Viscoplasticity with a saturation stress: distinguishing features of the model

Abstract

Alexandrov, S; Mishuris, G. Viscoplasticity with a saturation stress: distinguishing features of the model. Archives of Applied Mechanics. 2007, 77(1), 35-47Viscoplastic models including a saturation stress are considered. The existence of the saturation stress significantly changes the mathematical structure of solutions near maximum friction surfaces (surfaces where the friction stress is equal to the local shear yield stress). The main features of solutions based on such theories are: (a) sliding must occur at the maximum friction surfaces under certain conditions, (b) the velocity field may be singular in the vicinity of maximum friction surfaces. The objective of the present paper is to study these features of solutions. The mathematical structure obtained is considered to be advantageous for a class of materials and may lead to a convergence of viscoplastic solutions to the corresponding rigid perfectly plastic solutions. It seems that the latter is of importance for the construction of a unified theory that could describe the material behavior in the range from rate-independent plasticity to viscoplasticity. In the present paper, the study of the main features of the model is based on the exact closed-form solution to the problem of flow between two coaxial rotating cylinders. In the case of sliding, in addition to the aforementioned features, the asymptotic behavior of the velocity field in the vicinity of the maximum friction surface is found for a class of constitutive laws.Peer reviewe

Qualitative behaviour of viscoplastic solutions in the vicinity of maximum-friction surfaces

“…Forȧ = 0 the statement of the problem under consideration is reduced to that of the Couette flow studied for viscoplastic models with a saturation stress in [12]. It is of interest to compare the latter solution and the solution given in the present paper asȧ → 0.…”

“…(1)-(3), (9) and the boundary conditions (10)- (12). It contains an undetermined function τ (a) which must be found from the friction boundary condition.…”

“…However, the assumption that σ Y → σ s < ∞ as ξ eq → ∞ (models of the second group) can significantly change the solution behaviour near the maximum-friction surfaces. In particular, it has been demonstrated in [12] by means of the exact solution to a particular plane-strain problem that the velocity field can be singular and its behaviour can be the same as in the case of rigid perfectly plastic solutions. Moreover, it has been shown that any set of experimental data can be approximated by a model of the second group with the same accuracy as by a conventional model.…”

“…Moreover, it has been shown that any set of experimental data can be approximated by a model of the second group with the same accuracy as by a conventional model. A disadvantage of the solution considered in [12] is that the normal strain rates vanish at the friction surface (in a local Cartesian coordinate system one axis of which is orthogonal to the friction surface). This may have a significant effect on the solution behaviour at the friction surface [13].…”

Prediction of mixed-mode fracture based on an elasto–plastic energy balance criterion

“…For adiabatic processes, the softening effect is due to both phenomena and is very high, while for isothermal processes the softening is generated only by micro-damage and is smaller. It is noteworthy to stress that the micro-damage process is influenced very much by thermomechanical effects [12,13].…”