塑性不安定規準

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The criteria of localized necking were proposed by Hill and Storen and Rice, and they are very famous for their ability in predicting sheet formability. Though Hill's analysis cannot be applied to sheet formability under biaxial stretching, the one by Storen and Rice gives the impression that it can be applied to biaxial stretching. However, detailed examination reveals that both analyses are identical in their assumptions of equilibrium and deformation rate. Therefore, the analysis by Storen and Rice remains within the sphere of Hill's analysis, and it also cannot be applied fundamentally to biaxial stretching. Localized necking is a phenomenon where velocity gradient or strain rate becomes discontinuous on a necking plane, and force equilibrium must be maintained on both sides of the plane. However, the published analyses were insufficient with respect to the equilibrium and mode of the necking plane. Rigorous treatment for them is demonstrated. Diffuse necking proposed by Swift is represented by the criterion that in-plane loads become simultaneously stationary under plane stress. However, the loads obtained based on the criterion, in general, are not stationary. Then, the origin of the unreasonable results is discussed, and an alternative criterion is proposed which can yield a rigid solution in addition to plastic solutions. All the criteria in diffuse and localized necking are involved in the universal criteria obtained from the permissible condition for multiple solutions.
一般社団法人日本機械学会の論文
1995-08-25

塑性不安定規準

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