Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 3. Creep Curves

Abstract

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model for shear flow of thixotropic viscoelastic-plastic media, which takes into account the mutual influence of the deformation process and structure evolution, is continued. A set of two nonlinear differential equations describing the processes of shear at a constant rate and stress relaxation is obtained. Equation set describing creep is derived; a general solution of the Cauchy problem for the set is constructed in an explicit form (the equations of the families of creep, and structuredness curves are derived). For arbitrary six material parameters and (increasing) material function that govern the model, basic properties of the families stress-strain curves at constant strain rates, stress relaxation curves and creep curves generated by the model, and the features of structuredness evolution under these types of loading are analytically studied. The dependences of these curves on time, shear rate, stress level, initial strain, and initial structuredness of the material, as well as on the material parameters and function of the model, are studied. Several indicators of the applicability of the model are found which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (unusual properties) are generated by a change in structuredness in comparison with typical stress-strain curves, relaxation curves, and creep curves of structurally stable materials. In particular, it is proved that creep curves always increase in time and have oblique asymptote, and structuredness under constant stress is always monotonous (unlike other loading modes), but can decrease or increase depending on the relation between the stress level and initial structuredness. The same condition controls creep curves to be convex up or down: at a certain (calculated) critical load creep curves change from convexity up (under smaller loads) to convexity down, and the structuredness becomes ascending instead of descending. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves, strain rate and strain hardening, flow under constant stress and so on.