Small Scale Yielding at a Crack Normal to the Interface Between an Elastic and a Yielding Material
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SMALL SCALE YIELDING AT A CRACK NORMAL TO THE INTERFACE BETWEEN AN ELASTIC AND A YIELDING MATERIAL Ming Y. He, R. M. McMeeking and Ning T. Zhang Materials Department & Mechanical Engineering Department, College of Engineering University of California, Santa Barbara, CA 93106 ABSTRACT By using the elastic singular field as a prescribed loading condition, small scale yielding solutions are obtained for a crack normal to the interface between a brittle and a ductile material. Results for both a crack in the brittle material and one in the ductile material are obtained by finite element analysis. The crack tip fields obtained by the finite element analysis are compared with the asymptotic solutions. It is found that near the tip the stress fields approach the asymptotic solutions. If the crack is in the brittle material, the high triaxial stresses are developed near the interface ahead of the crack tip. 1. INTRODUCTION Thin films of metals, ceramics and polymers bonded to substrates are typically subject to appreciable residual stress, which can cause cracking of the films. Many analytical, numerical and experimental investigations have been conducted recently. However, comprehensive elastic-plastic analyses for cracks in films are not available. One purpose of our study is to provide one specific solution. The problem analyzed in this paper is shown in Figure 1. A perpendicular crack meets an interface between two dissimilar materials. Loads are applied which tend to open the crack (mode I loading). The tip is at the interface. One material is purely elastic and the other is elastic-perfectly plastic. By using the elastic singular field as a prescribed boundary condition, small scale yielding solutions are obtained by finite element analysis and compared with the asymptotic fields. 2. ASYMPTOTIC FIELDS The plane strain asymptotic stress fields for a crack normal to the interface between an elastic and an elastic-perfectly plastic material when the crack tip is at the interface have been given by [1]. The results are quoted here as follows: Problem A: If the crack is in the yielded material as in Figure la, the asymptotic solutions for the stresses in the perfectly plastic material are given in polar coordinates by [21 as=k(1+
2
20J, 2
22
"•"(1)
4
Ore= k
Mat. Res. Soc. Symp. Proc. Vol. 239. @1992 Materials Research Society
586
and k(l + cos20)] a, = k(1- cos20) CO=
445
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