The fracture energy of bimaterial interfaces
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I.
INTRODUCTION
THE fracture
energy of interfaces between dissimilar materials, Fi, exerts a critical influence on many problems of technological importance, particularly the mechanical properties of composites tl'E'sl and the decohesion of films and coatings, [3-7) as well as the strength of bonds, t8,9] The specific role of the fracture energy is first outlined for several of these problems, as needed to provide a conceptual framework for studies of Fi. Subject to this background and with the adoption of a practicable mechanics formulation for characterizing interface cracks, methods for measuring F~ on bimaterial systems of interest are described. Experimental measurements and observations of interface fractures are presented, as well as atomistic, chemical, and microstructural features of typical interfaces. Preliminary attempts are then made to relate F~ to the salient characteristics of interfaces, using the appropriate models. The conceptual framework for addressing the interface fracture energy derives from notions already established for interpreting the fracture energy of brittle solids. (~~ The most basic contribution to Fi, which often leverages all others, is the work of adhesion, Wad, and the effect on that quantity of segregants at the interface, as given by tl~ Fo = Waa - E (Ag~ - Ag~
11]
i
where ci is the concentration of segregant per unit area of interface and Ag ~ is the Gibbs free energy of segregation. The subscript i refers to the interface and s to A.G. EVANS, Professor, is with the Materials Department, University of California, Santa Barbara, CA 93106. M. ROHLE is with the Max Planck Institiit fiir Metallforschung, Stuttgart, Federal Republic of Germany. B.J. DALGLEISH is with Materials Development, Berkeley Laboratory, Berkeley, CA. P.G. CHARALAMBIDES is with the Department of Mechanical Engineering, Michigan State University, East Lansing, MI. This paper is based on a presentation made in the symposium "Interface Science and Engineering" presented during the 1988 World Materials Congress and the TMS Fall Meeting, Chicago, IL, September 26-29, 1988, under the auspices of the ASM-MSD Surfaces and Interfaces Committee and the TMS Electronic Device Materials Committee. METALLURGICALTRANSACTIONSA
the free surface. For a planar interface in a system having constituents with linear constitutive characteristics, [HI Fi = ~Fo
[21
where ~ is a quantity (1 -~ ~ ~ 10) which characterizes the nonequilibrium thermodynamic state of the surface created by fracture. Nonlinearity of either constituent and nonplanarity of the interface introduce other multiplicative contributions to Fi, based on crack shielding and dissipation. The roughness-related shielding is manifest in a parameter, [12] X = E H 2 / L F0
[3]
where H is the amplitude, L is the wavelength of roughness, and E is Young's modulus. Plasticity occurring in one of the bonded layers can cause plastic dissipation, governed by a nondimensional parameter Its,14] = EFo/y2h
[4]
where Y is the yield strength and h the thickness of the du
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