平板上压制筋条的塑性流动问题

王仁

doi:10.6052/0459-1879-1957-1-1957-014

平板上压制筋条的塑性流动问题

王仁

北京大学数学力学系

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出版历程
- 刊出日期: 1957-02-24

PLASTIC FLOW IN THE EXTRUSION OF RIBS ON FLAT PLATES

WANG JEN

Poking University

摘要

摘要: 本文考虑从一块平板上压制出平行筋条的塑性流动问题,这里是把它当作一个理想刚塑性的平面应变问题来处理的.文中假设下压平板和平板之间是足够粗糙的,因而没有相对滑动.而在上压板和平板之间,则考虑了两个情形:即摩擦系数μ=0及μ≥0.175的情形;前者相当于完全光滑的压板,而后者相当于完全粗糙的压板,也就是没有相对滑动的情形.在不同的h/d比值下(h为平板厚度,2d为筋条宽度),都找出了滑移线状的圆形和它们所对应的速度圆及应力圆.文中指出这些解都是满足应力和应变条件的完全解.根据这些解可以求出在上压板上的压力分布和不同收缩比时的平均压力.文中把这些结果和众所周知的反挤情形加以比较,后者相当于本文的一个极端情形.事实上,可以说本文考虑了在反挤时底面的影响.苏联学者依留幸(Ильюшин)最近提出了一个近似方法,他的结果也和本文的正确解作了比较,证明当收缩比很大的时候,他的近似解是相当精确的.最后还将变形分布的情形,用方格的变形表示出来,这使我们能一目了然.

Abstract: We consider the extrusion of ribs on thin flat plates as a problem in the theory of plane strain for perfectly plastic-ringid materials. These assamptions imply that ι≥2(w+d), (Fig. 1), and that the effect of work hardening being distributed over the deformed regions.The problem is one of coining. The anthor is unaware of other solutions treated in the prosent manner, except a similar initial motion problem given in Ref. 15. However, if the thickness h of the plastic material is large compared to the width of the extruded bar d, the flow region will be concentrated around the die and this is the familiar problem of inverted extrusion (Ref. 16) has recently given an approximate solution to the present problem. His results are discussed in section 4.

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参考文献(18)

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