基于对数应力率大应变本构关系的参数标定研究

Calibration of Parameters in Large Strain Constitutive Model with Logarithmic Stress Rate

在所有率型弹塑性本构模型中,只有对数应力率对应的本构模型能够满足自适应准则。基于对数应力率,采用实心圆轴扭转实验,对大应变弹塑性本构模型中的参数标定问题进行了讨论。推导出了考虑Swift效应时端部自由实心圆轴扭转变形的变形率、对数旋率、Kirchhoff应力及Kirchhoff应力的对数应力率。对于等向强化大应变弹塑性本构关系,给出了由实心圆轴扭转实验标定的、基于Kirchhoff应力对数应力率的本构关系中塑性刚度函数的表达式。分析了扭转圆轴的Swift效应对塑性刚度函数的影响。结果表明,实心圆轴扭转的轴向伸长变形和径向变形对基于对数应力率大应变本构关系中的塑性刚度函数都有影响。当不考虑Swift效应时,所得塑性刚度函数表达式与不考虑Swift效应时基于Jaumann应力率的塑性刚度函数表达式相同。

Among all rate type elastoplastic constitutive models, only those with the newly discovered logarithmic stress rate fulfill self consistency criterion. Solid shafts torsion test was used to determine large deformation elasto-plastic behavior because of the plastic stability of the solid torsion specimen. An isotropic hardening elasto-plastic constitutive model with the logarithmic stress rate was studied by the aid of solid cylindrical shafts torsion test within large strain range. The deformation rate, the logarithmic spin, the Kirchhoff stress and the logarithmic stress rate of Kirchhoff stress were obtained in torsion of free-end solid shafts when considering Swift effect. According to the results obtained from solid cylindrical torsion test, the plastic rigidity function in the isotropic hardening elasto-plastic constitutive model was determined within large strain range. The constitutive model was compared with the constitutive models with Jaumann stress rates. The results show that the Swift effect on finite strain constitutive relationship is related to the varying rate of axial deformation and radius deformation to shear strain.