泡沫金属双向承载的力学模型

Mechanical model for metallic foams under biaxial loads

根据开孔泡沫金属材料的结构特点提出其抽象化的新型简化结构模型,即“八面体模型”,在此基础上建立起该类材料在双向拉伸条件下的力学分析模型。从该分析模型出发,推导得出了该类材料在双向拉伸破坏时两向名义应力与孔率三者的数学关系式。结果表明:该关系式还可进一步描述成“偏应力”、“平均应力”和孔率三者之间的关系。本理论模型与Gibson和Ashby的有关理论体系的不同之处是,前者可直接运用“梁理论”进行方便的分析和推演,而后者则不能。验证实验结果显示,本理论模型的数学关系与实际数据吻合良好。

Based on the structural feature of the open-cell metallic foam, an abstract and simplified structure model （i. e. the ＂octahedron model＂） was put forward, and the mechanical model was further established for this three-dimensional reticulated high-porosity foam under biaxial tension. From this structure-property model, the mathematical relationship between biaxial nominal failure stresses and porosity was deduced and eventually derived for this material. This relationship can be further expressed as the mathematical relationship among the nominal failure ＂deviatoric stress＂, the nominal failure ＂average stress＂ and porosity, but the concepts both of the ＂deviatoric stress＂ and the ＂average stress＂ can appear just from the mathematical treatment. Here, the difference of the present theoretical model from that presented by Gibson and Ashby is that, the former can directly use the ＂beam theory＂ conveniently whereas the latter can not. The results indicate that the mathematical relationship from the present model is in good agreement with the practical data.