13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- calculated by solving numerically a system of integral equations [9]. Here, as well as in [9-12] the attempts were made to estimate the coefficients of elastic clamping analytically, and semi-analytically. 2. Problem formulation Consider elastic half-plane (substrate) with adjusted layer (coating) of thickness h having elastic properties, different from the properties of substrate. The layer is perfectly glued to the half-plane everywhere except a section of length, 2b, along which it is delaminated. The Cartesian coordinate system is chosen with x-axis being parallel the half-plane boundary, and y-axis coinciding with its external normal, the origin of the coordinate frame coinciding with the delamination centre. Thus the half-plane occupies area / 2 y h <− , the layer does / 2 / 2 h y h − < < , the delamination does , / 2 b x b y h − < < =− . The Young moduli and Poisson ratios of the coating and substrate are , , ,s s E Eν ν, respectively. The layer is assumed to be subjected to the tensile eigenstrain causing compressive stresses, 0σ, acting along the boundary. Such a situation takes place while heating the system in question if thermal extension of the layer is higher than the one of the half-plane. On reaching by the compressive stress some particular level of crσ , the system loses stability and the layer bends (Figure 1). The problem is to find the value of stress, 0 cr σ σ = , corresponding to the loss of stability . Fig. 1. Geometrical configuration. The problem was solved in [6] numerically, using FEM, the value of crσ being presented as products of corresponding values, calculated for the clamped plane 0 crσ and a coefficient σγ 0 cr cr σ σ σ γ = (1) Magnitude of 0 crσ may be calculated using elementary methods. Thus for the clamped plate of length 0 2b the critical stress is [13]: h 2b x δ y
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