基于应力的广义Jaumann导数的大变形本构关系

Large Deformation Constitutive Relationship with Generalized Jaumann Stress Rate

研究了用实心圆轴扭转实验标定大变形弹塑性本构关系的问题.首先进行了A3钢的单向拉伸和纯扭转实验,分析了两种实验的应力应变曲线特性,给出了实心圆轴扭转实验中变形率d、相对旋率Ω和广义Jaumann导数的具体形式.然后以应力的广义Jaumann导数作为客观导数,应用等向强化J2流动塑性理论,建立了由扭转实验的τ—γ曲线标定的大变形本构关系形式.结果表明,对应广义Jaumann应力导数的扭转大变形本构关系与对应Jaumann应力导数的本构关系形式相同.

In this paper, large deformation elastoviscoplastic constitutive relationship is discussed by the aid of torsion test with cylinder specimens. Firstly, unidirectional tension test and simply torsion test with A3 steel are completed, and deformation rate d, relative spin Ω and generalized Jaumann stress rate for torsion problem are given. Secondly, isotropic hardening models and J2 flowing plasticity theory are used in the literature and large deformation constitutive equation with generalized Jaumann stress rate is developed on the basis of torsion test. The result indicates that torsion elastoviscoplastic constitutive equation with generalized Jaumann rate is agreeable with constitutive equation with Jaumann objective rate.