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TECHNICAL PAPERS

Effect of Residual Stress on Cavitation Instabilities in Constrained Metal Wires

[+] Author and Article Information
Viggo Tvergaard

Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark

J. Appl. Mech 71(4), 560-566 (Sep 07, 2004) (7 pages) doi:10.1115/1.1767845 History: Received November 24, 2003; Revised March 08, 2004; Online September 07, 2004
Copyright © 2004 by ASME
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References

Bishop,  R. F., Hill,  R., and Mott,  N. F., 1945, “The Theory of Indentation and Hardness Tests,” Proc. Phys. Soc. London, 57, pp. 147–159.
Huang,  Y., Hutchinson,  J. W., and Tvergaard,  V., 1991, “Cavitation Instabilities in Elastic-Plastic Solids,” J. Mech. Phys. Solids, 39, pp. 223–241.
Tvergaard,  V., Huang,  Y., and Hutchinson,  J. W., 1992, “Cavitation Instabilities in a Power Hardening Elastic-Plastic Solid,” Eur. J. Mech. A/Solids, 11, pp. 215–231.
Ball,  J. M., 1982, “Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity,” Philos. Trans. R. Soc. London, Ser. A, A306, pp. 557–610.
Horgan,  C. O., and Abeyaratne,  R., 1986, “A Bifurcation Problem for a Compressible Nonlinearly Elastic Medium: Growth of a Microvoid,” J. Elast., 16, pp. 189–200.
Chou-Wang,  M.-S., and Horgan,  C. O., 1989, “Void Nucleation and Growth for a Class of Incompressible Nonlinearly Elastic Materials,” Int. J. Solids Struct., 25, pp. 1239–1254.
Flinn, B., Rühle, M., and Evans, A. G., 1989, “Toughening in Composites of Al2O3 Reinforced With Al,” Materials Department Report, University of California, Santa Barbara, CA.
Tvergaard,  V., 1995, “Cavity Growth in Ductile Particles Bridging a Brittle Matrix Crack,” Int. J. Fract., 72, pp. 277–292.
Ashby,  M. F., Blunt,  F. J., and Bannister,  M., 1989, “Flow Characteristics of Highly Constrained Metal Wires,” Acta Metall., 37, pp. 1847–1857.
Dalgleish,  B. J., Trumble,  K. P., and Evans,  A. G., 1989, “The Strength and Fracture of Alumina Bonded With Aluminum Alloys,” Acta Metall., 37, pp. 1923–1931.
Tvergaard,  V., 1991, “Failure by Ductile Cavity Growth at a Metal-Ceramic Interface,” Acta Metall. Mater., 39, pp. 419–426.
Tvergaard,  V., 1997, “Studies of Void Growth in a Thin Ductile Layer Between Ceramics,” Comput. Mech., 20, pp. 186–191.
Tvergaard,  V., 2000, “Interface Failure by Cavity Growth to Coalescence,” Int. J. Mech. Sci., 42, pp. 381–395.
Pedersen,  T. O̸., 1998, “Remeshing in Analysis of Large Plastic Deformations,” Comput. Struct., 67, pp. 279–288.
Hutchinson, J. W., 1973, “Finite Strain Analysis of Elastic-Plastic Solids and Structures,” Numerical Solution of Nonlinear Structural Problems, R. F. Hartung, ed., 17 , ASME, New York.
Tvergaard,  V., 1982, “On Localization in Ductile Materials Containing Spherical Voids,” Int. J. Fract., 18, pp. 237–252.
Tvergaard,  V., 1976, “Effect of Thickness Inhomogeneities in Internally Pressurized Elastic-Plastic Spherical Shells,” J. Mech. Phys. Solids, 24, pp. 291–304.
Tvergaard,  V., 1992, “Effect of Ductile Particle Debonding During Crack-Bridging in Ceramics,” Int. J. Mech. Sci., 34, pp. 635–649.

Figures

Grahic Jump Location
Sketch of the tensile test specimen used by Ashby et al. 9
Grahic Jump Location
Axisymmetric model of the half test specimen analyzed, showing the initial dimensions, the coordinate system and a finite element mesh. The ductile wire occupies the region 0≤x2≤A0.
Grahic Jump Location
Effect of different residual stress levels for initial void size Rv/A0=0.01 and crack-tip radius Rc/A0=0.01, with metal wire material parameters σy/E=0.003, ν=0.3 and N=0.1. (a) Average nominal stress versus end displacement. (b) Void volume growth.
Grahic Jump Location
Deformed meshes at four different stages for σmR=0. The initial void size and crack tip radius are Rv/A0=0.01 and Rc/A0=0.01, and parameters for the metal wire are σy/E=0.003, ν=0.3, and N=0.1. (a) Initial mesh. (b) Stage where V/V0=100. (c) Stage where V/V0=104. (d) End of computation.
Grahic Jump Location
Comparison of deformed meshes for two different values of σmR. The initial void size and crack-tip radius are Rv/A0=0.01 and Rc/A0=0.01, and parameters for the metal wire are σy/E=0.003, ν=0.3 and N=0.1. (a) Stage where V/V0=104 for σmR=0. (b) Stage where V/V0=104 for σmRy=4.07. (c) End of computation for σmR=0. (d) End of computation for σmRy=4.07.
Grahic Jump Location
Effect of different values of the initial void size, for σmRy=2.72 and Rc/A0=0.01. Parameters for the metal wire are σy/E=0.003, ν=0.3 and N=0.1. (a) Average nominal stress versus end displacement. (b) Void volume growth.
Grahic Jump Location
Effect of different values of the initial crack-tip radius, for σmRy=2.72 and Rv/A0=0.01. Parameters for the metal wire are σy/E=0.003, ν=0.3 and N=0.1. (a) Average nominal stress versus end displacement. (b) Void volume growth.
Grahic Jump Location
Effect of different residual stress levels for initial void size Rv/A0=0.01 and crack-tip radius Rc/A0=0.01, with metal wire material parameters σy/E=0.0004, ν=0.42 and N=0.2. (a) Average nominal stress versus end displacement. (b) Void volume growth.
Grahic Jump Location
Comparison of deformed meshes for two different values of σmR. The initial void size and crack-tip radius are Rv/A0=0.01 and Rc/A0=0.01, and parameters for the metal wire are σy/E=0.0004, ν=0.42 and N=0.2. (a) Stage where V/V0=104 for σmR=0. (b) Stage where V/V0=104 for σmRy=8.22. (c) End of computation for σmR=0. (d) End of computation for σmRy=8.22.
Grahic Jump Location
Effect of different crack-tip radii, for the initial void size Rv/A0=0.01, with metal wire material parameters σy/E=0.0004, ν=0.42 and N=0.2. (a) Average nominal stress versus end displacement. (b) Void volume growth.

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