# Interface Crack Between Two Elastic Layers

A semi-infinite interface crack between two infinite isotropic elastic layers under general edge loading conditions is considered. The problem can be solved analytically except for a single real scalar independent of loading, which is then extracted from the numerical solution for one particular loading combination. Two applications of the basic solution are made which illustrate its utility: interface cracking driven by residual stress in a thin film on a substrate, and an analysis of a test specimen proposed recently for measuring interface toughness.

## interface crack between two elastic layers

Jun Lei, Pengbo Sun, and Tinh Quoc Bui. "Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic composites." Curved and Layered Structures 2.1 (2015): null. .

@articleJunLei2015,abstract = To determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack opening displacements across crack faces, which is convenient for numerical applications, especially for BEM. Meantime, an alternative extrapolation formula based on the path-independent J-integral and displacement ratios was presented which may be more adaptable for any domain-based numerical techniques like FEM. A numerical example was presented to show the correctness of these formulae.,author = Jun Lei, Pengbo Sun, Tinh Quoc Bui,journal = Curved and Layered Structures,keywords = displacement extrapolation formula; fracture parameters; magnetoelectroelastic; interfacial crack; J integral,language = eng,number = 1,pages = null,title = Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic composites,url = ,volume = 2,year = 2015,

TY - JOURAU - Jun LeiAU - Pengbo SunAU - Tinh Quoc BuiTI - Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic compositesJO - Curved and Layered StructuresPY - 2015VL - 2IS - 1SP - nullAB - To determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack opening displacements across crack faces, which is convenient for numerical applications, especially for BEM. Meantime, an alternative extrapolation formula based on the path-independent J-integral and displacement ratios was presented which may be more adaptable for any domain-based numerical techniques like FEM. A numerical example was presented to show the correctness of these __formulae.LA__ - engKW - displacement extrapolation formula; fracture parameters; magnetoelectroelastic; interfacial crack; J integralUR - ER -

Sourki, R., Ayatollahi, M., & Monfared, M. M. (2018). Mode III fracture analysis of a non-homogeneous layer bonded to an elastic half-plane weakened by multiple interface cracks. Scientia Iranica, 25(5), 2570-2581. doi: 10.24200/sci.2017.4493

R. Sourki; M. Ayatollahi; M. M. Monfared. "Mode III fracture analysis of a non-homogeneous layer bonded to an elastic half-plane weakened by multiple interface cracks". Scientia Iranica, 25, 5, 2018, 2570-2581. doi: 10.24200/sci.2017.4493

Sourki, R., Ayatollahi, M., Monfared, M. M. (2018). 'Mode III fracture analysis of a non-homogeneous layer bonded to an elastic half-plane weakened by multiple interface cracks', Scientia Iranica, 25(5), pp. 2570-2581. doi: 10.24200/sci.2017.4493

Sourki, R., Ayatollahi, M., Monfared, M. M. Mode III fracture analysis of a non-homogeneous layer bonded to an elastic half-plane weakened by multiple interface cracks. Scientia Iranica, 2018; 25(5): 2570-2581. doi: 10.24200/sci.2017.4493

By application of the theory of complex variable functions, asymmetrical dynamic propagation problem on the edges of mode III interface crack subjected to superimpose loads was studied. Analytical solutions of the stresses displacements and dynamic stress intensity factors are obtained by means of self- similar functions. The problems researched can be facilely transformed into Riemann-Hilbert problems and their closed solutions are attained rather simple according to this measure. After those solutions are utilized by superposition theorem, the solutions of arbitrarily complex problems can be gained.

Surface cracking and debonding are among the most important modes of failure in FGM coatings. In the first part of this lecture the analytical benchmark problem for a FGM coating bonded to a homogeneous substrate will be considered. It will be assumed that the mechanical properties of the bond coat are approximately same as that of the substrate and the coating contains a surface crack perpendicular to the boundary. The composite medium may be under mechanical or thermal loading. The stress intensity factors for three typical crack geometries, namely ah will be presented, where a and h are, respectively, the crack length and coating thickness. Also presented will be the results of the nonlinear crack/contact problem in which, despite the positive stress intensity factor at the crack tip, due to the compressive stress near the boundary, the crack may actually be closed near and at the coating surface. The primary objective of the study is to investigate the influence of the crack-component geometry, the nature of the external loads and the material inhomogeneity parameter on the stress intensity factor. The second part of the lecture will deal with the debonding of FGM coatings. It will be assumed that the debonding crack initiates at a stress-free boundary and propagates along the nominal interface. Due to the formation of a thin oxide layer, the interface will be assumed to be the weak fracture plane. The composite medium having finite dimensions will be under steady-state heat conduction with convective heating at the FGM surface, forced cooling at the substrate surface and very weak convective cooling at the ends. An additional important factor considered in this problem will be the influence of partial insulation across the crack surfaces on the temperature distribution, total heat flow and the strain energy release rate. In heat transfer problems involving cracks it is generally assumed that the crack surfaces are either fully insulated or fully conducting.

The fracture and damage behaviour of high temperature materials can be essentially modified by realising well-defined property gradients. Crack propagation perpendicular and parallel to the heated surface are the crucial phenomena. Crack propagation parallel to the surface leads to delamination and damage. A gradient effect based on fracture mechanics is demonstrated with the modelling of thermal barrier coatings (TBCs), taking into account the effective material properties derived in a self-consistent way. It is shown that the energy release rate G for delamination in TBCs under stationary heat flow can be reduced by grading towards decreasing thermal misfit between TBC and the substrate, even though the coating must be made thicker for compensation of the higher thermal conductivity. According to the fracture criterion, G has to be compared with the critical energy release rate Gc. Therefore, information on Gc has to be gathered. Damage is avoided by keeping G below Gc. The 4-point bending test after Charalambides has been modified such that Gc of the delamination crack of thin layers can be measured. The G required for crack propagation is obtained by attaching a stiffening layer to the TBC. As another advantage of this modification, segmentation of the layer and plastic deformation of the substrate are avoided. The experiment is analysed by FEM. In order to measure Gc, one needs the critical load and the crack length. The latter is derived by FEM from the measured compliance of the sample. With the providing of fracture mechanical material parameters and the optimization of a material gradient by minimization of G/Gc, this example is meant to contribute to improving the performance of layered systems and thermal barrier coatings in particular.

A basic set of design criteria was determined for elastic/elastic-plastic microlaminates, composed of alternating micron-scale metal and intermetallic layers. An analysis combining the finite element method of constrained metal deformation and a large scale bridging was used to calculate the effect of various microscale fracture processes and composite parameters on the stress-displacement function, s(u), of the ductile layer and both the corresponding resistance curve toughness and fracture strength of composite specimens with specified flaw sizes. Microscale processes included residual stresses, tunnel crack growth, fracture path selection (e.g., slanted and offset cracks), internal inclusion debonding/microvoid damage and effective layer debonding by brittle matrix splitting. The constituent parameters included ductile layer strength, strain hardening exponents and intrinsic brittle matrix toughness. The effect of loading rate, fracture mode and statistical distributions in key parameters were also modeled. Fracture strength is enhanced by a high metal layer strength and strain hardening, and, for small initial flaw sizes, by tensile residual stress and a high degree of deformation constraint. Voids in the ductile layers reduce fracture strength at large flaw sizes; for large voids, the fracture strength is reduced at all flaw sizes. Interfacial debonding or splitting cracks in the elastic layers reduce constraint, which, along with layer thickness, decreases the fracture strength for small flaws and increases it for larger cracks. 350c69d7ab

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