Method of weaving a double polyaxial fabric and double polyaxial fabric
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- CALLAS JOÃO CARLOS
- Filing Date
- 2025-11-18
- Publication Date
- 2026-06-25
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Figure BR2025050530_25062026_PF_FP_ABST
Abstract
Description
"METHOD OF WEAVING A DOUBLE POLYAXIAL FABRIC AND DOUBLE POLYAXIAL FABRIC"FIELD OF THE INVENTION
[0001] The present invention relates to a method of weaving a double polyaxial fabric consisting of continuous filament yarns in the warp direction ( longitudinal direction) and weft direction ( transverse direction) , with the warp yarns having tangling points , wherein the layers of the double polyaxial fabric are j oined directly during weaving thereof , rather than by j oining separate layers obtained individually . The present invention also relates to the double polyaxial fabric made from said method .BACKGORUND OF THE INVENTION
[0002] The weaving technology is widely used to produce fabrics for various purposes , including ballistic applications . Currently, ballistic fabrics are predominantly made using aramid yarns and the plain weaving technique , of fering recogni zed strength and protection properties . However, these fabrics face several performance and cost limitations that restrain their ef fectiveness in ballistic applications .
[0003] One of the main limitations of aramid fabrics is the high material cost , which directly impacts the final price of the products . Furthermore , aramid yarns are sensitive to moisture , which can s igni ficantly reduce their strength, service li fe , and, consequently, their ballistic performance . To mitigate this problem, it is necessary to apply special repellent resins or sealed casings , increasing the cost and complexity of production . Another critical issueis the low tenacity of aramid yarns compared to more modern alternatives, which requires the use of a greater number of layers to achieve the required strength, resulting in heavier end products that are less suitable for applications such as ballistic protection solutions.
[0004] The plain weaving technique used in aramid fabrics also has structural disadvantages. Plain weaves create significant voids between the warp and weft yarns, which reduces uniformity and increases the need for adhesives to bond the layers in the process of forming ballistic plates or blankets. This additional use of adhesives results in heavier, stiffer, and more expensive products. The high density of aramid (1.44 g / cm3) compared to other materials exacerbates the weight problem, making the fabrics less competitive .
[0005] Ultra-high molecular weight polyethylene (UHMWPE) yarns are also known for their superior performance in protective applications, including ballistics. This material has higher tenacity and tensile strength than aramid, allowing for the creation of lighter and more efficient fabrics with smaller number of layers. Furthermore, UHMWPE has a significantly lower density (0.93 g / cm3) , which contributes to reducing the overall weight of ballistic plates. Another advantage of UHMWPE is its moisture resistance, eliminating the need for additional liquid protection treatments, simplifying the production process and reducing costs.
[0006] Even more promising is the possibility of integrating UHMWPE into the double-weaving process, whereintwo layers of fabric are joined directly during manufacturing. In this approach, binder yarns are strategically inserted to connect the two sets of warp and weft, creating a stable and uniform three-dimensional structure. This method eliminates the need for adhesives to join layers, resulting in lighter fabrics with better ballistic performance, while also improving weight distribution and structural efficiency.
[0007] However, although the benefits of UHMWPE are widely recognized, there are still no reports of its application in textile structures based on double weaves for exclusive use in ballistic armor. This technological gap represents a significant opportunity for the development of new fabrics that combine the intrinsic advantages of UHMWPE with the benefits of double-weaving. Such innovation would enable the advancement of lighter, stronger, and more affordable ballistic products, meeting the growing demand for more efficient and modern armor solutions.
[0008] To solve existing technical problems, the present invention aims to provide a method of weaving a double polyaxial fabric consisting of continuous filament yarns in the warp and weft directions, with the warp yarns having tangle points, wherein the layers of the double polyaxial fabric are joined directly during weaving thereof by double plain or twill weaves, rather than by joining separate layers obtained individually.
[0009] Furthermore, the present invention also aims to provide a double polyaxial fabric made from said method.
[0010] Some prior art documents describe weaving methods for producing double ballistic fabrics and the fabrics thus obtained.
[0011] Brazilian patent No. BR 11 2012 007306 0, published on April 7, 2011, in the name of BARRDAY INC., describes a method and apparatus for producing multilayer fabric for ballistic applications. The fabric is made by interweaving two distinct sets of yarns to form the layers. The layers can be secured together without the use of adhesives or stitching, avoiding problems such as fraying or damage to the yarns .
