复合材料粘弹性本构关系与热应力松弛规律研究 Ⅰ:理论分析

STUDY ON THE THERMAL STRESS RELAXATION AND CONSTITUTIVE EQUATIONS OF VISCOELASTIC COMPOSITE MATERIALS,PART I:GENERAL THEORY

基于均匀化理论研究了复合材料粘弹性分析的多尺度方法,以及复合材料等效热应力松弛规律。引入了等效粘弹性热应力系数张量和等效时变热膨胀系数的概念,建立了含温度变化的复合材料热粘弹性本构关系,并给出了基于均匀化理论的复合材料粘弹性松弛模量、等效热应力松弛系数和等效时变热膨胀系数的预测方法。对特殊复合材料的粘弹性性质进行了分析,结果表明:(1)复合材料的粘弹性本构关系具有与常规材料的本构关系类似的形式,但一般复合材料的热应力松弛规律与常规材料不同,其热膨胀不能瞬时完成,而具有明显的时变性质;(2)空心材料的热膨胀具有瞬时性质,其等效时变热膨胀系数与基体材料的热膨胀系数相同,其热应力松弛规律与基体材料的松弛规律相同;(3)当各组分材料的松弛模量的各分量可分解成不同的系数与相同的时间函数的乘积时,复合材料的等效时变热膨胀系数与时间无关,其松弛规律与常规材料的松弛规律完全相同。

Based on the homogenization theory, the multi-scale analysis methods of the viscoelastic property, and the effective thermal stress relaxation laws are studied. By defining the concepts, the effective thermal stress relaxation modulus (ETSRM) and the effective time-dependent coefficients of thermal expansion (ETCTE), the thermal viscoelastic constitutive equation is expressed in the same form as that of conventional materials. Besides, a homogenization-based method for predicting the effective viscoelastic relaxation modulus, ETSRM and ETCET is given. It is pointed out that, for viscoelastic composite materials, the thermal expansion coefficients are time-dependent, and the thermal expansion process can not be completed instantaneously, exhibiting an obvious time-delay effect. The analysis of several kinds of special composite materials shows that: (1) The thermal expansion of porous material has an instantaneous character, its ETCTE is the same as that of the matrix material which is time-independent, and its thermal stress relaxation law is also the same as that of the matrix material; (2) For a special kind of composite materials of which the relaxation moduli of all the components can be expressed as the products of different individual time-independent coefficients and a same time-dependent function, the effective time-dependent thermal expansion coefficient is time-independent, and the character of the relaxation laws is the same as that of conventional materials.