不完美界面聚合物基纤维复合材料的黏弹性行为

Viscoelastic behavior of fiber-reinforced polymer matrix composites with imperfect interface

为预测具有不完美界面的聚合物基纤维增强复合材料在时域下的黏弹性响应,在细观力学均匀化模型的基础上,研究了基体黏弹性对复合材料宏/细观特性的影响。根据弹性-黏弹性对应原理建立了基于均匀化理论的复合材料黏弹性性能评估方法,即将边值问题和材料均匀化本构引入Laplace域中进行求解,然后将材料的宏/细观响应通过性能较稳定的Zakian方法转化到时域当中,从而避免对含有积分形式的黏弹性本构进行分步迭代。另外,与经典唯象理论以及数值方法不同,细观力学方法LEHT采用了Trefftz概念,即通过求解偏微分方程得到微元体内部位移和应力的解析表达。引入带有刚度的弹簧模型用于描述界面处的损伤情况,并与纤维/基体的解析表达的函数正交性结合,实现了界面的精确模拟。最后通过周期性变分原理对晶胞施加周期性边界条件,并建立宏观均匀化本构用于预测材料的宏观性能。结果表明:该方法不仅能实现材料长期性能的高效预测,同时还原了代表性晶胞内的局部应力重分布来解释宏观模量衰退的影响。

To predict the viscoelastic responses of fiber-reinforced polymer matrix composites with imperfect interface in the time domain,the effects of viscoelasticity of polymers on the macroscopic/mesoscopic properties of composites are studied on the basis of the micromechanics model.According to the elastic-viscoelastic correspondence principle,a viscoelastic property evaluation method of composites based on the homogenization theory is developed.The boundary value problem and the materials′homogenization constitutive equation are introduced into the Laplace domain,and then the macro/meso responses of the materials are transformed into the time domain by Zakian′s method with relatively stable performance,thus avoiding the step-by-step iteration of the viscoelastic constitutive with integral form.Different from the classical phenomenological theory and other numerical methods,the present work adopts the Trefftz concept that employs the complete elastic solutions with unknown coefficients to represent the internal trial displacement/stress fields.A spring model with stiffness is introduced to describe the interfacial damage,combined with the functional orthogonality of the analytical expression of fiber/matrix,and the accurate simulation of the interface was realized.Finally,the periodic boundary conditions are applied to the cells by the periodic variational principle,and the macroscopic homogenization constitutive is established to predict the macroscopic properties of materials.The results show that the proposed method can not only realize the efficient prediction of the long-term properties of composites,but also restore the local stress redistribution within unit cells to illustrate the effect of macroscopic modulus degradation.