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A uniform analysis of plane-strain bending for different rigid/plastic and elastic/ plastic constitutive laws is performed. In most cases numerical treatment is reduced to solving an ordinary differential equation. The solutions obtained either coincide with known exact solutions or show the same tendencies as known approximate solutions. In addition, new solutions are obtained, including an elastic/plastic solution at large strains. The throughthickness distribution of the principal stresses and the variation in the bending moment as well as the thickness of the layer with a time-like parameter are illustrated.

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

To determine a workability diagram for bulk metal forming processes, it is proposed to use experiments in which fracture occurs at a free surface. A good example of such experiments is an upsetting test with profiled dies. An advantage of this method is that fracture conditions are formulated in terms of strain components whereas stresses are excluded using an exact theoretical solution. In the present study three axisymmetric upsetting tests, with flat dies and with conical dies, are carried out to determine the strain to fracture. The method proposed is then combined with these experimental data to find an approximation to the workability diagram of a tool steel.

The main objective of the present paper is to compare, by means of a problem permitting a closed-form solution, qualitative behaviour of solutions based on three models of pressure-dependent plasticity, the coaxial model, the double-shearing model, and the double-slip and rotation model. The constitutive equations of each model reduce to classical metal plasticity at specific values of input parameters. Nevertheless, the solution behaviour essentially depends on the model chosen, independently of how close the input parameters are to these specific values. In particular, such features of the solutions as non-uniqueness, non-existence and singularity are emphasized. It is concluded that the double-slip and rotation model only retains all features inherent to classical plasticity. r

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