International Journal of Fracture, Vol. 15, No. 2, April 1979 © 1979 Sijthotf & Noordhoff International Publishers Alphen aan den Rijn, The Netherlands 135 Evaluation of stress intensity factors for bimaterial bodies using numerical crack flank displacement data R.E. SMELSER* Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA (Received February 24, 1978; in revised form April 14, 1978) ABSTRACT Methods for obtaining stress intensity factors for bimaterial bodies using numerical crack flank displace- ment data are presented and compared. The stress analysis of a cracked bimaterial is reviewed. The analysis results in a data reduction scheme for the stress intensity factors via the crack flank displacement data. The data reduction scheme produces adequate resolution of the magnitude of the complex stress intensity factor but is incapable of resolving the angle when the moduli of the adjoining materials are close. An extended form of the J-integral is shown to provide increased accuracy for the magnitude of the complex stress intensity factor without yielding the angle. 1. Introduction The presence of cracks along the interface of multimaterial domains presents special analytical problems not encountered in cracked homogeneous bodies. In single material bodies, stress intensification arises solely from a geometric discontinuity, the crack. The multimaterial body, in contrast, produces stress intensification from a geometric discontinuity and a material discontinuity. These discontinuities induce both an opening mode, KI, and a shearing mode, K~, intensification for single mode loading. This coupling of stress intensification was first demonstrated by Williams [I]. He also showed that the stresses behave in an oscillatory manner as the crack tip is approached. Further analysis of cracked bimaterial bodies by Erdogan [2,3], Rice and Sih [4,5], England [6], and more recently Goree and Venezia [7] has yielded stress intensity factors for some simple geometries and loadings. Because of the complexity of these analyses, numerical procedures are a necessity when stress intensities are desired for more general configurations and loadings. An early numerical analysis for a crack lying perpendicular to, but not touching, the bimaterial interface was presented by Leverenz [8]. In this work, he presented stress intensity correction factors which demonstrated the effect of an interface on the crack tip stress field. Recently, Lin and Mar [9] have used a special hybrid crack tip finite element to obtain stress intensity factors for both the interface crack and the perpendicular crack touching the interface. Stern and Hong [10, 11] have extended the contour integral method of Stern [12] to bimaterials with interfacial cracks. While the numerical techniques of Lin and Mar and Stern and Hong yield KI and KH in- dependently, they do require complicated computational procedures. Thus, alternate methods for obtaining KI and K~I are desirable. One such alternative is to use displacement fields provided by numerical solu- tions. A method commonly used in studying cracked bodies involves the (displace- * Formerly Graduate Research Assistant, Department of Mechanical Engineering, Carnegie-Mellon Uni- versity, Pittsburgh, Pennsylvania. 0376-9429/79/020135-09500.20/0 Int. Journ. o/Fracture, 15 (1979) 135-143