σ x1 x2 Figure 1: Schematic illustration of two overlapping plates bonded in a finite zone. The thin plate is loaded by a constant normal traction, σ11 = σ, as indicated. FRACTURE MECHANICS The edge of the bond zone is regarded as an interface crack front, which is subject to combined mode I, II and III loading. For the plate thickness, h, smaller than the extent of the bond zone, the energy release rate, G, and the mode I, II and III contributions to G can be calculated by the coupling of an inner, fracture mechanics based solution close to the crack tip with an outer solution for the stress state in the plate. The relations between the combined mode I/II and the mode III energy release rates and the normal stress, σnn, and shear stress, σnt, in the plate along the crack front are given by [6] 2 2 I/II III I / II nn III nt 1- 1+ G=G G ,G = h , G = h 2E E ν + σ 2 ν σ (1) where E and ν are the Young’s modulus and the Poisson’s ratio for the plate, respectively. A family of interface fracture criteria formulated in [6] for non-oscillating singular crack tip fields is applied here in the form I 2 II 3 III 1c G + G + G = G λ λ (2) where λ2 and λ3 denote parameters between 0 and 1 adjusting the relative contributions of mode II and III to the fracture criterion, and G1c is the mode I fracture toughness of the bond. For λ2 = λ3 = 1 the fracture criterion is the Griffith criterion, while for λ2 = λ3 = 0 the fracture criterion is independent of mode II and III. The criterion (2) has been applied to thin film debonding problems in e.g. [6] and Jensen and Thouless [7]. It contains as a special case the fracture criterion applied for spot welds in Radaj [8] and [3]. The fracture criterion captures the mixed mode dependence of interface fracture toughness due to, for instance, plastic deformation at the crack tip or rough crack faces contacting under mode II and III dominant loading conditions. For the present problem, which probably represents the simplest case possible since the stress state in the plate is planar so that the ratio between the mode I and mode II energy release rate along the crack front is constant, (1) and (2) reduces to 2 2 nn nt c F + k = 2 ≡ σ σ σ (3)
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