On semi-infinite interface crack in bi-material elastic layer

Устинов, К. Б.

doi:10.1016/j.euromechsol.2019.01.013

Cited by 25 publications

(35 citation statements)

References 34 publications

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“…It follows from here that both sides of (35) are equal to a single function holomorphic in the whole plane p. Moreover, it may be concluded from (30) and (25) that both sides of (35) tend to zero as p → ∞ in the half-planes Re p > 0 and Re p < 0, respectively, and, hence, the single holomorphic function should be equal to zero. Thus, the general solution is…”

Section: Solution To the Non-homogeneous Problemmentioning

confidence: 64%

“…Here is a constant vector to be determined. The function in the right-hand side of (42) is of the most general type, because multiple poles at p = −1 and poles at other points of the line Re p = −1 are not allowed (26), (27), and presence of terms with p k , k ≥ 0 would violate the condition (25). It is follows from (42) that…”

Section: Solution Of the Homogeneous Problemmentioning

confidence: 99%

“…Note, that violating this condition appears to be an insurmountable obstacle in obtaining analytical solutions for geometries different from the very basic ones (e.g. [24, 25]). The reason seems to lie in the appearance of oscillating singularity in that case [26].…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to the solutions in [1][2][3][4], the problem in question in the present study is formulated not only as non-homogeneous, but also as homogeneous. Such consideration, although possibly less precise for particular boundary conditions, may yield much simpler solutions allowing analysis of their key features [24,25,[33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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Certain cases of elastic equilibrium of a composed wedge with an interface crack

Устинов¹

2020

Mathematics and Mechanics of Solids

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Problems of interface cracks starting from the common corner points of pairs of perfectly glued wedges of different isotropic elastic materials are addressed. It is demonstrated that for a few particular configurations and a restrictive condition imposed on values of elastic constants (corresponding to vanishing of the second Dundurs parameter), the problem of elastic equilibrium may be solved by Khrapkov’s method. These configurations are: (i) the wedges forming a half-plane; (ii) the wedges forming a plane; (iii) one of the wedges being a half-plane. In all cases, the external boundaries are supposed to be free of stresses. By applying Mellin’s transform for all three configurations the problem has been reduced to vector Riemann’s problem, and the matrix coefficient has been factorized for the case of the mentioned restrictive condition. The first configuration, i.e. the problem of an inclined edge crack located along the boundary separating two wedges of different elastic isotropic materials forming a half-plane is considered in more detail. The solution has been obtained for both uniform (corresponding to remote loading) and non-uniform (loading applied at the crack faces) problems. Numerical results are presented and compared with the available results obtained by other authors for particular cases. The obtained solutions appear especially valuable for analysing extreme cases of parameters.

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Section: Solution To the Non-homogeneous Problemmentioning

confidence: 64%

Section: Solution Of the Homogeneous Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Certain cases of elastic equilibrium of a composed wedge with an interface crack

Устинов¹

2020

Mathematics and Mechanics of Solids

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“…The extension allows for accurate and efficient calculation of the fracture parameters, avoiding case specific numerical calculations, in a large number of fracture tests used for material characterization, e.g., Double-Cantilever Beam tests, mixed-mode bending tests, end-notched flexural tests, four-point bending, and inverted four-point bending tests. Analytical solutions for bi-material beams with h 1 /h 2 = 1 and β = 0 have been recently derived in [61], and semi-analytical solutions for beams with h 1 /h 2 = 1 and β = 0 are presented in [62].…”

Section: Discussionmentioning

confidence: 99%

Fracture Mechanics Solutions for Interfacial Cracks between Compressible Thin Layers and Substrates

et al. 2019

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The decohesion of coatings, thin films, or layers used to protect or strengthen technological and structural components causes the loss of their functions. In this paper, analytical, computational, and semi-analytical 2D solutions are derived for the energy release rate and mode-mixity phase angle of an edge-delamination crack between a thin layer and an infinitely deep substrate. The thin layer is subjected to general edge loading: axial and shear forces and bending moment. The solutions are presented in terms of elementary crack tip loads and apply to a wide range of material combinations, with a large mismatch of the elastic constants (isotropic materials with Dundurs’ parameters − 1 ≤ α ≤ 1 and − 0.4 ≤ β ≤ 0.4 ). Results show that for stiff layers over soft substrates ( α → 1 ), the effects of material compressibility are weak, and the assumption of substrate incompressibility is accurate; for other combinations, including soft layers over stiff substrates ( α → − 1 ), the effects may be relevant and problem specific. The solutions are applicable to edge- and buckling-delamination of thin layers bonded to thick substrates, to mixed-mode fracture characterization test methods, and as benchmark cases.

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

Устинов

Idrisov

2020

Z Angew Math Mech

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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.

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On semi-infinite interface crack in bi-material elastic layer

Cited by 25 publications

References 34 publications

Certain cases of elastic equilibrium of a composed wedge with an interface crack

Certain cases of elastic equilibrium of a composed wedge with an interface crack

Fracture Mechanics Solutions for Interfacial Cracks between Compressible Thin Layers and Substrates

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

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