 1 to 17, wherein the foldable substrate achieves a parallel plate spacing of 1 mm to 6 mm.

[0039] Aspect 19. The foldable substrate according to any one of aspects 1 to 17, wherein the foldable substrate achieves a parallel plate spacing of 3 mm.

[0040] Aspect 20. The foldable substrate of any one of aspects 1 to 19, wherein a first transition width of the first transition region is from about 100 microns to about 5 millimeters.

[0041] Aspect 21. A foldable substrate according to any one of Aspects 1 to 20, wherein the first compressive stress region includes a first maximum compressive stress of approximately 400 MPa or greater, the second compressive stress region includes a second maximum compressive stress, the third compressive stress region includes a third maximum compressive stress of approximately 400 MPa or greater, and the fourth compressive stress region includes a fourth maximum compressive stress.

[0042] Aspect 22. The foldable substrate of aspect 21, wherein the second maximum compressive stress is about 400 MPa or greater, and the fourth maximum compressive stress is about 400 MPa or greater.

[0043] Aspect 23. The foldable substrate of any one of aspects 1 to 22, wherein the substrate thickness is in a range from about 50 microns to about 2 millimeters.

[0044] Aspect 24. The foldable substrate of any one of aspects 1 to 22, wherein the substrate thickness is in a range from about 100 microns to about 200 microns.

[0045] Aspect 25. The foldable substrate of any one of aspects 1 to 24, wherein the center thickness is in a range from about 25 microns to about 120 microns.

[0046] Aspect 26. The foldable substrate of any one of aspects 1 to 24, wherein the center thickness is in a range from about 25 microns to about 60 microns.

[0047] Aspect 27. The foldable substrate of any one of aspects 1 to 26, wherein the foldable substrate comprises a glass substrate.

[0048] Aspect 28. The foldable substrate of any one of aspects 1 to 26, wherein the foldable substrate comprises a ceramic substrate.

[0049] Aspect 29. A consumer electronic product comprising:

[0050] a housing comprising a front surface, a rear surface, and side surfaces;

[0051] an electrical assembly at least partially located within the housing, the electrical assembly including a controller, a memory, and a display, the display located at or adjacent to a front surface of the housing; and

[0052] a cover plate disposed above the display,

[0053] Wherein at least one of a portion of the housing or the cover comprises a foldable substrate according to any one of aspects 1 to 28. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The above and other features and advantages of various aspects of the present disclosure will be better understood when the following detailed description is read with reference to the accompanying drawings, in which:

[0055] Figure 1 is a schematic diagram of an example foldable device in a planar configuration according to various aspects, where the schematic diagram of the folded configuration can be as shown. Figure 6 As shown;

[0056] Figure 2 A foldable device according to various aspects includes a foldable substrate along Figure 1 A cross-sectional view taken along line 2-2;

[0057] Figure 3 A foldable device according to various aspects includes a foldable substrate along Figure 1 An alternative cross-sectional view along line 2-2 of FIG.

[0058] Figures 4A-4C 5A-5C show a foldable device along Figure 1 An alternative cross-sectional view along line 2-2 of FIG.

[0059] Figure 6 is a schematic diagram of an example foldable device according to aspects of the present disclosure in a folded configuration, wherein the schematic diagram of the planar configuration may be as shown in FIG. Figure 1 As shown;

[0060] Figure 7 is a test device used to determine the minimum parallel plate spacing of an example foldable substrate along Figure 6 Cross-sectional view of line 7-7, illustrating a foldable substrate that is in a planar configuration Figure 2 a folded configuration of the foldable device as shown;

[0061] Figure 8 is a test device used to determine the minimum parallel plate spacing of an example foldable substrate along Figure 6 Cross-sectional view of line 7-7, illustrating a foldable substrate that is in a planar configuration Figure 3 a folded configuration of the foldable device as shown;

[0062] Figure 9 Presentation Figure 2-3 , 4A-4C and 5A-5C (e.g., Examples 1-6 and Comparative Example AA), wherein the horizontal axis (e.g., x-axis) and the vertical axis (e.g., y-axis) correspond to the physical distance from the midpoint of the folded configuration in mm;

[0063] Figure 10 Presentation Figure 2-3 and 7-8, wherein the horizontal axis (e.g., x-axis) and the vertical axis (e.g., y-axis) correspond to the physical distance from the midpoint of the folded configuration of Examples 7-8 in mm; and

[0064] Figure 11 Presenting stress (in megapascals) on the left vertical axis (e.g., the left y-axis) as a function of the angular position (in radians and degrees, on the horizontal axis (e.g., the x-axis)) of the foldable substrate in the folded configuration for Example 9 and Comparative Example BB, while the right vertical axis (e.g., the right y-axis) corresponds to the local thickness in micrometers (μm);

[0065] Figure 12 is a schematic plan view of an example consumer electronic device according to various aspects;

[0066] Figure 13 yes Figure 12 a schematic perspective view of an example consumer electronic device;

[0067] Figure 14 is a schematic perspective diagram of a foldable consumer electronic product;

[0068] Figure 15 Presenting stress (in megapascals) on the vertical axis (e.g., y-axis) as a function of the angular position (in radians and degrees, on the horizontal axis (e.g., x-axis)) of the foldable substrate in the folded configuration for Example 12 and Comparative Examples AA and CC, while the right vertical axis (e.g., right y-axis) corresponds to the local thickness in micrometers (μm);

[0069] Figure 16 presents stress (in megapascals) on the vertical axis (e.g., y-axis) as a function of angular position (in radians and degrees, on the horizontal axis (e.g., x-axis)) of the foldable substrate in the folded configuration for Example 11 and Comparative Example AA, while the right vertical axis (e.g., right y-axis) corresponds to local thickness in micrometers (μm); and

[0070] Figure 17 The stress (in megapascals) on the vertical axis (e.g., y-axis) is presented as a function of the angular position (in radians and degrees, on the horizontal axis (e.g., x-axis)) of the foldable substrate in a folded configuration for Example 13 and Comparative Examples AA and DD, while the right vertical axis (e.g., right y-axis) corresponds to the local thickness in micrometers (μm).

[0071] Throughout this disclosure, the accompanying drawings are used to emphasize certain aspects. Therefore, unless otherwise explicitly stated, the relative sizes of different regions, parts, and substrates shown in the accompanying drawings should not be considered to be proportional to their actual relative sizes. DETAILED DESCRIPTION

[0072] Various aspects will now be described more fully hereinafter with reference to the accompanying drawings, in which example aspects are shown. Wherever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts.

[0073] Figure 1-3 , 4A-4C, 5A-5C, and 7-8 show views of foldable devices 101, 301, 403, 405, 407, 509, 511, 513, 601, and 801 including a foldable substrate 201 according to aspects of the present disclosure. Unless otherwise indicated, discussions of features of various aspects of one foldable device are equally applicable to corresponding features of any aspect of the present disclosure. For example, identical part numbers throughout the present disclosure may indicate that features identified in some aspects are identical to each other, and unless otherwise indicated, discussions of features identified in one aspect are equally applicable to features identified in any other aspect of the present disclosure.

[0074] Figure 2-3 , 4A-4C, and 5A-5C schematically illustrate example aspects of foldable devices 101, 301, 403, 405, 407, 509, 511, and 513 including a foldable substrate 201 according to aspects of the present disclosure in an unfolded (e.g., flat) configuration, while Figure 6-8 Example aspects of foldable devices 601 and 801 including a foldable substrate 201 according to aspects of the present disclosure are shown in a folded configuration. The foldable device 101 and the foldable substrate 201 include a first portion 221 and a second portion 231 with a central portion 281 and / or a folding region 271 positioned therebetween. Figure 3 、 4A -4C and 5A-5C, but it is understood that the central portion 281 and / or the folded area 271 can be attached to the same Figure 2 The corresponding parts shown are similar or identical to the first part 221 and / or the second part 231. Although not shown, it should be understood that the foldable substrate can be combined with one or more polymer parts, adhesive layers, coatings and / or display devices to form a foldable device.

[0075] Throughout this disclosure, reference is made to Figure 1, the width 103 of the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601 and / or 801 is taken to be the dimension of the foldable device taken between opposite edges of the foldable device in the direction 104 of the folding axis 102 of the foldable device, where the direction 104 also includes the direction of the width 103. Furthermore, throughout this disclosure, the length 105 of the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 is referred to as a dimension of the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 taken between opposite edges of the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 in a direction 106 that is perpendicular to the folding axis 102 of the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801. It should be understood that the direction 104 of the width 103 and / or the direction 106 of the length 105 can correspond to corresponding directions in the foldable substrate 201. In various aspects, such as Figure 1-3 As shown in FIG, the foldable device according to any aspect of the present disclosure may include a folding plane 109, which includes a folding axis 102 when the foldable device is in a planar configuration (e.g., see FIG. Figure 2-3 ). In other aspects, such as Figure 2-3 As shown in FIG, when the foldable device is in a planar configuration, the folding plane 109 can extend along the folding axis 102 in the direction of the substrate thickness 207 (e.g., see FIG. Figure 2-3 ). The folding plane 109 may include a central axis 107 of the foldable device. In various aspects, the foldable device may be folded about a folding axis 102 extending in a direction 104 of the width 103 in a direction 111 (see Figure 1 ) to form a folded configuration (see, for example, Figure 7-8 , corresponding to Figure 2-3folding configuration of the planar configuration shown). As shown, the foldable device and / or the foldable substrate may include a single folding axis, such that the foldable device and / or the foldable substrate can include a bifold, wherein, for example, the foldable device and / or the foldable substrate can be folded in half. In other aspects, the foldable device and / or the foldable substrate may include two or more folding axes, wherein each folding axis includes a corresponding central portion similar to or identical to the central portion 281 and / or folding zone 271 discussed herein. For example, providing two folding axes can enable the foldable device and / or the foldable substrate to include a trifold, wherein, for example, the foldable device and / or the foldable substrate can be folded into a first portion 221, a second portion 231, and a third portion similar to or identical to the first portion or the second portion, wherein a central portion 281, a folding zone 271, and another central portion similar to or identical to the central portion and / or folding zone are positioned between the first portion and the second portion, and between the second portion and the third portion, respectively.

[0076] The foldable substrate 201 may include a glass substrate and / or a ceramic substrate having a pencil hardness of 8H or higher, for example, 9H or higher. As used herein, pencil hardness is measured using ASTM D 3363-20 standard lead pencils. Providing a glass foldable substrate and / or a ceramic foldable substrate can enhance puncture resistance and / or impact resistance.

[0077] In various aspects, the foldable substrate 201 may include a glass substrate. As used herein, "glass" includes both glass and glass ceramics, wherein the glass ceramic has one or more crystalline phases and an amorphous residual glass phase. A glass material (e.g., a glass substrate) may include an amorphous material (e.g., glass) and optionally one or more crystalline materials (e.g., ceramics). Amorphous materials and glass materials may be strengthened. As used herein, the term "strengthening" may refer to a material that has been chemically strengthened, for example, by exchanging smaller ions with larger ions in the substrate surface, as discussed below. However, other strengthening methods, such as thermal tempering, or the mismatch of thermal expansion coefficients between parts of the substrate may be utilized to generate compressive stress and a central tension zone, thereby forming a strengthened substrate. Regardless of whether lithium oxide is contained, exemplary glass materials include soda-lime glass, alkali-aluminosilicate glass, alkali-containing borosilicate glass, alkali-containing aluminum borosilicate glass, alkali-containing phosphosilicate glass, and alkali-containing aluminum phosphosilicate glass. In various aspects, the glass-based material may include alkali-containing glass or alkali-free glass, either of which may be lithium-free or lithium-free. In various aspects, the glass material can be alkali-free and / or include a low content of alkali metals (e.g., about 10 mol% or less of RO, where RO includes LiO, NaO, KO, or the more extensive list provided below). In one or more aspects, the glass material can include, in mole percent (mol%), SiO in a range of about 40 mol% to about 80 mol%, AlO in a range of about 5 mol% to about 30 mol%, BO in a range of 0 mol% to about 10 mol%, ZrO in a range of 0 mol% to about 5 mol%, PO in a range of 0 mol% to about 15 mol%, TiO in a range of 0 mol% to about 2 mol%, RO in a range of 0 mol% to about 20 mol%, and RO in a range of 0 mol% to about 15 mol%. As used herein, RO may refer to alkali metal oxides, for example, LiO, NaO, KO, RbO, and CsO. As used herein, RO may refer to MgO, CaO, SrO, BaO, and ZnO. In various aspects, the glass substrate may also optionally include 0 mol% to about 2 mol% of NaSO, NaCl, NaF, NaBr, KSO, KCl, KF, KBr, AsO, SbO, SnO, FeO, Mn ...Examples of suitable glass-ceramics may include Li2O-Al2O3-SiO2 (i.e., LAS) glass-ceramics, MgO-Al2O3-SiO2 (i.e., MAS) glass-ceramics, ZnO×Al2O3×nSiO2 (i.e., ZAS), and / or glass-ceramics containing a primary crystalline phase comprising a β-quartz solid solution, β-spodumene, cordierite, petalite, and / or lithium disilicate. The glass-ceramic substrate may be strengthened using a chemical strengthening process. In one or more aspects, the MAS-based glass-ceramic substrate may be strengthened in a Li2SO4 molten salt, wherein 2Li may be added. + With Mg 2+ exchange.

[0078] In various aspects, the foldable substrate 201 may include a ceramic substrate. As used herein, "ceramic" includes both ceramics and glass ceramics, wherein the glass ceramic has one or more crystalline phases and an amorphous residual glass phase. The ceramic material can be strengthened (e.g., chemically strengthened). In various aspects, the ceramic material can be formed by heating the glass material to form a ceramic (e.g., crystalline) portion. In other aspects, the ceramic material may include one or more nucleating agents that can promote the formation of a crystalline phase. In various aspects, the ceramic material may include one or more oxides, nitrides, oxynitrides, carbides, borides, and / or silicides. Example aspects of ceramic oxides include zirconium oxide (ZrO2), zirconium (ZrSiO4), alkali metal oxides (e.g., sodium oxide (Na2O)), alkaline earth metal oxides (e.g., magnesium oxide (MgO)), titanium dioxide (TiO2), hafnium oxide (Hf2O), yttrium oxide (Y2O3), iron oxide, beryllium oxide, vanadium oxide (VO2), fused silica, mullite (a mineral comprising a combination of aluminum oxide and silicon dioxide), and spinel (MgAl2O4). Example aspects of ceramic nitrides include silicon nitride (Si3N4), aluminum nitride (AlN), gallium nitride (GaN), beryllium nitride (Be3N2), boron nitride (BN), tungsten nitride (WN), vanadium nitride, alkaline earth metal nitrides (e.g., magnesium nitride (Mg3N2)), nickel nitride, and tantalum nitride. Example aspects of oxynitride ceramics include silicon oxynitride, aluminum oxynitride, and SiAlON (a combination of aluminum oxide and silicon nitride, which may have Si 12-m-n Al m+n O n N 16-n 、Si 6-n Al n O n N 8-n or Si 2-n Al n O 1+ n N 2-n, wherein m, n, and resulting subscripts are all non-negative integers. Example aspects of carbides and carbon-containing ceramics include silicon carbide (SiC), tungsten carbide (WC), iron carbide, boron carbide (B4C), alkali metal carbides (e.g., lithium carbide (Li4C3)), alkaline earth metal carbides (e.g., magnesium carbide (Mg2C3)), and graphite. Example aspects of borides include chromium boride (CrB2), molybdenum boride (Mo2B5), tungsten boride (W2B5), iron boride, titanium boride, zirconium boride (ZrB2), hafnium boride (HfB2), vanadium boride (VB2), niobium boride (NbB2), and lanthanum boride (LaB6). Example aspects of silicides include molybdenum disilicide (MoSi2), tungsten disilicide (WSi2), titanium disilicide (TiSi2), nickel silicide (NiSi), alkaline earth silicides (e.g., sodium silicide (NaSi)), alkali metal silicides (e.g., magnesium silicide (Mg2Si)), hafnium disilicide (HfSi2), and platinum silicide (PtSi).

