Constitutive Equation of Cyclic Softening

Abstract

A constitutive equation of cyclic strain softening for materials with low internal stress levels was derived from the rate equation. The study showed that cyclic strain softening is associated with stress relaxation and that the two phenomena are parallel over a high stress and low temperature range where thermally activated plastic flow in the two processes can be approximated with activation over a single energy barrier. The constitutive parameters were identical in both processes, leading to the recommendation that stress relaxation can be employed to determine the experimental variables for the understanding of the cyclic softening process.

Rate Dependent Constitutive Equations of Cyclic Softening

“…The constitutive equation of cyclic strain softening for materials with low (or negligible) internal stress levels was derived in our previous paper [16]. The study showed that cyclic strain softening is a rate phenomenon, strongly dependent on the temperature and loading rate, and that it can be tested in stress relaxation.…”

“…In our previous papers [16,17] it was considered that plastic flow during cyclic strain softening is a thermally activated process and the constitutive equation describing the shear stress in function of time during cyclic strain softening was derived. It was shown that cyclic strain softening is associated with stress relaxation and that the two phenomena are parallel over a high stress and low temperature range where thermally activated plastic flow in the two processes can be approximated with activation over a single energy barrier.…”

“…Cyclic softening, like other plastic deformation processes is time and temperature dependent and, therefore, thermally activated [7,10,11,14,15,16]. In a specific stress and temperature range a single energy barrier may control the plastic flow.…”

“…However, it was established by Krausz and Eyring [11] that in the high stress and low temperature zone the activation volume is independent of stress and time: no structural change. Also, the evaluation of experimental results for some materials with low internal stress levels [11,16,18,19,20] have shown that when the total strain amplitude is small, the components of the shear stress rate due to mobile dislocation density (and/or microstructure) changes and to the internal stress rate are negligible compared to the component due to the change of the plastic strain rate. Hence, the applied shear stress rate in the high stress and low temperature range and during cyclic strain softening of these materials can be approximated as…”

“…Thermally activated dislocation movement ends -fades out -at strain rates several orders of magnitude below this [11,14]. and stress relaxation can be approximated with activation over a single energy barrier, (14) was used to evaluate the material structural characteristics (the activation volume and the activation free energy) [16] for cyclic strain softening. Consequently, the shear stress-time response during cyclic strain softening can be calculated from (13) using the structural characteristics evaluated from stress relaxation.…”