The application of an anisotropic yield function of the sixth degree to orthotropic material

Abstract

By combining Drucker's yield function with Hill's quadratic yield function, an anisotropic yield function of the sixth degree is proposed. The effects of the third deviatoric stress invariant and initial anisotropy are also included. Experimental evaluation is made on 1050 aluminium tubes under multiaxial stress states. The tubes in the as-received condition are subjected to progressive reductions in the hot extruding and cold drawing processes. They are annealed by heating at 200 °C for 1 h. By applying proportionally combined loadings of axial load, internal pressure, and torsion to the specimens, a change of yield stress with a rotation of the principal stress axes and a difference between the directions of the principal stress and principal strain increment are examined. In the tension-internal pressure stress field, it is found that this aluminum tube exhibits orthotropic anisotropy of high strength in the tangential direction. The yield surface in the tension-torsion stress field lies outside von Mises’ yield surface. The torsional yield stress deviates considerably from von Mises criterion. Such behavioural characteristics can be expressed precisely by the proposed yield function. In addition, it is experimentally verified that the normality rule is obeyed in strain behaviour.