TY - JOUR

T1 - Plane strain asymptotic fields of a crack growing along an elastic-elastic power-law creeping bi-material interface

AU - Taher, M.

AU - Saif, A.

AU - Hui, C. Y.

N1 - Funding Information:
This researchw as conducted using the resourceso f the Cornell Theory Center, which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State Science and Technology Foundation and members of the Corporate Research Institute. Additional computing facilities provided by the Materials Scicncc Ccntcr, Cornell University is acknowledged. Special thanks arc cxtcndcd to Professor Andy Ruina of Theoretical and Applied Mechanics, Cornell University, for his valuable comments and insights, without which the work would not have reached this state. The authors would like to thank Professor Aravas for the stimulating discussions on crack growth problems during his visit at Cornell.

PY - 1994/2

Y1 - 1994/2

N2 - Plane strain asymptotic stress and strain fields near the tip of a crack growing quasi-statically along the interface of a linear elastic and an incompressible elastic power law creeping material is studied. The solutions for the stress and strain fields are found to be in the separable forms, γij, ∼ a ̇ BE+r 1 (n-1) γ ̃ij(θ,n,β) and ε{lunate}ij ∼ a ̇ BE+r 1 (n-1) ε{lunate} ̃ij(θ,n,β), whenn ≥ 3. Heren and B are the power law creeping exponent and coefficient respectively, E+ and E- are moduli of elasticity of the elastic-creeping and elastic materials, β = E+ E-, r is the radial distance from the moving tip and θ is the angle measured from the interface. The amplitude of the field is determined by the crack tip velocity, a, and material parameters. The angular functions \ ̃gsij(θ, n, β) and \ ̃geij exhibit only two modes, one of which is close to pure mode I and the other one is close to pure mode II ; arbitrary mode mixity cannot be prescribed. For a given β, there is a corresponding n, close to n = 3, at which the two solutions coalesce into one. Below this value of n no real separable solution exists. We also studied the special case of a quasi-statically growing crack in a homogeneous elastic power law creeping material. We find that only pure modes I and II are possible near the tip, and the amplitude of the field is determined by a and material parameters. Thus the near tip field is independent of the far field loading conditions for both the bi-material and the homogeneous cases. For 1≤n< 3, the elastic strain dominates the creep strain so that the near tip stress field of the growing interface crack is given by the classical bimaterial complex K field and therefore has an oscillatory singularity. The complex K in this case depends not only on the specimen geometry and the applied load, but also on the crack growth history.

AB - Plane strain asymptotic stress and strain fields near the tip of a crack growing quasi-statically along the interface of a linear elastic and an incompressible elastic power law creeping material is studied. The solutions for the stress and strain fields are found to be in the separable forms, γij, ∼ a ̇ BE+r 1 (n-1) γ ̃ij(θ,n,β) and ε{lunate}ij ∼ a ̇ BE+r 1 (n-1) ε{lunate} ̃ij(θ,n,β), whenn ≥ 3. Heren and B are the power law creeping exponent and coefficient respectively, E+ and E- are moduli of elasticity of the elastic-creeping and elastic materials, β = E+ E-, r is the radial distance from the moving tip and θ is the angle measured from the interface. The amplitude of the field is determined by the crack tip velocity, a, and material parameters. The angular functions \ ̃gsij(θ, n, β) and \ ̃geij exhibit only two modes, one of which is close to pure mode I and the other one is close to pure mode II ; arbitrary mode mixity cannot be prescribed. For a given β, there is a corresponding n, close to n = 3, at which the two solutions coalesce into one. Below this value of n no real separable solution exists. We also studied the special case of a quasi-statically growing crack in a homogeneous elastic power law creeping material. We find that only pure modes I and II are possible near the tip, and the amplitude of the field is determined by a and material parameters. Thus the near tip field is independent of the far field loading conditions for both the bi-material and the homogeneous cases. For 1≤n< 3, the elastic strain dominates the creep strain so that the near tip stress field of the growing interface crack is given by the classical bimaterial complex K field and therefore has an oscillatory singularity. The complex K in this case depends not only on the specimen geometry and the applied load, but also on the crack growth history.

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U2 - 10.1016/0022-5096(94)90008-6

DO - 10.1016/0022-5096(94)90008-6

M3 - Article

AN - SCOPUS:38149146609

SN - 0022-5096

VL - 42

SP - 181

EP - 214

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

IS - 2

ER -