The stress state around two spatially arranged ellipsoidal inclusions — A case study for high-speed tool steel

Abstract High-speed tool steel can be regarded as a particle reinforced composite consisting of carbides embedded in a martensitic matrix. The internal stress distribution in such a material shows a significant dependency on various parameters such as geometry, material and arrangement of the inclusion as well as external loading conditions. The interaction of two such inclusions, approximated as ellipsoids, is investigated. Finite-element models of representative volume elements serve as the basis for the calculations. In order to reduce computing time the case studies are carried out in two dimensions using plane-stress elements. In the first step the influence of the excentricity, Young's modulus and angular position of only one ellipse on the stress field is calculated for uni- and biaxial tension, shear load and thermal load, respectively. In a second step the position of a second inclusion relative to the first one is taken into account which adds further degrees of freedom to the problem. For selected cases the results are validated by means of three-dimensional finite-element calculations. The major principal stress along the contour of the inclusion in the presence of a second ellipse will be compared with the case of the single ellipse. Additionally the direction of the principal stress vector which is of great interest with respect to the fracture-mechanical behavior of brittle materials is ascertained. For each load-case a critical configuration and the failure mechanism most likely to occur will be pointed out.