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Ductile crack growth – I. A numerical study using computational cells with microstructurally-based length scales. (English) Zbl 0879.73047
Many metals which fail by a void growth mechanism display a macroscopically planar fracture process zone of one or two void spacings in thickness characterized by intense plastic flow in the ligaments between the voids; outside this region, the voids exhibit little or no growth. To model this process, a material layer containing a pre-existing population of similar sized voids is assumed. The thickness of the layer, \(D\), can be identified with the mean spacing between the voids. This layer is represented by an aggregate of computational cells of linear dimension \(D\). Each cell contains a single void of some initial volume. The Gurson constitutive relation for dilatant plasticity describes the hole growth in a cell resulting in material softening and, ultimately, loss of stress carrying capacity.
Finite element calculations are carried out to determine crack growth resistance curves for plane strain, mode I crack growth under small scale yielding. The parameters affecting fracture resistance are discussed emphasizing the roles of microstructural parameters and continuum properties of the material.

74R99 Fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
74A60 Micromechanical theories
74M25 Micromechanics of solids
Full Text: DOI
[1] Andersson, H., Analysis of a model for void growth and coalescence ahead of a moving crack tip, J. mech. phys. solids, 25, 217-233, (1977)
[2] Aoki, S.; Kishimoto, K.; Takeya, A.; Sakata, M., Effects of microvoids on crack blunting and initiation in ductile materials, Int. J. fract., 24, 267-278, (1984)
[3] Aravas, N.; McMeeking, R.M., Microvoid growth and failure in the ligament between a hole and a blunt crack tip, Int. J. fract., 29, 21-38, (1985)
[4] Becker, R.; Needleman, A.; Suresh, S.; Tvergaard, V.; Vasudevan, A.K., An analysis of ductile failure by grain boundary void growth, Acta metall., 37, 99-120, (1989)
[5] Betegon, C.; Hancock, J.W., Two-parameter characterization of elastic-plastic crack-tip fields, J. appl. mech., 58, 104-110, (1991)
[6] Brown, L.M.; Embury, J.D., The initiation and growth of voids at second phase particles, (), 164-169
[7] Cottrell, A.H., Mechanisms of fracture, (), 1-27
[8] Du, Z.-Z.; Hancock, J.W., The effect of non-singular stresses on crack-tip constraint, J. mech. phys. solids, 39, 555-567, (1991)
[9] Griffith, A.A., The phenomenon of rupture and flow in solids, Phil. trans. R. soc. (lond.), A221, 163-198, (1920)
[10] Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth: part I-yield criteria and flow rules for porous ductile media, J. engng mater. technol., 99, 2-15, (1977)
[11] Hancock, J.W.; Reuter, W.G.; Parks, D.M., Constraint and toughness parameterized by T. constraint effects in fracture, (), 21-40
[12] Irwin, G.R., Fracture mechanics, (), 557-591
[13] Joyce, J.A.; Link, R.E., Effects of tensile loading on upper shelf fracture toughness, ()
[14] Lemaitre, J., A continuous damage mechanics model for ductile fracture, J. engng mater. technol., 107, 83-89, (1985)
[15] Li, F.Z.; Shih, C.F.; Needleman, A., A comparison of methods for calculating energy release rates, Engng fract. mech., 21, 405-421, (1985)
[16] Needleman, A.; Tvergaard, V., An analysis of ductile rupture modes at a crack tip, J. mech. phys. solids, 35, 151-183, (1987) · Zbl 0601.73106
[17] Needleman, A.; Tvergaard, V.; Hutchinson, J.W., Void growth in plastic solids, (), 145-178
[18] O’Dowd, N.P.; Shih, C.F., Family of crack-tip fields characterized by a triaxiality parameter-I. structure of fields, J. mech. phys. solids, 39, 989-1015, (1991)
[19] O’Dowd, N.P.; Shih, C.F., Family of crack-tip fields characterized by a triaxiality parameter-II. fracture applications, J. mech. phys. solids, 40, 939-963, (1992)
[20] O’Dowd, N.P.; Shih, C.F.; Dodds, R.H., The role of geometry and crack growth on constraint and implications for ductile/brittle fracture, ()
[21] Pineau, A., Global and local approaches of fracture-transferability of laboratory test results to components, (), 197-234
[22] Rice, J.R., A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. appl. mech., 35, 379-386, (1968)
[23] Rice, J.R.; Drugan, W.J.; Sham, T.-L., Elastic-plastic analysis of growing cracks, (), 189-221 · Zbl 0496.73086
[24] Rice, J.R.; Johnson, M.A., The role of large crack tip geometry changes in plane strain fracture, (), 641-672
[25] Ritchie, R.O.; Knott, J.F.; Rice, J.R., On the relationship between critical tensile stress and fracture toughness in mild steel, J. mech. phys. solids, 21, 395-410, (1973)
[26] Rousselier, G., Ductile fracture models and their potential in local approach of fracture, Nucl. engng design, 105, 97-111, (1987)
[27] Rousselier, G.; Devaux, J.-C.; Mottet, G.; Devesa, G., A methodology for ductile fracture analysis based on damage mechanics: an illustration of a local approach of fracture, (), 332-354
[28] Shih, C.F.; Xia, L., Modeling crack growth resistance using computational cells with microstructurally-based length scales, () · Zbl 0879.73047
[29] Tvergaard, V., Influence of void nucleation on ductile shear fracture at a free surface, J. mech. phys. solids, 30, 399-425, (1982) · Zbl 0496.73087
[30] Tvergaard, V., Material failure by void growth to coalescence, Adv. appl. mech., 27, 83-151, (1990) · Zbl 0728.73058
[31] Tvergaard, V.; Hutchinson, J.W., The relation between crack growth resistance and fracture process parameters in elastic-plastic solids, J. mech. phys. solids, 40, 1377-1397, (1992) · Zbl 0775.73218
[32] Tvergaard, V.; Hutchinson, J.W., Effect of T-stress on mode I crack growth resistance in a ductile solid, Int. J. solids struct., 31, 823-833, (1994) · Zbl 0800.73334
[33] Varias, A.G.; Shih, C.F., Quasi-static crack advance under a range of constraints-steady-state fields based on a characteristic length, J. mech. phys. solids, 41, 835-861, (1993)
[34] Xia, L.; Shih, C.F., Ductile crack growth-II. strain rate, void nucleation and crack path tortuosity effects, (1994), In preparation
[35] Xia, L.; Shih, C.F.; Hutchinson, J.W., A computational approach to ductile crack growth under large scale yielding conditions, J. mech. phys. solids, (1994), (in press)
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