弹塑性材料杆的相变分析

针对弹塑性材料的相变问题，对弹塑性杆中的相变分别进行了小变形和大变形分析．分析表明，相变可以在能应变软化的弹塑性杆中发生，相变的Maxwell应力、弹性相和弹塑性相的应变都可以被确定．对任一条假设的应变软化曲线，Maxwell应力直线和应变软化曲线所围面积的代数和总等于零，这和Ericksen对非线性弹性杆相变研究得到的结论一致．数值算例表明，跨越弹塑性杆相变界面的应变跳越一般很大，这时用小变形分析导致的误差也很大，必须应用大变形理论对弹塑性杆的相变进行分析．

Analysis of Phase Transformations in Bars Composed of Elastoplastic Materials

In view of phase transformations of elastoplastic materials, phase transformations in elastoplastic bars were investigated for both infinitesimal deformation and finite deformation in present paper. It is verified that phase transformations can definitely occur in elastoplastic bars with strain-softening behavior, the Maxwell stress and the strains inside both elastic and plastic phases can be determined. It is proved that for any assumed strain-softening curve the algebraic sum of areas enclosed by the Maxwell stress straight line and the strain-softening curve is always equal to zero, which agrees with the result given by Ericksen for nonlinear elastic bars. Numerical examples demonstrate that the jump of strains across interfaces between phases in bars is usually very large, the error of the analysis due to using infinitesimal deformation theory is also very large, and it is necessary to apply the finite deformation theory in the analysis of phase transformations of elastoplastic bars.