Summary
A survey is presented on theoretical solutions to elastoplastic treatments in failure mechanics, in which the plastic zones are simulated as slip bands. Some experimental studies are discussed on plastic-strain localization in thin layers near cracks. Two-dimensional treatments of plastic band growth in bodies with cracks are considered for the conditions of planar stress, planar strain, and longitudinal shear, together with the corresponding axisymmetric and three-dimensional treatments. A note is also made of papers in which the plasticity band model is used for the bending of plates and shells containing cracks.
Similar content being viewed by others
Literature cited
P. M. Vitvitskii, V. V. Panasyuk, and S. Ya. Yarema, “Plastic strain near cracks and failure criteria: review,” Probl. Prochn., No. 2, 3–18 (1973).
V. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids,8, No. 2, 100–104 (1960).
M. Ya. Leonov, P. M. Vitvitskii, and S. Ya. Yarema, “A theoretical and experimental study on elastoplastic strains on stretching a plate containing a slit,” in: Plate and Shell Theory [in Russian], Izd. AN Ukr. SSR, Kiev (1962), pp. 196–199.
G. I. Kornilov and S. Ya. Yarema, “Planar specimens with crack-type stress concentrators for experimental research on plasticity bands,” in: Aspects of the Mechanics of Real Solids, Issue 1 [in Russian], Izd. AN Ukr. SSR, Kiev (1962), pp. 29–36.
M. Ya. Leonov, P. M. Vitvitskii, and S. Ya. Yarema, “Plasticity bands in stretching a plate containing a crack-type stress concentrator,” Dokl. Akad. Nauk SSSR,148, No. 3, 541–544 (1963).
S. Ya. Yarema, “A study on plasticity bands in stretching a plate containing a stress concentrator,” in: Aspects of the Mechanics of Real Solids, Issue 2 [in Russian], Naukova Dumka, Kiev (1964), pp. 177–190.
G. T. Hahn and A. R. Rosenfield, “Local yielding and extension of a crack under plane stress,” Acta Met.,13, No. 3, 293–306 (1965).
J. Rice, “Mathematical methods in failure mechanics,” in: Failure [Russian translation], Vol. 2, Mir, Moscow (1975), pp. 204–335.
P. M. Vitvitskii, V. V. Panasyuk, and S. Ya. Yarema, “Plastic deformation around cracks and fracture criteria,” Eng. Fract. Mech.,7, No. 3, 305–319 (1975).
V. Z. Parton and E. M. Morozov, Mechanics of Elastoplastic Failure [in Russian], Nauka, Moscow (1985).
M. P. Savruk, Two-Dimensional Elastic Treatments for a Body Containing Cracks [in Russian], Naukova Dumka, Kiev (1981).
V. V. Panasyuk, M. P. Savruk, I. V. Prokopchuk, and A. M. Danilovich, “Planar elastoplastic treatment for a body containing cracks with plastic strain localization in thin layers,” Fiz.-Khim. Mekh. Mater., No. 5, 35–42 (1991).
V. V. Panasyuk, A. E. Andreikiv, and V. Z. Parton, Principles of Material Failure Mechanics (Handbook) [in Russian], Vol. 1, Naukova Dumka, Kiev (1988).
Y. J. Sun, O. S. Lee, and A. S. Kobayashi, “Crack tip plasticity under mixed mode loading,” Proc. ICF Int. Symp. Fract. Mech., Beijing. Utrecht (1984), pp. 502–588.
C. Atkinson and C. Bastero, “Plastic relaxation at a crack tip by asymmetric slip,” Proc. R. Soc., A418, No. 1854, 261–280 (1988).
C. Bastero and C. Atkinson, “Incipient yielding at a debond crack tip under mixed mode loading,” Int. J. Fract.,38, No. 3, 193–206 (1988).
P. M. Vitvitskii and M. Ya. Leonov, “Slip bands in inhomogeneous plate deformation,” in: Aspects of the Mechanics of Real Solids, Issue 1 [in Russian], Izd. AN Ukr. SSR, Kiev (1962), pp. 13–28.
M. Ya. Leonov and V. V. Panasyuk, “The growth of general cracks in a solid,” Porosh. Metall.,5, No. 4, 391–401 (1959).
M. Ya. Leonov, “A simplified model for a brittle solid,” Information Bulletin No. 1, Scientific Council on the Scientific Principles of Strength and Plasticity [in Russian], Izd. VINITI Akad. Nauk SSSR, Moscow (1960), pp. 16–17.