[0012] According to the Brazilian patent in question, these layers are joined together using security yarns that are interwoven with at least some of the upper yarns (yarns from an upper layer of the fabric) and some of the lower yarns (yarns from a lower layer of the fabric) , thus enabling the production of a multilayer fabric in a unified construction without the need for joining the different fabric layers after being formed individually.
[0013] On the other hand, according to the present invention, the fabric layers are not interwoven with security yarns, but rather with double plain or twill weaves of the same warp and weft yarns, joining the upper fabric to the lower fabric with a spacing to form the double fabric according to the invention.
[0014] Furthermore, the security yarns used to interweave the fabric layers in the Brazilian patent in question are not ballistic yarns and have lower denier, lowerstrength, and lower tenacity of the main yarns, that is, the warp and weft yarns.
[0015] Brazilian patent No. BR 11 2015 019791 4, published on July 18, 2017, in the name of TEIJIN ARAMID GMBH, describes a woven fabric structure with thermoplastic fibers and high-strength fibers. Thermoplastic fibers can be in the form of a woven fabric or a non-crimp fabric, preferably a unidirectional non-crimp fabric.
[0016] In the fabric structure according to the Brazilian patent in question, high-strength fibers are joined to the thermoplastic fibers by warp and / or weft yarns, forming a double fabric, without the need for any additional connecting agents such as adhesive films or foils.
[0017] However, according to the Brazilian patent in question, the fabric layers are joined by compacting the layers that form the fabric under specific temperatures and pressures, such as, during this compaction, the thermoplastic yarn that composes the fabric layers serves as an adhesive by melting with the temperature.
[0018] Thus, the weaving method for producing double fabrics in Brazilian patent No. BR 11 2015 019791 4 differs completely from the method according to the present invention, since in the latter, the layers that form the double fabric are woven together during the weaving process using double plain or twill weaves.
[0019] As can be seen, although the prior art reveals methods for weaving double fabrics, no reference is made to a method of weaving a double polyaxial fabric consisting of continuous filament yarns in the warp direction(longitudinal direction) and weft direction (transverse direction) , with the warp yarns having tangling points, in which the layers of the double polyaxial fabric are joined directly during weaving thereof, rather than by joining separate layers obtained individually.
[0020] Furthermore, the prior art documents do not describe a double polyaxial fabric made from said method with improved ballistic properties, such as the fabric according to the present invention.SUMMARY OF THE INVENTION
[0021] The present invention provides significant advantages over the methods for weaving double fabrics and the fabrics thus obtained described above.
[0022] It is an objective of the present invention to provide a method of weaving a double polyaxial fabric comprising the following steps: a) subjecting continuous filament yarns bobbins to be used in the warp direction to tangling (i) ; b) accommodating the tangled yarns from step a) into bobbins (ii) ; c) transferring (iii) the yarns accommodated on the bobbins to a spool, forming a warp yarn blanket; d) introducing into the loom the yarns of the warp blanket in the warp direction (iva) and the weft yarns in the transverse direction (ivb) ; e) weaving (v) the double polyaxial fabric by interlacing the warp yarns of the formed blanket with the weft yarns, in which the weft yarns are inserted into the loom in the transverse direction; f) obtaining the double polyaxial fabric (vi) , in which the double polyaxial fabric comprises two fabric layers, the fabric layers being directly joined in step e) by means ofdouble plain or double twill weaves; and in which the weft yarns are non-tangled continuous filament yarns.
[0023] It is also an object of the present invention to provide a double polyaxial fabric with double plain or twill weaves made of continuous filament yarns, in which the double polyaxial fabric has a total number of warp yarns of 60-220 yarns / 10 cm of fabric, a total number of weft yarns of 80-220 yarns / 10 cm of fabric, and a total basis weight of 300 to 1000 g / m2.BRIEF DESCRIPTION OF THE DRAWINGS
[0024] Figure 1 illustrates a process flow diagram of the method of weaving a double polyaxial fabric according to the present invention.
[0025] Figure 2 illustrates how the yarn tangling step is performed according to the method of the present invention .
[0026] Figure 3 illustrates the bobbins of tangled yarns, arranged in cages before proceeding to the warping step .
