Base material film for semiconductor manufacturing tape
A base film for semiconductor manufacturing tapes, using a homopolymer of 1-butene and low-density polyethylene, addresses issues of stretchability and rigidity, ensuring stable unwinding and processing stability by optimizing molecular properties and ratios.
Patent Information
- Application Number
- JP2025080936
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-05-14
- Publication Date
- 2025-07-17
- Estimated Expiration
- 2041-10-29
AI Technical Summary
Existing semiconductor manufacturing tapes face issues with insufficient uniform stretchability, rigidity, and processing stability due to necking, thickness variation, and unwinding instability, primarily attributed to the use of crystalline random polypropylene and low-viscosity butene copolymers.
A base film composed of a homopolymer of 1-butene and low-density polyethylene, with a specific mass ratio and molecular properties, including a density of 0.93 g/cm³ and a melt mass flow rate of 1.0 to 6.0 g/10 min, enhances uniform stretchability, rigidity, and processing stability.
The base film achieves excellent uniform stretchability, rigidity, and processing stability by preventing necking, reducing thickness variation, and ensuring stable unwinding during manufacturing processes.
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Abstract
Description
Technical Field
[0001] The present invention relates to a base film for a semiconductor manufacturing tape (hereinafter, may be simply referred to as "base film").
Background Art
[0002] As a method for manufacturing a semiconductor device such as an IC chip, for example, a wafer circuit in which a circuit is formed on a semiconductor wafer having a substantially disk shape is diced on a semiconductor manufacturing tape (dicing tape) for a wafer to obtain individual semiconductor devices. This method is widely used. After dicing, for example, the dicing tape is stretched to form a gap between semiconductor devices (that is, expanded), and then each semiconductor device is picked up by a robot or the like.
[0003] Further, as a semiconductor manufacturing tape for a wafer, a dicing / die attach film (DDAF) in which an adhesive layer is laminated on the adhesive layer of the above-described dicing tape is used. After the wafer circuit is diced on the dicing / die attach film, the dicing / die attach film is stretched to form a gap between semiconductor devices, and then the adhesive layer is photocured, and the semiconductor device is peeled off from the adhesive layer and picked up in a state where the adhesive layer is adhered.
[0004] A dicing tape and a dicing / die attach film generally include an adhesive layer for fixing a wafer and a base film containing polyolefin or the like. For example, the base film contains 30 to 100% by weight of an amorphous polyolefin having a content of propylene and / or 1-butene components of 50% by weight or more, 0 to 70% by weight of a crystalline polypropylene resin, and 0 to 70% by weight of a polyethylene resin. A dicing tape provided with a base film composed of a laminate of a polyolefin layer (intermediate layer) and a polyethylene resin layer (surface layer) formed of a polyethylene resin such as low density polyethylene laminated on both surfaces of the polyolefin layer has been proposed (see, for example, Patent Document 1).
[0005] Also, a base material film is proposed which is composed of a laminate including an intermediate layer containing at least 40% by mass or more of an amorphous polyolefin containing at least one component selected from the group consisting of ethylene, propylene, and 1-butene, and surface layers laminated on both sides of the intermediate layer and mainly composed of crystalline polyethylene (see, for example, Patent Document 2).
[0006] Also, a random copolymer of propylene with ethylene and / or an α-olefin having 4 to 8 carbon atoms, wherein the content of ethylene and / or the α-olefin having 4 to 8 carbon atoms is 6% by weight or more, and the density measured in accordance with ASTM D1505 is 885 kg / m 3 There is proposed a base material film composed of a laminate including an intermediate layer mainly composed of the following propylene-based random copolymer (β), and surface layers laminated on both sides of the intermediate layer and mainly composed of a propylene-based random copolymer (α) having a lower content of ethylene and / or an α-olefin having 4 to 8 carbon atoms and a higher density than the propylene-based random copolymer (β) (see, for example, Patent Document 3).
Prior Art Documents
Patent Documents
[0007]
Patent Document 1
Patent Document 2
Patent Document 3
Summary of the Invention
Problems to be Solved by the Invention
[0008] However, in the base film described in Patent Document 1 above, since crystalline random polypropylene is added in an amount equal to or greater than that of the amorphous butene copolymer, necking occurs when the base film is stretched, and there is a problem that the uniform stretchability (uniform expandability) of the base film is insufficient. Further, since a low-viscosity butene copolymer is used, the thickness variation due to discharge variations such as draw resonance when forming the base film becomes large, and there is a problem that the processing stability of the base film is insufficient.
