An analysis of cracks in ductile single crystals—I. Anti-plane shear

Abstract The problem of a stationary mathematically sharp semi-infinite crack in an FCC crystal is considered. We adopt a geometrically rigorous formulation of crystalline plasticity accounting for finite deformations and finite lattice rotations, as well as for the full three-dimensional crystallographic geometry of the crystal. A comparison of results with earlier small-strain solutions reveals some notable differences. These include the expected development of finite deformations and rotations near the crack tip, but also discrepancies such as a considerable spread of the plastic zones. In addition, nearly self-similar, square-root singular fields are obtained within the portion of the plastic zone where the crystal is in a state of high positive hardening. The results suggest that both finite-deformation and lattice rotation effects, as well as the details of the hardening law, strongly influence the structure of the solution.

[1]  A. Needleman,et al.  A tangent modulus method for rate dependent solids , 1984 .

[2]  Alan Needleman,et al.  An analysis of nonuniform and localized deformation in ductile single crystals , 1982 .

[3]  S. Chang,et al.  Dislocation‐free zone model of fracture comparison with experiments , 1982 .

[4]  The emergence of shear bands in plane strain , 1981 .

[5]  M. Ortiz,et al.  Formulation of implicit finite element methods for multiplicative finite deformation plasticity , 1990 .

[6]  J. Mandel,et al.  Plasticité classique et viscoplasticité , 1972 .

[7]  John R. Rice,et al.  Crack tip singular fields in ductile crystals with taylor power-law hardening , 1989 .

[8]  R. Asaro,et al.  Micromechanics of Crystals and Polycrystals , 1983 .

[9]  Anthony Kelly,et al.  Ductile and brittle crystals , 1967 .

[10]  S. Panchanadeeswaran,et al.  Crystal Rotations Represented as Rodrigues Vectors , 1989 .

[11]  J. Rice,et al.  Anti-plane shear cracks in ideally plastic crystals , 1985 .

[12]  T. R. Hughes,et al.  Mathematical foundations of elasticity , 1982 .

[13]  J. Rice,et al.  Constitutive analysis of elastic-plastic crystals at arbitrary strain , 1972 .

[14]  J. Rice.  TENSILE CRACK TIP FIELDS IN ELASTIC-IDEALLY PLASTIC CRYSTALS , 1987 .

[15]  Alan Needleman,et al.  Material rate dependence and localized deformation in crystalline solids , 1983 .

[16]  J. Rice,et al.  Crack tip singular fields in ductile crystals with taylor power-law hardening. I: Anti-plane shear , 1988 .

[17]  R. Asaro,et al.  Geometrical effects in the inhomogeneous deformation of ductile single crystals , 1979 .

[18]  James R. Rice,et al.  Ductile versus brittle behaviour of crystals , 1974 .

[19]  J. C. Simo,et al.  Remarks on rate constitutive equations for finite deformation problems: computational implications , 1984 .

[20]  I.-H. Lin,et al.  Cleavage, dislocation emission, and shielding for cracks under general loading , 1986 .

[21]  John R. Rice,et al.  Stresses Due to a Sharp Notch in a Work-Hardening Elastic-Plastic Material Loaded by Longitudinal Shear , 1967 .

[22]  John Arthur Simmons,et al.  FUNDAMENTAL ASPECTS OF DISLOCATION THEORY. VOLUME II. Conference Held at Gaithersburg, Maryland, April 21--25, 1969. , 1970 .

[23]  V. Vítek.  Yielding from a crack with finite root-radius loaded in uniform tension , 1976 .

[24]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[25]  Johannes Weertman,et al.  Fracture mechanics: A unified view for Griffith-Irwin-Orowan cracks , 1978 .

[26]  J. C. Rice,et al.  On numerically accurate finite element solutions in the fully plastic range , 1990 .

[27]  Robert M. McMeeking,et al.  Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture , 1977 .

[28]  Cristian Teodosiu,et al.  Elastic Models of Crystal Defects , 1982 .

[29]  Brian Moran,et al.  Energy release rate along a three-dimensional crack front in a thermally stressed body , 1986, International Journal of Fracture.

[30]  J. Rice.  On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals , 1970 .

[31]  James R. Rice,et al.  Strain localization in ductile single crystals , 1977 .

[32]  S. V. Harren,et al.  Micro and macroscopic aspects of shear band formation in internally nitrided single crystals of Fe-Ti-Mn alloys , 1988 .

[33]  M. Ortiz,et al.  An analysis of cracks in ductile single crystals—II. Mode I loading , 1992 .

[34]  S. Kobayashi,et al.  In situ fracture experiments in b.c.c. metals , 1980 .

[35]  J. Rice.  Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity , 1971 .

[36]  R. Asaro,et al.  An experimental study of shear localization in aluminum-copper single crystals , 1981 .

[37]  James R. Rice,et al.  Crack tip fields in ductile crystals , 1990 .

[38]  A. Needleman,et al.  A COMPARISON OF METHODS FOR CALCULATING ENERGY RELEASE RATES , 1985 .

[39]  K. S. Havner,et al.  On the mechanics of crystalline solids , 1973 .