28 S. Aduloju et al. 0 2 4 6 8 10 0 0.02 0.04 0.06 0.08 0.1 Relative SSC depth (λ) thickness ratio (τ ) αa=0.8 αr=0.8 αa=0.6 αr=0.6 αa=0.4 αr=0.4 αa=0.2 αr=0.2 αa=0 αr=0 αa=-0.2 αr=-0.2 αa=-0.4 αr=-0.4 αa=-0.8 αr=-0.8 Fig. 5.4 Relative SSC depth as function of film/substrate thickness The SSC depth and KI for bimaterial for different ’ parameters were explored and four additional bimaterial specimen designs were made to obtain KI that changes with propagation length so that crack velocities values rather than a single point be obtained. This could be realized by developing bimaterial specimens with varying thickness across its length. FRANC3D [11, 12] code receives a mesh model as input and performs adaptive mesh restructuring to incrementally advance a crack. The SSC propagations for the five new specimens were performed using Franc3D code interfaced with Abaqus. 3D geometry and initial Finite element discretization using quadratic quadrilateral elements were done in ABAQUS FE code while the initial crack lengths were specified in the Franc3D code. The 3-dimensional models for the five designs were realized by extruding the 2D model through a thickness of 1 mm. Finer discretization of the geometry with a high concentration of elements near the crack tip was done and stress intensity factors were calculated by the M-integral method [11, 12]. The local direction of the crack growth was predicted using the maximum Tensile stress criterion. 5.3 FE Model Validation Suo and Hutchinson’s analytic model was used as a benchmark to check the accuracy of the FE model. This was done by comparing the results obtained from studying the SSC in a system consisting of a thin film deposited on a glass substrate in Fig. 5.2. h1 represents the thickness of the film and h2 the thickness of the glass substrate. Figure 5.4 shows the relative SSC depth obtained for different film/substrate thickness ratio £. These values were obtained for eight different bonded materials where ’a and ’r represent the choice of first dundurs’ parameter for analytical and FE models. Figure 5.5 shows the effect of the difference in the Elastic mismatch on the relative SSC where £a and£r represent the choice of the thickness ratio used for analytical and FE models. The results obtained from the FE model in Figs. 5.4 and 5.5 compared well with the results obtained from Suo and Hutchinson analytic model [13]. 5.4 Bi-material Beam Finite Element Model The FE model was used to study SSC in the bottom material of bimaterial beam. h1 represents the thickness of the Schott B270 glass and h2 the thickness of the soda-lime glass. Figure 5.6 shows the axial stress contour plot across the bimaterial beam for h1 Dh2 D25.4mm and the initial crack depth of length 15 mm located at œD0.5., The cooling of the bimaterial beam from the bonding temperature puts the composite beam in bending because they are constrained to be the same length along the interface. The bottom material has lower CTE and contracts lesser than the top material. The contraction of the top material results in compressive stresses on the bottom material at the interface and the bottom material exert tensile stresses on the top material at the interface.
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