June 24-29, 2018
A set of analytical solutions has been obtained related to crack growth along the boundary of a layer adjusting to another layer or half-plane. In particular, for the second Dundur’s parameter vanishing the exact analytical solutions have been obtained for the two particular cases:
- semi-infinite crack separating two layers of equal thickness;
- semi-infinite crack separating a layers from a half-plane.
Two modes of stress intensity factors (SIFs) were obtained in terms of three force parameters: the total moment and two components (normal and shear) of the total force of stresses acting on the continuation of the crack line. The elastic clamping conditions [1-3] for a plate modelling the delaminated part of coating have also been obtained. According to these conditions the rotation angle and two components of displacement vector at the clamping point are related to the acting moment and two components of the total force by means of 3x3 matrix of compliance .
All functions involved are expressed in terms of single integrals of algebraic functions. For very small and very large ratios of Young’s moduli simple asymptotics are derived.
The obtained solutions has been applied for the problems of buckling driven delaminations. It has been shown that for a wide range of parameters the ratio of the buckling stress and the critical stress of a rigidly clamped plate is determined by a single non-dimensional parameter, composed by the ratio of the elastic constants of the coating and substrate, and the ratio of the delamination length and the coating thickness. The solution has ben generalized for anisotropic and multilayered structures.
The problem of coating delamination from the cylindrical compliant substrate has also been addressed. Two types of prolonged blisters have been considered – along axial and circumferential directions: for each type of blisters the energy release rates have been calculated for their propagation in both axial and circumferential direction. For both cases tendencies for blister elongation has been observed.
From the practical point of view the obtained results is appeared to be useful for calculation parameters of coatings including TBC and for verifying precision of the program codes designed and to be designed for solving the wider range of problems of the kind. The results may also be useful for other applications such as interpretations of the results of blister tests.
1. Cotterell B., Chen Z. Int J Fract. V.104 (2000) 169-179.
2. Yu H.-H., Hutchinson J. W. Int. J. Fract. V.113. (2002) 39–55.
3. Begley, M.R, Hutchinson, J.W." The Mechanics and Reliability of Films, Multilayers and Coatings" Cambridge University Press, (2017).
4. Ustinov K.B. Eng. Fail. Analysis V.48B (2015) 338-344
Konstantin B. Ustinov, "On coatings delamination; some analytical solutions" in "Thermal Barrier Coatings V", Prof. Dr. Robert Vaßen, Forschungszentrum Jülich GmbH, Germany Brian Hazel, Pratt & Whitney, USA Prof. Dr. Uwe Schulz, German Aerospace Center, Germany Dr. Michael J. Maloney, Pratt & Whitney, USA Dr. Ram Darolia, GE Aviation (Retired), USA Eds, ECI Symposium Series, (2018). http://dc.engconfintl.org/tbcv/9