An improved numerical prediction method of elastic properties based on two unit-cells models for 3D angle-interlock woven composites and experimental verification
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摘要: 为准确预测三维角联锁机织复合材料的宏观弹性性能,对基于CT图像几何参数实测数据建立的内单胞和面单胞细观实体模型进行数值分析,其中面单胞模型采用组合面单胞形式,并开展了三维角联锁机织超高分子量聚乙烯(UHMWPE)纤维/聚氨酯复合材料的经向拉伸实验。结果表明:基于两单胞模型预测该复合材料的宏观弹性模量与实验结果吻合较好,组合面单胞的经向拉伸模量小于内单胞;经向拉伸时复合材料在经纱间接触面处、纬纱沿宽度方向的端部和经纱与基体的交界面处易出现应力集中现象;当纬纱层数小于30层时,应该考虑表面区域对复合材料整体力学性能的影响。Abstract: To accurately predict the macroscopic elastic properties of 3D angle-interlock woven composites, interior and surface unit-cells mesoscopic solid models were established for numerical analysis based on the geometric parameters measured in CT images, and surface unit-cells were modeled in the form of integrated surface unit-cells. Then a tensile test in warp direction was conducted for 3D angle-interlock woven ultra-high molecular weight polyethylene (UHMWPE) fiber/polyurethane composites. The results show that the predicted macroscopic elastic modulus values of the composites based on two unit-cells models are in good agreement with the experimental values. The tensile modulus in the warp direction of the integrated surface unit-cells is smaller than that of the interior unit-cells. During the tensile test in the warp direction, stress concentration tends to occur at the interface among warp yarns, the end of weft yarns along the width and the interface between warp yarns and matrix. When the number of weft layers is less than 30, the effect of surface region on the overall mechanical properties of the composites should be considered.
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Key words:
- 3D woven composites /
- unit cells /
- elastic modulus /
- finite element analysis /
- tensile test
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图 11 三维角联锁机织UHWMPE纤维/聚氨酯复合材料经向拉伸模量和纤维体积含量随纬纱层数的变化规律
Case 1—Accurate modulus of composites obtained by interior unit-cell and integrated surface unit-cells models; Case 2—Accurate modulus of composites obtained by only interior unit-cell model
Figure 11. Change law of tensile modulus in warp direction and fiber volume fraction of 3D angle-interlock woven UHWMPE fiber/polyurethane composites with the number of weft layers
表 1 三维角联锁机织UHMWPE纤维/聚氨酯复合材料细观几何参数测量
Table 1. Mesoscopic geometric parameters’ measurements of 3D angle-interlock woven UHMWPE fiber/ polyurethane composites
Yarn Parameter Number of measurements Average value Variable coefficient Input value Weft Height Hw 408 0.492 mm 0.137 0.469 mm Width Ww 408 1.919 mm 0.042 1.919 mm Space Sw 306 3.651 mm 0.012 3.333* mm Warp Width Wj 300 1.139 mm 0.014 1.111* mm Height Hj 300 0.382 mm 0.143 0.398 mm Inclination θs 255 45.6° 0.074 Notes: * represents data obtained by equation (10). 表 2 UHMWPE纤维和聚氨酯力学性能参数
Table 2. Mechanical properties of UHMWPE fiber and polyurethane
UHWMPE fiber Ea*/GPa Et[19]/GPa Ga[19]/GPa 94 3.5 1.0 Gt[19]/GPa νa[19] νt[19] 1.2 0.29 0.45 Polyurethane Em*/MPa νm[19] 195 0.25 Notes:Ea, Ga and νa—Axial tensile modulus, shear modulus and Passion’s ratio of fiber, respectively;Et, Gt and νt—Transverse tensile modulus, shear modulus and Passion’s ratio of fiber, respectively;Em and νm—Modulus and Poisson’s ratio of matrix, respectively; * represents data obtained by experiments. 表 3 三维角联锁机织UHWMPE纤维/聚氨酯复合材料试件的经向拉伸模量实验结果
Table 3. Experimental results of tensile modulus in warp direction of 3D angle-interlock woven UHWMPE fiber/polyurethane composite specimens
Specimen Ex/GPa Average/GPa Variable coefficient/% No.1 2.02 2.19 5.34 No.2 2.14 No.3 2.27 No.4 2.33 No.5 2.20 Note:Ex—Tensile modulus in x direction. 表 4 三维角联锁机织UHWMPE纤维/聚氨酯复合材料弹性常数的数值预测值
Table 4. Results of elastic constants of 3D angle-interlock woven UHWMPE fiber/polyurethane composites by numerical analysis method
Elastic
constantInterior
unit-cellIntegrated surface
unit-cellOverall Ex/GPa 3.12 1.75 2.39 Ey/GPa 17.21 14.20 15.58 Ez/GPa 0.80 0.46 0.62 Gxz/GPa 0.79 0.29 0.52 Gyz/GPa 0.30 0.18 0.24 Gxy/GPa 0.31 0.20 0.25 νxz 0.35 0.30 0.32 νyz 0.01 0.01 0.01 νxy −0.06 −0.04 −0.05 Notes:Ex, Ey and Ez—Tensile moduli in x, y and z directions, respectively;Gxz, Gyz and Gxy—Shear moduli in xz, yz and xy directions, respectively;νxz, νyz and νxy—Poisson’s ratios in xz, yz and xy directions, respectively. -
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