Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I—Small Scale Yielding

[+] Author and Article Information
C. F. Shih, R. J. Asaro

Division of Engineering, Brown University, Providence, RI 02912

J. Appl. Mech 55(2), 299-316 (Jun 01, 1988) (18 pages) doi:10.1115/1.3173676 History: Received March 06, 1987; Revised December 04, 1987; Online July 21, 2009


Full-field numerical solutions for a crack which lies along the interface of an elastic-plastic medium and a rigid substrate are presented. The solutions are obtained using a small strain version of the J2 -deformation theory with power-law strain hardening. In the present article, results for loading causing only small scale yielding at the crack tip are described; in subsequent articles the mathematical structure of the crack-tip fields under small scale yielding and results for contained yielding and fully plastic behavior will be presented. We find that although the near-tip fields do not appear to have a separable singular form, of the HRR-type fields as in homogeneous media, they do, however, bear interesting similarities to certain mixed-mode HRR fields. Under small scale yielding, where the remote elastic fields are specified by a complex stress-concentration vector Q = |Q |eiφ with φ being the phase angle between the two in-plane stress modes, we find that the plastic fields are members of a family parameterized by a new phase angle ξ, ≡ φ + εln(QQ /σ0 2 L ) , and the fields nearly scale with the well-defined energy release rate as evaluated by the J-integral. Here σ0 is the reference yield stress and L is the total crack length (or a relevant length of the crack geometry). Numerical procedures appropriate for solving a general class of interface crack problems are also presented. A description of a numerical method for extracting the mixed mode stress intensities for cracks at interfaces and in homogeneous isotropic or anisotropic media, is included.

Copyright © 1988 by ASME
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