正交异性材料在R.Hill屈服准则下平面应力问题的特征场(h>2)

THE CHARACTERISTIC FIELD OF PLANE STRESS PROBLEM FOR THE ORTHOTROPIC MATERIALS UNDER R.HILL YIELD CRITERION (h>2)

大多数金属材料在承载时产生了各向异性强化的特点,因此,对这一类材料特性的深入研究显得十分必要,正确建立及分析理论模型将对在实际工程中的应用提供很好的理论依据。本文在R.Hill屈服准则下提出了无量纲化的解析应力解,讨论了屈服参数2>h时,正交异性材料平面应力问题的应力场及应力特征场,利用应力微分平衡方程得到了决定特征曲线特征的参数。结果说明特征线一般互不正交。特别地分析了平头冲压边界附近的情况,得到了各应力状态不同区域的应力特征场,应用数值分析的方法对过渡区进行了计算。

Many metal materials exhibit the properties of orthotropic hardening under loading. In this paper, the R.Hill yield criterion is used to discuss the characteristic field of plane stress problem for orthotropic materials. Dimensionless analytical solutions are obtained from the differential equations of equilibrium, and the coefficients of the characteristic curves are determined. It is found that the characteristic curves are not orthogonal generally. The stresses at press load boundary are studied and the characteristic fields of different stress state areas are obtained. Analysis of the transition area is also conducted using the numerical method.