A tensile bar is machined so that the diameter at one location is 1% smaller than that for the rest of the bar. The bar is tested at high temperature, so strain-hardening is negligible, but the strain-rate exponent is 0.25. When the strain in the reduced region is 0.20, what is the strain in the

Question

A tensile bar is machined so that the diameter at one location is 1% smaller than that for the rest of the bar. The bar is tested at high temperature, so strain-hardening is negligible, but the strain-rate exponent is 0.25. When the strain in the reduced region is 0.20, what is the strain in the larger region?

Accepted Answer

[latex] f=(\pi D^{2}_{1}/4 )/ (\pi D^{2}_{2}/4 )=(D_{1}/ D_{2})^2 =(0.99/1)^2 =0.98[/latex]. Substituting [latex]\varepsilon _{b}=0.20 [/latex] and [latex] f=0.98 [/latex] into Equation (7.8), [latex] \exp(- \varepsilon _{a}/m)- 1 =f^{1/m}\left[\exp (-\varepsilon _{a}/m)-1\right], \exp (- \varepsilon _{a}/0.25)=(0.98)^{1/.25}\left[\exp(-0.2/0.25)-1\right] + 1=0.492.\ \varepsilon _{a}=-0.25\ln (0.492)=0.177. [/latex]

Question 7.3: A tensile bar is machined so that the diameter at one locati......

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