Specification of the Parameters of an Exponential Heredity Kernel of the Endochronic Theory in Describing Ratcheting Under Biaxial Loading

Abstract

In this paper, a method is proposed for specifying the parameters of the exponential hereditary function kernels of the endochronic theory of plasticity to describe the ratcheting (cyclic creep) effect of metallic materials under stress-controlled complex non-proportional loading. The method involves the dependence of the difference of plastic moduli on the ratcheting rate on the steady-state portion of the cyclic stress–strain curve. The plastic moduli are determined at the points where the maximum stresses act in different half-cycles of asymmetric loading. It is believed that the greater the difference of plastic moduli towards the mean stress in the cycle, the greater the strain increment in each cycle of loading. The statements of our previously proposed approach were used to determine the rate of plastic strain accumulation at the steady-state stage of deformation under biaxial loading. This approach, based on the data of uniaxial experiments under cyclic asymmetric loading in tension–compression and reversed torsion with the known value of the cycle nonproportionality parameter, is developed to analyze the cyclic loading paths with equal mean and amplitude von Mises stress values. With some simplifications, the expression is proposed to determine the parameters of the exponential kernel of the hereditary function depending on the cyclic path geometry and the known ratcheting rate for the basic loading path. Similar values for the exponential kernel parameters of the hereditary function are obtained in terms of the difference of plastic moduli by using a simpler bilinear model of elastoplastic deformation. The obtained values of the hereditary function parameters were used to simulate the ratcheting effect under uniaxial and biaxial cyclic loading. The loading programs and data of experiments were taken from the literature. The results of simulation have shown that the parameters of the constitutive equations for cyclic plasticity obtained with this method allow one to describe satisfactorily the kinetics of the stress-strain state of metallic materials subjected to biaxial non-proportional loading under cyclic creep.