Document Zbl 0523.73088

On a proposal for a continuum with microstructure. (English) Zbl 0523.73088

Acta Mech. 45, 91-121 (1982).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0523.73088

MSC:

74A60	Micromechanical theories
74M25	Micromechanics of solids
74C99	Plastic materials, materials of stress-rate and internal-variable type
74A20	Theory of constitutive functions in solid mechanics

Keywords:

continuum with microstructure; continuum viewed as superimposed state composed of perfect lattice state; immobile dislocation state; mobile dislocation state; each state evolves continuously in space-time; transitions from one state to another take place spontaneously according to balance laws of effective mass and momentum; constitutive equations subjected to requirements of invariance; plastic strain; yield; identified in terms of parameters characterizing dislocation states; flow rules; yield surfaces; Tresca and von Mises plastic behavior; kinematic hardening; different responses in tension and compression; latent hardening; Bauschinger effect

Cite Review PDF

Full Text: DOI

References:

[1]	Aifantis, E. C.: A proposal for a continuum with microstructure. Mech. Res. Comm.5, 139-145 (1978). · doi:10.1016/0093-6413(78)90047-2
[2]	Aifantis, E. C.: Preliminaries on degradation and chemomechanics. In: Proc. NSF Workshop on a continuum mechanics approach to life and damage prediction (Stouffer, D. C., Krempl, E., Fitzgerald, J. E., eds.), pp. 159-173, Carrolton, Kentucky, May 4-7, 1980.
[3]	Aifantis, E. C.: Elementary physicochemical degradation processes (Invited). In: Proc. Int. Symp. on mechanical behavior of structured media, pp. 301-317, Carleton University, Ontario, Canada, May 18-21, 1981.
[4]	Read, W. T., Jr.: Dislocations in crystals. New York: McGraw-Hill 1953. · Zbl 0051.23003
[5]	Nabarro, F. R. N.: Theory of crystal dislocations. Oxford: Clarendon Press 1967.
[6]	Stein, D. L., Low, J. R.: Mobility of edge dislocations in silicon-iron crystals. J. Appl. Phys.31, 362-369 (1960). · doi:10.1063/1.1735574
[7]	Gillis, P. P., Gilman, J. J.: Dynamical dislocation theory of crystal plasticity. J. Appl. Phys.36, 3370-3380 (1965). · doi:10.1063/1.1702998
[8]	Kelly, J. M., Gillis, P. P.: The influence of a limiting dislocation flux on the mechanical response of polycrystalline metals. Int. J. of Solids and Structures10, 45-59 (1974). · Zbl 0267.73069 · doi:10.1016/0020-7683(74)90100-0
[9]	Conrad, H., Weidersich, H.: Activation energy for deformation of metals at low temperatures. Acta Met.8, 128-130 (1960). · doi:10.1016/0001-6160(60)90097-3
[10]	Li, J. C. M.: Kinetics and dynamics in dislocation plasticity. In: dislocation dynamics (Rosenfield, A. R., Hahn, G. T., Bement, A. L., jr., Jafee, R. I., eds.), pp. 87-116. McGraw-Hill 1968.
[11]	Hirth, J. P., Nix, W. D.: An analysis of the thermodynamics of dislocation glide. Phys. Stat. Sol.35, 177-188 (1969). · doi:10.1002/pssb.19690350116
[12]	Kochs, U. F., Argon, A. S., Ashby, M. F.: Progress in materials science, Vol. 19. Oxford: Pergamon Press 1964.
[13]	Krausz, A. S., Eyring, H.: Deformation kinetics, New York: Wiley and Sons 1975.
[14]	Mecking, H., Lucke, K.: A new aspect of the theory of flow stress and metals. Scripta Metallurgica4, 427-432 (1970). · doi:10.1016/0036-9748(70)90078-5
[15]	Gibbs, G. B.: A general dislocation model for high temperature creep. Phil. Mag.23, 771-780 (1971). · doi:10.1080/14786437108216987
[16]	Gibbs, G. B.: The thermodynamics of creep deformation. Phys. Stat. Sol.5, 693-696 (1964). · doi:10.1002/pssb.19640050323
[17]	Gibbs, G. B.: The thermodynamics of thermally activated dislocation glide. Phys. Stat. Sol.10, 507-512 (1965). · doi:10.1002/pssb.2220100212
[18]	Weertman, J.: Theory of steady State Creep based on dislocation climb. J. App. Phys.26, 1213-1221 (1955). · doi:10.1063/1.1721875
[19]	Weertman, J.: Dislocation climb theory of steady state creep. Am. Soc. met. Trans. Quart.61, 681-694 (1968).
[20]	Weertman, J.: Steady state creep through climb and glide. J. Appl. Phys.28, 362-369 (1957). · doi:10.1063/1.1722747
[21]	Orowan, E.: Problems of plastic gliding. Proc. Phys. Soc. (London)52, 8-21 (1940). · doi:10.1088/0959-5309/52/1/303
[22]	Johnston, W. G., Gilman, J. J.: Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J. Appl. Physics30, 129-144 (1959). · doi:10.1063/1.1735121
[23]	Webster, G. A.: A widely applicable dislocation model of creep. Phil. Mag.14, 775-783 (1966). · doi:10.1080/14786436608211971
[24]	Webster, G. A.: In support of a model of creep based on dislocation dynamics. Phil. Mag.14, 1303-1307 (1966). · doi:10.1080/14786436608224296
