复合材料蠕变本构关系及实验测定 Ⅰ.本构关系

CREEP CONSTITUTIVE EQUATION AND EXPERIMENTAL DETERMINATION OF COMPOSITE MATERIALS

蠕变是复合材料最重要的力学性能之一,实验表明:复合材料在蠕变条件下的变形可以分为弹性变形、粘弹性变形和粘塑性变形。应用不可逆过程的热力学和广义变量的概念可以分析材料的蠕变变形。本文首先回顾了热力学的基本方程;基于Schapery本构关系的假设和思路推导了蠕变本构关系的一般形式,其中包括弹性变形、粘弹性变形和粘塑性变形;考虑到广义力选取的不唯一性,本文提出了广义力选取的原则以使得到的本构关系尽可能地简单;由此本文给出了复合材料的一维蠕变,各向同性复合材料的二维蠕变和纤维增强复合材料平面内的蠕变的本构关系。

Creep is one of the most important mechanical behaviors of composite material.The results of creep-recovery experiments show that under creep condition deformation can be divided into three parts: elastic deformation, viscoelastic deformation which can recover slowly and visco-plastic deformation which cannot when the load is removed.The thermodynamics of irreverible processes and concept of generalized variables can be used to derive creep constitutive equation in which strain is expressed as observable variable.In this paper, the foundamental thermodynamics equations are reviewed.Based on the assumption and idea of Schapery's equation, the common formula of multi-dimensional creep constitutive equation is derived which includes elastic, viscoelastic and viscoplastic deformations. Considering that the generalized force is not unique, the authors proposed a principle for selecting variables so that the result is as simple as possible. According to such a principle, some special constitutive equations are presented, which include the equations for one-dimensional problems, two-dimensional problems of the isotropic material and the plane problems of fibre reinforced composite materials.