(北京師范大學(xué) 材料科學(xué)與工程系
射線束技術(shù)與材料改性教育部重點(diǎn)實(shí)驗(yàn)室， 北京100875)
摘 要: 根據(jù)開孔泡沫金屬材料的結(jié)構(gòu)特點(diǎn)提出其抽象化的新型簡化結(jié)構(gòu)模型， 即“八面體模型”， 在此基礎(chǔ)上建立起該類材料在雙向拉伸條件下的力學(xué)分析模型。從該分析模型出發(fā)， 推導(dǎo)得出了該類材料在雙向拉伸破壞時兩向名義應(yīng)力與孔率三者的數(shù)學(xué)關(guān)系式。 結(jié)果表明： 該關(guān)系式還可進(jìn)一步描述成“偏應(yīng)力”、 “平均應(yīng)力”和孔率三者之間的關(guān)系。本理論模型與Gibson和Ashby的有關(guān)理論體系的不同之處是，前者可直接運(yùn)用“梁理論”進(jìn)行方便的分析和推演， 而后者則不能。 驗(yàn)證實(shí)驗(yàn)結(jié)果顯示， 本理論模型的數(shù)學(xué)關(guān)系與實(shí)際數(shù)據(jù)吻合良好。
關(guān)鍵字: 泡沫金屬； 多孔金屬； 泡沫材料； 多孔材料
（The Key Laboratory of Beam Technology and Material Modification of
Ministry of Education, Department of Materials Science and Engineering,
Beijing Normal University, Beijing 100875, China）
Abstract: 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.
Key words: foamed metal; metallic foam; porous material; porous metals
