An investigation of plastic flow and differential work hardening in orthotropic brass tubes under fluid pressure and axial load

Abstract

Thin-walled closed tubes of 70-30 brass were homogeneously deformed to finite levels of strain by internal fluid pressure combined with external longitudinal load in arbitrary fixed ratios. Plastic orthotropy was present initially and remained coaxial with the principal stresses throughout every experiment. On the other hand, the successive contours of equal work in biaxial stress space changed their shapes progressively. The geometry of the entire family is represented here by a simple formula involving only work-dependent parameters. The modelling is complemented by an empirical stress-strain relation for each experiment; the parameters in this case are dependent only on the imposed load ratio.In the present constitutive analysis a primary role is assigned to the contours of equal work (and not to yield loci). That role is further enhanced by our observation that (with certain exceptions) the successive contours act instantaneously as plastic potentials. This means that the components of an infinitesimal increment of logarithmic strain are proportional to the components of the associated normal to the current contour in stress space. In coming to this conclusion we found it advantageous to call in aid the geometric principle of polar reciprocity; as this rarely features in the mechanics literature an exposition ab initio is included in the paper.