[0009] Further, in the base film described in Patent Document 2 above, since the rigidity of the base film is insufficient, there is a problem that the unwinding of the base material becomes unstable in the manufacturing process of the base film.
[0010] Further, in the base film described in Patent Document 3 above, since a semi-crystalline resin instead of an amorphous resin is used, necking occurs when forming the base film, and there is a problem that the uniform stretchability of the base film is insufficient. Further, since the rigidity of the base film is insufficient, there is a problem that the unwinding of the base material becomes unstable in the manufacturing process of the base film. Further, since the surface of the base film has high adhesiveness, the base film adheres to the conveying roll when the base film is conveyed, making it difficult to convey and wind up the base film, and blocking occurs when winding up the base film, and there is a problem that the processing stability is insufficient.
[0011] Therefore, the present invention has been made in view of the above problems, and an object thereof is to provide a base film for a semiconductor manufacturing tape having excellent uniform stretchability, rigidity, and processing stability.
Means for Solving the Problems
[0012] In order to achieve the above object, the base film for a semiconductor manufacturing tape of the present invention comprises a homopolymer of 1-butene and a density of 0.93 g / cm 3It contains low-density polyethylene as follows, the mass ratio of the homopolymer of 1-butene to low-density polyethylene is 1-butene homopolymer:low-density polyethylene = 10:90 to 70:30, the low-density polyethylene is linear low-density polyethylene, the melt mass flow rate (MFR) of the linear low-density polyethylene is 1.0 to 6.0 g / 10 min, and the ratio of the stress at 40% elongation to the stress at 20% elongation is 1 or more and 2 or less.
Effect of the Invention
[0013] According to the present invention, it becomes possible to provide a base film for a semiconductor manufacturing tape that is excellent in uniform stretchability, rigidity, and processing stability.
Brief Description of the Drawings
[0014]
Figure 1
Figure 2
Modes for Carrying Out the Invention
[0015] Hereinafter, the base film for a semiconductor manufacturing tape of the present invention will be specifically described. Note that the present invention is not limited to the following embodiments, and can be appropriately modified and applied without changing the gist of the present invention.
[0016] The base film of the present invention is a film formed of a polyolefin resin, and contains a homopolymer of 1-butene and low-density polyethylene having a density of 0.93 g / cm 3 as follows.
[0017] <Homopolymer of 1-Butene> In the present invention, as the polybutene, a homopolymer obtained by polymerizing 1-butene alone is used. This homopolymer of 1-butene has a high molecular weight and bulky side chains, and due to the strong intermolecular forces caused by these bulky side chains, despite being a crystalline polymer, it can improve the uniform stretchability of the base film in the same manner as in the case of an amorphous polymer.
[0018] Moreover, as the homopolymer of 1-butene used in this embodiment, those having a weight average molecular weight (Mw) of about 500,000 to 1,500,000 can be used.
[0019] The above-mentioned "weight average molecular weight" refers to the value calculated in accordance with JIS K 7252-1:2016.
[0020] And since the homopolymer of 1-butene used in the present invention has a high molecular weight, it has low surface tackiness and can be used as a surface layer. Also, compared with amorphous polyolefins, it has high rigidity, so in the manufacturing process of the base film, it is possible to provide a base film having high rigidity that allows the base material to be unwound.
[0021] In addition, although the homopolymer of 1-butene used in the present invention has a high molecular weight, it can be molded with a general-purpose extruder. Since the high molecular weight component reduces the surface tackiness of the film, it is possible to suppress adhesion to the conveying rolls when conveying the base film, and to suppress blocking when winding up the base film and draw resonance when forming the base film, thereby improving the processing stability of the base film.
[0022] From the above, by using a homopolymer of 1-butene as the resin for forming the base film, it is possible to improve the uniform stretchability, rigidity, and processing stability of the base film.
