Plastic flow of crystals

Publisher Summary This chapter provides an overview of plastic flow of crystals. Plastic flow under multiple slip, particularly in metallic crystals, has been widely studied by materials scientists and applied mechanicians since the early 1900s. Finite strain crystal plasticity is a rigorous nonlinear continuum theory. With few exceptions, subtleties of this theory such as multislip hardening and non-Schmid effects have not been tested sufficiently in critical experiments. In particular, through the interplay between small secondary slips and hardening, there is now compelling evidence that important effects largely have been ignored. Furthermore, because intermetallic compounds are currently of growing interest in high-temperature applications, non-Schmid effects, which are also important in BCC metals and alloys, should also be considered more seriously. In this chapter, recent studies of multiple-slip interactions and hardening are brought together within a time-independent theory, and their influence on strain localization is explored. It discusses in detail about yield behavior including non-Schmid effects. Flow behavior including non-Schmid effects is elaborated. Concepts of hardening behavior and strain localization are also explained in the chapter.

[1]  J. Children LX. An abstract of the characters of Ochsenheimer's genera of the lepidoptera of Europe; with a list of the species of each genus, and reference to one or more of their respective icones , 1828 .

[2]  John W. Hutchinson,et al.  Elastic-plastic behaviour of polycrystalline metals and composites , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  A. Kelly,et al.  Deformation of age-hardened aluminium alloy crystals—II. Fracture , 1964 .

[4]  John W. Hutchinson,et al.  A class of phenomenological corner theories of plasticity , 1979 .

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

[6]  K. S. Havner,et al.  Theoretical latent hardening in crystals—I. General equations for tension and compression with application to F.C.C. crystals in tension , 1979 .

[7]  J. Garstone,et al.  Easy glide of cubic metal crystals , 1956 .

[8]  J. Bishop VI. A theoretical examination of the plastic deformation of crystals by glide , 1953 .

[9]  P. Franciosi,et al.  Latent hardening in copper and aluminium single crystals , 1980 .

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

[11]  T. Mitchell,et al.  The detection of secondary slip during the deformation of copper and α-brass single crystals , 1964 .

[12]  D. Pope,et al.  The asymmetry of cyclic hardening in Ni3(Al,Nb) single crystals , 1985 .

[13]  D. C. Stouffer,et al.  A Constitutive Model for the Inelastic Multiaxial Response of Rene’ 80 at 871C and 982C , 1990 .

[14]  J. Bassani,et al.  Non-Schmid yield behavior in single crystals , 1992 .

[15]  K. S. Havner,et al.  Further Investigation of a New Hardening Law in Crystal Plasticity , 1978 .

[16]  C. F. Elam Tensile Tests on Alloy Crystals. Part IV. A Copper Alloy Containing Five Per Cent. Aluminium , 1927 .

[17]  M. J. Sewell A plastic flow rule at a yield vertex , 1974 .

[18]  J. Bassani,et al.  Non-associated plastic flow in single crystals , 1992 .

[19]  D. C. Drucker,et al.  Continuum Plasticity Theory in Relation to Solid Solution, Dispersion, and Precipitation Hardening , 1967 .

[20]  R. Hill,et al.  XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. , 1951 .

[21]  D. Kuhlmann-wilsdorf,et al.  Dislocation behavior in fatigue V: Breakdown of loop patches and formation of persistent slip bands and of dislocation cells , 1980 .

[22]  J. Mandel,et al.  Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques , 1973 .

[23]  P. Jackson,et al.  Latent Hardening and the Flow Stress in Copper Single Crystals , 1967 .

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

[25]  K. S. Havner,et al.  A quantitative study of a crystalline aggregate model , 1973 .

[26]  John W. Hutchinson,et al.  Bifurcation phenomena in the plane tension test , 1975 .

[27]  K. S. Havner,et al.  A simple mathematical theory of finite distortional latent hardening in single crystals , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[28]  K. S. Havner The Theory of Finite Plastic Deformation of Crystalline Solids , 1982 .

[29]  J. L. Bassani Single Crystal Hardening , 1990 .

[30]  U. F. Kocks The relation between polycrystal deformation and single-crystal deformation , 1970 .

[31]  W. T. Koiter Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface , 1953 .

[32]  R. Clifton,et al.  On the computation of plastic stress-strain relations for polycrystalline metals , 1977 .