[0027] Figure 4 illustrates a spool of warp yarns formed after transferring the tangled yarns from the bobbins to the spool.
[0028] Figure 5 shows the flow diagram of the weaving process on the looms.
[0029] Figure 6 illustrates the right side of a double polyaxial fabric with 3X1 double twill weaves according to the present invention.
[0030] Figure 7 illustrates the back side of a double polyaxial fabric with 3X1 double twill weaves according to the present invention.
[0031] Figure 8 illustrates the right side of a double polyaxial fabric with double plain weave according to the invention.
[0032] Figure 9 illustrates the back side of a double polyaxial fabric with double plain weave according to the invention . DETAILED DESCRIPTION OF THE INVENTION
[0033] Although the present invention may be susceptible to different embodiments, a preferred embodiment is shown in the following detailed description, with the understanding that this description should be considered an exemplification of the principles of the invention and is not intended to limit the present invention to what has been illustrated and described herein.
[0034] In one embodiment, the present invention relates to a method of weaving a double polyaxial fabric comprising the following steps: a) subjecting continuous filament yarns bobbins to be used in the warp direction to tangling (i) ; b) accommodating the tangled yarns from step a) into bobbins (ii) ; c) transferring (iii) the yarns accommodated on the bobbins to a spool, forming a warp yarn blanket; d) introducing into the loom the yarns of the warp blanket in the warp direction (iva) and the weft yarns in the transverse direction (ivb) ; e) weaving (v) the double polyaxial fabric by interlacing the warp yarns of the formed blanket with the weft yarns, in which the weft yarns areinserted into the loom in the transverse direction; f) obtaining the double polyaxial fabric (vi) , in which the double polyaxial fabric comprises two fabric layers, the fabric layers being directly joined in step e) by means of double plain or double twill weaves; and in which the weft yarns are non-tangled continuous filament yarns.
[0035] According to the present invention, the continuous filament yarns that constitute said fabric may be continuous filament yarns of any suitable material such as ultra-high molecular weight polyethylene (UHMWPE) , aramid, pure graphene or hybrids, wherein the hybrid continuous filament yarns are selected from the group comprising continuous filament yarns of graphene and polymers or graphene and carbon fibers, provided that they have a yarn linear density value of 400 to 3000 Denier and tenacity values of 12 to 150 cN / dtex.
[0036] In a preferred embodiment, the yarns used in the method according to the present invention are ultra-high molecular weight polyethylene (UHMWPE) yarns with a yarn linear density value of 1600 Denier, tenacity of 31 to 42 cN / Dtex, tensile strength of 551.57 to 660 N, final elongation of 3.0 to 4.0%, and Young's Modulus of 1100 to 1400 g / den, which are yarns that have an exceptional strength-to-weight ratio, being significantly lighter than other ballistic materials, such as aramid, while offering high tensile strength. Furthermore, they have superior impact resistance, effectively absorbing and dissipating projectile energy.
[0037] Table 1 below reflects the main physical properties of the UHMWPE yarns preferred for carrying out the method according to the present invention, containing 480 filaments.Table 1
[0038] Another advantage of this type of yarn is its chemical and environmental resistance, which extends its durability and performance in adverse conditions. These yarns also feature low density and high flexibility, allowing for the creation of lighter and more comfortable ballistic protection .
[0039] The yarns to be used in the warp direction are initially subjected to a tangling step, as shown in Figure 2. This step consists of inserting spools of continuous filament yarns into an interlacing machine to interlace the filaments of these yarns. A flow of air is blown directly onto the surface of the yarn. The air is blown through the inflation point (1) at a pressure of 0.15 to 0.5MPa (1.5 to 5 bar) , preferably 0.45 MPa (4.5 bar) , having as a final result a number of tangling / interlacing points of 10to 20 points / meter of yarn, preferably 15 tangling points / meter of yarn.
[0040] In a preferred embodiment of the method according to the invention, a standard P431 insert is used for air injection during the tangling step. This insert is specifically designed for 1600 Denier UHMWPE yarns. This insert controls the air flow to create slight tangling / interlacing points (2) in the yarn.
[0041] Tangling is essential for the continuity of the method, as it overcomes the problem of f ilamentation of UHMWPE yarns caused by static and friction generated during the weaving process. This f ilamentation causes the accumulation of broken filaments in the yarn until it breaks completely, which is known as "bushing".
