弹塑性形式一致的航空颗粒增强复合材料细观力学模型
A CONSISTENT ELASTOPLASTIC MICROMECHANICAL MODEL FOR AERONAUTICAL PARTICLE-REINFORCED COMPOSITES
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摘要: 颗粒增强复合材料在一些重要航空部件中已得到应用, 其弹塑性行为的精确预测对材料和结构设计至关重要, 也是复合材料力学领域长期致力于解决的科学难题. 为此, 本文基于应力集中系数, 建立了一种弹塑性形式一致的颗粒增强复合材料细观力学本构模型. 首先, 利用经典细观力学方法, 推导了线弹性阶段描述颗粒与基体相互作用的桥联张量, 以预测复合材料的线弹性响应. 在此基础上, 将桥联张量直接拓展至塑性变形阶段, 建立了适用于塑性行为的均匀化方法, 进而使得塑性本构模型与弹性具有一致的表示形式. 同时, 推导得到应力集中系数的解析表达式, 修正了复合材料的有效初始屈服行为, 实现了对颗粒增强复合材料弹塑性行为的理论预测. 该模型因直接从线弹性细观力学模型拓展得到, 形式简洁、参数物理意义明确, 便于实际航空工程应用. 为验证模型的有效性, 构建了颗粒增强复合材料的代表性体积单元模型, 并开展数值仿真分析. 结果表明, 所建立的本构模型具有良好的预测精度. 此外, 通过与试验结果对比, 进一步验证了该模型能够准确描述真实复合材料的弹塑性行为.Abstract: Particle-reinforced composites have been used in some important aeronautical components, and the accurate prediction of their elastoplastic behavior is essential for material and structural design. This remains a key scientific challenge in the field of composite mechanics. In this paper, a micromechanical constitutive model with a consistent elastoplastic formulation for particle-reinforced composites is established based on the stress concentration factor. First, using classical micromechanical methods, the bridging tensor that describes the interaction between the particle and matrix in the linear elastic stage is derived to predict the linear elastic response of the composite. On this basis, the bridging tensor is directly extended to the plastic deformation stage, establishing a homogenization method applicable to plastic behavior, thereby achieving a constitutive model for the plastic regime that maintains the same form as that for the elastic regime. An analytical expression for the stress concentration factor is subsequently derived, which corrects the effective initial yield behavior of the composite and enables theoretical prediction of the elastoplastic behavior of particle-reinforced composites. Since the proposed model is extended directly from a linear elastic micromechanics framework, it features a concise formulation with physically meaningful parameters, facilitating its application in aeronautical engineering practice. To validate the model, representative volume elements of the composite are constructed, and numerical simulations are performed. The results demonstrate that the proposed constitutive model achieves good predictive accuracy. Furthermore, comparisons with experimental data confirm that the model accurately captures the elastoplastic behavior of real composite materials.
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