Bimaterial interface

The mechanics of fracture along bimaterial interfaces have been studied extensively. Excellent reviews have been published [18]. The stress and deformation field near the tip of a crack lying along a bimaterial interface can be uniquely characterized by means of the complex stress intensity factor K = Kl + iK2. K and K2 have the dimension (Pa m112 " ) and are functions of the sample geometry, applied loading and material properties, i = is the imaginary number and is a dimensionless material constant defined below. 

Labossiere, P.E.W., Dunn, M.L., and Cunningham, S.J., Application of bimaterial interface comer failure mechanics to silicon/glass anodic bonds, Jourruil of the Mechanics and Physics of Solids 2002, 50,405-433. 

The stress measure and closed within parentheses is defined so that (6.29) reduces to (6.28) in the limit as the film becomes very thick. It is likely that glide is accomplished by the thermally activated motion of kinks along the threading segment (Tuppen and Gibbings (1990) Hull et al. (1991)). A free surface or bimaterial interface may offer a better site for kink formation than interior points along the dislocation line, and this is an influence on relaxation that cannot be addressed directly by approaches based on continuum mechanics. 

P.G. Charalambides, J. Lund, A.G. Evans, R.M. McMeeking, A test specimen for determining the fracture resistance of bimaterial interfaces, J. Appl. Mechanics, 56 (1989) 77 82... 

Fig. 7. Crack-lip coordinate system for a crack at a bimaterial interface.

Evans, A.G. and Hutchinson, J.W., Effects of non-planaiity on the mixed mode fracture resistance of bimaterial interfaces. Int. J. Solids Struct., 20,455—466 (1989). 

If we restrict ourselves to 2D problems, a crack along a bimaterial interface will generally be in a state of combined mode I, in which stresses ahead of the crack tip tend to open the crack, and mode II, in which stresses ahead of the crack tip tend to shear the crack faces (there are some limitations to this interpretation of mode mix for cases where the materials have large differences in mechanical properties, and this will be discussed in the following section). Following the work of Hutchinson and Suo, the mode mix is often expressed as a phase angle, defined as [55] ... 

Geubelle, P.H. and Knauss, W.G.. Crack propagation at and near bimaterial interfaces linear analysis. J. Appl. Mech., 61,560-566 (1994). 

Cracks at, or near, interfaces - The above has considered the aspect of cracks located in bulk material, but a second important case is that of cracks at, or very close to, a bimaterial interface. However, an immediate problem arises namely, that when the joint is subjected to solely tensile loads applied normal to the crack, which is located along or parallel to the interface, then these will induce both tensile and shear stresses around the crack tip. Therefore, both Ku and terms are needed to describe the stress field the subscript i indicating a crack at, or near, the interface. Similarly, an applied pure shear stress will also induce both such terms. However, these Kn and Km terms no longer have the clearly defined physical significance, as for the bulk material case and illustrated in Fig. 7.3. Mathematical modelling has shown [21-27] that, for linear-elastic materials, the local stresses ahead of the crack tip at a bimaterial interface are proportional to ... 

However, it is also clear from the discussions in the present chapter that there are many areas in the application of fracture mechanics to the failure of adhesive joints which are far from fully understood. For example, the theoretical problems of dealing with cracks at, or near, bimaterial interfaces and the dependence of the measured values of Gc and Kc upon the joint geometry have yet to be completely understood and modelled. Thus, if the aims of predicting the short- and long-term behaviour of adhesive joints from the behaviour of the bulk adhesive material are to be realized, considerable work remains to be done. 

A. Agrawal and A. M. Karlsson, Obtaining Mode Mixity for a Bimaterial Interface Crack Using the Virtual Crack Closure Technique, Int. J. Fract., 141,75 - 98,2006. 

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