On delamination of bi‐layers composed by orthotropic materials: Exact analytical solutions for some particular cases

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 101; no. 4
• Main Authors: Ustinov, K. B., Idrisov, D. M.
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01-04-2021
• Subjects: anisotropy; Axes (reference lines); bi‐layer; Dimensionless numbers; elastic mismatch; Elastic properties; Exact solutions; Infinity; interface crack; Interfacial cracks; Mathematical analysis; matrix factorization; Modulus of elasticity; Parameters; scaling; Stress intensity factors; Tensors; Thickness
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.202000239

Earlier [1, 2, 3], exact analytical solutions were obtained for three configurations of composed bi‐layers with semi‐infinite interface cracks: (i) the bilayer composed of two isotropic layers of equal thicknesses; (ii) an orthotropic layer with the central semi‐infinite crack; (iii) an isotropic layer on isotropic half‐plane of a different material (may be considered as a bilayer, the thickness of one of its layers tending to infinity). In all cases the second Dundur's parameter were supposed to be equal to zero. Here by using a scaling technique all three solutions have been extended to cover wider range of elastic and geometric parameters (elastic constants and thicknesses). In particular, a 2‐D problem of a bilayer composed by dissimilar anisotropic layers partly separated by semi‐infinite crack arbitrary loaded at infinity is considered. The principle axes of elasticity tensor for both layers are supposed to coincide with the geometrical axes. The problem involves 10 constants: four elastic constants for each layer and two thicknesses of the layers. By choosing the proper scales for length and for elastic moduli, the number of dimensionless constants is reduced to 8. By using a scaling technique exact analytical solutions are obtained for two subclasses of the problem with four conditions imposed on the parameters for each case, so that four out of eight parameters remain arbitrary. Similarly a solution is obtained for 2‐D problem of a layer on a half‐plane partly separated by semi‐infinite crack arbitrary loaded at infinity. For all considered cases two modes of stress intensity factors are found in terms of four integral characteristics of the external loads.
Earlier [1, 2, 3], exact analytical solutions were obtained for three configurations of composed bi‐layers with semi‐infinite interface cracks: (i) the bilayer composed of two isotropic layers of equal thicknesses; (ii) an orthotropic layer with the central semi‐infinite crack; (iii) an isotropic layer on isotropic half‐plane of a different material (may be considered as a bilayer, the thickness of one of its layers tending to infinity). In all cases the second Dundur's parameter were supposed to be equal to zero….