[0023] <Low-density polyethylene> In the present invention, the density of the low-density polyethylene is 0.930 g / cm 3The following applies. When the density is 0.930 g / cm 3 In the following cases, since an excessive increase in crystallinity is suppressed and flexibility is improved, the isotropy of the base film can be improved. When the density is greater than 0.930 g / cm 3 In the case where it is greater, since the crystallinity increases excessively, the isotropy may decrease, and since the rigidity becomes too large, the pick-up property of the semiconductor device may decrease, and the semiconductor device may be damaged.
[0024] Also, from the viewpoint of improving processing stability, the density of the low-density polyethylene is preferably 0.860 g / cm 3 or more, more preferably 0.880 g / cm 3 or more.
[0025] Also, since linear low-density polyethylene has side-chain branches in the linear structure of high-density polyethylene, compared with high-density polyethylene, the crystallinity does not become too high and it is excellent in flexibility.
[0026] Note that, from the viewpoint of strength, linear low-density polyethylene produced using a metallocene catalyst or a Ziegler catalyst may be used.
[0027] Also, the melt mass flow rate (MFR) of the linear low-density polyethylene is preferably 0.5 to 7.5 g / 10 min, more preferably 1.0 to 6.0 g / 10 min, and even more preferably 2.0 to 5.0 g / 10 min. When the melt mass flow rate (MFR) is 0.5 g / 10 min or more, the molecular weight is not too large, and flexibility and processability can be improved. When it is 7.5 g / 10 min or less, the molecular weight is not too small, and processing stability can be improved.
[0028] Note that the above melt mass flow rate is obtained by measuring in accordance with the provisions of JIS K7210:1999.
[0029] From the above, as the resin for forming the base film, with a density of 0.93 g / cm 3By using low-density polyethylene as described below, the flexibility and isotropy of the base film can be improved.
[0030] <Base film> In the base film of the present invention, the mass ratio of the homopolymer of 1-butene to low-density polyethylene is in the range of homopolymer of 1-butene: low-density polyethylene = 10:90 to 70:30. By setting the mass ratio of the homopolymer of 1-butene to low-density polyethylene within this range, the occurrence of necking during the formation of the base film can be prevented, enabling uniform expansion, and enabling the unwinding of the base material during the manufacturing process of the base film. Furthermore, it becomes possible to prevent the occurrence of blocking when winding up the base film and the thickness variation due to draw resonance when forming the base film. Therefore, it becomes possible to provide a base film excellent in uniform stretchability, rigidity, and processing stability.
[0031] Also, in the base film of the present invention, from the viewpoint of further improving the uniform stretchability of the base film, in the machine axis (longitudinal) direction (hereinafter referred to as "MD") of the base film and the direction orthogonal thereto (hereinafter referred to as "TD"), the ratio of the stress (at 40% elongation) to the stress (at 20% elongation) (that is, the elongation rate of the base film) is preferably 1 or more and 2 or less, more preferably 1.05 or more and 1.8 or less, and even more preferably 1.1 or more and 1.7 or less. When the elongation rate of the base film is greater than 2, it may become difficult to maintain expansion ring due to excessive stress increase. When the elongation rate of the base film is less than 1, necking may occur, making uniform expansion difficult.
[0032] Further, the stress (at 25% elongation) in MD and TD is preferably 5 MPa or more and 20 MPa or less, more preferably 6 MPa or more and 15 MPa or less, and even more preferably 7 MPa or more and 13 MPa or less. When the stress is greater than 20 MPa, the rigidity becomes too high, resulting in a decrease in the pick-up property of the semiconductor device and possible damage to the semiconductor device. When the stress is less than 5 MPa, the rigidity is low, making it difficult to unwind the base material during the manufacturing process of the base film and possibly reducing the coatability of the adhesive.
[0033] Also, from the perspective of suppressing the occurrence of slack due to the isotropy of the base film during expansion, the ratio of the stress in MD (at 25% elongation) to the stress in TD (at 25% elongation) (i.e., the stress ratio of the base film at 25% elongation) is preferably 0.8 or more and 1.3 or less, more preferably 0.85 or more and 1.15 or less, and even more preferably 0.9 or more and 1.1 or less.
[0034] Note that the above "stress" refers to the stress measured in accordance with JIS K7161-2:2014.
[0035] The thickness of the base film is preferably 50 to 300 μm, more preferably 80 to 150 μm. If the thickness of the base film is 50 μm or more, the handleability is improved, and if the thickness is 300 μm or less, the flexibility (expandability) can be improved. In the case of the base film for wafers, the thickness of the base film is preferably 50 to 150 μm, more preferably 70 to 100 μm.