[0079] Throughout this disclosure, elastic modulus (e.g., Young's modulus) and / or Poisson's ratio are measured using ISO 527-1:2019. Throughout this disclosure, Young's modulus of glass and ceramic materials is measured using the resonant ultrasonic spectroscopy technique described in ASTM E2001-13, entitled "Standard Guide for Resonant Ultrasound Spectroscopy for Defect Detection in Both Metallic and Non-metallic Parts." In various aspects, the elastic modulus of the foldable substrate 201 can be in the range of about 10 GPa to about 100 GPa, about 40 GPa to about 100 GPa, about 60 GPa to about 100 GPa, about 60 GPa to about 80 GPa, about 80 GPa to about 100 GPa, or any range or sub-range therebetween.

[0080] Unless otherwise indicated, transmittance values are measured using a BYK Haze-Gard Dual (BYK Gardner). In various aspects, the foldable substrate 201 can be optically transparent. As used herein, "optically transparent" or "optically clear" means an average transmittance of 70% or greater through a 1.0 mm thick sheet of material in the wavelength range of 400 nm to 700 nm. In various aspects, an "optically transparent material" or "optically clear material" can have an average transmittance of 75% or greater, 80% or greater, 85% or greater, or 90% or greater, 92% or greater, 94% or greater, or 96% or greater through a 1.0 mm thick sheet of material in the wavelength range of 400 nm to 700 nm. The average transmittance in the wavelength range of 400 nm to 700 nm is calculated by measuring the transmittance at integer wavelengths from about 400 nm to about 700 nm and averaging the measured values.

[0081] like Figure 2-3 As shown in , 4A-4C and 5A-C, the foldable device 101, 301, 403, 405, 407, 509, 511 and / or 513 includes a foldable substrate 201, which includes a first major surface 203 and a second major surface 205 opposite to the first major surface 203. Figure 2-3 As shown in , 4A-4C and 5A-5C, the first major surface 203 can extend along the first plane 204. The second major surface 205 can extend along the second plane 206. In various aspects, as Figure 3 As shown, the second major surface 205 may be discontinuous, for example, divided into a plurality of surfaces having a plurality of teeth 311 separated by a corresponding plurality of grooves. Figure 3 、 4A -4C and 5A-5C, the center portion 281 and / or the folded area 271 may be attached to Figure 2The substrate 204 may be formed on a first portion 221 and / or a second portion 231 that are similar or identical to the corresponding portions shown. In various aspects, as shown, the second plane 206 may be parallel to the first plane 204. As used herein, the substrate thickness 207 may be defined between the first major surface 203 and the second major surface 205 as the distance between the first plane 204 and the second plane 206. In various aspects, the substrate thickness 207 can be about 10 micrometers (μm) or greater, about 25 μm or greater, about 40 μm or greater, about 50 μm or greater, about 60 μm or greater, about 70 μm or greater, about 80 μm or greater, about 90 μm or greater, about 100 μm or greater, about 125 μm or greater, about 150 μm or greater, about 200 μm or greater, about 300 μm or greater, about 2 millimeters (mm) or less, about 1 mm or less, about 800 μm or less, about 500 μm or less, about 300 μm or less, about 200 μm or less, about 180 μm or less, or about 160 μm or less. In various aspects, the substrate thickness 207 can be in the range of about 10 μm to about 2 mm, about 25 μm to about 2 mm, about 40 μm to about 2 mm, about 50 μm to about 2 mm, about 60 μm to about 2 mm, about 70 μm to about 2 mm, about 70 μm to about 1 mm, about 70 μm to about 800 μm, about 80 μm to about 500 μm, about 90 μm to about 500 μm, about 100 μm to about 200 μm, about 125 μm to about 200 μm, about 150 μm to about 200 μm, about 150 μm to about 160 μm, or any range or sub-range therebetween.

[0082] like Figure 2 As shown in FIG, the first portion 221 of the foldable substrate 201 may include a first surface area 223 and a second surface area 225 opposite to the first surface area 223. Figure 2The foldable device 101 of FIG. 1 depicts a first portion 221, with the understanding that, unless otherwise noted, such description of the first portion 221 also applies to any aspect of the present disclosure. In various aspects, as shown, the first surface area 223 can comprise a flat surface, and / or the second surface area 225 of the first portion 221 can comprise a flat surface. In other aspects, as shown, the second surface area 225 can be parallel to the first surface area 223. In various aspects, as shown, the first major surface 203 can comprise the first surface area 223, and the second major surface 205 can comprise the second surface area 225. In other aspects, the first surface area 223 can extend along the first plane 204. In other aspects, the second surface area 225 can extend along the second plane 206. In various aspects, the substrate thickness 207 can correspond to the distance between the first surface area 223 of the first portion 221 and the second surface area 225 of the first portion 221. In various aspects, the substrate thickness 207 can be substantially uniform across the first surface area 223. In various aspects, the first thickness defined between the first surface area 223 and the second surface area 225 can be within one or more of the ranges discussed above with respect to the substrate thickness 207. In other aspects, the first thickness can comprise the substrate thickness 207. In other aspects, the first thickness of the first portion 221 can be substantially uniform across its corresponding length (i.e., in the direction 106 of the length 105 of the foldable device) and / or its corresponding width (i.e., in the direction 104 of the width 103 of the foldable device) between the first surface area 223 and the second surface area 225. As discussed above, it should be understood that Figure 3 、 4A -4C and 5A-5C may also include a first portion 221 that is similar or identical to the first portion attached to the central portion 281 and / or the folding region 271 described above in this paragraph.

[0083] like Figure 2 As shown in FIG, the second portion 231 of the foldable substrate 201 may include a third surface area 233 and a fourth surface area 235 opposite to the third surface area 233. Figure 2The foldable device 101 of FIG. 1 depicts a second portion 231, with the understanding that, unless otherwise noted, such description of the second portion 231 also applies to any aspect of the present disclosure. In various aspects, as shown, the third surface area 233 of the second portion 231 may comprise a flat surface, and / or the fourth surface area 235 of the second portion 231 may comprise a flat surface. In other aspects, the third surface area 233 of the second portion 231 may be coplanar with the first surface area 223 of the first portion 221. In other aspects, as shown, the fourth surface area 235 may be parallel to the third surface area 233. In other aspects, the fourth surface area 235 of the second portion 231 may be coplanar with the second surface area 225 of the first portion 221. A second thickness may be defined between the third surface area 233 of the second portion 231 and the fourth surface area 235 of the second portion 231. In various aspects, the second thickness may be within the ranges discussed above with respect to the substrate thickness 207. In other aspects, the second thickness may comprise the substrate thickness 207. In other aspects, as shown, the second thickness can be substantially equal to the substrate thickness 207 (e.g., the first thickness). In various aspects, the second thickness of the second portion 231 can be substantially uniform between the third surface area 233 and the fourth surface area 235. As discussed above, it should be understood that Figure 3 、 4A -4C and 5A-5C may also include a second portion 231 that is similar or identical to the second portion attached to the central portion 281 and / or the folding region 271 described above in this paragraph.

[0084] like Figure 2 As shown in , the foldable substrate 201 may include a central portion 281 located between the first portion 221 and the second portion 231. In various aspects, as Figure 2-3 As shown in , the central portion 281 may include a folding area 271 including a first folding surface area 273 or 373 and / or a second folding surface area 275 opposite the first folding surface area 273 or 373. In various aspects, as Figure 2 As shown in , the center portion may also include a first transition zone 212, a second transition zone 242 and / or one or more concave surface areas 253, 255, 263 and / or 265, which attach the folding zone 271 to the first part 221 and / or the second part 231.

[0085] In various aspects, such as Figure 2As shown in , the central portion 281 may include a central thickness 217, which is defined as the minimum thickness of the foldable substrate 201 in the direction 202 of the substrate thickness 207 of the central portion 281 of the foldable substrate 201. Therefore, the central thickness 217 is less than the substrate thickness 207. For example, as Figure 2 , central thickness 217 is located between first concave surface region 253 and second concave surface region 255. Additionally, central thickness 217 can be located at other locations that can be symmetrical about folding plane 109, such as between third and fourth concave surface regions 263, 265 that can be symmetrical with first and second concave surface regions 253, 255 when reflected across folding plane 109.

[0086] In various aspects, the center thickness 217 can be about 1 μm or more, about 5 μm or more, about 10 μm or more, about 25 μm or more, about 40 μm or more, about 120 μm or less, about 100 μm or less, about 80 μm or less, about 60 μm or less, or about 50 μm or less. In various aspects, the center thickness 217 can be in the range of about 1 μm to about 120 μm, about 5 μm to about 120 μm, about 10 μm to about 120 μm, about 10 μm to about 120 μm, about 25 μm to about 120 μm, about 25 μm to about 100 μm, about 25 μm to about 80 μm, about 25 μm to about 60 μm, about 40 μm to about 60 μm, or any range or sub-range therebetween. In various aspects, the center thickness 217 can be about 10 μm or more, about 20 μm or more, about 30 μm or more, about 40 μm or more, about 50 μm or more, or about 60 μm or more less than the substrate thickness 207. In various aspects, the center thickness 217, expressed as a percentage of the substrate thickness 207, can be about 0.5% or more, about 1% or more, about 2% or more, about 5% or more, about 6% or more, about 40% or less, about 30% or less, about 20% or less, about 13% or less, about 10% or less, or about 8% or less. In various aspects, the center thickness 217, expressed as a percentage of the substrate thickness 207, can be in the range of about 0.5% to about 40%, about 0.5% to about 30%, about 0.5% to about 20%, about 0.5% to about 13%, about 1% to about 13%, about 1% to about 10%, about 2% to about 10%, about 2% to about 8%, about 5% to about 8%, about 6% to about 8%, or any range or sub-range therebetween.

[0087] In various aspects, such as Figure 2 As shown in , the first transition region 212 may include a first transition surface region 213 extending from a first surface region 223 and / or a second transition surface region 215 extending from a second surface region 225. In various aspects, as Figure 2As shown in , the thickness of the first transition region 212 can decrease from the substrate thickness 207 of the first portion 221 to the center thickness 217. In various aspects, as Figure 2 As shown in FIG, second transition region 242 may include a third transition surface region 243 extending from third surface region 233 and / or a fourth transition surface region 245 extending from fourth surface region 235. In other aspects, as shown, the thickness of first transition region 212 and / or second transition region 242 may decrease smoothly, monotonically, and / or smoothly and monotonically from substrate thickness 207 of first portion 221 to central thickness 217. As used herein, a smooth decrease in thickness refers to a smooth (e.g., gradual) change in cross-sectional area, rather than an abrupt (e.g., step-like) change in thickness. As used herein, a monotonically decreasing thickness in a direction refers to a decrease in thickness for a portion of time while remaining constant, decreasing, or both (i.e., the thickness decreases in the direction but never increases) for the remainder of the time. The smooth shape of the first and / or second transition regions may reduce optical distortion. A monotonically decreasing thickness of the first and / or second transition regions may reduce the incidence of mechanical instability and / or reduce the visibility of the transition regions.

[0088] In various aspects, such as Figure 2 As shown in FIG, first transition surface region 213 may include a linearly inclined surface extending from first surface region 223. In various aspects, although not shown, the first transition surface region may include an upwardly concave shape, for example, where the local slope of the first transition surface region smoothly transitions to first concave surface region 253, while the local slope of the first transition surface region is significantly different from the slope of first surface region 223. In various aspects, although not shown, the first transition surface region may include an S-shaped shape. In various aspects, although not shown, the local slope of the first transition surface region at the midpoint of the first transition surface region may be greater than where the first transition surface region meets first concave surface region 253 and where the first transition surface region meets first surface region 223. In various aspects, although not shown, the first transition surface region may include an upwardly convex shape, for example, where the local slope of the first transition surface region smoothly transitions to the slope of first surface region 223, while the local slope of the first transition surface region is significantly different from the slope of first concave surface region 253. In various aspects, the second transition surface region can include one of the shapes or characteristics discussed above in this paragraph for the first transition surface region. Figure 2 As shown in FIG, second transition surface region 215 may include a linearly inclined surface extending between second surface regions 225 (eg, extending from second surface regions 225 to second concave surface region 255).

[0089] In various aspects, such as Figure 2 As shown in FIG, third transition surface region 243 may include a linearly inclined surface extending from third surface region 233. In various aspects, although not shown, the third transition surface region may include an upwardly concave shape, for example, where the local slope of the first transition surface region smoothly transitions to the third concave surface region 263, while the local slope of the third transition surface region is significantly different from the slope of third surface region 233. In various aspects, although not shown, the third transition surface region may include an S-shaped shape. In various aspects, although not shown, the local slope of the third transition surface region at the midpoint of the third transition surface region may be greater than where the third transition surface region meets the third concave surface region 263 and where the second transition surface region meets the third surface region 233. In various aspects, although not shown, the third transition surface region may include an upwardly convex shape, for example, where the local slope of the third transition surface region smoothly transitions to the slope of the third surface region 233, while the local slope of the third transition surface region is significantly different from the slope of the third concave surface region 263. In various aspects, the fourth transition surface region can include one of the shapes or characteristics discussed above in this paragraph for the third transition surface region. Figure 2 As shown in FIG, fourth transition surface region 245 may include a linearly inclined surface extending from between fourth surface regions 235 (eg, from fourth surface region 235 to fourth concave surface region 265).

[0090] In various aspects, such as Figure 2As shown in the figure, the first concave surface area 253 can be recessed from the first major surface 203 by a first distance 257. In other aspects, the first distance 257 can be about 30 μm or more, about 40 μm or more, about 50 μm or more, about 70 μm or more, about 100 μm or more, about 1 mm or less, about 800 μm or less, about 500 μm or less, about 300 μm or less, about 100 μm or less, or about 60 μm or less. In other aspects, the first distance 257 can be in the range of about 30 μm to about 1 mm, from about 30 μm to about 800 μm, about 30 μm to about 500 μm, about 40 μm to about 300 μm, about 50 μm to about 100 μm, about 50 μm to about 60 μm, or any range or sub-range therebetween. In various aspects, as shown, the second concave surface area 255 can be recessed from the second major surface 205. In other aspects, the second concave surface region 255 can be recessed a distance from the second major surface 205 that is within one or more of the ranges discussed above in this paragraph and / or is equal to the first distance. In various aspects, as shown, the first concave surface region 253 and / or the second concave surface region 255 can be planar and / or parallel to the first plane 204 and / or the second plane 206 along which the first major surface 203 and / or the second major surface 205 extend, respectively.

[0091] In various aspects, such as Figure 2 As shown in FIG, third concave surface region 263 can be recessed from first major surface 203 by a second distance 267. In other aspects, second distance 267 can be within one or more of the ranges discussed above for first distance 257. In other aspects, second distance 267 can be substantially equal to first distance 257. In various aspects, as shown, fourth concave surface region 265 can be recessed from second major surface 205. In other aspects, fourth concave surface region 265 can be recessed from second major surface 205 by a distance within one or more of the ranges discussed above for first distance 257 and / or second distance 267. In various aspects, as shown, third concave surface region 263 and / or fourth concave surface region 265 can be planar and / or parallel to first plane 204 and / or second plane 206, along which first major surface 203 and / or second major surface 205 extend, respectively.

