13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- coating and substrate being of the same material were obtained in [12]. The results were obtained on the base of solution of the matrix Wiener-Hopf problem [17], which was extended to describe displacements. The extraction of the coefficient 22 a for this case was made before [18], [19]. 3-D case was considered in [20]. It follows from the results of [5] that the value for 12 a does not effectively depend on the ratio elastic moduli, unless very soft substrates. For this case value 12 3 a = (22) was obtained [12]. It was also obtained (ibid.) the value for 13 a for the case of the same moduli of coating and substrate 13 1 3 a = + (23) The obtained formula for 11 a appeared rather awkward to be represented here. An intent look at the results for 11 a reveals that all points may be represented as a single master curve (Fig 3) with rather good accuracy. Fig. 3. Numerically obtained master curve for 11 a on the base of results [5]. The curve may be fitted by one of the following (purely approximating) formulae 1/4 1/4 3 3 11 11 1/5 1/6 11 3 11 1 3 3 2 2 2 1 4 3 S S S S S S S E b E b E a a E h E h E E b E E b E a a E h E E h E ⎡ ⎤ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ⎢ ⎥ = + = ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ⎢ ⎥ = − = − ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ (24)
RkJQdWJsaXNoZXIy MjM0NDE=