[0036] <Manufacturing Method> The base film of the present invention is manufactured by using a resin material containing the above-mentioned homopolymer of 1-butene and a low-density polyethylene having a density of 0.93 g / cm 3 or less, and extruding and molding the resin material at a predetermined temperature using, for example, an extruder equipped with a T-die. Note that the base film of the present invention may also be manufactured by a known calendar method or inflation method.
[0037] <Other forms> The base film of the present invention may contain various additives. As the additives, known additives commonly used in semiconductor manufacturing tapes can be used. For example, crosslinking aids, antistatic agents, heat stabilizers, antioxidants, ultraviolet absorbers, lubricants, antiblocking agents, colorants, etc. can be mentioned. In addition, these additives may be used alone or in combination of two or more.
[0038] In addition, examples of the crosslinking aid include triallyl isocyanurate, etc. When the base film contains a crosslinking aid, the content of the crosslinking aid in the base film is preferably 0.05 to 5 parts by mass, more preferably 1 to 3 parts by mass, based on 100 parts by mass of the resin forming the base film.
Examples
[0039] Hereinafter, the present invention will be described based on examples. The present invention is not limited to these examples, and these examples can be modified and changed based on the gist of the present invention, and they are not excluded from the scope of the present invention.
[0040] The materials used for producing the base film are shown below. (1) LLDPE-1: Linear low-density polyethylene, melting point: 120 °C, density: 0.913 g / cm 3 , MFR: 2.0 g / 10 min (2) LLDPE-2: Linear low-density polyethylene, melting point: 108 °C, density: 0.921 g / cm 3 , MFR: 2.5 g / 10 min (3) LLDPE-3: Linear low-density polyethylene, melting point: 93 °C, density: 0.903 g / cm 3 , MFR: 2.0 g / 10 min (4) LLDPE-4: Linear low-density polyethylene, melting point: 124 °C, density: 0.936 g / cm 3 , MFR: 2.0 g / 10 min (5) LLDPE-5: Linear low-density polyethylene, density: 0.923 g / cm3 , MFR: 0.5 g / 10 min (manufactured by Prime Polymer Co., Ltd., trade name: Ultrex (registered trademark) 2005HC) (6) LDPE-1: Low-density polyethylene, melting point: 108 °C, density: 0.918 g / cm 3 , MFR: 7.5 g / 10 min (manufactured by Ube Maruzen PE Co., Ltd., trade name: UBE Polyethylene L719) (7) LDPE-2: Low-density polyethylene, melting point: 110 °C, density: 0.922 g / cm 3 , MFR: 5.0 g / 10 min (manufactured by Ube Maruzen PE Co., Ltd., trade name: UBE Polyethylene F522N) (8) PP Elastomer 1: Propylene-based elastomer, density: 0.889 g / cm 3 , MFR: 8.0 g / 10 min (at 230 °C), polyethylene content 4% (manufactured by ExxonMobil, trade name: Vistamaxx (registered trademark) 3588FL) (9) PP Elastomer 2: Propylene-based elastomer, density: 0.862 g / cm 3 , MFR: 3.0 g / 10 min (at 230 °C), polyethylene content: 16% (manufactured by ExxonMobil, trade name: Vistamaxx (registered trademark) 6102FL) (10) Amorphous polyolefin + crystalline polypropylene (1-butene·propylene copolymer: crystalline polypropylene = 50:50): density: 0.880 g / cm 3 , MFR: 11.7 g / 10 min (manufactured by Dainichi Kasei Co., Ltd., trade name: Pelicon CAP350S) (11) 1-Bu: Homopolymer of 1-butene, melting point: 128 °C, density: 0.920 g / cm 3 , MFR: 0.5 g / 10 min
[0041] (Example 1) (Preparation of Substrate Film) First, each material shown in Table 1 was blended to prepare a resin material for Example 1 having the composition (parts by mass) shown in Table 1. Next, this resin material was extruded using a three-layer coextrusion machine through a T-die under the conditions of a die temperature of 180 - 200 °C and a chill roll temperature of 40 °C to obtain a substrate film having the thickness shown in Table 1.
