Pergamon Acta metall, mater. Vol. 43, No. 3, pp. 1149-1156, 1995 Copyright (C 1995 ElsevierScienceLtd 0956-7151(94)00308-4 Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00 THE EFFECT OF FLAWS ON THE PROPAGATION OF CRACKS AT BI-MATERIALS INFERFACES A. A. MAMMOLI 1, A. L. GRAHAM 2, I. E. REIMANIS 2 and D. L. TULLOCK 2 ~Department of Mechanical and Materials Engineering, The University of Western Australia, Nedlands, WA 6009. Australia and 2Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A. (Recewed 20May 1994) Abstract---This study uses the boundary element method to investigate the effects of interfacial flaws on the propagation of a crack at or near an interface between two elastic, isotropic materials. These calculations reveal that flaws tend to deflect cracks approaching the interface from their original trajectory if the distance between the flaw and crack tip is small in relation to the flaw size. It is found that the higher the elastic mismatch parameter, the more crack trajectories are attracted to flaws. Other calculations show that materials with interfacial flaws have a significantly increased tendency to deflect cracks along the interface as compared to defect-free materials. I. INTRODUCTION Debonding is an important phenomenon in com- posite materials, and it is essential for the activation of toughening mechanisms such as crack bridging and frictional energy dissipation (fibre pullout) [1]. Interface debonding is frequently desired so that the reinforcement phase is left intact, to inhibit further opening of the crack tip. Debonding is usually in- itiated by the deflection of a crack along an interface. The role of interfaces in crack deflection has been examined by a number of workers, both experimen- tally [1 11] and theoretically [12 14]. The relative tendency for a crack to deflect along the interface or propagate into the reinforcement is known to depend on the elastic anisotropy between the materials, the relative fracture energies of the interface and reinforcement, the residual stress, and the angle of the approaching crack with respect to the interface [12, 13, 15]. The criteria are widely accepted and utilized by the structural composites community [l]. For plane strain, the elastic properties of a com- posite, composed of two elastic, isotropic materials can be fully defined by Dundurs parameters [16] and ft. In this study, the elastic mismatch parameter is defined as #2(1 -- vl) -- ]/1(1 -- v2) ~. - (1) tt2(l -- v I) -I- J/1 (1 -- v2) where fl~ and /~2 are the shear moduli of materials 1 and 2, and v~ and v 2 are their respective Poisson's ratios. To simplify the calculations and to reduce the number of variables, fl was kept at 0. In the types of problems discussed here, fl is frequently assumed to be 0 [12, 15], and has been shown to have an insignifi- cant effect on crack deflection criteria [13]. The convention we adopt is such that the main crack is always in material 1, so that a positive value of c~ represents a crack in a compliant material approach- ing the interface with a stiffer material (see Fig. 1). Consider a crack in the matrix phase of a com- posite material approaching the reinforcement phase. A necessary condition for a crack to deflect along the interface is ri(~) < % = ~(0) (2) F~ .~p where Fi(0) is the interface toughness at a phase angle of loading, ~, Fs is the toughness of the reinforcement phase, aJd is the energy release rate for a crack deflected at the interface and ~p is the energy release rate for a penetrating crack. The energy release rate ratio ~(~) is a function of the elastic properties of the materials on either side of the interface and of the loading conditions. If the ratio of the interface toughness to the reinforcement toughness, Fi( ~)/F s, lies below the ~(~) curve, then deflection will occur. Deflection can be achieved by lowering the Fi(~)/Fs ratio, through appropriate interface coatings, or by shifting the ~(~) curve upwards. Local microstructural changes, such as crystallographic twinning, discontinuous second phases or flaws, which are often present at bimaterial interfaces [1, 2, 6, 7, 11], might be predicted to affect ~(0). In this paper it is demonstrated that flaws can facilitate deflection by the latter method. None of the studies described above has examined the effect of interface flaws on crack deflection in composites, yet there is evidence that these flaws can significantly influence the behaviour of a crack at or near the interface [6, 171. Interface flaws are also important in controlling other mechanical properties in brittle matrix composites, for example multiple 1149