Conditions of yield and cyclic plasticity around inclusions

In this paper the stress field in the proximity of a circular (cylindrical) inclusion is considered. The conditions for in-plane plastic flow in the m atrix are examined from a classical elasticity solution obtained by Goodier . Elementary cases are considered such as remote loading ranging from pure tensile and pure shear to equibiaxial tension. For proportional loading, it is argued that the upper bound to the shakedown limit is always twice the elastic limit; therefore, within the limits of our assumptions, if the elas tic stress concentration for the equivalent stress is greater than two, the re is a possibility of cyclic plasticity before bulk yielding, which means that possibly an arbitrarily large plastic strain can cumulate with increas ingly high risk of exhaustion of ductility and void nucleation or detachmen t of the interface. Consequently, conditions under which it is possible to reach twice the elas tic limit before full-scale yielding are shown in the Dundurs plane represe nting all possible combinations of elastic parameters. Following these line s, it is shown that there is no possibility of cyclic plasticity under remo te shear; there is a limited area of the Dundurs plane for tension, includi ng the hole case; finally, in the equibiaxial limiting case, cyclic plastic ity is always possible for any combination of elastic properties.