[0042] <Evaluation of the presence or absence of yield point> Using the produced base film, samples for measurement were obtained in accordance with JIS K7161-2:2014. Next, the obtained samples for measurement were set in a tensile testing machine (manufactured by Shimadzu Corporation, product name: AG-5000A) so that the distance between the gripping tools was 40 mm, and a tensile test was conducted at a tensile speed of 300 mm / min in an environment with a temperature of 23°C and a relative humidity of 40% in accordance with JIS K7161-2:2014.
[0043] Then, in the S-S curves (stress-strain curves) of MD and TD, those in which no yield point was confirmed during the elongation from an elongation rate of 0% to 100% (no necking occurred and uniform expansion was possible) were marked as 〇, and those in which a yield point was confirmed (necking occurred and uniform expansion was impossible) were marked as ×. The above results are shown in Table 1.
[0044] Note that the S-S curves (stress-strain curves) of MD and TD in the base film of this example are shown in FIGS. 1 to 2. As shown in FIGS. 1 to 2, it can be seen that there is no yield point in the S-S curves (stress-strain curves) of MD and TD during the elongation from an elongation rate of 0% to 100%.
[0045] <Measurement of stress in MD and TD> Using the produced base film, samples for measurement were obtained in accordance with JIS K7161-2:2014. Next, the obtained samples for measurement were set in a tensile testing machine (manufactured by Shimadzu Corporation, product name: AG-5000A) so that the distance between the gripping tools was 40 mm, and a tensile test was conducted at a tensile speed of 300 mm / min in an environment with a temperature of 23°C and a relative humidity of 40% in accordance with JIS K7161-2:2014.
[0046] Then, the stress at 25% elongation (25% stress) in the MD and TD of the base film was measured, and the ratio of the stress in the MD (at 25% elongation) to the stress in the TD (at 25% elongation) (i.e., the stress ratio of the base film at 25% elongation) was calculated. The above results are shown in Table 1.
[0047] Similarly, the stress at 20% elongation (20% stress) and the stress at 40% elongation (40% stress) in the MD and TD of the base film were measured, and the ratio of the stress at 40% elongation to the stress at 20% elongation in the MD (i.e., the elongation rate of the base film in the MD) and the ratio of the stress at 40% elongation to the stress at 20% elongation in the TD (i.e., the elongation rate of the base film in the TD) were calculated. The above results are shown in Table 1.
[0048] <Rigidity Evaluation> Using the produced base film, the rigidity was evaluated. More specifically, in the manufacturing process of the base film, when the unwinding of the base material is possible, it is marked as 〇 (the rigidity of the base film is excellent), and when the unwinding of the base material is unstable in the manufacturing process of the base film, it is marked as × (the rigidity of the base film is poor). The above results are shown in Table 1.
[0049] <Processing Stability Evaluation> Using the produced base film, the processing stability was evaluated. More specifically, when it is possible to suppress the adhesion of the base film to the transport roll during the transport of the base film, and at the same time, it is possible to prevent blocking during the winding of the base film and thickness variation due to draw resonance during the forming of the base film, it is marked as 〇 (the processing stability of the base film is excellent). When the base film adheres to the transport roll during the transport of the base film, making it difficult to transport and wind the base film, or when the thickness variation due to draw resonance during the forming of the base film is large, it is marked as × (the processing stability of the base film is poor). The above results are shown in Table 1.
[0050] (Examples 2 - 9, Comparative Examples 1 - 3) A base film having the thickness shown in Tables 1 to 2 was produced in the same manner as in Example 1 above, except that the composition of the resin component was changed to the composition (parts by mass) shown in Tables 1 to 2.
[0051] Then, in the same manner as in Example 1 above, evaluation of the presence or absence of a yield point, measurement of stress in the MD and TD directions, rigidity evaluation, and process stability evaluation were carried out. The above results are shown in Tables 1 to 2.
[0052] (Comparative Examples 4 to 6) First, in each comparative example, each material shown in Table 3 was blended to prepare a resin material for forming a surface layer and a resin material for forming an intermediate layer having the composition (parts by mass) shown in Table 3.