P. M. Vitvitskii and M. Ya. Leonov, “Griffiths' failure theory,” ibid., pp. 14–15.
V. V. Panasyuk, “Crack widening theory in brittle-body deformation,” Dokl. Akad. Nauk Ukr. SSR, No. 9, 1105–1109 (1960).
V. V. Panasyuk, “Determining stresses and strains near a minute crack,” in: Aspects of Machine Science and Strength in Engineering, Issue 6 [in Russian], Izd. AN Ukr. SSR, Kiev (1960), pp. 114–127.
P. M. Vitvitskii and M. Ya. Leonov, “Failure of a plate containing a slit,” Prikl. Mekh.,7, No. 5, 516–520 (1961).
M. Ya. Leonov, “Elements of brittle failure theory,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 85–92 (1961).
A. A. Wells, “Critical tip opening displacement as a fracture criterion,” Proc. Crack Propagation Symp., Cranfield, 1961, Vol. 1, Cranfield (1962), pp. 210–221.
A. A. Wells, “The application of fracture mechanics at and beyond general yielding,” Brit. Weld. J.,10, No. 11, 563–570 (1963).
V. V. Panasyuk, Limiting Equilibrium in a Brittle Body Containing Cracks [in Russian], Naukova Dumka, Kiev (1968).
G. R. Egan and J. N. Robinson, “The application of elastic-plastic fracture mechanics parameters in fracture safe design,” Nucl. Eng. Design,45, No. 1, 133–158 (1978).
B. L. Karihaloo, “Fracture of solids containing arrays of cracks,” Eng. Fract. Mech.,12, No. 1, 49–77 (1979).
C. Atkinson, “Stress singularities and fracture mechanics,” Appl. Mech. Rev.,32, No. 2, 123–135 (1979).
L. H. Larsson, “Use of EPFM in design,” Advances in Elastoplastic Fracture Mechanics, London (1980), pp. 261–278.
V. V. Panasyuk, “Current aspects of failure mechanics,” Fiz.-Khim. Mekh. Mater., No. 2, 7–27 (1982).
H. Chr. Zeislmayr, “Elastoplastic failure mechanics,” in: Static Strength and Failure Mechanics for Steels [Russian translation], Moscow (1986), pp. 298–316.
G. P. Chrepanov, Brittle-Failure Mechanics [in Russian], Nauka, Moscow (1974).
T. Ekobori, The Scientific Principles of Strength and Failure in Materials [Russian translation], Naukova Dumka, Kiev (1978).
J. F. Nott, The Principles of Failure Mechanics [Russian translation], Metallurgiya, Moscow (1978).
J. Broek, The Principles of Failure Mechanics [Russian translation], Vysshaya Shkola, Moscow (1980).
M. Ya. Leonov, The Mechanics of Deformation and Failure [in Russian], Ilim, Frunze (1981).
A. E. Andreikiv, Three-Dimensional Aspects of Cracking Theory [in Russian], Naukova Dumka, Kiev (1982).
B. D. Annin and G. P. Cherepanov, An Elastoplastic Treatment [in Russian], Nauka, Novosibirsk (1903).
V. M. Mirsalimov, Failure in Elastic and Elastoplastic Bodies Containing Cracks [in Russian], Elm, Baku (1984).
M. Shiratori, T. Miyoshi, and H. Matsushita, The Computational Mechanics of Failure [Russian translation], Mir, Moscow (1986).
V. M. Mirsalimov, Non-One-Dimensional Elastoplastic Problems [in Russian], Nauka, Moscow (1987).
C. Hellan, Introduction to Failure Mechanics [Russian translation], Mir, Moscow (1988).
I. M. Kershtein, V. D. Klyushnikov, E. V. Lomakin, and S. A. Shesterikov, Principles of Experimental Failure Mechanics [in Russian], Izd. Mosk. Univ., Moscow (1989).
L. I. Slepyan, Crack Mechanics [in Russian], Sudostroenie, Leningrad (1990).
J. N. Goodier and F. A. Field, “Plastic energy dissipation in crack propagation,” Fracture of Solids, J. Wiley Interscience, New York-London (1963), pp. 103–118.