[0092] In various aspects, a first transition width 214 of the first transition region 212 is defined between a first portion 221 including the substrate thickness 207 and a fold region 271 where the local thickness increases (e.g., increases from a central thickness 217). In other aspects, the first transition width 214 can be about 100 μm or greater, about 200 μm or greater, about 300 μm or greater, about 500 μm or greater, about 700 μm or greater, about 1 mm or greater, about 5 mm or less, about 4 mm or less, about 3 mm or less, about 1 mm or less, about 800 μm or less, or about 600 μm or less. In other aspects, the first transition width 214 can be in the range of about 100 μm to about 5 mm, about 100 μm to about 4 mm, about 200 μm to about 3 mm, about 300 μm to about 1 mm, about 500 μm to about 1 mm, about 500 μm to about 800 μm, about 500 μm to about 600 μm, or any range or sub-range therebetween. In various aspects, the second transition width 244 of the second transition region 242 is defined between the second portion 231 including the substrate thickness 207 and the fold region 271 where the local thickness begins to increase (e.g., from the central thickness 217). In other aspects, the second transition width 244 can be within one or more of the ranges discussed above in this paragraph for the first transition width 214 and / or be substantially equal to the first transition width 214.

[0093] Providing opposing first grooves (e.g., between first concave surface region 253 and / or third concave surface region 263 and first plane 204) and second grooves (e.g., between second concave surface region 255 and / or fourth concave surface region 265 and second plane 206) can reduce bending-induced strain in any material positioned in the first groove and / or second groove, compared to a single groove in which the surface is concave by the sum of the first and second distances. Reducing bending-induced strain in the material positioned in the first groove and / or second groove can allow for a wider range of usable materials because the strain requirements of the material are reduced. For example, a harder and / or more rigid material can be positioned in the first groove, which can improve the impact resistance, puncture resistance, abrasion resistance, and / or scratch resistance of the foldable device.

[0094] In various aspects, such as Figure 2As shown in FIG, fold region 271 can be located between first transition region 212 and second transition region 242. In various aspects, as shown, fold region 271 includes a first fold surface area 273 and a second fold surface area 275 opposite first fold surface area 273. In other aspects, as shown, the local thickness of fold region 271 in direction 202 of substrate thickness 207 between first fold surface area 273 and second fold surface area 275 increases as the distance from the centerline of fold region 271 (e.g., fold plane 109) decreases. As used herein, "local thickness" refers to the thickness measured in direction 202 at a given location (in direction 106), rather than the average distance between surfaces. In other aspects, the local thickness of fold region 271 can range from a center thickness 217 (e.g., at a boundary with first transition region 212 and / or second transition region 242) to substantially the substrate thickness 207 (e.g., at fold plane 109—the centerline—of fold region 271). In other aspects, the local thickness of the fold region 271 varies with position in the direction 106 (e.g., along the fold width 274 of the fold region 271) in proportion to the cube root of the sine of the fractional position. In still other aspects, the fractional position is scaled to vary over the fold width 274 from 0 (at one end of the fold region 271—at the boundary between the first transition region 212) to π radians (at the other end of the fold region 271—at the boundary between the second transition region 242). As used herein, "fold width" is measured as the distance in the direction 106 between the fold region 271 and the boundary of the first transition region 212 and the second transition region 242. In other aspects, as shown, the foldable substrate 201 can be symmetrical about a plane that is equidistant from the first major surface 203 and the second major surface 205 (i.e., parallel to and equidistant from the first plane 204 and the second plane 206), and / or the foldable substrate 201 can be symmetrical about a plane that extends through the centerline of the fold region 271 (e.g., the fold plane 109) and is equidistant from the first portion 221 and the second portion 231. In other aspects, as discussed below, the foldable substrate 201 can be folded into a folded configuration (see Figure 7-8 ), the folded configuration is substantially circular (e.g., when folded about a centerline of the fold region 271 (e.g., fold plane 109) in a parallel plate test, as described below), and / or the portion of the substrate that is bent in the folded configuration can be substantially equal to a fold width 274 of the fold region 271 (e.g., the fold width 274 can be substantially equal to approximately 1.6 times the minimum parallel plate spacing of the foldable substrate 201 in a parallel plate test, as described below).

[0095] The inventors of the present application have determined that the thickness profile of the folding region 271 described herein (e.g., the profile of the local thickness) can unexpectedly enable the foldable substrate 201 to fold into a substantially circular folded configuration (e.g., see Figure 7-8 and / or in a parallel plate test). Without being bound by theory, a substrate having a uniform thickness in the substrate fold region will have an elliptical folded configuration, and its substrate fold length may be about 2.2 times the corresponding parallel plate spacing as measured in a parallel plate test (described below). In contrast, a foldable substrate of the present disclosure having a substantially circular configuration may have a fold length of about 1.6 times the corresponding parallel plate spacing. Additionally, a substrate having a uniform thickness may have a non-uniform stress distribution in the folded configuration, which may increase the incidence of device damage and / or failure compared to the stress distribution of a foldable substrate having the thickness profile described herein when folded.

[0096] Without being bound by theory, for a substrate bent at two points (as in a parallel plate test), the relationship between the change in position along the substrate (s) and the direction the substrate is facing (θ) is

[0097]

[0098] Where E is the elastic modulus (e.g., Young's modulus), I is the moment of inertia of the substrate cross section (perpendicular to the direction of the path s), and F is the applied bending force. For a rectangular cross section, I = wh 3 / 12, where w is the substrate width and h is the substrate thickness (or local thickness). To determine the local thickness profile that produces a constant variation in the folding zone (i.e., in a circular configuration where the radius ), the expression can be rearranged as

[0099]

[0100] The coordinate system can then be changed from angular directions (θ) to Cartesian coordinates (x) (e.g., in Figure 7-8 ), is

[0101]

[0102] This outline is Figure 2 The folding area 271 shown in FIG is reflected as a local thickness profile between the first folding surface area 273 and the second folding surface area 275 (e.g., where each surface has half the magnitude shown in the above equation). In addition, as discussed below, the shape of the first folding surface area 373 that does not include the plurality of teeth 311 is also based on this profile.

[0103] like Figure 2-3As shown in FIG, the local thickness profile increases toward the fold plane 109. In contrast, conventional thickness profiles are either constant or decrease toward the fold plane. Unexpectedly, the local thickness increase profile of the present disclosure enables a rounded fold profile, thereby reducing the length of the fold zone and reducing stress concentrations along the bend.

[0104] Figure 3 1 shows a cross-sectional view of a foldable device 301 including a plurality of teeth 311 according to aspects of the present disclosure. In various aspects, as Figure 3 As shown in FIG, the plurality of teeth 311 can extend from the first folding surface area 373, but in other aspects, the plurality of teeth can extend from both sides of the foldable substrate. In other aspects, as shown, the folding area 271 containing the plurality of teeth 311 is defined based on the local thickness profile of the first folding surface area 373 that does not contain the plurality of teeth 311, where the thickness is equal to the center thickness (e.g., Figure 2 The local thickness of the central thickness 217 shown in FIG is increased. In various aspects, as Figure 3 As shown in , the local thickness of the fold region 271 that does not include the plurality of teeth 311 (e.g., the profile of the first fold surface area 373) increases as the distance from the centerline of the fold region 271 (e.g., the fold plane 109) decreases. In other aspects, the local thickness of the fold region 271 (e.g., the local thickness profile) varies with position along the fold width 274 of the fold region 271, proportional to the cube root of the sine of the fractional position, as described above, where the fractional position is scaled to vary over the range of 0 to π radians over the fold width 274, as described above. In various aspects, as shown, the fold region 271 is symmetrical about a plane (e.g., the fold plane 109) that extends through the centerline of the fold region 271 (e.g., equidistant with respect to the first portion and the second portion). In various aspects, as Figure 8 As shown, in the parallel plate test (described below), the center line of the folding area (e.g., Figure 3 The folded configuration of the foldable substrate 201 folded about the folding plane 109 shown in FIG. 1 is substantially circular. In various aspects, as discussed above, in a parallel plate test (described below), the folded width 274 of the folding region 271 can be substantially equal to the minimum parallel plate spacing 711 of the foldable substrate 201 (see FIG. Figure 8 ).

[0105] In various aspects, such as Figure 3As shown in FIG, one or more of the teeth 313a-313e of the plurality of teeth 311 may include a local thickness (e.g., a surface of the one or more teeth may extend along the first plane 204) that is substantially equal to the substrate thickness 207 (e.g., within 5% or less), although in other aspects, the local thickness of one of the plurality of teeth may be less than the substrate thickness 207. In other aspects, as shown, all of the teeth 313a-313e of the plurality of teeth 311 may include substantially the same local thickness profile, and in still other aspects, the local thickness profile may include a local thickness 417 that is substantially equal to the substrate thickness 207 (see FIG. Figures 4A-4C and 5A-5C). In other aspects, as shown, the first folding surface area 373 can be opposite the second folding surface area, which can be part of the second major surface 205, but in other aspects, the second folding surface area can be a mirror image of the first folding surface area, or have a Figure 2 、 4A 5A-5C for the first folding surface area. In various aspects, as shown, the cross-sectional shape of one or more teeth 313a-313e in the plurality of teeth 311 can be substantially rectangular (e.g., linear), but in other aspects, the cross-sectional shape can be curved (e.g., elliptical), curvilinear, or a combination thereof.

[0106] Figure 3 、 4A -4C and 5A-5C illustrate various patterns of the plurality of grooves in the foldable devices 301, 403, 405, 407, 509, 511, and / or 513, which, for example, in some aspects can be combined with the shape of the first folding surface area 273 or 373 and / or the second folding surface area 275. In various aspects, as shown, one or more teeth of the plurality of teeth (e.g., teeth 313a-313e) include widths 315, 413a, 413c, 423a-b, 433a-b, 543a-b, 523a-b, and / or 533a-b. In other aspects, as shown, Figure 3 、 4C , 5A and 5B, the widths 315, 433a-b, 543a-b and / or 523a-b of all teeth (e.g., of the plurality of teeth) in the fold region 271 and / or the central portion 281 can be substantially the same. Alternatively, in other aspects, such as Figures 4A-4C As shown in 5C and 5D, different teeth in the plurality of teeth may have widths that vary as the distance between the teeth and the centerline varies. In still other aspects, as shown in Figures 4A-4BAs shown in , the width 413a or 423a of the first tooth can be greater than the width 413c or 423b of the second tooth, wherein the first tooth is closer to the centerline (e.g., the dashed line, the folding plane 109) than the second tooth. For example, the width of different teeth can decrease (e.g., monotonically decrease) as the distance from the centerline increases. Alternatively, in still other aspects, as Figure 5C As shown in the figure, the width 533a of the first tooth can be less than the width 533b of the second tooth, wherein the first tooth is closer to the center line (e.g., dotted line, folding plane 109) than the second tooth. For example, as shown in the figure, the width of different teeth can increase (e.g., monotonically) as the distance from the center line increases. In other aspects, the width of the one or more teeth can be about 10 μm or greater, about 20 μm or greater, about 30 μm or greater, about 40 μm or greater, about 50 μm or greater, about 70 μm or greater, about 100 μm or greater, about 500 μm or less, about 300 μm or less, about 200 μm or less, about 100 μm or less, about 80 μm or less, about 60 μm or less, or about 40 μm or less. In other aspects, the width of the one or more teeth can be in the range of about 10 μm to about 500 μm, about 10 μm to about 300 μm, about 20 μm to about 200 μm, about 30 μm to about 100 μm, about 40 μm to about 80 μm, about 40 μm to about 60 μm, or any range or sub-range therebetween.

[0107] In various aspects, such as Figure 3 、 4A -4C and 5A-5C, the distance 317, 415a-b, 425a-b, 435a-b, 545a-b, 525a-b and / or 535a-b can be defined between a pair of adjacent teeth. Figure 3 , groove 323b is located between the pair of adjacent teeth 313c and 313d. Similarly, grooves 323a and 323c are adjacent to teeth 313a and 313e, respectively. In other aspects, as Figure 3 and 5A As shown in , the distances 317 and 543a-b between a pair of adjacent teeth can be substantially the same for all adjacent pairs of teeth (e.g., of the plurality of teeth) in the fold region 271 and / or the central portion 281. Alternatively, in other aspects, such as Figures 4A-4C As shown in Figures 5B-5C, the distance between adjacent pairs of teeth in different pairs of adjacent teeth can vary as the distance between the adjacent pairs of teeth and the center line varies. In still other aspects, as shown in Figures 5B-5C, the distance between adjacent pairs of teeth in different pairs of adjacent teeth can vary as the distance between the adjacent pairs of teeth and the center line varies. Figures 4A-4CAs shown in , the distance 415a, 425a, or 435a between a first pair of adjacent teeth can be less than the distance 413b, 425b, or 435b between a second pair of adjacent teeth, where the first pair of adjacent teeth is closer to the centerline (e.g., the dashed line, the folding plane 109) than the second pair of adjacent teeth. For example, the distance between adjacent pairs of teeth in different pairs of adjacent teeth can increase (e.g., monotonically increase) as the distance between the adjacent pairs of teeth and the centerline increases. In yet other aspects, as Figures 5B-5C As shown in FIG, the distance 525a or 435a between a first pair of adjacent teeth can be greater than the distance 525b or 535b between a second pair of adjacent teeth, where the first pair of adjacent teeth is closer to the centerline (e.g., dashed line, folding plane 109) than the second pair of adjacent teeth. For example, the distance between adjacent pairs of teeth in different pairs of adjacent teeth can decrease (e.g., monotonically decrease) as the distance between the adjacent pairs of teeth from the centerline increases. In other aspects, the distance between a pair of adjacent teeth can be about 10 μm or more, about 20 μm or more, about 30 μm or more, about 40 μm or more, about 50 μm or more, about 70 μm or more, about 100 μm or more, about 500 μm or less, about 300 μm or less, about 200 μm or less, about 100 μm or less, about 80 μm or less, about 60 μm or less, or about 40 μm or less. In other aspects, the distance between a pair of adjacent teeth can be in the range of about 10 μm to about 500 μm, about 10 μm to about 300 μm, about 20 μm to about 200 μm, about 30 μm to about 100 μm, about 40 μm to about 80 μm, about 40 μm to about 60 μm, or any range or sub-range therebetween.

[0108] In various aspects, such as Figure 3 、 4A , 4B, 5A and 5C, the spacing (e.g., spacing 319) of the plurality of teeth (e.g., plurality of teeth 311) (i.e., the sum of the width of a tooth and the distance between the tooth and another tooth as a pair of adjacent teeth) can be substantially the same for all teeth (e.g., of the plurality of teeth) in the folding region 271 and / or the central portion 281. In other aspects, as Figure 3 and 5A As shown in , the spacing can be substantially the same by having teeth of substantially uniform width and substantially uniform distances between adjacent pairs of teeth. Alternatively, in other aspects, such as Figure 4A 、 4B As shown in FIG5 and FIG5C , the spacing can be substantially the same by varying the width of the teeth to offset variations in the distance between adjacent pairs of teeth. Figure 4C and 5B As shown in , the spacing of the plurality of teeth may vary as the distance from the center line (eg, folding plane 109) varies. For example, as shown in Figure 4C and 5B As shown in , the spacing can be changed by changing the distance between adjacent pairs of teeth, but the spacing can also be changed by changing the width of the teeth. Figure 4C As shown, the spacing at the first position can be smaller than the spacing at the second position, wherein the first position is closer to the centerline (e.g., folding plane 109) than the second position. For example, the spacing of the plurality of teeth can increase (e.g., monotonically increase) as the distance from the centerline (e.g., folding plane 109) increases. Alternatively, in other aspects, such as Figure 5B As shown in , the spacing at a first position can be greater than the spacing at a second position, where the first position is closer to the centerline (e.g., folding plane 109) than the second position. For example, the spacing of the plurality of teeth can decrease (e.g., monotonically) as the distance from the centerline (e.g., folding plane 109) increases. In various aspects, the spacing can be about 20 μm or more, about 30 μm or more, about 40 μm or more, about 50 μm or more, about 70 μm or more, about 100 μm or more, about 150 μm or more, 200 μm or more, about 1,000 μm or less, about 800 μm or less, about 600 μm or less, about 500 μm or less, about 300 μm or less, about 200 μm or less, about 100 μm or less, about 80 μm or less, about 60 μm or less, or about 40 μm or less. In various aspects, the pitch can be in the range of about 20 μm to about 1,000 μm, about 20 μm to about 800 μm, about 30 μm to about 600 μm, about 40 μm to about 500 μm, about 50 μm to about 300 μm, about 70 μm to about 200 μm, about 150 μm to about 200 μm, or any range or sub-range therebetween.

