Heterogeneity of plastic strain around an ellipsoidal inclusion in an ideal plastic matrix

A matrix which contains an inclusion with different mechanical properties features a heterogeneous strain distribution during plastic deformation. This problem is studied for spherical or ellipsoidal inclusions embedded in an ideal plastic matrix without strain rate sensitivity. An Eshelby-type solution is deliberately not used, because judged inappropriate for this case, at least when adjustable parameters are to be avoided. Instead of using finite element simulations, a more approximate, but less computer time intensive upper bound analysis is performed. The results are used for the calibration of an approximate, but general formula which allows for very rapid calculations in future applications. In this first paper, the results for spherical inclusions are given. They are discussed in terms of the following topics: metal matrix composites reinforced by hard particles; relaxed constraints Taylor models for the prediction of deformation textures; self-consistent models; geometrically necessary disolocations as introduced by Ashby. An interesting result is that relaxed constraints models should not only be used when the grains are elongated, but also when they are equiaxed.status: publishe