[0053] Next, using a co-extrusion machine for three-layer with a T-die, the resin material for forming the surface layer and the resin material for forming the intermediate layer were simultaneously extruded and molded under the conditions of 180 to 200 °C and a chill roll temperature of 40 °C, to obtain a base film having the thickness shown in Table 3 (i.e., the ratio of the intermediate layer to the entire base film is 80%) and having a three-layer structure laminated in the order of surface layer / intermediate layer / surface layer.
[0054] Then, in the same manner as in Example 1 above, evaluation of the presence or absence of a yield point, measurement of stress in the MD and TD directions, rigidity evaluation, and process stability evaluation were carried out. The above results are shown in Table 3.
[0055] [Table 1]
[0056] [Table 2]
[0057] [Table 3]
[0058] As shown in Table 1, the homopolymer of 1-butene and the low-density polyethylene having a density of 0.93 g / cm 3 hereinafter, in the base films of Examples 1 to 9 containing the low-density polyethylene and having a mass ratio of the homopolymer of 1-butene to the low-density polyethylene of homopolymer of 1-butene: low-density polyethylene = 10:90 to 70:30, no yield point was confirmed, and it was found that they have excellent uniform stretchability and excellent rigidity and processing stability.
[0059] On the other hand, as shown in Table 2, in the base film of Comparative Example 1, the mass ratio of the homopolymer of 1-butene to the low-density polyethylene was homopolymer of 1-butene: low-density polyethylene = 80:20, and since the content of the 1-butene homopolymer was large, a yield point was confirmed, and in TD, the ratio of the stress (at 40% elongation) to the stress (at 20% elongation) was less than 1, and it was found that the uniform stretchability was poor.
[0060] Also, as shown in Table 2, in the base film of Comparative Example 2, since the homopolymer of 1-butene was not contained, a yield point was confirmed, the uniform stretchability was poor, and the processing stability was also poor.
[0061] Also, as shown in Table 2, in the base film of Comparative Example 3, since the density of the low-density polyethylene was greater than 0.93 g / cm 3 (0.936 g / cm 3 ), a yield point was confirmed, and in TD, the ratio of the stress (at 40% elongation) to the stress (at 20% elongation) was less than 1, and it was found that the uniform stretchability was poor.
[0062] Also, as shown in Table 3, in the base film of Comparative Example 4, since the homopolymer of 1-butene is not contained, the yield point is confirmed, and it can be seen that the uniform elongation property is poor. Also, since the ratio of the stress in the MD (at 25% elongation) to the stress in the TD (at 25% elongation) is greater than 1.3, it can be seen that the film lacks isotropy. Also, since a low-viscosity butene copolymer is used, when forming the base film, the thickness variation due to draw resonance becomes large, and it can be seen that the processing stability is poor.
[0063] Also, as shown in Table 3, in the base film of Comparative Example 5, the homopolymer of 1-butene is not contained, and since the stress in the TD (at 25% elongation) is less than 5 MPa, in the manufacturing process of the base film, the unwinding of the base material becomes unstable, and it can be seen that the rigidity is poor.
[0064] Also, as shown in Table 3, in the base film of Comparative Example 6, the homopolymer of 1-butene is not contained, and in the MD and TD, since the ratio of the stress (at 40% elongation) to the stress (at 20% elongation) is less than 1, the yield point is confirmed, and it can be seen that the uniform elongation property is poor. Also, since the stress in the MD and TD (at 25% elongation) is less than 5 MPa, in the manufacturing process of the base film, the unwinding of the base material becomes unstable, and it can be seen that the rigidity is poor. Also, since the surface of the film has high adhesiveness, when transporting the base film, the base film adheres to the transport roll, making the transport and winding of the base film difficult, and it can be seen that the processing stability is poor.
Industrial Applicability
[0065] As described above, the present invention is suitable for a base film for a semiconductor manufacturing tape.
Claims
Claim 1 a homopolymer of 1-butene, and Low-density polyethylene having a density of 0.93 g / cm 3 or less, and the mass ratio of the homopolymer of 1-butene to the low density polyethylene is 10:90 to 70:30 for the homopolymer of 1-butene:low density polyethylene, the low density polyethylene is linear low density polyethylene, the melt mass flow rate (MFR) of the linear low density polyethylene is 1.0 to 6.0 g / 10 min, a base film for a semiconductor manufacturing tape, characterized in that the ratio of the stress (at 40% elongation) to the stress (at 20% elongation) is 1 or more and 2 or less.
Citation Information
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