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Question: example 62 transition from sliding to sticking friction in upsetting...

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EXAMPLE 6.2 Transition from sliding to sticking friction in upsetting In plane-strain upsetting, the frictional stress cannot be higher than the shear yield stress, k, of the workpiece material. Thus, there may be a distance x in Fig. 6.4 where a transition occurs from sliding to sticking friction. Derive an expression for xin terms of a, b, and μ only. Solution. The shear stress at the interface due to friction can be expressed as However, the shear stress cannot exceed the yield shear stress, k, of the material, which, for plane strain, is Y/2. The pressure curve in Fig. 6.5 is given by Eq. (6.13); thus, in the limit, we have or (a - x) 2μ Hence, Note that, as expected, the magnitude of x decreases as μ decreases. How- ever, the pressures must be sufficiently high to cause sticking: that is, the a/h ratio must be high. For example,let a 10 mm and b 1 min. Then, for μ-02, x 7.71 mm, and for μ-04, x-9.72 mm. Lid ricticn
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