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

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 yield ing and associated volume expansion in tempered martensite, Acta Metall. 23 (1975) 885-893] and others also show a pronounced strength-differential ef fect between compression and tension (S-D effect), and furthermore a sensit ivity of the flow stress to the hydrostatic pressure. These macroscopic phe nomena 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 a ssociated volume expansion in tempered martensite, Acta Metall. 23 (1975) 8 85-893] as a consequence of plastic deformation. For simulation of the abov e observations in this work a yield function dependent on the three basic i nvariants of a reduced stress tenser and a process vector is proposed. Addi tionally the yield function is generalized towards the incorporation of a d amaging void growth effect due to hydrostatic stresses. Concerning numerica l aspects, the resulting local problem with 15 unknowns is reduced to an eq uivalent three-dimensional problem, and for the finite-element equilibrium iteration the algorithmic tangent operator is derived. Two examples illustr ate the capability of the proposed model. (C) 2001 Elsevier Science B.V. Al l rights reserved.