一维拉伸本构方程不能直接推广到二维胀形力学问题

Yuquan Song, Shumei Liu
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引用次数: 5

摘要

超塑性成形已广泛应用于制造形状复杂、精度高的零部件。而超塑性地层处于多应力状态。长期以来,单轴拉伸本构方程被直接推广到处理多应力状态。这样做是否可行,需要从理论上加以证明。本文首先总结了变m超塑性拉伸胀形本构方程的建立过程,并基于连续介质塑性力学的基本原理,利用自由胀形的等效应力δ和等效应变率ε的解析表达式,导出了超塑性自由胀形的最佳加载规律的解析表达式。通过对比典型超塑性合金ZnAl22的定量结果,表明一维拉伸本构方程不能直接推广到二维胀形定量力学问题;只有基于胀形应力状态的超塑性胀形本构方程才能用于处理胀形的定量力学问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
One-dimensional tensile constitutive equation cannot be directly generalized to deal with two-dimensional bulging mechanical problems
Superplastic forming has been extensively applied to manufacture parts and components with complex shapes or high-precisions. However, superplastic formation is in multi-stress state. In a long time, uniaxial tensile constitutive equation has been directly generalized to deal with multi-stress state. Whether so doing is feasible or not needs to be proved in theory. This paper first summarizes the establishing processes of superplastic tensile and bulging constitutive equation with variable m, and, using the analytical expressions of equivalent stress δ and equivalent strain rate ε of free bulge based on the fundamentals of continuum medium plastic mechanics, derives the analytical expressions of optimum loading rules for superplastic free bulge. By comparing the quantitative results on typical superplastic alloy ZnAl22, it is shown that one-dimensional tensile constitutive equations cannot be directly generalized to deal with two-dimensional bulging quantitative mechanical problems; only superplastic bulging constitutive equation based on bulging stress state can be used to treat the quantitative mechanical problems of bulge.
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