一种考虑微尺度金属材料损伤的应变梯度理论

The mechanical performances of metallic materials with micron-order characteristic lengths exhibit significant size effects. The strain gradient theory is one of feasible approaches characterizing the micro-size effects of metallic materials. However, the existing strain gradient theories almost assume a perfectly elasto-plastic deformation of materials, without considering the damage and fracture behaviors induced by micro-scale materials. This project aims to develop a strain gradient theory characterizing the deformation and damage behaviors of micro-scale metallic materials. Firstly, we will carry out several micro-scale damage tests, in order to study the size effects of mechanical behaviors of differently micro-scale metallic materials from loading to fracture, and the damage behaviors of materials will be quantitatively characterized. Secondly, we will introduce damage parameter into a low-order strain gradient plasticity theory, and derive the strain gradient constitutive equation considering the damage effects and the damage evolution equation, so that a complete damage strain gradient theory is established. Finally, we will use the damage strain gradient theory to characterize differently experimental phenomena, in order to verify the theoretical model. The damage and failure behaviors of micro-scaled metallic materials will be described, based on which the effects of micro-scale damage on the materials’ mechanical performances will be revealed. The relevance of damage to the intrinsic lengths and characteristic lengths will also be analyzed. The achievements in this project should be helpful to provide more comprehensively theoretical guidance for the safe service of micro-scale metallic material structures.

特征尺寸为微米量级的金属材料，其力学性能表现出明显的尺度效应，应变梯度理论是一种刻画金属材料微尺度效应的可行工具之一。然而，已有应变梯度理论基本都假设材料发生完美弹塑性变形，未考虑微尺度材料变形引起损伤的破坏行为。本项目旨在发展一种表征微尺度金属材料变形及损伤力学行为的应变梯度理论。首先，开展若干微尺度损伤实验，研究不同微尺度金属材料从加载到破坏过程中力学行为的尺寸效应，并定量表征材料的损伤行为。其次，将损伤参量引入低阶塑性应变梯度理论，建立考虑损伤效应的应变梯度本构方程和损伤演化方程，形成完整的损伤应变梯度理论。最后，应用损伤应变梯度理论表征不同的实验现象，验证理论模型，描述微尺度金属材料的损伤失效行为，揭示微尺度损伤对材料力学性能的影响，并分析材料损伤与内禀长度和材料特征尺度的相关性。本项目成果有望为微尺度金属材料结构安全服役提供更全面的理论指导。

特征尺寸为微米量级的金属材料，其力学性能表现出明显的尺度效应，应变梯度理论是一种刻画金属材料微尺度效应的可行工具之一。然而，已有应变梯度理论基本都假设材料发生完美弹塑性变形，未考虑微尺度材料变形引起损伤的破坏行为，特别是对于微米颗粒增强金属基复合材料，理论预测结果与实验数据存在较明显误差。本项目基于C-W低阶应变梯度理论和连续介质损伤力学发展了一种考虑损伤的低阶应变梯度理论，该理论模型中不包含任何高阶应力和高阶应变率，应变梯度仅作为内变量影响材料切线硬化模量，而材料弹性模量与内禀长度都受损伤的影响。运用该理论分析了细丝扭转与微薄臂梁弯曲问题，发现随结构变形增大，材料刚度逐渐减小，理论预测与实验数据吻合；进一步利用该理论描述微米颗粒增强金属基复合材料内部的基体损伤行为，并结合考虑界面脱胶机制的非线性细观力学模型，解析预测了复合材料的服役行为，相应理论结果与实验数据符合较好，精确刻画了颗粒的尺寸效应、基体的损伤效应及界面脱胶的影响。本项目研究成果能够为精准预测微尺度金属材料力学行为提供有效的理论工具，为微米器件及微颗粒增强先进复合材料体系的优化设计提供理论指导，并发展了微尺度力学和损伤力学。