Relaxation of the Combined Stress System of Tension and Torsion

Abstract

Most of the studies on the stress relaxation of metals reported so far are relevant to the relaxation of uniaxial tensile stress. The more general problem of complex stress relaxation has hitherto attracted but little attension and only a few works on this have been reported by E. A. Davis, J. Marin and A. E. Johnson et al. The experimental works in these investigations were carried out with only two materials, alminum and magnesium alloys. However, no information of this sort is available on steel yet.In the present study, the relaxation tests for combined tension and torsion stresses were carried out on the thin-walled tube of a low alloy steel (21/4Cr-1Mo) at 500°C. In the experiment, the stress ratio of torsional stress τ to axial tensile stress σ was kept at constant value ranging from zero (simple tension test) to infinity (pure torsion test) during the tests. For the relaxation condition, the total axial strain was maintained constant for the cases of simple tension and combined stress system and the total torsional strain for the test of pure shear. The analysis was also made by using the von Mises effective stress and effective strain rate for multiaxial stress state in order to elucidate the correlation between the relaxations under the complex stress system and that under simple tensile stress. The results of the experiment and the analysis are summarized as follows.The von Mises effective stress relaxation of complex stress system under the condition of constant total axial strain is equivalent to that of the tension test under the same initial stress. Under the condition of constant total shear strain, the effective stress of combined stress state relaxes ranidly [2(1+ν)/3]1/n times more than the tension test, where ν is the Poisson's ratio and n is the exponent of time dependence of the creep strain expressed in a power function. It is impossible in general to maintain the total strains in many directions at the same time under the condition of constant stress ratio, hence it is to be noticed that stress relaxation depends on its relaxation condition of strain.