N. Alexandrova

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.

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.

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.

Analytical treatment of tube drawing with a mandrel

Abstract An upper-bound analysis is used to estimate the required power in tube drawing and ironing of rigid, perfectly plastic material through a conical die. The frictional stresses exerted by the die and the mandrel on the material have constant values. The proposed kinematically admissible velocity field accounts for the singular behaviour of the real velocity field in the vicinity of the maximum friction surface. An optimal die angle is determined. The analysis agrees favourably with experiments and other theoretical solutions.

Fracture analysis of tube drawing with a mandrel

Abstract Hill’s general method and a fracture criterion based on a workability diagram have been used to determine whether the material would fail during the ironing/drawing processes. The material is assumed to be rigid, perfectly plastic passing through a conical die. The frictional stresses exerted by the die and the mandrel on the material have constant values. Computer software “Mathematica-3” is adopted to calculate the distribution of the equivalent strain and mean stress throughout the specimen. For the given product geometry the analysis proposed is capable of predicting the occurrence of fracture in the product. Results agree favorably with experiments and other solutions obtained by the finite element method.

Elastic-plastic stress distributions and limit angular velocities in rotating hyperbolic annular discs:

Abstract Plastic analytical stress analysis of a rotating annular disc with its contours being free from the radial pressure and with specifically variable thickness is presented in terms of the Mises-yield criterion and its associated flow rule. The hyperbolic form of thickness variation is considered and optimized towards the maximum rotational speed and favourable stress combinations. Radial and circumferential stress distributions in the disc both in the intermediate elastic-plastic and in the limit plastic states are obtained. As a particular case, limit elastic angular velocity parameter is derived. The influences of rotational speed as well as the discs thickness profile on the plastic solution and size of elastic-plastic zone are demonstrated and discussed. The results obtained may be used for the correct implementation of numerical codes and preliminary engineering design.

Deformation and Stress Analysis of an Anisotropic Rotating Annular Disk

The plane state of stress in a rotating elastic-perfectly plastic anisotropic annular disk of constant thickness and density is studied. It is shown that the key design geometric parameters of the disk, namely, its mean radius and width, influence the stress and strain distributions. To explicitly get the total strain field, including elastic and plastic regions, a new, original, semi-analytical method is developed. The disk material is assumed to be elastically and plastically anisotropic, obeying the Hills quadratic yield criterion in the plastic zone and the generalized Hookes law in the elastic zone. The results may be used in a preliminary design of rotating disks as well as in implementation of numerical codes.

Preliminary Design of a Composite Material Flywheel

Flywheel rotor performance monitoring and damage detection are increasingly gaining the interest of manufacturers of aircraft engines. This is primary due to the fact that there is a necessity for improving safety during operation as well as a need for lower maintenance costs. Applied techniques for damage detection and health monitoring of rotors are essential for engine safety, reliability and life prediction. Preliminary design of such a flywheel studied here is based on a simple model of annular rotating disk with stress-free boundary conditions. In addition to the critical rotational speed, the paper analyses the influence of the leading design parameter - material plastic anisotropy - on the development of plastic zone and stress/strain distributions.