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TECHNICAL PAPERS

A Surface Crack in a Graded Medium Under General Loading Conditions

[+] Author and Article Information
S. Dag

F. Erdogan

Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015

J. Appl. Mech 69(5), 580-588 (Aug 16, 2002) (9 pages) doi:10.1115/1.1488661 History: Received April 02, 2001; Revised November 14, 2001; Online August 16, 2002
Copyright © 2002 by ASME
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References

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Erdogan,  F., and Wu,  B. H., 1997, “The Surface Crack Problem for a Plate With Functionally Graded Properties,” ASME J. Appl. Mech., 64, pp. 449–456.
Erdogan,  F., and Wu,  B. H., 1996, “Crack Problems in FGM Layers under Thermal Stresses,” J. Therm. Stresses, 19, pp. 237–265.
Kasmalkar M., 1997, “The Surface Crack Problem for a Functionally Graded Coating Bonded to a Homogeneous Layer,” Ph.D. dissertation, Lehigh University, Bethlehem, PA.
Jin,  Z. H., and Batra,  R. C., 1996, “Interface Cracking Between Functionally Graded Coatings and a Substrate Under Antiplane Shear,” Int. J. Eng. Sci., 34, pp. 1705–1716.
Wang,  X. Y., Wang,  D., and Zou,  Z. Z., 1996, “On the Griffith Crack in a Nonhomogeneous Interlayer of Adjoining Two Different Elastic Materials,” Int. J. Fract., 79, pp. R51–R56.
Gao,  H., 1991, “Fracture Analysis of Non-Homogeneous Materials via a Moduli Perturbation Approach,” Int. J. Solids Struct., 27, pp. 1663–1682.
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Nozaki,  H., and Shindo,  Y., 1998, “Effect of Interface Layers on Elastic Wave Propagation in a Fiber Reinforced Metal-Matrix Composite,” Int. J. Eng. Sci., 36, pp. 383–394.
Erdogan,  F., 1995, “Fracture Mechanics of Functionally Graded Materials,” Composites Eng., 5, pp. 753–770.
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Dag, S., 2001, “Crack and Contact Problems in Graded Materials,” Ph.D. dissertation, Lehigh University, Bethlehem, PA.
Koiter,  W. T., 1965, discussion of “Rectangular Tensile Sheet With Symmetrical Edge Cracks,” Trans. ASME, J. Appl. Mech. 87, pp. 237–238.
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Figures

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Surface crack in a graded medium
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Convergence of the numerical results for small values of the nonhomogeneity parameter
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Normalized mode I stress intensity factors, κ=2, μ(x)=μ0 exp(γx)
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Normalized mode II stress intensity factors, κ=2, μ(x)=μ0 exp(γx)
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Normalized modes I and II stress intensity factors for fixed grip tensile and shear loading, κ=1.8, μ(x)=μ0 exp(γx),σ=8μ0ε0/(κ+1),τ=8μ0γ0/(κ+1)
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The influence of Poisson’s ratio on the normalized mode I stress intensity factor in a graded half-plane with a surface crack; the case of plane strain, p(x)=σ0,q(x)=0,μ(x)=μ0 exp(γx)
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The influence of Poisson’s ratio on the normalized mode II stress intensity factor in a graded half-plane with a surface crack; the case of plane strain, p(x)=0,q(x)=τ0,μ(x)=μ0 exp(γx)
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Normal crack opening displacement, v*(x)=v(x,+0)−v(x,−0),p(x)=σ0,q(x)=0, κ=2, μ=μ0 exp(γx)
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Tangential crack opening displacement, u*(x)=u(x,+0)−u(x,−0),p(x)=0,q(x)=τ0, κ=2, μ=μ0 exp(γx)
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Normal crack opening displacement for fixed grip loading, v*(x)=v(x,+0)−v(x,−0),σ=8μ0ε0/(κ+1), κ=2, μ=μ0 exp(γx)
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Tangential crack opening displacement for fixed grip loading, u*(x)=u(x,+0)−u(x,−0),τ=8μ0γ0/(κ+1), κ=2, μ(x)=μ0 exp(γx)
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A graded half-plane with a surface crack loaded by a sliding rigid circular stamp
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Mode I stress intensity factors for a graded half-plane loaded by a sliding circular stamp as shown in Fig. 12, (b−a)/R=0.1,d/R=0.1, η=0.4, κ=2, μ(x)=μ0 exp(γx)
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Mode II stress intensity factors for a graded half-plane loaded by a sliding circular stamp as shown in Fig. 12, (b−a)/R=0.1,d/R=0.1, η=0.4, κ=2, μ(x)=μ0 exp(γx)
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Normalized force required for a given contact area (b−a)/R=0.1,d/R=0.1, η=0.4, κ=2, μ(x)=μ0 exp(γx)

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