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Reaz A Chaudhuri - One of the best experts on this subject based on the ideXlab platform.
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On three-dimensional singular Stress Field at the front of a planar rigid inclusion (anticrack) in an orthorhombic mono-crystalline plate
International Journal of Fracture, 2012Co-Authors: Reaz A ChaudhuriAbstract:A novel eigenfunction expansion technique, based in part on separation of the thickness-variable and partly on the Eshelby–Stroh type affine transformation, is developed to derive three-dimensional Asymptotic Stress Field in the vicinity of the front of a semi-infinite through-thickness anticrack reinforcing an infinite orthorhombic single crystal plate, of finite thickness and subjected to far-Field mode I/II loadings. Anticrack-face boundary conditions and those that are prescribed on the top and bottom (free or fixed) surfaces of the plate are exactly satisfied. The present investigation considers six through-anticrack systems reinforcing orthorhombic single crystal plates. Explicit expressions for the singular Stresses in the vicinity of the front of a through-thickness anticrack reinforcing an orthorhombic plate, subjected to far-Field mode I/II loadings, are presented. Finally, hitherto largely unavailable results, pertaining to the through-thickness variations of Stress singularity coefficients corresponding to symmetric and skew-symmetric sinusoidal loads that also satisfy the boundary conditions on the top and bottom surfaces of an orthorhombic mono-crystalline plate under investigation, bridge a longstanding gap in the Stress singularity/fracture mechanics literature.
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three dimensional singular Stress Field at the front of a crack weakening a unidirectional fiber reinforced composite plate
Composite Structures, 2011Co-Authors: Reaz A ChaudhuriAbstract:Abstract An eigenfunction expansion technique, based in part on separation of the thickness-variable and partly on the Eshelby–Stroh type affine transformation, is employed to derive hitherto unavailable three-dimensional Asymptotic Stress Field in the vicinity of the front of a semi-infinite through-thickness crack weakening an infinite transversely isotropic unidirectional fiber reinforced composite plate, of finite thickness and subjected to far-Field mode I/II loadings. Crack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed or lubricated) surfaces of the lamina are exactly satisfied. The present investigation considers mainly two through-crack systems – (i) (0 1 0)[0 0 1] with the [1 0 0] propagation direction, and (ii) ( 1 ¯ 0 0 ) [ 0 0 1 ] with the [0 1 0] propagation direction. Explicit expressions for the singular Stresses in the vicinity of the front of a through-thickness crack weakening a transversely isotropic unidirectional fiber reinforced composite plate, subjected to far-Field mode I/II loadings, are presented. Hitherto unavailable numerical results, pertaining to the through-thickness variations of Stress intensity factors for saw-tooth load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the cracked unidirectional fiber reinforced composite (transversely isotropic) plates under investigation, bridge a longstanding gap in the fracture mechanics literature.
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on three dimensional singular Stress residual Stress Fields at the front of a crack anticrack in an orthotropic orthorhombic plate under anti plane shear loading
Composite Structures, 2010Co-Authors: Reaz A ChaudhuriAbstract:Abstract A novel eigenfunction expansion technique, based in part on separation of the thickness-variable, is developed to derive three-dimensional Asymptotic Stress Field in the vicinity of the front of a semi-infinite through-thickness crack/anticrack weakening/reinforcing an infinite orthotropic/orthorhombic plate, of finite thickness and subjected to far-Field anti-plane shear loading. Crack/anticrack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed and lubricated) surfaces of the orthotropic plate are exactly satisfied. Five different through-thickness crack/anticrack-face boundary conditions are considered: (i) slit crack, (ii) anticrack or perfectly bonded rigid inclusion, (iii) transversely rigid inclusion (longitudinal slip permitted), (iv) rigid inclusion in part perfectly bonded, the remainder with slip, and (v) rigid inclusion located alongside a crack. Explicit expressions for the singular Stress Fields in the vicinity of the fronts of the through-thickness cracks, anticracks or mixed crack–anticrack type discontinuities, weakening/reinforcing orthotropic/orthorhombic plates, subjected to far-Field anti-plane shear (mode III) loadings, are presented. In addition, singular residual Stress Fields in the vicinity of the fronts of these cracks, anticracks and similar discontinuities are also discussed.
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three dimensional Asymptotic Stress Field at the front of an unsymmetric bimaterial wedge associated with matrix cracking or fiber break
Composite Structures, 2007Co-Authors: Reaz A Chaudhuri, Souhsiung Jack ChiuAbstract:Abstract A combined approach for prediction of the singular Stress Fields at the interfacial fronts of fiber breaks and matrix cracks is presented. A recently developed eigenfunction expansion method is employed for obtaining three-dimensional Asymptotic displacement and Stress Fields in the vicinity of a point located at the front of a bimaterial wedge of general (unsymmetric) geometrical configuration (with respect to bimaterial interface), and subjected to extension/bending (mode I) and in-plane shear/twisting (mode II) far Field loading and free–free wedge-side boundary condition. Each material is isotropic and elastic, but with different material properties. The material 2 (fiber in the case of matrix cracking or matrix in the case of fiber break) is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying matrix cracking or fiber break incidence angles at the interfaces. Numerical results pertaining to the variation of the lowest eigenvalues (or Stress singularities) for various wedge aperture angles of the material 1, subjected to the afore-mentioned wedge-side boundary condition, are also presented. Variation of the same with the shear moduli ratio of the component material phases is also an important part of the present investigation. The conclusion drawn from the present Asymptotic analysis of the matrix cracking problem is in agreement with that of an earlier investigation based on the energy based criterion. Similar conclusion drawn from the present Asymptotic analysis of fiber break problem is in agreement with that of an energy based criterion derived here in analogy to the corresponding matrix crack problem by another investigator.