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

[34]  Bernard Budiansky,et al.  THEORETICAL PREDICTION OF PLASTIC STRAINS OF POLYCRYSTALS , 1961 .

[35]  M. Ortiz,et al.  A finite element method for localized failure analysis , 1987 .

[36]  Doris Kuhlmann-Wilsdorf,et al.  Theory of plastic deformation: - properties of low energy dislocation structures , 1989 .

[37]  M. J. Sewell A yield-surface corner lowers the buckling stress of an elastic-plastic plate under compression , 1973 .

[38]  W. Lomer A dislocation reaction in the face-centred cubic lattice , 1951 .

[39]  R. Davis,et al.  Effect of orientation on the plastic deformation of aluminum single crystals and bicrystals , 1957 .

[40]  Elias C. Aifantis,et al.  On the geometry of slip and spin in finite plastic deformation , 1991 .

[41]  Otto T. Bruhns,et al.  Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strain , 1981 .

[42]  David P. Pope,et al.  A theory of the anomalous yield behavior in L12 ordered alloys , 1984 .

[43]  J. Rice Localization of plastic deformation , 1976 .

[44]  G. Taylor,et al.  The Plastic Extension and Fracture of Aluminium Crystals , 1925 .

[45]  R. Hill Generalized constitutive relations for incremental deformation of metal crystals by multislip , 1966 .

[46]  R. E. Green,et al.  Continuous X-ray diffraction measurement of lattice rotation during tensile deformation of aluminium crystals , 1980 .

[47]  D. Peirce Shear band bifurcations in ductile single crystals , 1983 .

[48]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[49]  T. Takasugi,et al.  Plastic flow of Co3 Ti single crystals , 1987 .

[50]  Alan Needleman,et al.  Non-normality and bifurcation in plane strain tension and compression , 1979 .

[51]  D. Pope,et al.  Mechanical properties of Ni3AI and nickel-base alloys with high volume fraction of γ' , 1984 .

[52]  Rodney Hill,et al.  Continuum micro-mechanics of elastoplastic polycrystals , 1965 .

[53]  P. L. Pratt,et al.  Plastic Deformation and Work-Hardening in NaCl , 1964 .

[54]  R. Cahn,et al.  A study of primary and conjugate slip in crystals of alpha-brass , 1955 .

[55]  V. Vítek,et al.  Asymmetry of plastic flow in Ni3Ga single crystals , 1987 .

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

[57]  John L. Bassani,et al.  Latent hardening in single crystals. II. Analytical characterization and predictions , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[58]  R. E. Green,et al.  An experimental study of the double slip deformation hypothesis for face-centred cubic single crystals , 1967 .

[59]  F. D. Rosi Stress-Strain Characteristics and Slip-Band Formation In Metal Crystals: Effect of Crystal Orientation , 1954 .

[60]  J. Mandel Generalisation de la theorie de plasticite de W. T. Koiter , 1965 .

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

[62]  Z. S. Basinski Thermally activated glide in face-centred cubic metals and its application to the theory of strain hardening , 1959 .

[63]  K. S. Havner,et al.  A theory of minimum plastic spin in crystal mechanics , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[64]  A. Zaoui,et al.  Multislip tests on copper crystals: A junctions hardening effect , 1982 .

[65]  J. Christian Some surprising features of the plastic deformation of body-centered cubic metals and alloys , 1983 .

[66]  R. Hill,et al.  CXXVIII. A theoretical derivation of the plastic properties of a polycrystalline face-centred metal , 1951 .

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

[68]  D. Stouffer,et al.  A Crystallographic Model for the Tensile and Fatigue Response for René N4 at 982°C , 1990 .

[69]  André Zaoui,et al.  Multislip in f.c.c. crystals a theoretical approach compared with experimental data , 1982 .

[70]  J. Washburn,et al.  Strain hardening of latent slip systems in zinc crystals , 1954 .

[71]  Z. S. Basinski,et al.  Fundamental aspects of low amplitude cyclic deformation in face-centred cubic crystals , 1992 .

[72]  D. Pope,et al.  Effect of boron additions on the ductility and fracture behavior of Ni3Al single crystals , 1991 .

[73]  K. S. Havner,et al.  Perspectives in the mechanics of elastoplastic crystals , 1982 .

[74]  R. Hill Acceleration waves in solids , 1962 .