动态多轴加载下泡沫金属的本构关系研究

There exits the change of volume under deformation of random cellular materials, such as metallic foams and polymeric foams, are essentially different from unchanged plastic volume of corresponding matrix materials. In the dynamic multi-axial loadings, the existing full or incremental constitutive relationship of metallic foams is not suitable for complex loading requirements. This project will take metallic foams as the main research object, obtain the yielding criterion, the effects of multiple strain rates and the characterization of subsequent yielding surface of metallic foams under multi-axial loadings as breakthrough points, and determine the intact yielding surface in the space of principal stresses and the constitutive relationship of metallic foams under multi-axial loadings as main targets. Based on multi-axial loading experiments and numerical simulative experiments, the influences of multi-axial strain rates on the yielding surface and the constitutive relationship will be investigated, and characterization methods of yielding surface and constitutive relationship, in which the effect of multi-axial strain rates is taken into account, will be developed. The research project will not only help to better understand the yielding surface, constitutive relationship and strain rate effect of metallic foams as well as the corresponding formation mechanism and to lay a firm theoretical foundation for extensive application of this type of materials, but also promote the development of basic research on impact dynamics, experimental mechanics and meso-mechanics. Thus, it has important theoretical and practical implications.

泡沫金属、泡沫塑料等随机多胞材料的变形伴随有明显的体积变化，它与密实金属塑性体积不变完全不同，在动态多轴加载下，现有的无论全量型还是增量型本构关系远未能适合复杂加载需求。本项目拟以泡沫金属为主要分析对象，以泡沫金属在多轴加载下的屈服判据、多轴轴率效应和后继屈服面表征等关键问题为突破点，以确定泡沫金属在主应力空间中的完整屈服面和多轴加载下的本构关系为目标。通过开展多轴动静态实验和数值模拟实验，探索多轴应变率对屈服面与本构关系的影响，发展包含多轴应变率的屈服面和本构关系的表征方法。本项目研究将不仅有助于确切地了解泡沫金属的屈服面和本构关系及应变率效应，为此类材料的广泛应用打下坚实的理论基础，还能促进冲击动力学、实验力学和细观力学等相关基础研究的发展，有重要的理论和实际意义。

泡沫金属近年来工程中应用越加广泛，但由于其细观结构复杂及多轴实验数据难以获取，使得已有的泡沫金属屈服面、本构方程和破坏面未能在多轴加载条件下得到充分验证。本项目以泡沫金属的多轴加载实验及其Voronoi细观模型为基础，重点探究了泡沫金属多轴加载下的本构关系。建立兼容单轴加载的多轴加载下的屈服准则，创新性地在覆盖主应力和主应变许可空间内表征泡沫初始屈服面，以及揭示了初始屈服面随初始密度的变化规律；在建立兼容单轴加载下的适合多轴加载的破坏准则，同样地在主应力和主应变许可空间给出泡沫金属破坏面，指出破坏面破缺区域及其边界方程；从传统的金属塑性理论出发，建立了适用于各向同性的多孔材料的塑性流动本构，并给出应力及应变的后继屈服演化方程，通过各向同性多孔金属模型及泡沫金属模型对理论进行验证。该本构方程是在拓展经典金属材料塑性流动假设基础上，结合数值分析而建立的，不仅指出现有经典泡沫金属本构关系理论的局限性，也克服了其仅仅依赖数值模拟实验的经验性，具有较好的普适性。同时本项目建立的合适多轴加载的屈服和破坏判据，不仅适用于泡沫金属，对一般性的多胞材料也具有重要的参考价值。项目执行期间总共发表论文14篇，培养博士研究生2名，硕士研究生2名，项目负责人获中国力学学会2021年度自然科学二等奖（排名第二）。