An Experimental Study of Stress Singularities at a Sharp Corner in a Contact Problem

-The photoelastic method was used to investigate the nature of the local stress field at a sharp corner of a wedge that was compressed against a larger body. Planar wedge specimens made of photoelastic material were compressed against a half plane (larger body) of identical material at various load levels. Several wedge angles were studied. The nature of the singular stress field postulated by linear elastic analysis was verified and the strength of the singularity was obtained by plotting the variation of fringe order as a function of radial distance from the sharp corner on a logarithmic scale. The experimental results were found to be in good agreement with the theoretical predictions. The effect of interface friction and the effect of rounding off the sharp edge are briefly discussed. I n t r o d u c t i o n In past years, the singular nature of the stress field near a re-entrant corner defined by contact of two bodies has been accounted for by a stress-intensity factor. By using a numerical technique such as the finite-element method based on linear-elastic theory, one can obtain a detailed description of the near-field stress distribution. However, mesh refinement near the re-entrant corner will not lead to convergent stresses near the corner. Indeed, the finer the mesh, the higher the stresses become near the corner. Many engineers in the field of engine design are somewhat skeptical about the predictions of singular stress fields. Indeed many believe that they do not exist, since problems have not occurred with current designs. One way to overcome this uncertainty is to conduct some simple model experiments. In this paper, we describe a set of experiments that are aimed at characterizing the singular stress field. One goal was too compare the experimental results with the theoretical predictions. A second was to investigate practical redesigns (e.g., chamfers, radii) that might reduce stress intensities at the contact point. The results obtained are compared with theory (Dundurs and E.C. Miniatt is Graduate Research Assistant, A.M. Waas is Assistant Professor of Aerospace Engineering, and W.J. Anderson is Professor of Aerospace Engineering, Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109-2140. Original manuscript submitted." September 22, 1989. Final manuscript received: May 10, 1990. Lee'). A discussion of the effects of frictional contact is also presented. T h e o r y The configuration being studied is shown in Fig. 1. A semi-infinite body B1 is compressed by an indenter B2, in the form of a wedge with a sharp corner encompassing an angle 3'. The half plane and the wedge have material properties /~,, gl and #2, x2 respectively. ~ denotes the shear modulus while x -4 3 u for plane strain with denoting Poisson's ratio. This problem was originally studied by Dundurs and Lee' for the case of frictionless contact. The case with friction was later studied by Theocaris and Gdoutos. 2 Comninou 3 extended this study and carried out a more detailed analysis that showed the presence of logarithmic singularities. Results which are relevant to the present study are presented in this section. According to the analysis in Ref. 3, singularities in the stress field are related to the real roots of the determinant associated with the Mellin transform of the elastic field. Details of the analysis are given in Refs. 3 and 5. This determinant is expressed as D(p: ' r ,c~,f3,Q) = 8(1 + p ) sin (p~r)F(p:7,a,t3,0)