Analysis of shear bands in a dynamically loaded viscoplastic cylinder containing two rigid inclusions

Summary

We study plane strain thermomechanical deformations of a hollow circular cylinder containing two rigid non-heat-conducting ellipsoidal inclusions placed on a radial line symmetrically with respect to the center. These inclusions can be viewed as precipitates or second phase particles in an alloy. The material of the cylinder is presumed to exhibit thermal softening, but strain and strain-rate hardening. The impact load applied on the inner surface of the cylinder is modeled by prescribing a radial velocity and zero tangential tractions at material particles situated on the inner surface. Rigid body motion of the inclusion is considered and no slip condition between the inclusion and the cylinder material is imposed.

It is found that shear bands initiate from points adjacent to inclusion tips near the inner surface of the cylinder and propagate toward this surface. At inclusion tips near the outer surface of the cylinder, the maximum principal logarithmic strain and the temperature are high and the effective stress is low, but severe deformations there do not propagate outward.