Question 6.7: Draw the three-dimensional Mohr’s circle diagrams for the st......
Draw the three-dimensional Mohr’s circle diagrams for the stresses and plastic strains in a body loaded under plane-strain tension, \varepsilon _{y}=0 , with \sigma _{z}=0 . Assume the von Mises yield criterion.
From the flow rules, \varepsilon _{y}=0= \lambda [\sigma_{y}-(1/2)( \sigma_{x}+\sigma_{z})] with \varepsilon _{y} =0 and \sigma _{z}=0 , \sigma _{y}=1/2 (\sigma_{x} ) . The Mohr’s stress circles are determined by the principal stresses, \sigma_{x} , \sigma _{y}=1/2 (\sigma_{x} ) , and \sigma _{z}=0 . For plastic flow, \varepsilon _{x}+ \varepsilon _{y}+\varepsilon _{z}=0, so with \varepsilon _{y}=0, \varepsilon _{z}=- \varepsilon _{x}. The Mohr’s strain circles (Figure 6.4) are determined by the principal strains, \varepsilon _{x} , \varepsilon _{y} =0, and \varepsilon _{z}=- \varepsilon _{x}.
