13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 0k b π = (10) Substituting Eq. (1), Eq. (5), Eq. (8), Eq. (10) into Eq. (7) gives 0 tan 0 d σ σ π γ π β γ + = (11) Here ( ) 3 * * s h b E E β= (12) Dependence of σγ on β according to this model is also presented on Figure 2. The most probable reason for the slight systematical divergence seems to be in underestimation of the critical stresses in numerical calculations. 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Figure 2. Dependence of relative critical stress on geometrical and elastic parameters: purple dashed line – solution Eq. (11); green dashed line (short dashes) – Eq. (18); solid red thin line – Eq. (26); dots – numerical solution [9] 4. Generalization for the case of multilayered coating and substrate The above model is easily generalized for the case of anisotropic (orthotropic) and multilayered coating and substrate. For anisotropic phases all the above formulae remain valid with replacing the values of effective moduli Eq. (9) of coating and substrate by the values corresponding to anisotropic media. Thus for substrate instead of the second formula of Eq. (9) we have ( ) { } 1/2 * 22 66 11 11 22 2 2 sE − ⎡ ⎤ = β β + β + β β ⎣ ⎦ (13) Here ij β are components of compliance tensor written in matrix form (eg [14]), axis 1x is
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