[0042] This step is performed exclusively for warp yarns, as these yarns suffer from this f ilamentation problem from the warping step, where the yarn placed in the warp cage has direct contact with the tensioners and warp yarn separation reeds, to the weaving process itself on the loom, where these yarns pass through tension rollers, frame heddles, and the reed that is moving, generating high levels of friction. The weft yarns, on the other hand, are inserted into the loom directly across the fabric and, therefore, are not subjected to friction that affects yarn quality.
[0043] To ensure that the tangling process produces a satisfactory interlaced yarn for use in the weaving method according to the present invention, a Fadis Textile Machine Sincro Multipla Jet Premium - Y05M interlacing machine isused, with the parameters set according to Table 1, which may vary according to the type of interlacing machine used.Table 2
[0044] After the tangle process, the tangled yarns are placed on several bobbins that are placed on the warpmachine cage, as shown in Figure 3. The yarns are then transferred from these bobbins to a spool, as shown in Figure 4, so they can be inserted into the loom for the subsequent weaving steps.
[0045] The combination of these multiple yarn bobbins, grouped in parallel, forms a web of yarns on the spool, which is called warp yarns.
[0046] After this preparation, the warp yarns are fed to the loom for the weaving process.
[0047] The method according to the present invention can be performed in a Jacquard loom or a Ratier rapier loom for weft yarn insertion.
[0048] Figure 5 illustrates a representative diagram of the weaving process according to the invention on a Ratier rapier loom.
[0049] In this scheme, the warp yarns are inserted into the loom from behind it (A) and then passed through a tensioning cylinder (B) , where the tension is adjusted according to the desired fabric.
[0050] After this, the warp yarns are passed through the loom's crossbar separator bars (C) , so that each yarn has an inverse sequence to its adjacent yarn, thus forming two yarn planes, where the yarn sequence is separated into even and odd yarns. The purpose of this step is to keep the yarns in the same sequence, avoiding tangling with adjacent yarns and facilitating yarn location in the event of a loom break .
[0051] After passing through the crossbar separator bars, the yarns are passed one by one through the heddles ofthe loom frames (D and E) , which are wires arranged in parallel and supported by the frames. As each yarn passes through the loom's heddles, as the frames move up and down according to the loom's machine programming (tables 3 and 5 below) , an opening called a shed (F) forms through which the weft yarns will be inserted, in the transverse direction, forming the interlacing of the warp and weft yarns to form the double polyaxial fabric with double plain or twill weaves according to the invention.
[0052] Immediately after the weft yarn is inserted through the system of grippers that carries the yarn from one side to the other in the transverse direction of the fabric, the reed (G) moves back and forth on the loom, pressing a weft yarn against the previous weft yarn, compacting the weft yarns, which is called the loom's beat- up .
[0053] After the warp and weft yarns are interlaced, and after the loom's reed beat-up, the fabric itself is formed, which then passes through the loom' s tensioning assembly (H) .
[0054] Finally, after passing through the tensioning assembly, the fabric is wound onto a cylinder (I) , thus completing the weaving process and obtaining the double polyaxial fabric.
[0055] In a second embodiment, the present invention provides a double polyaxial fabric obtained through the described method, wherein said double polyaxial fabric has a total warp yarn linear density of 60-220 yarns / lOcm of double fabric, preferably 140 yarns / lOcm of double fabric or70 yarns / lOcm for each face / side of the double fabric, a total weft yarn linear density of 80-220 yarns / lOcm of double fabric, preferably 150 yarns / lOcm of fabric or 75 yarns / lOcm for each face / side of the double fabric, and a total basis weight of 300 to 1000 g / m2, preferably 520 g / m2.
[0056] By "number of yarns for each face / side of the double fabric" it is meant that, in a double fabric according to the invention containing, for example, a total number of yarns of 140 yarns / 10 cm of the double fabric itself, each individual side of the double fabric has half the total number of yarns, that is, 70 yarns on the back side and 70 yarns on the front side.
[0057] The warp yarns that are interlaced with the weft yarns to form the double polyaxial fabric according to the invention are the yarns that have undergone the tangling process and then been subjected to the warping, while the weft yarns are the natural yarns, that is, those that have not undergone the tangling step.
