A numerical method for determining the strain rate intensity factor under plane strain conditions

Abstract

Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous.

Analysis of the maximum friction condition for green body forming in an ANSYS environment

“…The maximum shear stress condition could be probably implemented into ANSYS directly if the developers adopt the respective special singular element. This task has been already recognized as important (see [33]). This would allow researchers to test the concept of the strain rate intensity factor recently proposed in [34,35].…”

Generation of a Layer of Severe Plastic Deformation near Friction Surfaces in Upsetting of Steel Specimens

“…However, to the best of authors' knowledge, no attempts have been made to determine the strain rate intensity factor by means of this method. To date the only accurate method for calculating the strain rate intensity factor is based on the method of characteristics [28]. However, its validity is restricted to plane strain problems.…”

Improvement of control algorithm for mobile robot using multi-layer sensor fusion

“…Starting from Prandtl-Nadai solution for rigid perfectly plastic material [1,2], various analytical solutions, extended or generalized, for a strip of single material or piece-wise homogeneous materials have been given [3 -6]. However, the corresponding numerical solutions have only been implemented for a strip of single rigid perfectly plastic material, among which it is necessary to mention the solutions in [7][8] for stress and velocity and the solution for the distribution of the strain rate intensity factor along maximum friction surfaces [9]. These solutions were based on the theory of characteristics -also known as method of characteristics -due to the equations governing plastic flow in plane strain are hyperbolic and the characteristics for the stresses and the velocities coincide, furthermore, they coincide with the slip-lines for which the general theory is presented in [2,10].…”