[0109] In various aspects, such as Figure 3 and 4A -4C, the centerline (e.g., the dashed line, folding plane 109) may not hit a tooth in the plurality of teeth (i.e., the location 411, 421, or 431 where the centerline hits is not a tooth). Figures 5A-5C As shown in , the centerline (e.g., the dotted line, folding plane 109) may hit a tooth in the plurality of teeth (i.e., the location 541, 521, or 531 where the centerline hits is a tooth). As discussed below with reference to examples, arranging the plurality of grooves so that the centerline does not hit a tooth in the plurality of teeth can reduce bending-induced stress on the foldable substrate. In various aspects, as Figures 4A-4C 5A-5C , the minimum thickness 419 of the foldable substrate (e.g., foldable devices 403 , 405 , 407 , 509 , 511 , and / or 513 ) can be substantially equal to the center thickness 217 .

[0110] In various aspects, although not shown, the cross-sectional shape of the teeth in the plurality of teeth can be rounded (e.g., at the top, rather than the angular corners shown herein). Providing rounded corners to the cross-sectional shape of the teeth in the plurality of teeth can reduce stress concentrations at the tooth corners, thereby reducing the maximum bending stress associated with folding to a predetermined parallel plate spacing, and / or increasing the reliability of folding the foldable substrate and / or foldable device. In addition, providing a plurality of teeth (e.g., comprising substantially the thickness of the substrate) can increase the puncture resistance of the folding region (e.g., because the thickness of the plurality of teeth is increased relative to the first folding surface area 373), and the folding region (not including teeth) can include the local thickness increase profile discussed above, which can facilitate folding into a substantially circular folding configuration. In various aspects, although not shown, the local thickness of the first folding surface area 373 between adjacent pairs of teeth can be substantially constant (as Figures 4A-4C and 5A-5C, rather than as shown Figure 3 ed (e.g., the fold plane 109), while the local thickness profile (excluding the plurality of teeth) can still increase with increasing distance from the centerline (e.g., the fold plane 109) (e.g., approximately the cube root of the sinusoidal profile discussed above), forming a stepped thickness profile (wherein the average and substantially constant local thickness between adjacent pairs of teeth has different local thickness values based on the distance of the adjacent pairs of teeth from the centerline). In other aspects, providing a plurality of substantially constant local thicknesses between corresponding adjacent pairs of teeth in the plurality of teeth can simplify manufacturing, for example, so that the local thickness between a pair of adjacent teeth can be formed in a single etching step (e.g., the portion corresponding to the pair of adjacent teeth is masked).

[0111] A predetermined parallel plate spacing can be achieved with a foldable device and / or foldable substrate using minimal force. In a parallel plate test, according to the present disclosure, the above-described Figure 7-8 The parallel plate device 701 is used to measure the "bending force" of a foldable device and / or a foldable substrate. Figure 2-3 ) into a curved (e.g., folded) configuration including a predetermined parallel plate spacing (e.g., see Figure 7-8In various aspects, the bending force, including the minimum force to bend the foldable device and / or the foldable substrate from a flat configuration to a parallel-plate spacing of 6 mm (e.g., when the maximum thickness of the foldable substrate is about 70 μm or greater), can be about 0.24 Newtons per millimeter width (N / mm) or less, about 0.22 N / mm or less, about 0.20 N / mm or less, about 0.18 N / mm or less, about 0.01 N / mm or greater, about 0.05 N / mm or greater, about 0.10 N / mm or greater, or about 0.15 N / mm or greater on the foldable substrate. In various aspects, the bending force comprising the minimum force to bend the foldable device and / or foldable substrate from a flat configuration to a parallel plate spacing of 6 mm (e.g., when the maximum thickness of the foldable substrate is about 70 μm or greater) can be in the range of about 0.01 N / mm to about 0.24 N / mm, about 0.05 N / mm to about 0.22 N / mm, about 0.10 N / mm to about 0.20 N / mm, about 0.15 N / mm to about 0.18 N / mm, or any range or sub-range therebetween. In various aspects, the bending force of a foldable substrate comprising a thickness profile associated with a first folding surface area having a maximum thickness according to aspects of the present disclosure can be 20% or more, 25% or more, or 30% or more, for example, in the range of about 20% to about 75%, about 25% to about 50%, or about 30% to about 40%, or any range or sub-range therebetween, than a comparative bending force of a substrate having a uniform thickness equal to the maximum thickness at the same parallel plate spacing (e.g., 6 mm).

[0112] Aspects of the present disclosure may include consumer electronic products. The consumer electronic product may include a front surface, a rear surface, and side surfaces. The consumer electronic product may also include an electrical component at least partially located within a housing. The electrical component may include a controller, a memory, and a display. The display may be located at or adjacent to the front surface of the housing. The display may include a liquid crystal display (LCD), an electrophoretic display (EPD), an organic light emitting diode (OLED) display, or a plasma display panel (PDP). The consumer electronic product may include a cover plate positioned above the display. In various aspects, at least one of a portion of the housing or the cover plate includes a foldable device discussed throughout this disclosure. The consumer electronic product may include a portable electronic device, such as a smartphone, a tablet computer, a wearable device, or a laptop computer.

[0113] The foldable devices disclosed herein can be incorporated into another article, such as an article with a display (or display article) (e.g., consumer electronics, including mobile phones, tablets, computers, navigation systems, wearable devices (e.g., watches), etc.), a building article, a transportation article (e.g., a car, train, airplane, marine vessel, etc.), an electrical article, or any article that may benefit from some transparency, scratch resistance, wear resistance, or a combination thereof. An exemplary article having any of the foldable devices disclosed herein is shown in FIG. Figure 12-13 The example method steps shown in are discussed in detail. Figure 12-13 A consumer electronic device 1200 is shown including a housing 1202 having a front surface 1204, a rear surface 1206, and side surfaces 1208. Although not shown, the consumer electronic device may include electrical components at least partially within or completely within the housing. For example, the electrical components may include at least a controller, a memory, and a display. Figure 12-13 , display 1210 can be located at or adjacent to the front surface of housing 1202. The consumer electronic device can include a cover substrate 1212 at or above the front surface of housing 1202, such that the cover substrate is above display 1210. In various aspects, at least one of cover substrate 1212 or a portion of housing 1202 can include any of the foldable devices disclosed herein, such as a foldable substrate.

[0114] and, Figure 14 A perspective view of a foldable consumer electronic product 1401 is schematically shown. According to aspects of the present disclosure, the consumer electronic product 1401 can include a foldable device 101, 301, 403, 405, 407, 509, 511, and / or 513 and / or a foldable substrate 201. As shown, the consumer electronic product 1401 can include a front surface 1403 and a side surface 1405. The consumer electronic product 1401 can include electronic components, including a display 1402 that can be viewed through and / or at the front surface 1403. In various aspects, as shown, the consumer electronic product 1401 can be folded along a direction 1412 to form a folded configuration with a first end 1427 and a second end 1437 (opposite the first end 1427) closer together (compared to the unfolded configuration). Additionally, as shown, consumer electronic product 1401 can be folded so that front surface 1403 and / or display 1402 face toward itself, but the consumer electronic product can be folded in the opposite direction of direction 1412 so that in the folded configuration, front surface 1403 is external to the consumer electronic product. Figure 1 As discussed, Figure 14The consumer electronic product 1401 shown in FIG can be folded about a folding axis 102, with a central portion 1481 located on the folding axis. The central portion 1481 can include the central portion 281 and / or the folding region 271 (e.g., as described above with reference to FIG). Figure 2-3 The central portion and / or folding area of the foldable device 101 and / or 301 as discussed. Figure 14 As shown, the center portion is located between a first portion 1421 including a first end 1427 and a second portion 1431 including a second end 1437. The position of the folding axis 102 can determine a first distance 1413 between the first end 1427 and the folding axis 102 (e.g., in direction 106) relative to a second distance 1415 between the second end 1437 and the folding axis 102 (e.g., in direction 1408). The total length of the consumer electronic product (e.g., Figure 1 The length 105 in ( 105 ) may be the sum of the first distance 1413 and the second distance 1415 . Also, as shown, the consumer electronic product is depicted in a folded or partially folded configuration, wherein the front surface 1403 forms an angle A about the fold axis 102 .

[0115] In various aspects, the foldable substrate 201 including a glass substrate and / or a ceramic substrate may include one or more compressive stress regions. In various aspects, the compressive stress regions may be generated by chemical strengthening. Chemical strengthening may include an ion exchange process in which ions in a surface layer are replaced or exchanged with larger ions having the same valence or oxidation state. Methods of chemical strengthening will be discussed later. Without being bound by theory, chemically strengthening the first portion 221, the second portion 231, the central portion 281 and / or the folding region 271 may achieve good impact resistance and / or puncture resistance (e.g., not being damaged when the pen is dropped from a height of about 15 centimeters (cm) or more, about 20 cm or more, or about 50 cm or more). Without being bound by theory, chemically strengthening the first portion 221, the second portion 231, the central portion 281 and / or the folding region 271 can achieve a smaller bend radius (e.g., less than about 10 mm or less, about 5 mm or less, or about 3 mm or less) because the compressive stress generated by the chemical strengthening can offset the tensile stress caused by the bending on the outermost surface of the substrate. The compressive stress zone can extend into a portion of the first portion and / or the second portion to a depth referred to as the depth of compression (DOC). As used herein, the depth of compression refers to the depth at which the stress in the chemically strengthened substrate and / or portion described herein changes from compressive stress to tensile stress. The depth of compression can be measured using a surface stress gauge or a scattered light polarizer (SCALP, where the values reported here use a SCALP-5 manufactured by Glasstress, Estonia), depending on the ion exchange treatment and the thickness of the article being measured. If the stress in the substrate and / or portion is generated by exchanging potassium ions into the substrate, the depth of compression is measured using a surface stress meter, such as an FSM-6000 (Orihara Industrial Co., Ltd. (Japan)). Unless otherwise specified, compressive stress (including surface CS) is measured by a surface stress meter (FSM) using a commercially available instrument manufactured by Orihara Corporation (e.g., FSM-6000). Surface stress measurements rely on accurate measurement of the stress-optical coefficient (SOC), which is related to the birefringence of the glass. Unless otherwise specified, SOC is measured according to Procedure C (Glass Disc Method) entitled "Standard Test Method for Measurement of Glass Stress-Optical Coefficient" described in ASTM Standard C770-16, the contents of which are incorporated herein by reference in their entirety. If the stress is generated by exchanging sodium ions into the substrate and the thickness of the article being measured exceeds about 400 μm, the depth of compression and central tension (CT) can be measured using SCALP.If the stress in the substrate and / or portion is generated by exchanging potassium and sodium ions into the substrate and / or portion and the thickness of the measured article exceeds about 400 μm, then the compression depth and CT are measured by SCALP. Without being bound by theory, the exchange depth of the sodium ions can indicate the compression depth, while the exchange depth of the potassium ions can indicate a change in the magnitude of the compressive stress (rather than a change from compressive stress to tensile stress). A graphical representation of the stress distribution can also be derived using a refractive near field (RNF; the RNF method is described in U.S. Patent No. 8,854,623, entitled "Systems and methods for measuring a profile characteristic of a glass sample," which is incorporated herein by reference in its entirety) method. When the graphical representation of the stress distribution is derived using the RNF method, the maximum central tension value provided by SCALP is utilized in the RNF method. The graphical representation of the stress distribution derived by the RNF is force balanced and calibrated based on the maximum central tension value provided by the SCALP measurement. As used herein, "depth of layer" (DOL) refers to the depth to which ions have been exchanged into the substrate and / or part (e.g., sodium, potassium). Throughout this disclosure, DOL is measured according to ASTM C-1422. Without wishing to be bound by theory, DOL is generally greater than or equal to the corresponding DOC. Through the present disclosure, when the maximum central tension cannot be directly measured by SCALP (e.g., when the thickness of the measured article is less than about 400 μm), the maximum central tension can be approximated by the product of the maximum compressive stress and the compression depth divided by the difference between the substrate thickness and twice the compression depth, where the compressive stress and compression depth are measured by FSM.

[0116] In various aspects, the first portion 221, including the glass portion and / or the ceramic portion, can include a first compressive stress zone at the first surface region 223, which can extend from the first surface region 223 to a first compression depth. In various aspects, the first portion 221, including the first glass and / or ceramic portion, can include a second compressive stress zone at the second surface region 225, which can extend from the second surface region 225 to a second compression depth. In various aspects, the first compression depth and / or the second compression depth, expressed as a percentage of the substrate thickness 207, can be about 5% or more, about 10% or more, about 12% or more, about 15% or more, about 30% or less, about 25% or less, about 22% or less, about 20% or less, about 17% or less, or about 15% or less. In various aspects, the first compression depth and / or the second compression depth, expressed as a percentage of the substrate thickness 207, can be in a range of about 5% to about 30%, about 10% to about 25%, about 10% to about 22%, about 12% to about 20%, about 12% to about 17%, about 15% to about 17%, or any range or sub-range therebetween. In various aspects, the first compression depth and / or the second compression depth can be about 1 μm or more, about 10 μm or more, about 15 μm or more, about 20 μm or more, about 25 μm or more, about 30 μm or more, about 200 μm or less, about 150 μm or less, about 100 μm or less, about 60 μm or less, about 45 μm or less, about 30 μm or less, or about 20 μm or less. In various aspects, the first compression depth and / or the second compression depth can be in the range of about 1 μm to about 200 μm, about 1 μm to about 150 μm, about 10 μm to about 100 μm, about 15 μm to about 600 μm, about 20 to about 45 μm, about 20 μm to about 30 μm, or any range or sub-range therebetween. By making the first portion including the first glass and / or ceramic portion include a first compression depth and / or a second compression depth in the range of about 1% to about 30% of the first thickness, good impact resistance and / or puncture resistance can be achieved.

[0117] In various aspects, the first compressive stress region can include a maximum first compressive stress. In various aspects, the second compressive stress region can include a maximum second compressive stress. In other aspects, the maximum first compressive stress and / or the maximum second compressive stress can be about 100 MPa (megapascals) or greater, about 300 MPa or greater, 400 MPa or greater, about 500 MPa or greater, about 600 MPa or greater, about 700 MPa or greater, about 1,500 MPa or less, about 1,200 MPa or less, about 1,000 MPa or less, or about 800 MPa or less. In other aspects, the maximum first compressive stress and / or the maximum second compressive stress can be in the range of about 100 MPa to about 1,500 MPa, about 100 MPa to about 1,200 MPa, about 300 MPa to about 1,200 MPa, about 300 MPa to about 1,000 MPa, about 400 MPa to about 1,000 MPa, about 500 MPa to about 1,000 MPa, about 600 MPa to about 900 MPa, about 700 MPa to about 800 MPa, or any range or sub-range therebetween. By having the maximum first compressive stress and / or the maximum second compressive stress in the range of about 100 MPa to about 1,500 MPa, good impact resistance and / or puncture resistance can be achieved.

