偏应力张量第二及第三不变量在塑性加工中的作用

塑性变形时物体内一点的应力张量的分量随坐标变化而改变,但其应力张量不变量却是固定不变的,因此应力张量不变量可以反映物体变形状态的实质。文章阐述了偏应力张量第二不变量J2的大小可用来判断物体所处的弹塑性状态;偏应力张量第三不变量J3的正负可用来定性的判断物体所处的应变类型。由此对通常认为比较抽象的偏应力张量不变量的意义与作用有更深层次的理解。并且通过数值模拟的方法,采用偏应力张量不变量对圆环压缩和环壳液压胀形过程中金属的变形进行了分析,模拟结果和实验现象一致。

Effects of the second and third invariants of the stress deviator on metal forming

In the deformation body,the components of stress tensor at a point are difference with the variation of the coordinate system,while the values of invariants of the stress tensor are same.Therefore,the invariants of the stress tensor can reflect the characteristics the state of deformation.This paper illustrates that the value of the second invariant of the stress deviator can be used to judge the plastic or elastic state of the body,and the sign of the third invariant of the stress deviator can be used to judge the deformation type of body.So,a deeper understanding of the significance and the role of the invariants of the stress deviator which are considered more abstractly has been given.Moreover,the invariants of the stress deviator were employed to analyze the metal deformation process of ring compression and hydro-bulging toroidal shell by numerical simulation,and also the simulated and experimented results have a good agreement.