Tension-compression asymmetry effects on the plastic response in bending: new theoretical and numerical results

Abstract

At present, the analysis and interpretation of the bending response of isotropic elastic/plastic metallic materials is done based on the assumption that yielding and subsequent plastic deformation under tension and compression are the same. In this paper, we put into evidence analytically and verified through F.E. analyses that even a slight tension-compression asymmetry in yielding of isotropic pressure-insensitive materials leads to very specific behaviour under four-point bending. For this purpose, the isotropic version of Cazacu et al. [1] yield criterion is used. This yield criterion is pressure-insensitive, accounts for third-invariant effects, and involves a unique parameter k which depends solely on the ratio between the yield stress in simple tension and compression, σT/σC; k = 0 corresponding to the von Mises criterion. The theoretical analysis shows that for a material with σT < σC, yielding first occurs in tension at the bottom outer fiber while for a material with σT > σC yielding sets in at the top outer fiber. As the moment is further increased, a single plastic zone spreads into the cross section starting from the fiber where min (σT, σC) is first reached, the neutral axis being no longer located at the mid-height of the beam, but moving continuously during bending. If the applied load is sufficiently large, yielding also occurs at the other outer fiber and the plastic domain is comprised of two zones, one in tension and the other in compression. The extent of the plastic zones in tension and compression is not the same, namely the extent of each zone and the critical value of the moment when these two zones join being dictated by the tension-compression asymmetry ratio of the material. Most importantly, the stresses in the cross section during loading, and consequently the distribution of residual stresses that remain after unloading are completely different than in the case of a von Mises material. To the author's knowledge these features of the plastic response in bending, which are confirmed by F.E. analyses, have not been previously identified or reported.