A TRANSVERSELY ISOTROPIC VISCO-HYPERELASTIC CONSTITUTIVE MODEL FOR SHORT FIBER REINFORCED EPDM
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摘要: 短纤维增强三元乙丙橡胶包覆薄膜，是一种应用于固体火箭发动机缠绕包覆装药的新型复合材料。为了描述其在工作过程中受振动、冲击等载荷作用时的力学行为，基于黏弹性理论和纤维增强连续介质力学理论，提出了一种考虑应变率强化效应的横观各向同性黏-超弹本构模型。模型中应变能函数被分解为超弹性应变能和黏性应变能，其中超弹性应变能包括表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能，黏性应变能采用表征橡胶和纤维黏性响应的宏观唯象模型。选取表征各应变能的函数形式，经过数学变换、替代、叠加，求解确定最终的应力应变形式，明确模型参数获取的具体步骤，将预测结果与实验结果对比分析，准确性较高。研究表明：该模型能有效预测材料在低应变率下纤维方向为0°~45°的非线性率相关力学特性；模型形式易于实现有限元开发，对固体火箭发动机装药结构完整性分析具有参考价值。Abstract: Short fiber reinforced EPDM inhibitor film is a new type composite material, which has been applied in solid rocket motor winding and coating. Based on viscoelastic theory and fiber reinforced continuum mechanics theory, a transversely isotropic visco-hyperelastic constitutive model is proposed to describe strain rate dependent mechanical behaviors under vibration, impact and other loading conditions. The strain energy function is decomposed into hyperelastic strain energy and viscous strain energy, in which hyperelastic strain energy includes two parts: representing the strain energy from isotropic rubber matrix and anisotropic fiber tensile deformation. A macro-phenomenological model is proposed to characterize the viscous response from rubber matrix and fibers. Then, select the function form of each strain energy. After a series of mathematical transformation, substitution and superposition, the final form of stress and strain is determined. Moreover, the specific steps to obtain model parameters are defined. Finally, the predicted and experimental results are compared and analyzed, which indicates high accuracy of the proposed model. Studies show that it can effectively predict their nonlinear and strain rate dependent mechanical behaviors in the fiber direction from 0° to 45° at low strain rate. It is concluded that the proposed model is easy to realize finite element development, which has reference value for the structural integrity analysis of solid rocket motor.
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Key words:
- EPDM /
- transversely isotropic /
- visco-hyperelastic /
- constitutive model
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图 2 短纤维增强EPDM单轴拉伸变形
Figure 2. Uniaxial tensile deformation of short fiber reinforced EPDM
图 5 不同应变率下的应力-应变曲线对比
Figure 5. Comparison of stress-strain curve under different strain rates
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