A New Numerical Method for the Analysis of Stress Concentration in Tension Specimen

Abstract

Analyzing the stress concentration in the critical region of a mixed boundary value elastic problem has always been an important area of interest in applied mechanics. In most of the cases, the problems were circumvented using a numerical solution. A numerical approach has been used to solve elastic problems of arbitrary shaped bodies subjected to mixed boundary conditions. The formulation of displacement potential function is used in finite difference method to determine the stress concentration factors in the critical point of fillet region of tension specimen. In this paper, ASTM D 638 type І, II, III, IV and specimens of other proposed dimensions are analyzed. A relationship between stress concentration factor and width-fillet ratio (w/r) has been established. It is also observed that width ratio (W/w) has no effect on stress concentration factor for higher fillet radius. But for lower fillet radius, width ratio has significant effect on stress concentration factor. It is suggested that single arc tension specimen (ASTM D 638 type I, II, and III) can be used instead of double arc specimen (ASTM D 638 type IV) since complicated geometry of double arc tension specimen cannot help to reduce stress concentration in the specimen during tensile test. The results obtained have been presented graphically and are in good agreement with the available results in the literature.

Keywords: Finite difference technique, Displacement potential function, Stress concentration factor