等周长屈服准则求解三维锻压力

目的 获得三维锻压力的解析解。方法 用线性的等周长屈服准则对三维锻压过程进行了力学分析，先建立了一个考虑变形外端影响的运动许可速度场，再利用等周长屈服准则对该速度场进行分析，依次求出了内部变形功率、剪切功率、摩擦功率以及总功率。最终，根据上界定理，导出了锻压力的解析解。同时，为验证解析解的正确性，将其理论值与相应的纯铅压缩试验结果进行了比较。结果 对比表明，计算出的理论锻压力比实测值高，但二者的相对误差小于15%。结论 基于EP屈服准则和所提出的速度场得到的理论锻压力是可行的。

Calculation of Three-dimensional Forging Force by Equal Perimeter Yield Criterion

The work aims to obtain the analytical solution of three-dimensional forging force. A linear yield criterion, called equal perimeter yield criterion, was applied to analyze three-dimensional forging process. A kinematically admissible velocity field in which the effect of external zone was considered was established. Then, the velocity field was analyzed with the EP yield criterion to obtain the internal deformation power, shear power, friction power, and the total power. Ultimately, an analytical solution of the forging force was derived according to the upper bound theory. Experimental results of pure lead compression were used to compare with the theoretical value to validate the analytical solution. Comparison showed that the calculated total forging forces were higher than the measured ones; however, their relative errors were less than 15%. It implies that the theoretical forging force obtained by the EP yield criterion and the proposed velocity field is feasible.