陶瓷基复合材料层合板的非线性损伤本构理论
NONLINEAR DAMAGE CONSTITUTIVE THEORY FOR CERAMIC MATRIX COMPOSITE LAMINATES
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摘要: 复杂应力本构关系模型是结构设计与性能评估的理论基础. 针对易损-非线性陶瓷基复合材料(CMC)层合板在组合加载下的变形响应, 在正交各向异性单层材料主方向损伤演化特性和应力-应变行为表征的基础上, 给出了不同角度单层非材料主方向的损伤柔度矩阵和损伤刚度矩阵的数学表达; 进一步考虑损伤层合板的非线性变形响应特性, 将其中面应变和曲率划分为弹性部分和非弹性部分, 对经典层合板理论进行拓展与改进, 分别描述了层合板的弹性变形和非弹性变形, 并最终给出了非线性CMC层合板的广义内力-变形物理方程, 从而丰富和发展了非线性复合材料的表征理论, 为复杂外载下CMC层合板变形行为的分析预测提供了新的模型和方法. 作为特例, 给出了正交对称CMC层合板的应变-内力关系的具体表达式, 并采用2D-C/SiC复合材料层合板, 模拟计算了轴向和偏轴拉伸载荷下材料的应力-应变行为, 验证了本构模型的合理性和适用性.Abstract: The constitutive model under complex stress is the theoretical basis for the design and performance evaluation of composite structures. This study focuses on the mechanical response of damageable and nonlinear ceramic matrix composite (CMC) laminates under combined loadings. Firstly, the expressions of off-axis damage compliance and damage stiffness matrices of single CMC layer as functions of fiber angle were represented on the basis of its on-axis orthotropic characteristics of damage evolution behavior and stress-strain response. In the following, the nonlinear strain response mechanisms of damaged laminated plate was considered and the deformation variable in terms of the mid-plane strain and curvature were divided into elastic and inelastic parts, respectively. Further, the classical laminate theory (CLT) was extended and improved, and the elastic deformation as well as the inelastic one of a laminated plate were formulated, respectively. Finally, the physical equation of the generalized internal force versus deformation of nonlinear CMC laminated plates was presented, which would supplement and enrich the mechanical characterization theory for nonlinear composite materials. In other words, it will serve as a new model and methodology for analyzing and predicting the deformation behavior of CMC laminates under complex external load. For orthogonal symmetric CMC laminates as a special case, the specific expressions of the relationship between mid-plane strain and internal force is presented. On this bases, the stress-strain behavior of a 2D-C/SiC composite laminate under on- and off-axis tension is simulated, and the reasonability and applicability of the constitutive model is verified.