AN INVESTIGATION OF PLASTIC-FLOW AND DIFFERENTIAL WORK-HARDENING IN ORTHOTROPIC BRASS TUBES UNDER FLUID PRESSURE AND AXIAL LOAD

Thin-walled closed tubes of 70-30 brass were homogeneously deformed to finite levels of strain by internal fluid pressure combined with exte rnal longitudinal load in arbitrary fixed ratios. Plastic orthotropy w as present initially and remained coaxial with the principal stresses throughout every experiment. On the other hand, the successive contour s of equal work in biaxial stress space changed their shapes progressi vely. The geometry of the entire family is represented here by a simpl e formula involving only work-dependent parameters. The modelling is c omplemented by an empirical stress-strain relation for each experiment ; the parameters in this case are dependent only on the imposed load r atio. In the present constitutive analysis a primary role is assigned to the contours of equal work (and not to yield loci). That role is fu rther enhanced by our observation that (with certain exceptions) the s uccessive contours act instantaneously as plastic potentials. This mea ns that the components of an infinitesimal increment of logarithmic st rain are proportional to the components of the associated normal to th e current contour in stress space. In coming to this conclusion we fou nd it advantageous to call in aid the geometric principle of polar rec iprocity; as this rarely features in the mechanics literature an expos ition ab initio is included in the paper.