[0118] In various aspects, the first portion 221 can include one or more alkali metal ions at a first depth associated with the first compressive stress region. In various aspects, the first portion 221 can include one or more alkali metal ions at a second depth associated with the second compressive stress region and the second compression depth. As used herein, the one or more alkali metal ions at a certain depth can include sodium, potassium, rubidium, cesium, and / or francium. In various aspects, the one or more alkali metal ions at the first depth and / or the one or more alkali metal ions at the second depth include potassium. In various aspects, the first depth and / or the second depth, expressed as a percentage of the substrate thickness 207, can be approximately 5% or greater, approximately 10% or greater, approximately 12% or greater, approximately 15% or greater, approximately 30% or less, approximately 25% or less, approximately 22% or less, approximately 20% or less, approximately 17% or less, or approximately 15% or less. In various aspects, the first layer depth and / or the second layer depth, expressed as a percentage of the substrate thickness 207, can be in the range of about 5% to about 30%, about 10% to about 25%, about 10% to about 22%, about 12% to about 20%, about 12% to about 17%, about 15% to about 17%, or any range or sub-range therebetween. In various aspects, the first layer depth of the one or more alkali metal ions and / or the second layer depth of the one or more alkali metal ions can be about 1 μm or more, about 10 μm or more, about 15 μm or more, about 20 μm or more, about 25 μm or more, about 30 μm or more, about 200 μm or less, about 150 μm or less, about 100 μm or less, about 60 μm or less, about 45 μm or less, about 30 μm or less, or about 20 μm or less. In various aspects, the first layer depth of one or more alkali metal ions and / or the second layer depth of one or more alkali metal ions can be in the range of about 1 μm to about 200 μm, about 1 μm to about 150 μm, about 10 μm to about 100 μm, about 15 μm to about 600 μm, about 20 μm to about 45 μm, about 20 μm to about 30 μm, or any range or sub-range therebetween.

[0119] In various aspects, the first portion 221 can include a first tensile stress region. In various aspects, the first tensile stress region can be located between the first compressive stress region and the second compressive stress region. In various aspects, the first tensile stress region can include a maximum first tensile stress. In other aspects, the maximum first tensile stress can be about 10 MPa or greater, about 20 MPa or greater, about 30 MPa or greater, about 100 MPa or less, about 80 MPa or less, or about 60 MPa or less. In other aspects, the maximum first tensile stress can be in the range of about 10 MPa to about 100 MPa, about 10 MPa to about 80 MPa, about 10 MPa to about 60 MPa, about 20 MPa to about 100 MPa, about 20 MPa to about 80 MPa, about 20 MPa to about 60 MPa, about 30 MPa to about 100 MPa, about 30 MPa to about 80 MPa, about 30 MPa to about 60 MPa, or any range or sub-range therebetween. Having a maximum first tensile stress in the range of about 10 MPa to about 100 MPa can achieve good impact resistance and / or puncture resistance while providing low energy consumption to fracture, as discussed below.

[0120] In various aspects, the second portion 231, including the second glass and / or ceramic portion, can include a third compressive stress zone at a third surface region 233, which can extend from the third surface region 233 to a third compression depth. In various aspects, the second portion 231, including the second glass and / or ceramic portion, can include a fourth compressive stress zone at a fourth surface region 235, which can extend from the fourth surface region 235 to a fourth compression depth. In various aspects, the third compression depth and / or the fourth compression depth, expressed as a percentage of the substrate thickness 207, can be within one or more of the ranges discussed above for the first compression depth and / or the second compression depth. In other aspects, the third compression depth can be substantially equal to the fourth compression depth. In various aspects, the third compression depth and / or the fourth compression depth can be within one or more of the ranges discussed above for the first compression depth and / or the second compression depth. By having the second portion, including the glass and / or ceramic portion, include a third compression depth and / or a fourth compression depth within a range of approximately 1% to approximately 30% of the substrate thickness, good impact resistance and / or puncture resistance can be achieved.

[0121] In various aspects, the third compressive stress region can include a maximum third compressive stress. In various aspects, the fourth compressive stress region can include a maximum fourth compressive stress. In other aspects, the maximum third compressive stress and / or the maximum fourth compressive stress can be within one or more of the ranges discussed above for the maximum first compressive stress and / or the maximum second compressive stress. By setting the maximum third compressive stress and / or the maximum fourth compressive stress within a range of about 100 MPa to about 1,500 MPa, good impact resistance and / or puncture resistance can be achieved.

[0122] In various aspects, the second portion 231 can include one or more alkali metal ions at a third depth associated with the third compressive stress region and the third compression depth. In various aspects, the second portion 231 can include one or more alkali metal ions at a fourth depth associated with the fourth compressive stress region and the fourth compression depth. In various aspects, the one or more alkali ions at the third depth and / or one or more of the one or more alkali ions at the fourth depth include potassium. In various aspects, the third depth and / or the fourth depth, expressed as a percentage of the substrate thickness 207, can be within one or more of the ranges discussed above for the first depth and / or the second depth expressed as a percentage of the substrate thickness 207. In various aspects, the third depth of the one or more alkali metal ions and / or the fourth depth of the one or more alkali metal ions can be the first depth and / or the second depth.

[0123] In various aspects, the second portion 231 can include a second tensile stress region. In various aspects, the second tensile stress region can be located between the third compressive stress region and the fourth compressive stress region. In various aspects, the second tensile stress region can include a maximum second tensile stress. In other aspects, the maximum second tensile stress can be within one or more of the ranges discussed above for the maximum first tensile stress. In various aspects, the maximum first tensile stress can be substantially equal to the maximum second tensile stress. Having the maximum second tensile stress within a range of about 10 MPa to about 100 MPa can achieve good impact resistance and / or puncture resistance while providing low-energy fracture, as discussed below.

[0124] In various aspects, the first compression depth can be substantially equal to the third compression depth. In various aspects, the second compression depth can be substantially equal to the fourth compression depth. In various aspects, the maximum first compressive stress can be substantially equal to the maximum third compressive stress. In various aspects, the maximum second compressive stress can be substantially equal to the maximum fourth compressive stress. In various aspects, the first layer depth of the one or more alkali metal ions can be substantially equal to the third layer depth of the one or more alkali metal ions. In various aspects, the second layer depth of the one or more alkali metal ions can be substantially equal to the fourth layer depth of the one or more alkali metal ions.

[0125] In various aspects, the central portion 281 and / or the fold region 271 can be one or more compressive stress regions. In other aspects, there can be a first fold compressive stress region extending from the first fold surface area 273 to a first fold compression depth, and / or there can be a second fold compressive stress region extending from the second fold surface area 275 to a second fold compression depth. In other aspects, the first fold compressive stress region and / or the second fold compressive stress region can be within the fold region 271 of the central portion 281 (e.g., can be coextensive with the first fold surface area 273 and / or the second fold surface area 275). In other aspects, the first fold compression depth and / or the second fold compression depth, expressed as a percentage of the central thickness 217 or a local thickness, can be within one or more of the ranges discussed above for the first compression depth and / or the second compression depth expressed as a percentage of the substrate thickness 207. In other aspects, the first fold compression depth and / or the second fold compression depth, expressed as a percentage of the center thickness 217 or the local thickness, can be about 1% or more, about 2% or more, about 5% or more, about 8% or more, about 10% or more, about 12% or more, about 20% or less, about 17% or less, about 15% or less, about 12% or less, about 10% or less, about 7% or less, or about 5% or less. For example, the first fold compression depth and / or the second fold compression depth, expressed as a percentage of the center thickness 217 or the local thickness, can be in the range of about 1% to about 20%, about 2% to about 17%, about 5% to about 15%, about 7% to about 10%, or any range or sub-range therebetween. In other aspects, the first fold compression depth can be substantially equal to the second fold compression depth. In other aspects, the first fold compression depth and / or the second fold compression depth can be within one or more of the ranges discussed above for the first compression depth and / or the second compression depth. In other aspects, the first fold compression depth and / or the second fold compression depth can be about 1 μm or greater, about 2 μm or greater, about 4 μm or greater, about 6 μm or greater, about 20 μm or less, about 15 μm or less, about 10 μm or less, or about 8 μm or less. For example, the first fold compression depth and / or the second fold compression depth can be in the range of about 1 μm to about 20 μm, about 2 μm to about 15 μm, about 4 μm to about 10 μm, about 6 μm to about 8 μm, or any range or sub-range therebetween. Good impact resistance and / or puncture resistance can be achieved by having the central portion and / or folding area including the glass and / or ceramic portion include a first fold compression depth and / or a second fold compression depth in the range of about 1% to about 30% (e.g., about 1% to about 20%) of the central thickness or local thickness.

[0126] In various aspects, the first fold compressive stress region can include a maximum first fold compressive stress. In various aspects, the second fold compressive stress region can include a maximum second fold compressive stress. In other aspects, the maximum first fold compressive stress and / or the maximum second fold compressive stress can be within one or more of the ranges discussed above for the maximum first compressive stress and / or the maximum second compressive stress. By having the maximum first fold compressive stress and / or the maximum second fold compressive stress within a range of about 100 MPa to about 1,500 MPa, good impact resistance and / or puncture resistance can be achieved.

[0127] In various aspects, the central portion 281 and / or the fold region 271 can include one or more alkali metal ions at a first folding layer depth associated with a first folding compressive stress region and a first folding compression depth. In various aspects, the central portion 281 and / or the fold region 271 can include one or more alkali metal ions at a second folding layer depth associated with a second folding compressive stress region and a second folding compression depth. In various aspects, one or more of the one or more alkali ions at the first folding layer depth and / or one or more of the one or more alkali ions at the second folding layer depth include potassium. In various aspects, the first folding layer depth and / or the second folding layer depth, expressed as a percentage of the central thickness 217 or a local thickness, can be within one or more of the ranges discussed above for the first layer depth and / or the second layer depth expressed as a percentage of the substrate thickness 207.

[0128] In various aspects, the first fold depth and / or the second fold depth, expressed as a percentage of the central thickness 217 or the local thickness, can be about 1% or more, about 2% or more, about 5% or more, about 8% or more, about 10% or more, about 12% or more, about 20% or less, about 17% or less, about 15% or less, about 12% or less, about 10% or less, about 7% or less, or about 5% or less. For example, the first fold depth and / or the second fold depth, expressed as a percentage of the central thickness 217 or the local thickness, can be in the range of about 1% to about 20%, about 2% to about 17%, about 5% to about 15%, about 7% to about 10%, or any range or sub-range therebetween. In other aspects, the first fold depth can be substantially equal to the second fold depth. In other aspects, the first fold depth and / or the second fold depth can be within one or more of the ranges discussed above for the first layer depth and / or the second layer depth. In other aspects, the first folding layer depth and / or the second folding layer depth can be about 1 μm or more, about 2 μm or more, about 4 μm or more, about 6 μm or more, about 20 μm or less, about 15 μm or less, about 10 μm or less, or about 8 μm or less. For example, the first folding layer depth and / or the second folding layer depth can be in the range of about 1 μm to about 20 μm, about 2 μm to about 15 μm, about 4 μm to about 10 μm, about 6 μm to about 8 μm, or any range or sub-range therebetween.

[0129] In various aspects, the central portion 281 and / or the fold region 271 can include a fold tensile stress region. In various aspects, the fold tensile stress region can be located between the first fold compressive stress region and the second fold compressive stress region. In various aspects, the fold tensile stress region can include a maximum fold tensile stress. In other aspects, the maximum fold tensile stress can be about 125 MPa or greater, about 150 MPa or greater, about 200 MPa or greater, about 375 MPa or less, about 300 MPa or less, or about 250 MPa or less. In other aspects, the maximum folding tensile stress can be in the range of about 125 MPa to about 375 MPa, about 125 MPa to about 300 MPa, about 125 MPa to about 250 MPa, about 150 MPa to about 375 MPa, about 150 MPa to about 300 MPa, about 150 MPa to about 250 MPa, about 200 MPa to about 375 MPa, about 200 MPa to about 300 MPa, about 200 MPa to about 250 MPa, or any range or sub-range therebetween. Having the maximum folding tensile stress in the range of about 125 MPa to about 375 MPa can achieve a smaller minimum bend radius.

[0130] Figure 6-8Aspects of a foldable device 601 and / or 801 according to aspects of the present disclosure are schematically shown in a folded configuration. Figure 7 As shown in , the foldable device 601 is folded so that the second main surface 205 of the foldable substrate 201 is inside the folded foldable device 601. For example, the foldable device 101 can be folded to form the foldable device 601. For example, the display can be located on the side of the second main surface 205, and the audience can view the display from the side of the first main surface 203. Alternatively, the display can be located on the side of the first main surface 203, and the audience can view the display from the side of the second main surface 205. Figure 8 As shown in FIG, foldable device 801 is folded so that second major surface 205 of foldable substrate 201 is inside folded foldable device 801. For example, foldable device 301 can be folded to form foldable device 801. For example, a display can be located on a side of second major surface 205, and a viewer can view the display from a side of first major surface 203. Alternatively, a display can be located on a side of first major surface 203, and a viewer can view the display from a side of second major surface 205.

[0131] As used herein, "foldable" encompasses fully folding, partially folding, bending, flexing, or a combination thereof. As used herein, the terms "break," "destroy," and the like refer to breaking, damage, delamination, or crack propagation. Similarly, if a foldable device is maintained at a parallel plate spacing "X" for 24 hours at approximately 85°C and approximately 85% relative humidity without being damaged, then the foldable device is said to achieve, have, or include a parallel plate spacing "X."

[0132] As used herein, the "parallel plate spacing" of a foldable device and / or foldable substrate is the distance measured using the parallel plate device 701 (see FIG. Figure 6-8 ) is measured, the parallel plate device includes a pair of parallel rigid stainless steel plates 703, 705, including a first rigid stainless steel plate 703 and a second rigid stainless steel plate 705. When measuring the foldable substrate 201 (for example, the foldable substrate 201 is composed of Figure 2-3 When the "parallel plate spacing" of the foldable device 101 and / or 301) is shown in Figure 7 and 8As shown in , the foldable substrate 201 is placed between the pair of plates 703 and 705 so that the first major surface 203 is in contact with the pair of plates 703 and 705. When determining the "parallel plate spacing", the distance between the parallel plates is reduced at a rate of 50 μm / second until the parallel plate spacing 711 is equal to the "parallel plate spacing" to be tested. Then, the parallel plates are maintained at the "parallel plate spacing" to be tested for 24 hours at approximately 85°C and approximately 85% relative humidity. As used herein, the "minimum parallel plate spacing" is the minimum parallel plate spacing that the foldable device can withstand without being damaged under the conditions and configurations described above.

[0133] In various aspects, the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 and / or the foldable substrate 201 can achieve a parallel plate spacing of 100 mm or less, 50 mm or less, 20 mm or less, 10 mm or less, 5 mm or less, 4 mm or less, 3 mm or less, 2 mm or less, or 1 mm or less. In other aspects, the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 and / or the foldable substrate 201 can achieve a parallel plate spacing of 50 millimeters (mm), or 20 mm, or 10 mm, 8 mm, 6 mm, 5 mm, 4 mm, 3 mm, 2 mm, or 1 mm. In various aspects, the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601 and / or 801 and / or the foldable substrate 201 may include a minimum parallel plate spacing of about 40 mm or less, about 20 mm or less, about 10 mm or less, about 8 mm or less, about 6 mm or less, about 5 mm or less, about 4 mm or less, about 3 mm or less, about 2 mm or less, about 1 mm or less, about 1 mm or more, about 2 mm or more, about 3 mm or more, about 4 mm or more, about 5 mm or more, or about 10 mm or more. In various aspects, the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 and / or the foldable substrate 201 can include a minimum parallel plate spacing in the range of about 1 mm to about 40 mm, about 1 mm to about 20 mm, about 1 mm to about 10 mm, about 1 mm to about 5 mm, about 2 mm to about 3 mm, or any range or sub-range therebetween. In various aspects, the foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 and / or the foldable substrate 201 can achieve a minimum parallel plate spacing in the range of about 2 mm to about 40 mm, about 2 mm to about 20 mm, about 2 mm to about 10 mm, about 3 mm to about 10 mm, about 3 mm to about 8 mm, about 3 mm to about 6 mm, about 4 mm to about 5 mm, or any range or sub-range therebetween.