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three dimensional Asymptotic Stress Field in the vicinity of the circumference of a bimaterial penny shaped interfacial discontinuity
International Journal of Fracture, 2006Co-Authors: Reaz A ChaudhuriAbstract:An eigenfunction expansion method is presented to obtain three-dimensional Asymptotic Stress Fields in the vicinity of the circumference of a bimaterial penny-shaped interfacial discontinuity, e.g., crack, anticrack (infinitely rigid lamella), etc., located at the center, edge or corner, and subjected to the far-Field torsion (mode III), extension/bending (mode I), and sliding shear/twisting (mode II) loadings. Five different discontinuity-surface boundary conditions are considered: (1) bimaterial penny-shaped interface anticrack or perfectly bonded thin rigid inclusion, (2) bimaterial penny-shaped interfacial jammed contact, (3) bimaterial penny-shaped interface crack, (4) bimaterial penny-shaped interface crack with partial axisymmetric frictionless slip, and (5) bimaterial penny-shaped interface thin rigid inclusion alongside penny-shaped crack. Solutions to these cases except (3) are hitherto unavailable in the literature. Closed-form expressions for Stress intensity factors subjected to various far-Field loadings are also presented. Numerical results presented include the effect of the ratio of the shear moduli of the layer materials, and also Poisson’s ratios on the computed lowest real parts of eigenvalues for the case (5). Interesting and physically meaningful conclusions are also presented, especially with regard to cases (1) and (2).
Sumio Murakami - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Fields of Stress and damage of a mode i creep crack in steady state growth
International Journal of Solids and Structures, 2000Co-Authors: Sumio Murakami, T. HiranoAbstract:Abstract Asymptotic Fields of Stress, strain rate and damage of a mode I creep crack in steady-state growth are analyzed on the basis of Continuum Damage Mechanics by employing a semi-inverse method. A damage Field D x for steady-state crack growth represented by an undetermined power function rl of radius r from the crack tip is assumed first, and the corresponding Asymptotic Stress Field of a mode I crack in a non-linear creep damage material is analyzed by solving a two-point boundary value problem of non-linear differential equations. Then, the exponent l of undetermined damage Field is determined so that the assumed damage Field D x may be consistent with the resulting Asymptotic Stress Field and the damage evolution equation. Finally, the relations between exponent p of the Asymptotic Stress distribution and exponents n and m of power creep constitutive law and the power creep damage law are elucidated. The effects of material damage on the crack-tip Stress Field in non-linear materials are discussed in detail. Comparison between the results of the present analysis and those of earlier papers of fracture mechanics on the creep-crack growth analyses based on grain-boundary cavitation is also made.
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effects of local damage on Asymptotic Stress Field of a growing creep crack
Metals and Materials International, 1998Co-Authors: Sumio Murakami, T. Hirano, M. MizunoAbstract:A parametric study on the effects of local damage Field on the crack-tip Stress Field of a growing Mode I creep crack is performed in the framework of Continuum Damage Mechanics (CDM). According to the results of creep crack growth analysis based on CDM and Finite Element Method, the damage distribution1-(D/D cr)=h(θ)rm represented by a power law function of the radiusr from the crack tip is postulated for the damage variableD. The damage effects are incorporated into the Norton creep law by means of the hypothesis of strain equivalence of CDM. The resulting two-point boundary value problems of differential equations for the growing creep cracks in the states of plane strain and plane Stress are solved by means of a shooting method. For a given creep exponentn of the Norton law, the exponentp of the Asymptotic Stress Field σ ij ∞r p is found to be governed by the exponentm of the power law damage distributionr m.
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Asymptotic Stress Field of a mode i crack in a nolinear hardening damage material
Transactions of the Japan Society of Mechanical Engineers. A, 1998Co-Authors: Sumio MurakamiAbstract:The effects of the local damage Field on the Asymptotic crack-tip Stress Field of a Mode I crack in a nonlinear-hardening material are discussed. Three kinds of the damage distribution 1-(D/Dcr)=h (θ) rm represented by a power function of radius r from the crack-tip are postulated for the damage variable D, and the damage effects are included into the power hardening relation by means of the effective Stress concept of continuum damage mechanics. For a given strain hardening exponent n of the power hardening equation, the exponent p of the resulting Asymptotic Stress Fields σuvγp is found to be governed by the exponent m of the power-law damage distribution. When m increases, p is found to increase from a singular (negative) HRR exponent p=-1/(n+1) to a nonsingular (positive) value, which coincides with the previous analytical result for a Mode III crack in a linear elastic-damage material. A sufficient condition M>1/n for the nonsingular crack-tip Stress is obtained for both plane Stress and plane strain states. The effects of the strain hardening exponent n and the Stress states on the p-m-n relation are discussed in some details. The damage effects on θ-distribution of the Asymptotic Stress Fields are also discussed.
