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在St?ren-Rice成形极限理论模型的基础上,建立了基于Logan-Hosford屈服函数的塑性本构方程,将其引入成形极限推导获得极限应变的解析表达式。以两种铝合金板为对象,采用建立的极限应变表达式计算其成形极限曲线,并与实验数据进行对比;研究了屈服函数中的应力指数a和各向异性系数r对计算结果的影响。结果表明,应力指数a对负应变比区理论值影响较小,正应变比区理论值随应力指数a值的增大而减小,当应力指数a=4时理论结果与实验吻合较好;当应力指数a=2时,正应变比区理论值随各向异性系数r值的增大而减小,当应力指数a>2时理论结果对各向异性系数r值的变化不敏感。
Based on the St? Ren-Rice forming limit theory model, a plastic constitutive equation based on the Logan-Hosford yield function is established, which is introduced into the forming limit derivation to obtain the analytical expression of the ultimate strain. Two kinds of aluminum alloy plates were taken as object. The forming limit curve was calculated by the established ultimate strain expression and compared with the experimental data. The influence of stress index a and anisotropy coefficient r on the yield function was studied. The results show that the stress index a has a little influence on the theoretical value of negative strain ratio, and the theoretical value of normal strain ratio decreases with the increase of stress index a. The theoretical result is in good agreement with the experiment when the stress exponent a = 4; When the stress exponent a = 2, the theoretical value of the normal strain ratio decreases with the increase of the anisotropy coefficient r. When the stress exponent a> 2, the theoretical result is not sensitive to the change of the anisotropy coefficient r.