[0134] In various aspects, the folded width 274 of the folding region 271 of the foldable substrate 201 can be about 1 times or more, about 1.1 times or more, about 1.3 times or more, about 1.5 times or more, about 1.6 times or more, about 1.8 times or more, about 2 times or more, about 2.2 times or more, about 3 times or less, about 2.5 times or less, about 2 times or less, about 1.8 times or less, or about 1.5 times or less of the minimum parallel plate spacing. In various aspects, the folded width 274 of the folding region 271 of the foldable substrate 201, expressed as a multiple of the minimum parallel plate spacing, can be in the range of about 1 times to about 3 times, about 1.1 times to about 2.5 times, about 1.3 times to about 2.2 times, about 1.5 times to about 2 times, about 1.6 times to about 1.8 times, or any range or sub-range therebetween. Without being bound by theory, the length of the folded portion between the parallel plates in the circular configuration can be about 1.6 times the parallel plate spacing 711. Without being bound by theory, the length of the curved portion between the parallel plates in the elliptical configuration can be about 2.2 times the parallel plate spacing 711. In various aspects, the folded width 274 of the fold region 271 of the foldable substrate 201 can be about 1 mm or more, about 3 mm or more, about 5 mm or more, about 6 mm or more, about 8 mm or more, about 10 mm or more, about 15 mm or more, about 20 mm or more, about 100 mm or less, about 60 mm or less, about 50 mm or less, about 40 mm or less, about 35 mm or less, about 30 mm or less, about 25 mm or less, about 20 mm or less, about 15 mm or less, or about 10 mm or less. In various aspects, the folded width 274 of the folding region 271 of the foldable substrate 201 can be in the range of about 1 mm to about 100 mm, about 2 mm to about 60 mm, about 3 mm to about 50 mm, about 5 mm to about 40 mm, about 6 mm to about 35 mm, about 6 mm to about 30 mm, about 8 mm to about 25 mm, about 8 mm to about 20 mm, about 10 mm to about 15 mm, or any range or sub-range therebetween. Having the folded width within the ranges set forth above in this paragraph can facilitate folding of the foldable device without breaking.

[0135] As used herein, a central width of the central portion 281 of the foldable substrate 201 is defined between the first portion 221 and the second portion 231 in the direction 106 of the length 105. In various aspects, the central width of the central portion 281 of the foldable substrate 201 can extend from the first portion 221 to the second portion 231. In various aspects, the central width of the central portion 281 of the foldable substrate 201 can be about 1.4 times or more, about 1.6 times or more, about 2 times or more, about 2.2 times or more, about 3 times or less, or about 2.5 times or less of the minimum parallel plate spacing. In various aspects, the central width of the central portion 281 of the foldable substrate 201, expressed as a multiple of the minimum parallel plate spacing, can be in the range of about 1.4 times to about 3 times, about 1.6 times to about 3 times, about 1.6 times to about 2.5 times, about 2 times to about 2.5 times, about 2.2 times to about 2.5 times, about 2.2 times to about 3 times, or any range or sub-range therebetween. In various aspects, the central width of the central portion 281 of the foldable substrate 201 can be about 1 mm or greater, about 3 mm or greater, about 5 mm or greater, about 8 mm or greater, about 10 mm or greater, about 15 mm or greater, about 20 mm or greater, about 100 mm or less, about 60 mm or less, about 50 mm or less, about 40 mm or less, about 35 mm or less, about 30 mm or less, or about 25 mm or less. In various aspects, the center width of the center portion 281 of the foldable substrate 201 can be in the range of about 1 mm to about 100 mm, about 3 mm to about 100 mm, about 3 mm to about 60 mm, about 5 mm to about 60 mm, about 5 mm to about 50 mm, about 8 mm to about 50 mm, about 8 mm to about 40 mm, about 10 mm to about 40 mm, about 10 mm to about 35 mm, about 15 mm to about 35 mm, about 15 mm to about 30 mm, about 20 mm to about 30 mm, about 20 mm to about 25 mm, or any range or sub-range therebetween. In various aspects, the center width of the center portion 281 of the foldable substrate 201 can be about 2.8 mm or greater, about 6 mm or greater, about 9 mm or greater, about 60 mm or less, about 40 mm or less, or about 24 mm or less. In various aspects, the central width of the central portion 281 of the foldable substrate 201 can be in the range of about 2.8 mm to about 60 mm, about 2.8 mm to about 40 mm, about 2.8 mm to about 24 mm, about 6 mm to about 60 mm, about 6 mm to about 40 mm, about 6 mm to about 24 mm, about 9 mm to about 60 mm, about 9 mm to about 40 mm, about 9 mm to about 24 mm, or any range or sub-range therebetween. Having the width within the ranges set forth above in this paragraph can facilitate folding of the foldable device without breaking.

[0136] In various aspects, the central width of the central portion 281, expressed as a percentage of the length 105 of the foldable device, can be about 30% or more, about 35% or more, about 40% or more, about 45% or more, about 70% or less, about 60% or less, about 55% or less, or about 50% or less. In various aspects, the central width of the central portion 281, expressed as a percentage of the length 105 of the foldable device, can be in the range of about 30% to about 70%, about 35% to about 60%, about 40% to about 55%, about 45% to about 50%, or any range or sub-range therebetween. In various aspects, the central width of the central portion 281, expressed as a percentage of the length 105 of the foldable device, can be in the range of about 30% to about 70%, about 35% to about 60%, about 40% to about 55%, about 45% to about 50%, or any range or sub-range therebetween. In various aspects, the central width of the central portion 281 can be about 30 mm or more, about 35 mm or more, about 40 mm or more, about 45 mm or more, about 50 mm or more, about 100 mm or less, about 80 mm or less, about 70 mm or less, or about 60 mm or less. In various aspects, the center width of the center portion 281 can be in the range of about 30 mm to about 100 mm, about 35 mm to about 80 mm, about 40 mm to about 70 mm, about 45 mm to about 60 mm, about 50 mm to about 60 mm, or any range or sub-range therebetween.

[0137] In various aspects, the foldable substrate and / or foldable device can be rollable. As used herein, a foldable substrate or foldable device is "rollable" if the threshold parallel plate spacing that can be achieved over the length of the foldable substrate and / or foldable device is 10 mm or 10% of the length of the corresponding foldable substrate and / or foldable device, whichever is greater. For example, as shown in FIG. 37 , when the folded width 274 of the folding region 271 and / or the center width of the center portion 281 is greater than the length 105 extending in the direction 106 of the length 105 (see FIG. 37 ), the folded width 274 of the folding region 271 and / or the center width of the center portion 281 is greater than the length 105 extending in the direction 106 of the length 105 (see FIG. 37 ). Figure 1 ) is 10%, the foldable substrate 201 is considered "rollable".

[0138] The foldable device 101, 301, 403, 405, 407, 509, 511, 513, 601, and / or 801 may have impact resistance, defined as the ability of a region of the foldable device (e.g., a region including the first portion 221, a region including the second portion 231, a region including the folding region 271, and / or the central portion 281) to survive a pen drop from a certain height (e.g., 5 centimeters (cm) or more, 10 cm or more, 20 cm or more), as measured according to a "pen drop test." As used herein, a "pen drop test" refers to the ability of a sample of a foldable device to withstand a force applied to an exterior major surface (e.g., Figure 2-3The foldable device 101 or 301 shown in FIGURE 1 is a foldable device that is subjected to a load (i.e., from a pen dropped from a specific height) on the first major surface 203 or second major surface 205 of the foldable substrate 201 of the foldable device 101 or 301 shown in FIGURE 1, wherein the foldable device is configured with a 100 μm thick PET sheet attached to a 50 μm thick test adhesive layer, which is in turn attached to the surface of the foldable substrate opposite the outer major surface to be struck by the pen. Thus, the PET layer in the pen drop test is intended to simulate a foldable electronic display device (e.g., an OLED device). During the test, the foldable device bonded to the PET layer is placed on an aluminum plate (6063 aluminum alloy, polished to a surface roughness of 400 grit sandpaper) with the PET layer in contact with the aluminum plate. No tape is used on the side of the sample placed on the aluminum plate.

[0139] The pen drop test uses a tube to guide the pen to the outer surface of the foldable device. For foldable devices 101, 301, 403, 405, 407, 509, 511, 513, 601 and / or 801, the pen is guided to the outer major surface (e.g., Figure 2-3 The pen is placed on the first major surface 203 or the second major surface 205 of the foldable substrate 201 of the foldable device 101 or 301 shown in FIG, and the tube is placed in contact with the second major surface 205 of the foldable substrate 201 such that the longitudinal axis of the tube is substantially perpendicular to the outer major surface, wherein the longitudinal axis of the tube extends in the direction of gravity. The tube has an outer diameter of 1 inch (2.54 cm), an inner diameter of nine-sixteenths of an inch (1.4 cm), and a length of 90 cm. For each test, the pen was secured at a predetermined height using an acrylonitrile butadiene (ABS) spacer. After each drop, the tube was repositioned relative to the sample to guide the pen to a different impact location on the sample. The pen used in the pen drop test was a BIC Easy Glide pen, fine type, tungsten carbide ballpoint pen tip, with a diameter of 0.7 mm (0.68 mm) and a weight of 5.73 grams (g), including the pen cap.

[0140] In the pen drop test, the pen cap is attached to the top of the pen (i.e., the end opposite the tip) and the pen is dropped so that the ballpoint pen interacts with the test sample. Following the drop sequence for the pen drop test, the pen is dropped once at an initial height of 1 cm, followed by successive drops in 0.5 cm increments up to 20 cm, and then in 2 cm increments after 20 cm, until the test sample is destroyed. After each drop, the presence of any observable signs of breakage, breakage, or other damage to the sample is recorded, as well as the specific drop height. The pen drop test allows multiple samples to be tested according to the same drop sequence to generate a population with greater statistical precision. When performing the pen drop test, a new pen is used after every 5 drops and for each new sample tested. In addition, all pens are dropped at a random location at or near the center of the sample; no pen is dropped at or near the edge of the sample.

[0141] In the pen drop test, "failure" means the formation of a visible mechanical defect in the laminate. A mechanical defect can be a crack or plastic deformation (e.g., a surface indentation). Cracks can be surface cracks or through-cracks. Cracks can form on the inner or outer surface of the laminate. Cracks can extend through all or part of the foldable substrate 201 and / or coating. The minimum dimension of a visible mechanical defect is 0.2 mm or greater.

[0142] In various aspects, when the pen is dropped from a height of 10 centimeters (cm), 12 cm, 14 cm, 16 cm, or 20 cm, the foldable device is not damaged if the pen is dropped on the area including the first portion 221 or the second portion 231. In various aspects, the maximum pen drop height that the foldable device can withstand without damaging the area including the first portion 221 or the second portion 231 can be about 10 cm or more, about 12 cm or more, about 14 cm or more, about 16 cm or more, about 40 cm or less, or about 30 cm or less, about 20 cm or less, or about 18 cm or less. In various aspects, the maximum pen drop height that the foldable device can withstand without damaging the area including the first portion 221 or the second portion 231 can be in the range of about 10 cm to about 40 cm, about 12 cm to about 40 cm, about 12 cm to about 30 cm, about 14 cm to about 30 cm, about 14 cm to about 20 cm, about 16 cm to about 20 cm, about 18 cm to about 20 cm, or any range or sub-range therebetween.

[0143] In various aspects, the foldable device is not damaged if the pen is dropped on the central portion 281 and / or the folding region 271 (e.g., between the first portion 221 and the second portion 231) when the pen is dropped from a height of 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, or more. In various aspects, the maximum pen drop height that the foldable device can withstand without damaging the central portion 281 and / or the folding region 271 (e.g., between the first portion 221 and the second portion 231) can be about 1 cm or more, about 2 cm or more, about 3 cm or more, about 4 cm or more, about 20 cm or less, about 10 cm or less, about 8 cm or less, or about 6 cm or less. In various aspects, the maximum pen drop height that the foldable device can withstand without damaging the central portion 281 and / or the folding region 271 (e.g., between the first portion 221 and the second portion 231) can be in the range of about 1 cm to about 20 cm, about 2 cm to about 20 cm, about 2 cm to about 10 cm, about 3 cm to about 10 cm, about 3 cm to about 8 cm, about 4 cm to about 8 cm, about 4 cm to about 6 cm, or any range or sub-range therebetween. In various aspects, the maximum pen drop height that the foldable device can withstand without damaging the central portion 281 and / or the folding region 271 (e.g., between the first portion 221 and the second portion 231) can be in the range of about 1 cm to about 10 cm, about 1 cm to about 8 cm, about 1 cm to about 5 cm, about 2 cm to about 5 cm, about 3 cm to about 5 cm, about 4 cm to about 5 cm, or any range or sub-range therebetween.

[0144] Various aspects of manufacturing the foldable substrate of the present disclosure will now be discussed. In various aspects, an initial substrate (e.g., a monolithic substrate) can be provided by purchasing or otherwise obtaining a substrate or by forming a foldable substrate. In various aspects, the initial substrate can include a glass substrate and / or a ceramic substrate. In other aspects, the glass substrate and / or ceramic substrate can be provided by various strip forming processes, for example, trough drawing, underdrawing, melt underdrawing, overdrawing, pressing rollers, redrawing, or floating. In other aspects, a ceramic substrate can be provided by heating a glass substrate to crystallize one or more ceramic crystals.

[0145] In all aspects, Figures 4A-4CThe foldable substrates 403, 405, 407, 509, 511, and / or 513 shown in and / or 5A-5C can be formed by applying a patterned etch mask, wherein the position and length of each portion of the patterned etch mask is proportional to the width of the corresponding teeth in the plurality of teeth in the resulting foldable substrate to form a masked surface. The masked surface can then be etched (e.g., using an inorganic acid, using plasma dry etching) to form a first folding surface region having associated grooves defining the plurality of teeth. Alternatively, a laser (e.g., laser etching or laser ablation) can be used to define the plurality of teeth, rather than etching, to form the first folding surface region, wherein the plurality of teeth correspond to untreated portions of the surface.

[0146] In all aspects, Figure 3 The foldable substrate 301 shown in FIG can be formed by sequentially etching portions of the substrate. Portions of the initial substrate corresponding to portions of the first folding surface region 373 having substantially the same thickness can be exposed, while the remainder of the corresponding surface is masked (e.g., a uniform etching mask can be patterned using photolithography or a laser to expose the portion to be etched). For example, the exposed portion can correspond to the portion where the difference between the first folding surface region 373 and the top surface of the tooth, the first main surface 203, is the largest. The exposed portion can be etched (e.g., using an inorganic acid, using plasma dry etching) to form the corresponding portion of the first folding surface region 373. The etched portion is then masked (e.g., subsequently coated with a masking material while keeping the etching mask in place, or the etching mask is removed and a new etching mask is reapplied), and another portion of the first folding surface region 373 corresponding to another substantially constant thickness can be exposed (e.g., using photolithography or using a laser to expose the portion to be etched), where the exposed portion is etched to form the next set of portions of the first folding surface region 373. The above operation may be repeated as needed until the first folding surface area 373 and the plurality of teeth are formed.

