A modified superposition principle has been employed to describe creep in the nonlinear range under combined stresses which change abruptly from time to time. The stress function fij employed is derived from three integrals of the multi-integral theory for constant stress. Several means of treating the nonlinearity in stress when the stress changes are investigated. The most satisfactory of these considers that after a change in stress from σkl(1) to σkl(2) the creep may be described as the sum of the recovery resulting from removal of σkl(1) and the creep from application of σkl(2), the recovery being computed on the basis of superposition. Thus for a power function of time t where the strain ε=ε0+ε+tn and n is a constant the creep following a change in stress at time t1 is given by εij(t)=fij0(σkl(1))+[fij0(σkl(2))−fij0(σkl(1))]+fij+(σkl(1))tn+[fij+(σkl(2))−fij+(σkl(1))] (t−tl)n. Experiments on an unplasticized poly(vinyl chloride) include tension creep followed by multiple-step unloading; combined tension and torsion creep followed by multiple-step unloading; combined tension and torsion creep with several abrupt changes in combination of tension and torsion; and tension creep with partial unloading and reloading. The method describes the time dependence reasonably well in all cases, but the total strain following partial unloading from high combined stresses in the nonlinear range was substantially larger than predicted.
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Findley et al. (1967) studied this question.