T. Hirano - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Fields of Stress and damage of a mode i creep crack in steady state growth
International Journal of Solids and Structures, 2000Co-Authors: Sumio Murakami, T. HiranoAbstract:Abstract Asymptotic Fields of Stress, strain rate and damage of a mode I creep crack in steady-state growth are analyzed on the basis of Continuum Damage Mechanics by employing a semi-inverse method. A damage Field D x for steady-state crack growth represented by an undetermined power function rl of radius r from the crack tip is assumed first, and the corresponding Asymptotic Stress Field of a mode I crack in a non-linear creep damage material is analyzed by solving a two-point boundary value problem of non-linear differential equations. Then, the exponent l of undetermined damage Field is determined so that the assumed damage Field D x may be consistent with the resulting Asymptotic Stress Field and the damage evolution equation. Finally, the relations between exponent p of the Asymptotic Stress distribution and exponents n and m of power creep constitutive law and the power creep damage law are elucidated. The effects of material damage on the crack-tip Stress Field in non-linear materials are discussed in detail. Comparison between the results of the present analysis and those of earlier papers of fracture mechanics on the creep-crack growth analyses based on grain-boundary cavitation is also made.
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effects of local damage on Asymptotic Stress Field of a growing creep crack
Metals and Materials International, 1998Co-Authors: Sumio Murakami, T. Hirano, M. MizunoAbstract:A parametric study on the effects of local damage Field on the crack-tip Stress Field of a growing Mode I creep crack is performed in the framework of Continuum Damage Mechanics (CDM). According to the results of creep crack growth analysis based on CDM and Finite Element Method, the damage distribution1-(D/D cr)=h(θ)rm represented by a power law function of the radiusr from the crack tip is postulated for the damage variableD. The damage effects are incorporated into the Norton creep law by means of the hypothesis of strain equivalence of CDM. The resulting two-point boundary value problems of differential equations for the growing creep cracks in the states of plane strain and plane Stress are solved by means of a shooting method. For a given creep exponentn of the Norton law, the exponentp of the Asymptotic Stress Field σ ij ∞r p is found to be governed by the exponentm of the power law damage distributionr m.
Jack S H Chiu - One of the best experts on this subject based on the ideXlab platform.
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three dimensional Asymptotic Stress Field at the front of an unsymmetric bimaterial pie shaped wedge under antiplane shear loading
Composite Structures, 2002Co-Authors: Jack S H ChiuAbstract:Abstract Three-dimensional Asymptotic Stress Field in the vicinity of the front of a bimaterial pie-shaped wedge of general (unsymmetric) geometry is obtained by a recently developed eigenfunction expansion method. The bimaterial pie-shaped wedge is subjected to four combinations of wedge-side boundary conditions – free–free, clamped–clamped, free–clamped and clamped–free. Each material is isotropic and elastic, but with different material properties. Additionally, numerical results pertaining to the variation of the lowest eigenvalues (or Stress singularities) with respect to the wedge opening angle of the bimaterial wedge, subjected to the aforementioned wedge-side boundary conditions, are also presented. Dependence of the same on the material properties of the component material phases is also an important part of the present investigation.
Souhsiung Jack Chiu - One of the best experts on this subject based on the ideXlab platform.
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three dimensional Asymptotic Stress Field at the front of an unsymmetric bimaterial wedge associated with matrix cracking or fiber break
Composite Structures, 2007Co-Authors: Reaz A Chaudhuri, Souhsiung Jack ChiuAbstract:Abstract A combined approach for prediction of the singular Stress Fields at the interfacial fronts of fiber breaks and matrix cracks is presented. A recently developed eigenfunction expansion method is employed for obtaining three-dimensional Asymptotic displacement and Stress Fields in the vicinity of a point located at the front of a bimaterial wedge of general (unsymmetric) geometrical configuration (with respect to bimaterial interface), and subjected to extension/bending (mode I) and in-plane shear/twisting (mode II) far Field loading and free–free wedge-side boundary condition. Each material is isotropic and elastic, but with different material properties. The material 2 (fiber in the case of matrix cracking or matrix in the case of fiber break) is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying matrix cracking or fiber break incidence angles at the interfaces. Numerical results pertaining to the variation of the lowest eigenvalues (or Stress singularities) for various wedge aperture angles of the material 1, subjected to the afore-mentioned wedge-side boundary condition, are also presented. Variation of the same with the shear moduli ratio of the component material phases is also an important part of the present investigation. The conclusion drawn from the present Asymptotic analysis of the matrix cracking problem is in agreement with that of an earlier investigation based on the energy based criterion. Similar conclusion drawn from the present Asymptotic analysis of fiber break problem is in agreement with that of an energy based criterion derived here in analogy to the corresponding matrix crack problem by another investigator.