[0147] Alternatively, another method of forming a substrate by sequentially etching portions of the substrate will now be discussed. Figure 3The method of the foldable substrate 301 shown in . An initial patterned etch mask can be formed on the surface of the initial substrate, wherein the position and / or length of each portion of the initial patterned etch mask is proportional to the corresponding proportions (e.g., width, aspect ratio) and / or spacing of the resulting teeth in the plurality of teeth (e.g., a uniform etch mask can be patterned using photolithography or laser to expose the portions to be etched). The surface can be etched until the shallowest portion (e.g., the maximum local thickness) of the first folding surface region 373 is formed. Then, those portions corresponding to the predetermined local thickness of the first folding surface region 373 are masked (e.g., the initial patterned etch mask is modified, such as by placing a masking material in a plurality of grooves corresponding to the positions of the portions having the predetermined local thickness), and the surface is then etched until the next shallowest portion of the first folding surface region 373 is formed. The above operation can be repeated as needed until the first folding surface region 373 and the plurality of teeth are formed.

[0148] Alternatively, another method of forming a substrate by sequentially etching each portion of the substrate will now be discussed. Figure 3 The method of the foldable substrate 301 shown in . An initial patterned etch mask can be formed on the surface of the initial substrate. The exposed portion (between the portions of the initial patterned mask) can correspond to the portion of the first folding surface area 373 having the thinnest (e.g., smallest) local thickness (e.g., the difference between the local thickness of the resulting first main surface 203 and the first folding surface area 373 is the largest). The surface with the initial patterned etch mask is etched until the etch thickness is equal to the difference between the target local thickness and the next thinnest local thickness of the first folding surface area 373. The initial patterned etch mask is then further patterned (e.g., using a laser, using plasma) to reveal the portion of the surface corresponding to the next thinnest local thickness of the first folding surface area 373, and the surface with the further patterned etch mask is etched until there is a difference between the target thickness of the newly added portion and the next thinnest local thickness of the first folding surface area 373. The above operation can be repeated as needed until the first folding surface area 373 and the plurality of teeth are formed.

[0149] In all aspects, forming Figure 2 The method of the foldable substrate 201 shown in FIG can include processing portions of the substrate so that it roughly corresponds to the shape of the first folding surface area 273. The surface can then be treated with various solutions to minimize and / or eliminate surface defects and / or scratches caused by processing.

[0150] In all aspects, forming Figure 2The method of the foldable substrate 201 shown in can include locally damaging and / or weakening a network of glass material and / or ceramic material that can be etched (e.g., laser writing and / or sintering, scratching, photolithography), wherein the localized processing (e.g., localized damage and / or weakening) preferentially etches to form a predetermined first folding surface area 273.

[0151] Example

[0152] Various aspects will be further illustrated by the following examples. Examples 1-13 and Comparative Examples AA-DD included glass substrates (Composition 1, with the following nominal composition (in mol %): 63.6SiO2; 15.7Al2O3; 10.8Na2O; 6.2Li2O; 1.16ZnO; 0.04SnO2; and 2.5P2O5) having dimensions of 100 mm x 160 mm in a direction perpendicular to the thickness of the substrate. The shapes of the folding configurations and stress distributions of Examples 1-10 and AA-BB were simulated using finite element analysis (FEA), but the shapes of the folding configurations can be measured by physical methods (e.g., as described in "Study of Deformation Behavior of Multilayered Sheets Using Digital Image Correlation" (Procedia Manufacturing 47 (2020), 1257-1263)). The FEA simulations were performed with the following assumptions: the foldable substrate has an elastic modulus of 71 GPa and a Poisson’s ratio of 0.22; the adhesive layer has a Poisson’s ratio of 0.49; the polymer-based portion has a Poisson’s ratio of 0.49; all interfaces in the foldable device are perfectly bonded with no delamination; large deformation methods are applicable; and the temperature of all components is 23°C.

[0153] Figure 9 The folded configurations of Examples 1-6 and Comparative Example AA are shown folded to a parallel plate spacing of 6 mm according to the parallel plate test. Figure 9 In FIG. 1 , the horizontal axis 901 (i.e., the x-axis) corresponds to the position in the direction of the parallel plate spacing 711 (see FIG. Figure 7-8 ), the longitudinal axis 902 (i.e., the y-axis) corresponds to the position in the direction perpendicular to the direction of the parallel plate spacing 711 (see Figure 7-8). The origin (i.e., the intersection of 0 on the horizontal axis and 0 on the vertical axis) is defined as the location of the folded configuration at the midline between the parallel plates, corresponding to the vertex of the folded configuration. In Comparative Example AA, a uniform (e.g., monolithic) substrate thickness of 80 μm is included, no teeth, and no foldable surface area as described herein. In Examples 1-6, the substrate thickness is 150 μm, the center thickness is 80 μm, and there are multiple teeth, wherein the thickness of each tooth is equal to the substrate thickness. Examples 1-3 correspond to Figures 4A-4C The foldable device 403, 405 or 407 shown in FIG, and examples 4-6 correspond to Figures 5A-5C The foldable device 509, 511 or 513 shown in FIG. Figure 9 Curves 903, 905, 907, 909, 911, and 913 in FIG correspond to Examples 1-6, respectively. In Examples 1-6, the maximum tooth width is 100 μm and the maximum distance between adjacent pairs of teeth is 200 μm. Curve 917 corresponds to Comparative Example AA, and curve 915 corresponds to a circle with a radius of 3 mm (corresponding to a diameter of 6 mm and a parallel plate spacing). Figure 9 As shown, in curve 913 (Example 6), the tooth width increases as the distance from the center line increases, and its folded configuration is the least similar to the circular shape shown in curve 915. Curves 909, 911 and 917 (Examples 4-5 and Comparative Example AA) have approximately the same folded configuration. In curve 907 (Example 3), the distance between adjacent pairs of teeth decreases as the distance from the center line increases, which is closer to a circular configuration (curve 915) than Example AA (curve 917). In curves 903 and 905 (Examples 1-2), the tooth width decreases as the distance from the center line increases, and its folded configuration is closest to a circular profile (curve 915). Therefore, Figure 9 It is shown that for a foldable device (e.g., a foldable substrate) having multiple teeth in the folding region and / or center portion, a more circular folding configuration can be obtained when the tooth width decreases with increasing distance from the centerline, as in Examples 1-2.

[0154] The maximum stress values for Examples 1-6 and Comparative Example AA are shown in Table 1. As shown, Comparative Example AA has the lowest maximum folding stress value, which is expected because there is less material to bend (i.e., the volume of the foldable substrate and / or foldable device). The maximum folding stresses for Examples 4-6 are roughly the same. Example 2 has the highest maximum folding stress value, followed by Example 1, and then Example 3. Comparing this trend with the above Figure 9 Combined with the discussion of , it can be seen that the maximum folding stress increases roughly as the folding configuration approaches a circular profile. This is unexpected, as lower maximum folding stress values are generally considered desirable; however, as Figure 9As shown in , the lower maximum folding stress values are further away from the circular profile. Although the maximum folding stress of Example 1-2 is greater than that of Comparative Example AA (whose thickness corresponds to the center thickness - the minimum thickness of Example 1-2), as discussed below, for the same parallel plate spacing (see Figure 11 ) or smaller parallel plate spacing under the same applied force (see Table 2), Figure 2-3 The maximum folding stress of the foldable devices (e.g., Examples 7 and 9) is less than that of Comparative Example BB (whose thickness corresponds to the average thickness of Examples 7 and 9).

[0155] Table 1: Characteristics of Examples AB and AA

[0156]

[0157] Figure 10 The folded configuration of Examples 7-8 is shown folded to a parallel plate spacing of 6 mm according to the parallel plate test. Figure 10 In FIG. 1 , the horizontal axis 1001 (i.e., the x-axis) corresponds to the position in the direction of the parallel plate spacing 711 (see FIG. Figure 7-8 ), the longitudinal axis 1002 (i.e., the y-axis) corresponds to the position in the direction perpendicular to the direction of the parallel plate spacing 711 (see Figure 7-8 ). The origin (i.e., the intersection of 0 on the horizontal axis and 0 on the vertical axis) is defined as the location of the folded configuration at the midline between the parallel plates, corresponding to the vertex of the folded configuration. In Examples 7-8, the substrate thickness is 112.6 μm and the center thickness is 80 μm. Curve 1005 corresponds to Figure 2 In the example 7 of the foldable device 101 (e.g., foldable substrate) shown in FIG, curve 1007 corresponds to Figure 3 Example 8 of the foldable device 301 shown in FIG. Curve 1003 corresponds to a circle with a radius of 3 mm (corresponding to a diameter of 6 mm and a parallel plate spacing). Figure 10 As shown in , curves 1005 and 1007 are very close to the shape of the circular profile (curve 1003). Figure 10 The contours in Figure 2-3 The foldable devices 101 and 301 shown in FIG can achieve a substantially circular folded configuration. As discussed above, the ability to achieve a circular folded configuration is unexpected because Examples 7-8 have a greater local thickness near the midline in the folding region than the local thickness away from the midline. In addition, Figure 9 In the folded configuration shown in Figure 10 The results shown in are unexpected.

[0158] Table 2 presents the characteristics of Examples 9-10 and Comparative Example BB. Examples 9-10 correspond to Examples 7-8, respectively; however, the substrate thickness is 127 μm and the center thickness is 80 μm. Comparative Example BB includes a uniform (e.g., monolithic) substrate thickness of 112.6 μm, corresponding to the average thickness of Examples 7 and 9. Examples 9-10 are folded under an applied force of 67.3 Newtons (N). As shown in Table 2, Examples 9-10 achieve an effective (curvature) radius of 3 mm, but Example BB only achieves an effective (curvature) radius of 6 mm (a difference of 100%). The folding length of Example BB is 13.1 mm, which is reduced to 9.42 mm for Examples 9-10 (a reduction of 28%). The maximum folding stress of Example 9 is 1579 MPa, which is less than the maximum folding stress of Example BB. The maximum folding stress of Example 9 is lower than that of Example 10.

[0159] Table 2: Properties of Examples 9-10 and Comparative Example B

[0160]

[0161] Figure 11 The direction (θ) that the foldable substrate faces when the folded configuration changes from 90° (π / 2) to 180° (π) is shown, but it should be understood that the trend from 0° to 90° (π / 2) is a mirror image of the results shown. The horizontal axis 1101 (i.e., the x-axis) shows the direction (θ), the left vertical axis 1102 (i.e., the left y-axis) is the magnitude (i.e., absolute value) of the surface tension stress (unit: MPa), and the right vertical axis 1112 (i.e., the right y-axis) is the local thickness (unit: μm). Curve 1105 corresponds to Comparative Example BB, and curve 1107 corresponds to Example 7 (corresponding to Figure 2 Foldable device 101 shown in ). Figure 11 The results in FIG were measured when a force of 67.3 N was applied, as described above with reference to Table 2. Figure 11 As shown in FIG, at angles less than 135° (and within the range of 45° to 135° due to symmetry), curve 1107 has a lower stress magnitude (along vertical axis 1102) than curve 1105. Meanwhile, curves 1115 and 1117 use vertical axis 1112 instead of vertical axis 1102. Curve 1115 is a line at the average thickness of Examples 7 and 9 and Comparative Example AA. Curve 1117 shows the thickness profile.

[0162]

[0163] It is mentioned above as Figure 2 The folding surface area of the foldable device 101 shown in FIG is based on the discussion. In the range of 90° to 135° (or in the range of 45° to 135° due to symmetry), the thickness of this thickness profile (curve 1117) is greater than the average thickness (curve 1115). Figure 11 For the multiple sets of curves shown in , the regions where the stress in curve 1107 is less than the stress in 1105 (from 90° to 135° or from 45° to 135° due to symmetry) correspond to the same regions where curve 1117 is greater than curve 1115 (i.e., the local thickness of Example 7 is greater than that of Comparative Example BB). This indicates that the stress corresponding to the regions above the average thickness in curves 1107 and 1117 is actually less than that in the regions with thinner local thickness (see curves 1105 and 1117). Therefore, the thickness profile of the fold region of the present disclosure can reduce bending-induced stress compared to a substrate having a uniform thickness in the corresponding fold region, where the uniform thickness is equal to the average thickness of the thickness profile of the fold region of the present disclosure. As mentioned elsewhere, this is unexpected, as it is expected that a larger local thickness would correspond to a larger bending-induced stress.

[0164] Figure 15-17 The direction (θ) that the foldable substrate faces when the folded configuration changes from 90° (π / 2) to 180° (π) is shown, but it should be understood that the trend from 0° to 90° (π / 2) is a mirror image of the results shown. The horizontal axis 1501, 1601 or 1701 (i.e., the x-axis) shows the direction (θ), the left vertical axis 1502, 1602 or 1702 (i.e., the left y-axis) is the magnitude (i.e., absolute value) of the surface tension stress (unit: MPa), and the right vertical axis 1512, 1612 or 1712 (i.e., the right y-axis) is the local thickness (unit: μm). Figure 15-17 In the example 11-13, curve 1507, 1605 or 1705 corresponds to the stress of comparative example AA, and curve 1517, 1615 or 1715 shows the corresponding thickness profile of comparative example AA that is integral (ie, consistent) with the thickness of 80 μm. Figure 2 The discussed thickness profiles, with thickness ranges for Examples 11-13, are presented in Table 3.

[0165] like Figure 16 As shown in Table 3, Comparative Example AA (curve 1605) exhibits a maximum folding stress of 1191 MPa at a parallel plate spacing of 6 mm. Figure 16 In FIG. 1 , curve 1607 corresponds to the stress of Example 11, and curve 1617 shows the corresponding thickness profile of Example 11, which increases from 40 μm at the transition region (see 180° or π radians) to 96 μm at the center of the bend (see 90° or π / 2 radians) according to the above relationship. Figure 16As shown in Table 3, Example 11 exhibited a maximum folding stress of 1191 MPa at a parallel plate spacing of 6 mm. Thus, Example 11 and Comparative Example AA exhibited the same maximum folding stress (parallel plate spacing of 6 mm), but Example 11 had a greater thickness (96 μm at the middle of the folding zone) than Comparative Example AA (80 μm), which is believed to be a result of the thickness profile enabling Example 11 to achieve a circular bending profile (as opposed to the elliptical bending profile discussed above). The increased thickness of Example 11 at the ends of the folding zone (compared to Comparative Example AA) is believed to contribute to Example 11 having greater puncture resistance than Comparative Example AA.

[0166] Table 3: Properties of Examples 11-13 and Comparative Examples AA and CC-DD

[0167] Example Parallel plate spacing (mm) Thickness range (μm) Maximum folding stress (MPa) Bending force (N / mm) 11 6 40 to 96 1191 0.29 12 5 40 to 80 1191 0.24 13 6 80 to 120 1492 0.57 AA 6 80 1191 0.24 CC 6 40 596 0.03 DD 6 120 1787 0.82

[0168] exist Figure 15 In FIG. 1 , curve 1505 corresponds to the stress of Comparative Example CC, and curve 1515 shows the corresponding thickness profile of Comparative Example CC that is integral (ie, consistent) with a thickness of 40 μm. Figure 15 As shown in Table 3, Comparative Example CC (curve 1505) exhibits a maximum folding stress of 596 MPa at a parallel plate spacing of 6 mm. Figure 15 In the example 12, curve 1509 corresponds to the stress, and curve 1519 shows the corresponding thickness profile of Example 12, which increases from 40 μm at the transition region (see 180° or π radians) to 80 μm at the center of the bend (see 90° or π / 2 radians) according to the above relationship. Unlike Examples 11 and 13 and Comparative Examples AA and CC-DD, Example 12 is folded to a parallel plate spacing of 5 mm instead of 6 mm. Figure 15 As shown in Table 3, Example 12 exhibited a maximum folding stress of 1191 MPa at a parallel plate spacing of 5 mm. As shown in Table 3, the maximum folding stresses of Example 11 and Comparative Example AA at 6 mm were the same as that of Example 12 at a smaller parallel plate spacing of 5 mm. Therefore, Example 12 demonstrates that, under the same maximum folding stress, a thickness profile according to aspects of the present disclosure having a maximum thickness in the folding region (same as the overall thickness having the corresponding maximum thickness) can achieve a smaller parallel plate spacing compared to a comparative substrate having an overall thickness equal to the corresponding maximum thickness.