J. R. Rice, “Plastic yielding at a crack tip,” Proc. First Int. Conf. Fracture, Vol. 1, Sendai (1966), pp. 203–300.
G. V. Galatenko, “Extension of Dugdale's cracking model on the basis of classical yield surfaces,” Prikl. Mekh.,25, No. 6, 36–42 (1989).
G. V. Galatenko, “An extension of Dugdale's cracking model,” ibid.,25, No. 3, 53–50 (1909).
G. V. Galatenko, “Elastoplastic failure in an isotropic plate containing a crack under biaxial loading,” ibid.,25, No. 7, 86–91 (1989).
G. V. Galatenko, O. S. Dekhtyareva, and A. A. Kaminskii, “Elastoplastic failure in an orthotropic plate containing a crack under biaxial loading,” ibid.,26, No. 8, 93–99 (1990).
J. C. Newman, “Fracture of cracked plates under plane stress,” Eng. Fract. Mech.,1, No. 1, 137–154 (1960).
G. G. Chell, “A simple model of work hardening applied to post-yield fracture mechanics,” Int. J. Fract.,10, No. 1, 128–131 (1974).
V. V. Panasyuk, O. E. Andreikiv, “A computational model for a work-hardening elastoplastic body,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1094–1098 (1974).
B. L. Karihaloo, “Arrays of cracks in perfectly-plastic and strain-hardening materials,” Z. Angew. Math. Mech.,58, No. 7, 376–378 (1978).
A. A. Kaminskii and G. V. Galatenko, “Fatigue-crack growth in work-hardening materials,” Porosh. Metall.,20, No. 4, 54–60 (1984).
A. A. Kaminskii and V. N. Bastun, Work Hardening and Softening in Metals under Alternating Loading [in Russian], Naukova Dumka, Kiev (1985).
P. G. Clarin, “Fracture analysis of center cracked infinite plates of linearly softening materials,” Eng. Fract. Mech.,27, No. 2, 231–245 (1987).
Duan Shu-jin and K. Nakagawa, “A mathematical approach of fracture macromechanics for strain-softening material,” Eng. Fract. Mech.,34, No. 5/6, 1175–1182 (1989).
K. N. Ruoinko, “Conditions for plasticity bands to arise on stretching a plate containing a rectilinear slit,” in: Aspects of the Mechanics of Real Solids, Issue 2 [in Russian], Naukova Dumka, Kiev (1964), pp. 27–37.
A. A. Kaminskii, Failure Mechanics of Viscoelastic Bodies [in Russian], Naukova Dumka, Kiev (1980).
A. A. Kaminskii and D. A. Gavrilov, Polymer Failure Mechanics [in Russian], Naukova Dumka, Kiev (1988).
G. I. Bykovtsev, L. G. Lukashev, and S. L. Stepanov, “A model for failure in an ideally elastoplastic medium,” Probl. Prochn., No. 3, 72–75 (1982).
A. R. Rosenfield, P. K. Dai, and G. T. Hahn, “Crack extension and propagation under plane stress,” Proc. First Int. Conf. Fracture, Sendai (1966), Vol. 1, pp. 223–258.
P. M. Vitvitskii, “A general model for plastic-band growth and failure around stress concentrators in thin plates,” Fiz.-Khim. Mekh. Mater., No. 5, 51–57 (1984).
E. M. Morozov, “An extension of theδ k crack theory,” Prikl. Mekh.,6, No. 4, 128–131 (1970).
M. F. Kanninen, “An estimate of the limiting speed of a propagating ductile crack,” J. Mech. Phys. Solids,16, No. 4, 215–228 (1968).
T. Y. Fan, “Moving Dugdale model,” Z. Angew. Math. Phys.,38, No. 4, 630–641 (1987).
D. H. Chen and H. Nisitani, “Analysis of plasticity-induced crack closure by the extended body force method (comparison of various analytical results based on Dugdale hypothesis,” JSME Int. J. Ser. 1, No. 3, 598–605 (1988).
R. A. Schapery, “On the mechanics of crack closing and bonding in linear viscoelastic media,” Int. J. Fract.,39, No. 1–3, 163–109 (1989).
M. F. Kanninen, “A solution for a Dugdale crack subjected to a linearly varying tensile loading,” Int. J. Eng. Sci.,8, No. 1, 85–95 (1970).
