Question 6.2: Consider an isotropic material loaded so that the principal ......

Mechanical Behavior of Materials [1002814]

Consider an isotropic material loaded so that the principal stresses coincide with the x, y, and z axes. Assuming the von Mises yield criterion applies, make a plot of $\sigma_{y}$ versus $\sigma_{x}$ yield locus with $\sigma_{z}$ = 0.

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Let $\sigma_{x} =\sigma_{1}$ , $\sigma_{y} =\sigma_{2}$ , and $\sigma_{z} =0$ . Now $\alpha =\sigma_{2}/ \sigma_{1}$ . Figure 6.3 results from substituting several values of $\alpha$ into Equation (6.12),

$\sigma_{1} = Y/(1-\alpha +\alpha^{2} )^{1/2}.$ (6.12)

solving for $\sigma_{x}$ /Y and $\sigma_{y}$ /Y = $\alpha \sigma_{x}$ /Y, and then plotting.

6.2

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