Evolution behavior of major Poisson's ratio of 2D-C/SiC composites
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摘要: 泊松比是材料及其结构力学性能分析的重要参数之一。本文旨在研究2D-C/SiC复合材料主泊松比的非线性演化行为。首先，基于Mini复合材料模型与正交层压板模型，考虑纤维的横观各向同性性质，建立了2D-C/SiC复合材料的热残余应力计算模型；其次，应用剪滞理论与经典层压板理论，考虑材料的损伤与热残余应力释放机制，建立了2D-C/SiC复合材料的主泊松比计算模型；最后，通过试验表征了材料的应变响应及泊松比演化规律，并对理论模型进行了分析验证。结果表明，2D-C/SiC复合材料内部热残余应力较大，拉伸损伤过程中的热残余应力释放是负泊松比产生的原因；应力-应变曲线及泊松比演化曲线的模型预测结果均与试验曲线吻合较好，表明了理论分析模型的准确性与合理性。
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关键词:
- 陶瓷基复合材料 /
- 泊松比 /
- Mini复合材料模型 /
- 热残余应力
Abstract: Poisson's ratio is one of the important parameters in the analysis of mechanical properties of materials and structures. In this paper, the nonlinear evolution behavior of major Poisson's ratio of 2D-C/SiC composites was studied. Firstly, based on Mini composite model and cross-ply laminate model, the thermal residual stress calculation model of 2D-C/SiC composites was established considering the transverse isotropic property of fiber. Secondly, the major Poisson's ratio calculation model of 2D-C/SiC composites was established by using shear-lag theory and classical laminate theory while considering the damage and thermal residual stress release mechanisms of the material. Finally, the strain response and Poisson's ratio evolution of the material were characterized by experiments, and the theoretical model was analyzed and verified. The results show that the internal thermal residual stress of 2D-C/SiC composites is large, and the release of thermal residual stress during tensile damage is responsible for the negative Poisson's ratio. The model prediction results of stress-strain curve and Poisson's ratio evolution curve are in good agreement with the tested curves, which indicates the accuracy and reasonability of the theoretical analysis model. -
图 3 圆筒截面应力示意图
Figure 3. Schematic illustration of stresses on cylinder section
q—Fiber-matrix interface pressure; σφm—Circumferential stress in the matrix; ρ—Radial coordinate; φ—Angular coordinate
图 7 界面全部脱粘时的应力图
Figure 7. Stress diagram upon interface is completely debonded
L—Matrix crack spacing; Ld—Interface sliding length
图 8 2D-C/SiC复合材料拉伸试件形状和基本尺寸
Figure 8. Shape and basic dimensions of tensile specimen of 2D-C/SiC composites
R—Radius
图 9 2D-C/SiC复合材料纵向拉伸应力-应变曲线的试验值与预测值
Figure 9. Experimental and predicted longitudinal stress-strain curves of 2D-C/SiC composites
图 10 2D-C/SiC复合材料横向应变-应力曲线及其预测值
Figure 10. Tested and predicted transverse strain-stress curves of 2D-C/SiC composites
图 11 2D-C/SiC复合材料泊松比演化的试验曲线及其预测值
Figure 11. Tested and predicted evolution curves of Poisson's ratio of 2D-C/SiC composites
图 12 2D-C/SiC复合材料最终裂纹间距和开裂指数对横向应变的影响
Figure 12. Effects of ultimate crack spacing and cracking exponent on transverse strain of 2D-C/SiC composites
图 13 2D-C/SiC复合材料界面滑移应力、开裂指数和最终裂纹间距对泊松比曲线的影响
Figure 13. Effects of interface sliding stress, cracking exponent and final crack spacing on Poisson's ratio curves of 2D-C/SiC composites
表 1 2D-C/SiC复合材料模型基本参数
Table 1. Basic parameters of 2D-C/SiC composites model
Parameter Value Longitudinal modulus of fiber $ {E}_{1\mathrm{f}} $/GPa 230 Transverse modulus of fiber $ {E}_{2\mathrm{f}} $/GPa 14 Matrix modulus $ {E}_{\mathrm{m}} $/GPa 350 Fiber volume fraction $ {V}_{\mathrm{f}} $/vol% 40 Matrix volume fraction $ {V}_{\mathrm{m}} $/vol% 60 Fiber volume fraction in bundle $ {V}_{\mathrm{f}\mathrm{b}} $/vol% 70 Matrix volume fraction in bundle $ {V}_{\mathrm{m}\mathrm{b}} $/vol% 30 Axial Poisson's ratio of fiber $ {\nu }_{1\mathrm{f}} $ 20 Transverse Poisson's ratio of fiber $ {\nu }_{2\mathrm{f}} $ 0.07 Matrix Poisson's ratio $ {\nu }_{\mathrm{m}} $ 0.2 CTE of matrix $ {\alpha }_{\mathrm{m}} $/$ {(10}^{-6}\;{\mathrm{K}}^{-1}) $ 4.6 Axial CTE of fiber $ {\alpha }_{1\mathrm{f}} $/$ {(10}^{-6}\;{\mathrm{K}}^{-1}) $ 0 Transverse CTE of fiber $ {\alpha }_{2\mathrm{f}} $/$ {(10}^{-6}\;{\mathrm{K}}^{-1}) $ 8.8 Interface sliding stress $ \tau $/MPa 15 Final crack spacing $ {L}_{\mathrm{u}} $/μm 180 Initial crack spacing $ {L}_{0} $/μm 2000 Reference stress of matrix cracking $ {\sigma }_{\mathrm{R}} $/MPa 46 Minimum cracking stress $ {\sigma }^{*} $/MPa 256 Cracking exponent $ m $ 2.1 Note: CTE—Coefficient of thermal expansion. 
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表 2 2D-C/SiC复合材料试件尺寸和拉伸试验结果
Table 2. Specimen size and tensile test results of 2D-C/SiC composites
No. Width
/mmThickness
/mmModulus
/GPaStrength
/MPaL1 10.10 3.70 80.29 177.80 L2 10.12 3.68 99.86 232.20 L3 10.28 3.64 91.63 218.76 L4 10.14 3.66 117.42 231.48 L5 10.16 3.64 112.70 251.36 L6 10.22 3.62 126.83 256.80 L7 10.08 3.68 106.10 205.75 L8 10.12 3.66 91.49 233.00 Average − − 103.29 225.89
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