泡沫铝材料准静态本构关系的理论和实验研究

应用Chen和Lu提出的适用于可压缩弹塑性固体的唯象本构模型框架，建立了泡沫铝的准静态本构模型，推导了三维等比例加载和环向受约束轴向加载下的宏观应力-应变曲线. 对两种泡沫铝材料(开孔和闭孔)进行了4类准静态试验，即单轴压缩、三维静水压缩、三维等比例压缩和侧向受约束轴向压缩实验. 利用单轴压缩和三维静水压缩的实验结果得到了泡沫铝材料的本构参数曲线，并由此预测它在三维等比例压缩和侧向受约束轴向压缩情况下的响应. 理论预测与相应实验结果相比较，三维等比例压缩的结果比较吻合，但与侧向受约束轴向压缩的结果却相差很大. 分析表明，理论预测与侧向受约束轴向压缩实验结果的偏差是由于泡沫铝试件与约束筒之间的摩擦造成的. 研究结果说明, Chen-Lu模型能够很好地描述泡沫铝材料在压缩占主导的应力状态下的响应.

A theoretical and experimental study on the quasi-static constitutive model of aluminum foams

The phenomenological constitutive framework for compressible elasto-plastic solid presented by Chen and Lu is applied to an open-cell and a closed-cell aluminum foams to establish their quasi-static constitutive models. The macroscopic stress-strain curves for the aluminum foams under 3-D proportional and non-proportional loadings, respectively, are derived from the model. Four kinds of experiments, i.e., uniaxial compression, hydrostatic compression, lateral-constrained compression and 3-D proportional compression, are conducted. Constitutive parameter curves for the model are obtained from the uniaxial compression and hydrostatic compression tests and then applied to predict their responses under the other two loading conditions. It is found that the theoretical prediction agrees well with the experimental results for the case of 3-D proportional compression, but not for that of lateral-constrained compression. A simplified friction correction reveals that the deviation of the theoretical prediction from the experimental results for the lateral-constrained compression case is induced by friction between the specimen and the constraining sleeve. The present results show that the Chen and Lu model can describe the compression-dominant behavior of aluminum foams satisfactorily.