Elastoplastic antiplane problem for a half-space with wedge-shaped rounded cut (Q2771586)

Stresses in the half-space \(x>0\), \(-\infty<y<\infty\), \(-\infty<z<\infty\) with a symmetrical surface cut arise due to a uniform antiplane shear stress at infinity \(\tau_{xz}=0\), \(\tau_{yz}=\tau_\infty\). At some value of \(\tau_\infty\), which increases with the radius of cut rounding, a plastic zone develops in the vicinity of wedge vertex. A boundary-value problem for the function \(\tau(\zeta) =\tau_{yz}(x,y) +i\tau_{xz}(x,y)\) (\(\zeta=x+iy\)), which is analytic in the elastic portion of the half-space, is formulated. Then the Keldysh-Sedov problem for an auxiliary function is formulated and solved exactly. Parametric equations of the boundary between elastic and plastic zones are derived. The shape of plastic zone for different cut angles and different vertex curvatures is studied. Numerical examples are presented.