Strength difference in compression and tension and pressure dependence of yielding in elasto-plasticity Original Research Article

A characteristic of most metallic materials is nonlinear work-hardening for the flow stress, equal in tension and compression at first loading. On the contrary, triaxial experimental tests for high-strength steels by Spitzig et al. [W.A. Spitzig, R.J. Sober, O. Richmond, Pressure dependence of yielding and associated volume expansion in tempered martensite, Acta Metall. 23 (1975) 885–893] and others also show a pronounced strength-differential effect between compression and tension (S-D effect), and furthermore a sensitivity of the flow stress to the hydrostatic pressure. These macroscopic phenomena are related to volume expansion of the material by the authors in [W.A. Spitzig, R.J. Sober, O. Richmond, Pressure dependence of yielding and associated volume expansion in tempered martensite, Acta Metall. 23 (1975) 885–893] as a consequence of plastic deformation. For simulation of the above observations in this work a yield function dependent on the three basic invariants of a reduced stress tensor and a process vector is proposed. Additionally the yield function is generalized towards the incorporation of a damaging void growth effect due to hydrostatic stresses. Concerning numerical aspects, the resulting local problem with 15 unknowns is reduced to an equivalent three-dimensional problem, and for the finite-element equilibrium iteration the algorithmic tangent operator is derived. Two examples illustrate the capability of the proposed model.