Plastic Stress–Strain Relations and Yield Surfaces for Aluminium Alloys

Abstract

The theoretical study of the behaviour of materials in the ‘plastic’ state has progressed rapidly on the basis of a few assumptions, some of which are insufficiently well supported, and even occasionally contradicted, by available experimental evidence.

In the present work three types of experiment are carried out. In the first several different materials are ‘overstrained’ into the plastic region, either by tensile or by shear stresses, and then subjected to additional stresses, shear or tensile respectively, the modulus of resistance to the additional stresses being measured. Similar experiments have been carried out previously but the results are not wholly concordant. The present work indicates that for initially stress-free material the ‘incremental’ type of theory is well founded. An explanation for the behaviour of material in other conditions is suggested which does not involve the existence of ‘corners’ on the ‘yield surface‘overstrained’ into the plastic region, either by tensile or by shear stresses, and then subjected to additional stresses, shear or tensile respectively, the modulus of resistance to the additional stresses being measured. Similar experiments have been carried out previously but the results are not wholly concordant. The present work indicates that for initially stress-free material the ‘incremental’ type of theory is well founded. An explanation for the behaviour of material in other conditions is suggested which does not involve the existence of ‘corners’ on the ‘yield surface’.

In the second type of experiment one material is subjected to a complicated ‘stress history’, and the corresponding strains are measured. Certain improvements are made in relation to previous experimental techniques. The results indicate that the Reuss equations, used in conjunction with the Maxwell (or Mises-Hencky) flow function, give a very satisfactory prediction of the behaviour of this material.

In the third type of experiment, one material is subjected to varying ‘overstrains’ of a particular type and its subsequent ‘yield stress’ (or, more strictly, limit of proportionality) under different combinations of complex stress determined. The results indicate that in the case of this material the ‘subsequent yield surface’ to a first approximation translates in the direction of the overstrain, but is considerably modified in shape by strain-hardening and by the Bauschinger effect. It remains concave towards the inner (elastic) region but this region does not necessarily contain the stress-free origin.