Sergei Alexandrov

Thermal effects on the development of plastic zones in thin axisymmetric plates

A simple thermoelastic-plastic problem is solved analytically to show a thermal effect on the development of plastic zones in thin plates. The temperature field is assumed to be uniform but monotonically varying with the time. The material of the plate obeys the von Mises yield criterion with a constant yield stress. It is shown that a negligible rise of temperature may lead to a significant growth of the plastic zone. Even though stress analysis only is needed in the plastic zone to illustrate this effect, a complete closed-form solution to the problem is given.

Elastic–Plastic Stress Distribution in a Rotating Annular Disk

Abstract The plane state of stress in an elastic–plastic rotating annular disk was studied. The analysis was based on the Mises yield criterion and its associated flow rule. The radius of the elastic–plastic boundary was found as a function of angular velocity. In particular, it was shown that this radius is sensitive to the magnitude of the angular velocity. The method of stress analysis developed is illustrated by numerical results. A comparison with the solution obtained using the Tresca yield criterion is given.

Elastic-plastic stress distribution in a plastically anisotropic rotating disk

The plane state of stress in an elastic-plastic rotating anisotropic annular disk is studied. To incorporate the effect of anisotropy on the plastic flow, Hill s quadratic orthotropic yield criterion and its associated flow rule are adopted. A semi-analytical solution is obtained. The solution is illustrated by numerical calculations showing various aspects of the influence of plastic anisotropy on the stress distribution in the rotating disk.

An Approach to Prediction of Evolution of Material Properties in the Vicinity of Frictional Interfaces in Metal Forming

The quality of surface of the product of metal forming processes depends on physical processes in the vicinity of frictional interfaces between the material and tool. It is well known that material properties in a narrow layer in the vicinity of such interfaces are usually quite different from the properties in the bulk. It is therefore necessary to develop a special approach to account for this feature of the distribution of material properties. A possible approach is proposed in the present paper. It is based on the concept of strain rate intensity factor.

On the dead-zone formation and limit analysis in axially symmetric extrusion

For axisymmetric direct and indirect extrusion, a kinematically admissible velocity field based on a simple radial flow field combined with the asymptotic behaviour required of a real velocity field near a velocity discontinuity surface is proposed. The influence of the extrusion ratio on the shape of a dead zone and the extrusion pressure is investigated. The result obtained for the upper bound on the extrusion pressure is compared with other solutions. It is shown that using the asymptotic velocity field slightly improves the prediction of the extrusion pressure in comparison with the other solutions based on radial flow. The main advantages of the approach proposed are that it is applicable to a class of processes and that it accounts for the behaviour of a real velocity field in the vicinity of velocity discontinuity surfaces/maximum friction surfaces where various physical effects like local heating, recrystalization, and transformations occur.

Displacement Field and Strain Distribution in a Rotating Annular Disk

Abstract The displacement field and strain distribution in a thin rotating disk with constant thickness and density are found based on Mises’ yield criterion and its associated flow rule. The material of the disk is elastic-perfectly plastic and the assumption of plane stress is adopted. The solution is illustrated by an example.

The Strain Rate Intensity Factor and its Applications: A Review

The present paper concerns with the concept of the strain rate intensity factor in rigid plastic solids. The strain rate intensity factor is the coefficient of the principal singular term in the expansion of the equivalent strain rate in a series in the vicinity of maximum friction surfaces. Such singular velocity fields appear in solutions based on several rigid plastic models. Because of this singularity in the velocity field, many conventional evolution equations for material properties are not compatible with such rigid plastic solutions. On the other hand, qualitative behaviour of the singular rigid plastic solutions in the vicinity of maximum friction surfaces is in agreement with a number of experimental results. Therefore, the primary objective of research in this direction is to develop an approach to relate parameters of the singular velocity fields and parameters characterizing material properties. The approaches proposed in previous works are based on the strain rate intensity factor. In the case of analytical and semi-analytical solutions the strain rate intensity factor can be found by means of an asymptotic analysis of the solutions. A number of such solutions obtained by inverse methods are reviewed in the present paper and the strain rate intensity factor is found. An effect of process parameters on its magnitude is shown and discussed.

Ideal Flow in Plasticity

Ideal plastic flows constitute a class of solutions in the classical theory of plasticity based on, especially for bulk forming cases, Tresca’s yield criterion without hardening and its associated flow rule. They are defined by the condition that all material elements follow the minimum plastic work path, a condition which is believed to be advantageous for forming processes. Thus, the ideal flow theory has been proposed as the basis of procedures for the direct preliminary design of forming processes, which mainly involve plastic deformation. The aim of the present review is to provide a summary of both the theory of ideal flows and its applications. The theory includes steady and nonsteady flows, which are divided into three sections, respectively: plane-strain flows, axisymmetric flows, and three-dimensional flows. The role of the method of characteristics, including the computational aspect, is emphasized. The theory of ideal membrane flows is also included but separately because of its advanced applications based on finite element numerical codes. For membrane flows, restrictions on the constitutive behavior of materials are significantly relaxed so that more sophisticated anisotropic constitutive laws with hardening are accounted for. In applications, the ideal plastic flow theory provides not only process design guidelines for current forming processes under realistic tool constraints, but also proposes new ultimate optimum process information for futuristic processes.

On The Maximum Friction Law for Rigid/Plastic, Hardening Materials

For a rigid/plastic, hardening material model, it is shown that the velocity fields adjacent to surfaces of maximum friction must satisfy the sticking condition. This means that the stress boundary condition, the maximum friction law, may be replaced by the velocity boundary condition. Axisymmetric flows without rotation and planar flows are considered.

An analysis of the axisymmetric compression of viscous materials

Abstract The axisymmetric compression of a cylinder and ring of a viscous power-law material is studied. It is assumed that the friction stress attains its maximum value at sliding. However, an analysis of such a friction law has shown that the sliding condition contradicts other equations. Therefore, this friction law leads to the sticking condition and, thus, to the kinematic boundary conditions at the friction surface. In this case, there is a class of metal-forming processes for which an upper bound on the force required to deform the specimen of a viscous power-law material can be obtained. Numerical results are given for the axisymmetric compression of a cylinder and ring.