[0169] exist Figure 17 In FIG. 1 , curve 1707 corresponds to the stress of Comparative Example DD, and curve 1717 shows the corresponding thickness profile of Comparative Example DD that is integral (ie, consistent) with a thickness of 120 μm. Figure 17 As shown in Table 3, Comparative Example DD (curve 1707) exhibits a maximum folding stress of 1782 MPa at a parallel plate spacing of 6 mm. Figure 17In FIG. 1 , curve 1709 corresponds to the stress of Example 13, and curve 1719 shows the corresponding thickness profile of Example 13, which increases from 80 μm at the transition region (see 180° or π radians) to 120 μm at the center of the bend (see 90° or π / 2 radians) according to the above relationship. It is worth noting that the thickness of Example 13 is greater than that of Examples 11-12. Figure 17 As shown in Table 3, Example 13 exhibited a maximum folding stress of 1492 MPa at a parallel plate spacing of 6 mm. Thus, Example 13 and Comparative Example DD had the same maximum thickness in the folding region, but at the same parallel plate spacing of 6 mm, Example 13 exhibited a lower bending stress than Comparative Example DD, which is believed to be a result of the thickness profile enabling Example 13 to achieve a circular bending profile (as opposed to the elliptical bending profile discussed above).

[0170] Table 3 also presents the bending force corresponding to the minimum force required to bend the foldable substrate to achieve the minimum parallel plate spacing described in Table 3. As shown, Example 12 has a bending force of 0.24 N / mm to achieve a parallel plate spacing of 5 mm, while Example AA has the same bending force to achieve a larger parallel plate spacing of 6 mm. In addition, comparing Comparative Example DD and Example 13, which have the same maximum thickness, the bending force of Example 13 to achieve a parallel plate spacing of 6 mm is 0.57 N / mm, which is 30% less than the corresponding bending of Comparative Example DD. This shows that the thickness profile according to various aspects of the present disclosure can reduce the bending force to achieve a predetermined parallel plate spacing (e.g., by 20% or more or by 30% or more) compared to a substrate having a uniform thickness equal to the maximum thickness.

[0171] Based on the above observations, the foldable substrate can have a smaller minimum parallel plate spacing, higher impact resistance, higher durability, lower fatigue and lower incidence of mechanical instability. The substrate and / or portions may include glass and / or ceramic portions, which can provide good dimensional stability, reduced incidence of mechanical instability, good impact resistance and / or good puncture resistance. These portions may include glass and / or ceramic portions, including one or more compressive stress zones, which can further improve impact resistance and / or puncture resistance. By providing a substrate including a glass and / or ceramic substrate, such a substrate can also improve impact resistance and / or puncture resistance while promoting good folding performance. In various aspects, the substrate thickness can be large enough (e.g., from about 50 microns (micrometers or μm) to about 2 mm) to further enhance impact resistance and puncture resistance. Providing a foldable substrate including a central portion having a central thickness that is less than the thickness of the substrate (e.g., the first thickness of the first portion and / or the second thickness of the second portion) (e.g., less than about 10 μm or more) can achieve a smaller parallel plate spacing (e.g., about 10 mm or less, about 5 mm or less, or about 3 mm or less) based on the reduced thickness of the central portion, thereby achieving foldability and / or rollability of the foldable substrate and / or foldable device.

[0172] The inventors of the present application have determined that the local thickness profile of the folding zone described herein can unexpectedly enable a foldable substrate to fold into a substantially circular folded configuration (e.g., a folded length of approximately 1.6 times the corresponding parallel plate spacing). This is in contrast to the elliptical folding configuration of a substrate having a uniform thickness in the folding zone (e.g., a folded length of approximately 2.2 times the corresponding parallel plate spacing). Additionally, a substrate having a uniform thickness has a non-uniform stress distribution in the folded configuration, which may increase the incidence of device damage and / or destruction compared to the stress distribution of a foldable substrate having the thickness profile described herein when folded. Unexpectedly, the local increased thickness profile of the present disclosure can achieve a circular folding profile, thereby reducing the length of the folding zone and reducing stress concentration along the bend. For example, in various aspects, a smoothly varying surface can be provided in the folding zone to promote folding into a substantially circular folding configuration. Alternatively, in various aspects, a plurality of teeth (e.g., comprising substantially the thickness of the substrate) can increase the puncture resistance of the folding zone, while the folding zone (not comprising teeth) can include the local increased thickness profile discussed above, which can promote folding into a substantially circular folding configuration.

[0173] In various aspects, a foldable device and / or a foldable substrate may include one or more recesses, for example, a first central surface region recessed a first distance from a first major surface and / or a second central surface region recessed a second distance from a second major surface. Providing opposing first and second recesses can provide a central thickness that is less than the thickness of the substrate. Furthermore, providing opposing first and second recesses can reduce the maximum bending-induced strain of the foldable device, for example, between the central portion and the first and / or second portions, because the central portion including the central thickness can be closer to the mid-axis of the foldable device and / or foldable substrate than if only a single recess were provided. Furthermore, making the first distance substantially equal to the second distance can reduce the incidence of mechanical instability in the central portion, for example, because the foldable substrate is symmetrical about a plane including the midpoint of the substrate thickness and the central thickness. Furthermore, providing opposing first and second recesses can reduce the bending-induced strain of material positioned within the first and / or second recesses, compared to a single recess whose surface is recessed the sum of the first and second distances. Reducing the bending-induced strain of material positioned within the first and / or second recesses can enable a wider range of usable materials due to reduced strain requirements. For example, a harder and / or more rigid material can be positioned in the first groove, which can improve the impact resistance, puncture resistance, abrasion resistance, and / or scratch resistance of the foldable device. Additionally, controlling the properties of the first material positioned in the first groove and the second material positioned in the second groove can control the position of the intermediate axis of the foldable device and / or the foldable substrate, which can reduce (e.g., mitigate, eliminate) the occurrence of mechanical instability, device fatigue, and / or device damage.

[0174] In various aspects, a foldable device and / or a foldable substrate may include a first transition region attaching the central portion to the first portion and / or a second transition region attaching the central portion to the second portion. Providing a transition region with a smooth and / or monotonically decreasing (e.g., continuously decreasing) thickness can reduce stress concentrations in the transition region and / or avoid optical distortion. Providing a transition region of sufficient length (e.g., about 0.15 mm or longer, or about 0.3 mm or longer) can avoid optical distortion that can be generated by a sharp change in the thickness of the foldable substrate.

[0175] As used herein, directional terms such as up, down, right, left, front, back, top, bottom, are made with reference only to the drawings as drawn and are not intended to imply an absolute orientation.

[0176] It should be understood that the various aspects disclosed may involve features, elements or steps described in conjunction with the aspects. It should also be understood that although features, elements or steps are described with respect to one aspect, they can be interchanged or combined with alternative aspects in various combinations or arrangements not shown.

[0177] It should also be understood that, as used herein, the terms "the," "a," or "an" mean "at least one," and should not be limited to "only one" unless clearly indicated to the contrary. For example, reference to "a component" includes aspects having two or more such components unless the context clearly indicates otherwise. Similarly, "plurality" is intended to mean "more than one."

[0178] As used herein, the term "about" means that amount, size, formula, parameter and other quantity and feature are not exact and do not have to be exact, but can be approximate and / or larger or smaller as needed, thereby reflecting tolerance, conversion factor, rounding, measurement error and other factors known to those skilled in the art. In this article, ranges can be expressed as from "about" a specific value and / or to "about" another specific value. When such a range is expressed, each aspect includes from the specific value and / or to the other specific value. Similarly, when a value is expressed as an approximate value by using the antecedent "about", it should be understood that the specific value forms another aspect. Regardless of whether the numerical value or range endpoint in the specification states "about", the numerical value or range endpoint is intended to include two aspects: one modified by "about" and one not modified by "about". It should also be understood that the endpoint of each range is meaningful relative to the other endpoint and independently of the other endpoint.

[0179] As used herein, the terms "substantially," "substantially," and variations thereof are intended to indicate that the characteristic being described is equal to or approximately equal to a value or description. For example, a "substantially flat" surface is intended to indicate a flat or approximately flat surface. Furthermore, as defined above, "substantially similar" is intended to indicate that two values are equal or approximately equal. In various aspects, "substantially similar" can mean values that are within about 10% of each other, such as within about 5% of each other, or within about 2% of each other.

[0180] Unless otherwise expressly stated, it is in no way intended that any method described herein be construed as requiring that its steps be performed in a specific order. Therefore, if a method claim does not actually recite the order in which its steps are to be followed, or if the steps are not otherwise specifically recited in the claims or specification as being limited to a specific order, no specific order is intended to be inferred.

[0181] Although the transition phrase "comprising" may be used to disclose various features, elements, or steps of a particular aspect, it should be understood that alternative aspects are implicitly included, including those aspects that may be described using the transition phrases "consisting of" or "consisting essentially of. Thus, for example, a device comprising A+B+C implicitly includes alternative aspects where the device consists of A+B+C and where the device consists essentially of A+B+C. Unless otherwise indicated, as used herein, the terms "comprising" and "including" and variations thereof should be understood to be synonymous and open-ended.

[0182] The above-described aspects and features of these aspects are exemplary and may be provided alone or in any combination with any one or more features of the other aspects provided herein without departing from the scope of the present disclosure.

[0183] It is obvious to those skilled in the art that various modifications and variations can be made to the present disclosure without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is intended to cover modifications and variations of all aspects herein, provided that they are within the scope of the appended claims and their equivalents.

Claims

1. A foldable substrate comprising: a substrate thickness defined between a first major surface and a second major surface opposite the first major surface; a first portion comprising the substrate thickness, a first compressive stress region extending from the first major surface to a first compressive depth, and a second compressive stress region extending from the second major surface to a second compressive depth; a second portion comprising the substrate thickness, a third compressive stress region extending from the first major surface to a third compressive depth, and a fourth compressive stress region extending from the second major surface to a fourth compressive depth; as well as a central portion located between the first portion and the second portion, the central portion including a folding region located between a first transition region and a second transition region, the first transition region and the second transition region including a central thickness less than a thickness of the substrate, the folding region including a first folding surface area and a second folding surface area opposite the first folding surface area, a first folding compressive stress region extending from the first folding surface area to a first folding compression depth, a second folding compressive stress region extending from the second folding surface area to a second folding compression depth, a folding width of the folding region defined between the first transition region and the second transition region, and a local thickness of the folding region in a direction of the substrate thickness between the first folding surface area and the second folding surface area increasing as a distance from a centerline of the folding region decreases, The foldable substrate comprises a glass material or a ceramic material.

2. The foldable substrate of claim 1 , wherein the local thickness of the folding region varies between the center thickness and the substrate thickness, wherein the local thickness at the midline of the folding region is substantially equal to the substrate thickness.

3. The foldable substrate of claim 1 , wherein the local thickness of the fold zone as a function of position along the fold width of the fold zone is proportional to the cube root of the sine of a fractional position scaled to vary over the fold width of the fold zone in the range of 0 to π radians. 4 . The foldable substrate of claim 1 , wherein a thickness of the first transition region decreases smoothly from the substrate thickness to the center thickness as the distance from the first portion increases.

5. A foldable substrate comprising: a substrate thickness defined between a first major surface and a second major surface opposite the first major surface; a first portion comprising the substrate thickness, a first compressive stress region extending from the first major surface to a first compressive depth, and a second compressive stress region extending from the second major surface to a second compressive depth; a second portion comprising the substrate thickness, a third compressive stress region extending from the first major surface to a third compressive depth, and a fourth compressive stress region extending from the second major surface to a fourth compressive depth; as well as a central portion located between the first portion and the second portion, the central portion including a fold zone located between a first transition region and a second transition region, the first transition region and the second transition region including a central thickness that is less than a thickness of the substrate, the fold zone including a plurality of teeth extending from a first fold surface region, the first fold surface region opposing a second fold surface region, a fold width of the fold zone defined between the first transition region and the second transition region, and a local thickness of the fold zone between the first fold surface region and the second fold surface region that does not include the plurality of teeth that increases as the distance from a centerline of the fold zone decreases, The foldable substrate comprises a glass material or a ceramic material.

6. The foldable substrate of claim 5, wherein a tooth thickness of the teeth of the plurality of teeth is substantially equal to a thickness of the substrate. The foldable substrate of claim 5 , wherein the centerline of the folding region does not include a tooth of the plurality of teeth.

8. The foldable substrate of claim 5, wherein a first width of a first tooth of the plurality of teeth is greater than a second width of a second tooth of the plurality of teeth, and the first tooth is closer to the centerline of the folding region than the second tooth is to the centerline.

9. The foldable substrate of claim 5, wherein a first width of a first tooth of the plurality of teeth is smaller than a second width of a second tooth of the plurality of teeth, and the first tooth is closer to the centerline of the folding region than the second tooth is to the centerline.

10. The foldable substrate of claim 5 , wherein a first distance between a first pair of adjacent teeth in the plurality of teeth is less than a second distance between a second pair of adjacent teeth in the plurality of teeth, the first pair of adjacent teeth being closer to the centerline of the folding region than the second pair of adjacent teeth.

11. The foldable substrate of claim 5 , wherein a first distance between a first pair of adjacent teeth in the plurality of teeth is smaller than a second distance between a second pair of adjacent teeth in the plurality of teeth, the first pair of adjacent teeth being closer to the centerline of the folding zone than the second pair of adjacent teeth.

12. A foldable substrate according to claim 5, wherein the local thickness of the fold zone as a function of position along the fold width of the fold zone is proportional to the cube root of the sine of the fractional position, the fractional position being scaled to vary over the fold width of the fold zone in the range of 0 to π radians.

13. The foldable substrate of claim 5, wherein a thickness of the first transition region not including the plurality of teeth decreases smoothly from the substrate thickness to the center thickness as the distance from the first portion increases.

14. The foldable substrate of any one of claims 1 to 13, wherein the folding region is symmetrical about a plane extending through the midline of the folding region and equidistant from the first portion and the second portion.

15. A foldable substrate according to any one of claims 1 to 13, wherein the folded configuration of the foldable substrate folded about the centerline of the folding zone in a parallel plate test is substantially circular, and wherein the folded width of the folding zone is substantially equal to the minimum parallel plate spacing of the foldable substrate in the parallel plate test.

16. The foldable substrate according to any one of claims 1 to 13, wherein the foldable substrate achieves a parallel plate spacing of 3 mm.

17. The foldable substrate of any one of claims 1 to 13, wherein the first compressive stress region comprises a first maximum compressive stress of approximately 400 MPa or greater, the second compressive stress region comprises a second maximum compressive stress, the third compressive stress region comprises a third maximum compressive stress of approximately 400 MPa or greater, and the fourth compressive stress region comprises a fourth maximum compressive stress, wherein the second maximum compressive stress is approximately 400 MPa or greater and the fourth maximum compressive stress is approximately 400 MPa or greater.

18. The foldable substrate according to any one of claims 1 to 13, wherein the substrate thickness is in the range of about 50 micrometers to about 2 millimeters, preferably in the range of about 100 micrometers to about 200 micrometers.

19. The foldable substrate according to any one of claims 1 to 13, wherein the central thickness is in the range of about 25 microns to about 120 microns, preferably in the range of about 25 microns to about 60 microns.

20. A consumer electronic product comprising: a housing comprising a front surface, a rear surface, and side surfaces; an electrical assembly located at least partially within the housing, the electrical assembly including a controller, a memory, and a display, the display located at or adjacent to a front surface of the housing; as well as a cover plate disposed above the display, wherein at least one of a portion of the housing or the cover comprises a foldable substrate according to any one of claims 1 to 13.

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