[25]	Alexander, H., Haasen, P.: Dislocations and plastic flow in the diamond structure. Solid State Physics, Vol. 22 (Seitz, F., ed.), pp. 27-159 (1968).
[26]	Kelly, J. M., Gillis, P. P.: Thermodynamics and dislocation mechanics. J. Franklin Inst.297, 853-862 (1974). · Zbl 0315.73054 · doi:10.1016/0016-0032(74)90138-0
[27]	Kelly, J. M., Gillis, P. P.: Continuum descriptions of dislocations under stress reversals. J. of Appl. Phys.45, 1091-1096 (1974). · doi:10.1063/1.1663372
[28]	Sackett, S. J., Kelly, J. M., Gillis, P. P.: A probabilistic approach to polycrystalline plasticity. J. Franklin Inst.304, 33-63 (1977). · Zbl 0367.73099 · doi:10.1016/0016-0032(77)90105-3
[29]	Pilecki, S.: Introduction to the diffusional theory of metal fatigue. Third International Conference on Fracture, Munich,1, 241-245 (1973).
[30]	Pilecki, S., Analysis of the usefulness of diffusion equations for the description of dislocation mobility and related phenomena. Archives of Mechanics29, 505-517 (1977).
[31]	Pilecki, S.: Proliferation, diffusion and vanishing of dislocations in the course of the process of metal fatigue. Bull. de L’Academie Polon. des Sci.17, 489-496 (1969).
[32]	Rosenfield, A. R.: A continuous distribution of moving dislocations. Phil. Mag.24, 63-69 (1971). · doi:10.1080/14786437108216424
[33]	Nye, J. F.: Some geometrical relations in dislocated crystals. Acta Met.1, 153-162 (1953). · doi:10.1016/0001-6160(53)90054-6
[34]	Nye, J. F.: Plastic deformation of silver chloride. II. Photoelastic study of the internal stresses in glide packets. Proc. Roy. Soc.A 200, 47-66 (1949). · doi:10.1098/rspa.1949.0158
[35]	Mura, T.: On dynamic problems of continuous distribution of dislocations. Int. J. Eng. Sci.1, 371-381 (1963). · doi:10.1016/0020-7225(63)90014-4
[36]	Mura, T.: Continuous distributions of dislocations and the mathematical theory of plasticity. Phys. Stat. Sol.10, 447-453 (1965). · doi:10.1002/pssb.2220100205
[37]	Mura, T.: Continuous distributions of dislocations and the mathematical theory of plasticity (II). Phys. Stat. Sol.11, 683-688 (1965). · doi:10.1002/pssb.19650110220
[38]	Mura, T.: The continuum theory of dislocations. Adv. Mat. Res.3, 1-108 (1968). · Zbl 0187.49001
[39]	Lardner, R. W.: Plane strain plasticity of single crystals. Int. J. Eng. Sci.7, 417-425 (1969). · doi:10.1016/0020-7225(69)90075-5
[40]	Lardner, R. W.: Dislocation dynamics and the theory of the plasticity of single crystals. ZAMP20, 514-529 (1969). · Zbl 0175.23606 · doi:10.1007/BF01595044
[41]	Werne, R. W., Kelly, J. M.: A dislocation theory of isotropic polycrystalline plasticity. Int. J. Eng. Sci.16, 951-965 (1978). · Zbl 0391.73096 · doi:10.1016/0020-7225(78)90054-X
[42]	Eshelby, J. D.: The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. Roy. Soc. A241, 376-395 (1957). · Zbl 0079.39606 · doi:10.1098/rspa.1957.0133
[43]	Kroupa, F.: Continuous distribution of dislocation loops. Czech. J. Phys.B 12, 191-201 (1962). · doi:10.1007/BF02353850
[44]	Kroupa, F.: The interaction between prismatic dislocation loops and straight dislocations. Phil. Mag.1962, 783-801.
[45]	Peach, M. O., Koehler, J. S.: The forces exerted on dislocations and the stress fields exerted by them. Phys. Rev.80, 436-439 (1950). · Zbl 0039.23301 · doi:10.1103/PhysRev.80.436
[46]	Weertman, J.: The Peach-Koehler equation for the force on a dislocation modified for hydrostatic pressure. Phil. Mag.11, 1217-1223 (1965). · doi:10.1080/14786436508224930
[47]	Aifantis, E. C.: On the problems of diffusion in solids. Acta Mech.37, 265-296 (1980). · Zbl 0447.73002 · doi:10.1007/BF01202949
[48]	Aifantis, E. C.: The mechanics of diffusion in solids. TAM Report 440, UILU-ENG 80-6001, University of Illinois, Urbana, Illinois, 1980. · Zbl 0447.73002
[49]	Bammann, D. J., Aifantis, E. C.: Unpublished results.
[50]	Bardeen, J., Herring, C.: Diffusion in alloys and the Kirkendall effect, imperfections in nearly perfect crystals (Shockley, W., ed.), pp. 261-288, New York: Wiley 1952.
[51]	Bammann, D. J., Aifantis, E. C.: On the perfect lattice-dislocated state interaction. In: Proc. Int. Symp. on Mechanical Behavior of Structured Media, Carleton University, Ontario, Canada, May 18-21, 1981.
[52]	Weng, G. J., Phillips, A.: An investigation of yield surface based on dislocation mechanics. Int. J. Eng. Sci.15, 45-59 (1977). · Zbl 0346.73065 · doi:10.1016/0020-7225(77)90068-4
[53]	Aifantis, E. C.: Lecture Notes on Dislocations, University of Minnesota, Spring 1981.
[54]	Colios, J., Aifantis, E. C.: On the problem of a continuum theory of embrittlement. Res. Mechanica (in press).
[55]	Hildebrand, F. B.: Advanced calculus for applications. Englewood Cliffs, N.J.: Prentice-Hall 1976. · Zbl 0333.00003

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.