Abstract
As von Mises yield criterion and associated flow rule (AFR) are widely applied in metal forming field, a semitotal deformation consistent relationship between the stress and plastic strain components and the rule of dimensional changes of metal forming processes in a plane-stress state are obtained on the basis of them in this paper. The deduced consistent relationship may be easily used in forming interval of the workpiece. And the rule of dimensional changes can be understood through three plastic strain incremental circles on which the critical points can be easily determined on the same basis. Analysis of stress and plastic strain evolution of aluminum warm deep drawing process is conducted, and the advantage of nonisothermal warm forming process is revealed, indicating that this method has the potential in practical large deformation applications.
Highlights
The rule of metal forming process has been investigated since several decades ago
Mathematical Problems in Engineering stress and plastic strain components is deduced on the basis of von Mises yield criterion and the associated flow rule (AFR), and the rule of dimensional changes of metal forming processes in planestress state is discussed
The critical points on the circumferential plastic strain incremental circle can be found on the basis of these two points
Summary
The rule of metal forming process has been investigated since several decades ago. Two main theories were proposed, the law of minimum resistance [1] and the consistent relationship [2]. Mathematical Problems in Engineering stress and plastic strain components is deduced on the basis of von Mises yield criterion and the AFR, and the rule of dimensional changes of metal forming processes in planestress state is discussed. The dimensional changes of the blank can be determined by the following steps [2]: (i) determining the size of the yield locus by the value of σs; (ii) determining location of the loading point P on the yield locus; (iii) drawing line OP and extending it to meet the three plastic strain incremental circles; (iv) determining the tendency of the dimensional changes of this forming part in plane-stress state. The following gives an insight into analysis of stress and plastic strain evolution according to the proposed consistent relationship and the rule of dimensional changes of metal forming processes in plane-stress state.
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