[0058] As described above, the interlacing of the warp yarns with the weft yarns occurs according to a pattern defined on the machine that moves the warp frames and with a defined weft entry programmed on the loom's machine panel.
[0059] To make a double polyaxial fabric with 3x1 double twill weaves as shown in figures 6 and 7, the machine pattern and weft entry are defined according to table 3 programmed on the loom panel, and the general loom adjustment setup is according to table 4.Table 3Table 4do not use drop wires .
[0060] To make a double polyaxial fabric with double warp weaves as shown in figures 8 and 9, the machine pattern and weft entry are defined according to table 5 programmed on the loom panel, and the general loom adjustment setup is according to table 6.Table 5Table 6do not use drop wires .
[0061] This definition in tables 5 and 6 induces the loom to interlace the warp and weft yarns so that a double fabric is formed during weaving itsel f , that is , a fabric with two layers of fabric interconnected by a double twill or double plain weave , eliminating the need to produce individual layers for later j oining to obtain the same type of fabric .
[0062] When using the double polyaxial fabric of the present invention to form multi-layer armor plates , a reduced amount of adhesive is required to complete the j oining of the double fabric layers by 25 to 50% , compared to the amount of adhesive used in fabrics formed by conventional non-double fabric weaving methods .
[0063] Thus , the weaving method according to the present invention provides greater productivity by forming a double fabric immediately after leaving the loom, and reduces process costs for obtaining double fabrics , as it requires fewer production steps than conventional non-double fabric weaving methods .
[0064] Furthermore , j oining the fabric layers using double twill or double plain weaves during weaving allows the resulting double polyaxial fabric to have greater flexibility and a lighter weight compared to aramid fabricswith single weaves , which are commonly used as ballistic fabrics .EXAMPLES :
[0065] The following examples illustrate the comparative balli stic results for ballistic tests conducted in accordance with ABNT NBR 15000-2 and NI J STD 0101 . 04 standards , comparing the double multiaxial fabric with double twill and plain weaves of the present invention to aramid fabrics with plain weave bindings . The fabric according to the present invention used in the tests was manufactured with 1600-denier UHMPE yarns .Example 1 :
[0066] Example 1 was performed following the standard ABNT NBR 15000-2 - Armor Systems - Ballistic Protection Part 2 : Classi fication, Requirements , and Test Methods for Flat Materials in samples of conventional aramid ballistic armor and the new Double Polyaxial Fabric ballistic armor . Table 7 below describes in detail the test results :Table 7
[0067] From the table above , it can be seen that , for a ballistic limit test (V50 ) , the velocities at which the threats had a 50% chance of completely penetrating the samples were considerably higher for the armor made with the double polyaxial fabric according to the present invention, compared to the 9-layer aramid armor .Example 2 :
[0068] Example 2 was performed in accordance with standard NI J STD 0101 . 04 on vests already constructed with layers of the Double Polyaxial Fabric according to the present invention combined with layers of unidirectional nonwoven fabric made of continuous UHMWPE fibers and on hybrid vests made of aramid and UHMWPE with a simple textile construction . Table 8 below describes in detail the results of the tests performed :Table 8
[0069] From the table above , it can be seen that , for a ballistic limit test (V50 ) , the velocities at which the threats have a 50% chance of completely piercing the samples were cons iderably higher for the vest made with the double polyaxial fabric, since the vest with double polyaxial fabric is 10% lighter, according to the present invention, compared to the hybrid aramid and UHMWPE vest with standard textile construction .
[0070] Considering the ballistic tests presented above , the ef ficiency of the double polyaxial fabric according to the present invention and, consequently, of its production method is clear, since the probability of complete perforation of the vest for 9mm FMJ RN ammunition will only occur at velocities equal to or greater than 527 m / s , with a tolerance of 11 m / s , while the velocity of this ammunition under normal conditions is 340 to 420 m / s , that is , lower than the limit determined for the double polyaxial fabric according to the present invention .
[0071] Therefore , the embodiments presented in the present invention do not limit the totality of possibilities ; it is understood that various omis sions , substitutions , and changes may be made by a person skilled in the art , without departing from the spirit and scope of the present invention .
