浅谈“塑性力学”教学中的Lode应力参数拓展

Discussion on the Expansion of Lode Stress Parameters in the Teaching of Plasticity Course

从课堂教学的角度分析了当前塑性力学教材中Lode应力参数的局限性,给出了其计算公式在π平面内的拓展形式。结果显示,拓展后的Lode应力参数有6种不同的计算公式,传统Lode应力参数计算公式只是主应力次序是σ_(1)≥σ_(2)≥σ_(3)时的一种情况。当主应力次序不再为σ_(1)≥σ_(2)≥σ_(3)时,Lode应力参数的计算公式随之发生改变。同时,由于Lode应力参数是建立材料屈服条件的基础,所以采用研究结果可以在不确定主应力大小次序的情况下绘制屈服曲线。所探讨的结果拓展了Lode应力参数的计算公式形式,完善了π平面内屈服曲线的绘制途径。

The limitation of Lode stress parameters in the current plasticity textbook is analyzed from the perspective of classroom teaching. The expanded form of Lode stress parameter calculation formula in π plane is deduced in this paper. It is suggested that there are six formulas for the calculation of Lode stress parameter. The formula in the current plasticity textbook is one of the six cases when the principal stress sequence is. The form of Lode stress parameter formula could change according to the principal stress sequence. Meanwhile, since the Lode stress parameter is the basis for establishing the material yield criteria in the plasticity, the results of this paper can be used to draw the yield curve without determining the sequence of principal stress. Therefore, the results discussed in this paper can develop the formulas form of Lode stress parameter and improve the way of drawing the yield curve in π plane.