An Energy Approach to the Plasticity of a Two-Phase Composite Containing Aligned Inclusions
An Energy Approach to the Plasticity of a Two-Phase Composite Containing Aligned Inclusions
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DOI：
10.1115/1.2896040
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发表时间：
1995-12
期刊：
影响因子：
--
通讯作者：
Y. Qiu;G. Weng
中科院分区：
文献类型：
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作者：
Y. Qiu;G. Weng
基于线性比较复合材料（Tandon and Weng，1988）和韧性基体有效应力的能量准则（Qiu and Weng，1992），建立了一个非线性理论，用于估计含定向球状夹杂物的两相复合材料的应变势和总应力-应变关系。通过求解两个联立方程，一个是本构方程，另一个是有效应力与割线剪切模量的关系，确定了在给定外载荷作用下延性基体的塑性状态。然后，通过线性比较复合材料的有效性质，非线性系统的整体应变和应变势的评估。结果表明，对于含有排列孔洞或刚性夹杂的弹性不可压缩基体，导出的应变势分别精确地等于Ponte Castaneda（1991）的界或Willis（1977）型的估计。与平面应变双轴加载下的纤维增强复合材料的精确解的比较也显示出良好的一致性。该理论一般适用于浓度不高时的情况，并最终应用于研究碳化硅/铝系统的整体响应的纵横比依赖性。研究发现，在大多数类型的载荷下，两相复合材料的非线性塑性响应对夹杂物形状非常敏感，而弹性行为则更为敏感。
Based on a linear comparison composite (Tandon and Weng, 1988) and an energy criterion for the effective stress of the ductile matrix (Qiu and Weng, 1992), a nonlinear theory is developed to estimate the strain potential and the overall stress-strain relations of a two-phase composite containing aligned spheroidal inclusions. The plastic state of the ductile matrix under a given external load is determined by solving two simultaneous equations, one being its constitutive equation and the other the expression of its effective stress as a function of its secant shear modulus. Then by means of the effective properties of the linear comparison composite, the overall strain and strain potential of the nonlinear system are evaluated. It is demonstrated that, for an elastically incompressible matrix containing either aligned voids or rigid inclusions, the derived strain potential is exactly equal to Ponte Castaneda's (1991) bound or estimate, respectively, of Willis' (1977) type. Comparison with an exact solution of a fiber-reinforced composite under the plane-strain biaxial loading also shows an excellent agreement. The theory is generally intended for the condition when the concentration is not high, and is finally applied to examine the aspect-ratio dependence of the overall response for a silicon carbide/aluminum system. It is found that, more so than the elastic behavior, the nonlinear plastic response of the two-phase composite is very sensitive to the inclusion shape under most types of loading.