[0072] It is expressly anticipated that all combinations of elements that perform the same function in substantially the same manner to achieve the same results are within the scope of the invention . Substitutions of elements from one described embodiment to another are also fully intended and contemplated .
[0073] Those skilled in the art will appreciate the knowledge presented herein and will be able to reproduce the invention in the embodiments presented and in other variants as covered by the scope of the attached claims .
Claims
SET OF CLAIMS1. Method of weaving a double polyaxial fabric characterized by comprising the following steps: a) subjecting bobbins of continuous filament yarns to be used in the warp direction to tangling (i) ; b) arranging the tangled yarns from step a) onto bobbins (11) ; c) transferring (iii) the tangled yarns arranged on the bobbins to a spool, forming a warp yarn blanket; d) introducing into the loom the yarns of the warp blanket in the warp direction (iva) and the weft yarns in the transverse direction (ivb) ; e) weaving (v) the double polyaxial fabric by interlacing the warp yarns with the weft yarns; f) obtaining the double polyaxial fabric (vi) , wherein the double polyaxial fabric comprises two fabric layers, the fabric layers being directly joined in step e) by means of double plain or double twill weaves; and wherein the weft yarns are non-tangled continuous filament yarns.
2. Method, according to claim 1, characterized in that the continuous filament yarns have a yarn linear density value of 400 to 3000 Denier and a tenacity of 12 to 150 cN / dtex .
3. Method, according to claim 2, characterized in that the continuous filament yarns are UHMWPE yarns.
4. Method, according to claim 2, characterized in that the UHMWPE yarns have a yarn linear density value of 1600 Denier .
5. Method, according to claim 3, characterized in that the UHMWPE yarns have a tenacity of 31 to 42 cN / Dtex, a tensile strength of 551.57 to 660 N, a final elongation of 3.0 to 4.0% and a Young's modulus of 1100 to 1400 g / den.
6. Method, according to claim 3, characterized in that the UHMWPE yarns have a tenacity of 35 cN / Dtex, a tensile strength of 604.95 N, a final elongation of 3.5% and a Young's modulus of 1316 g / den.
7. Method, according to any one of the preceding claims, characterized in that, in step a) , air is blown through an inflation point (1) at a pressure of 1.5 to 5 Bar, preferably 4.5 Bar, by a standard P431 insert.
8. Method, according to any one of the preceding claims, characterized in that, in step a) , the number of tangling points in the yarn is of 10 to 20 points / meter of yarn, preferably 15 points / meter of yarn.
9. Method, according to any one of the preceding claims, characterized in that step d) is carried out on a Ratier rapier loom.
10. Double polyaxial fabric obtained by the method as defined in any one of claims 1 to 9, characterized in that it has a total warp yarn linear density of 60-220 threads / lOcm of fabric, a total weft yarn linear density of 80-220 threads / lOcm of fabric, and a total basis weight of 300 to 1000 g / m2.
11. Polyaxial fabric, according to claim 10, characterized in that the total warp yarn linear density is of 140 yarns / 10 cm of fabric or 70 yarns / 10 cm for each face / side of the double fabric.
12. Polyaxial fabric, according to claim 10, characterized in that the total weft yarn linear density is of 150 yarns / 10 cm of fabric or 75 yarns / 10 cm for each face / side of the double fabric.
13. Double polyaxial fabric, according to claim 10, characterized in that it has a total basis weight of 520 g / m2.
14. Polyaxial fabric, according to claim 10, characterized in that the continuous filament yarns that constitute said fabric have a yarn linear density of 400 to 3000 Denier and tenacity of 12 to 150 cN / dtex.
15. Polyaxial fabric, according to claim 14, characterized in that the continuous filament yarns are UHMWPE yarns .
16. Polyaxial fabric, according to claim 15, characterized in that the UHMWPE yarns have a yarn linear density of 1600 Denier.
17. Polyaxial fabric, according to claim 16, characterized in that the UHMWPE yarns have a tenacity of 31 to 42 cN / Dtex, a tensile strength of 551.57 to 660 N, a final elongation of 3.0 to 4.0%, and a Young's modulus of 1100 to 1400 g / den.
18. Polyaxial fabric, according to claim 17, characterized in that the PEUAPM yarns have a tenacity of 35 cN / Dtex, a tensile strength of 604.95 N, a final elongation of 3.5%, and a Young's modulus of 1316 g / den.