O. L. Bowie and P. G. Tracy, “On the solution of the Dugdale model,” Eng. Fract. Mech.,10, No. 2, 249–256 (1978).
P. M. Vitvits'kii, “Development of plastic strain around the ends of a slit in a thin plate stretched by localized forces,” Dokl. AN Ukr. SSR, Ser. A, No. 4, 316–320 (1969).
V. M. Mirsalimov, “Some aspects of constructive crack blocking,” Fiz.-Khim. Mekh. Mater., No. 1, 84–88 (1986).
V. V. Panasyuk, P. M. Vitetskii, and S. I. Kuten', “Plastic strain and failure in a plate weakened by an equal-armed cross-type crack,” Probl. Prochn., No. 5, 3–6 (1979).
P. M. Vitvitskii, “Slip bands in stretching a thin plate containing rectilinear slits,” in: Stress Concentration, Issue 1 [in Russian], Naukova Dumka, Kiev (1965), pp. 78–85.
E. Smith, “Fracture of stress concentrations,” Proc. First Int. Conf. Fracture, Sendai (1966), Vol. 1, pp. 133–151.
Y. M. Tsai and Zhang Peizhong, “Plastic zones for a pair of coplanar line cracks: theory and experiment,” Proc. Int. Conf. Exp. Mech., Beijing (1905), pp. 975–980.
P. S. Theocaris, “Dugdale models for two collinear unequal cracks,” Eng. Fract. Mech., No. 3, 545–559 (1983).
P. M. Vitvitskii, “Quasibrittle failure in a plate containing two semiinfinite slits,” Fiz.-Khim. Mekh. Mater., No. 6, 749–751 (1969).
P. M. Vitvitskii, “Elastoplastic strain and failure under localized forces in a plate containing external slits,” ibid., No. 3, 75–80 (1973).
M. Ya. Leonov and L. V. Onishko, “Brittle failure in a plate containing two closely spaced slits,” Prikl. Mekh., No. 6, 639–644 (1962).
M. Ya. Leonov and L. V. Onyshko, “Brittle failure in a plate containing two closely spaced slits,” in: Theory of Plates and Shells [in Russian], Izd. AN Ukr. SSR, Kiev (1962), pp. 200–203.
E. Smith, “The spread of plasticity between two cracks,” Int. J. Eng. Sci.,2, No. 4, 379–307 (1964).
B. A. Bilby, A. H. Cottrell, E. Smith, and K. H. Swinden, “Plastic yielding from sharp notches,” Proc. R. Soc.,A279, No. 1376, 1–9 (1964).
B. K. Bilby and K. H. Swinden, “Representation of plasticity at notches by linear dislocation arrays,” ibid.,A205, No. 1400, 22–33 (1965).
B. A. Kudryavtsev, V. Z. Parton, and G. P. Cherepanov, “Elastoplastic treatment for a plane containing rectilinear slits” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 174–176 (1969).
P. M. Vitvits'kii, “Elastoplastic equilibrium in a plate containing a periodic slit system,” Dokl. AN Ukr. SSR, Ser. A, No. 6, 524–527 (1970).
H. Nisitani and Y. Murakami, “Interaction of elastoplastic cracks subjected to a uniform tensile stress in an infinite or semiinfinite plate,” Mechanical Behavior of Materials, Vol. 1, Kyoto (1972), pp. 346–356.
V. V. Panasyuk, E. V. Buina, and T. R. Yas'kevich, “The limiting equilibrium state of a strip containing a crack,” Dokl. AN Ukr. SSR Ser. A, No. 10, 923–926 (1973).
V. V. Panasyuk, E. V. Buina, and T. R. Yas'kevich, “The limiting equilibrium of a strip containing a crack stretched by localized forces,” Fiz.-Khim. Mekh. Mater., No. 1, 71–74 (1974).
B. L. Karihaloo, “Spread plasticity from a stack of cracks under mode I conditions,” Int. J. Solids Struct.,13, No. 4, 376–375 (1977).
B. L. Karihaloo, “Fracture characteristics of solids containing stacked stress concentrations,” Proc. Int. Conf. Fract. Mech. and Technol., Vol. 2, Alphen aan den Rijn (1977), pp. 823–836.
E. Smith, “The spread of plasticity from stress concentrations,” Proc. R. Soc.,A202, No. 1390, 422–432 (1964).
B. L. Karihaloo, “Fracture characteristics of solids containing doubly periodic arrays of cracks,” ibid.,A360, No. 1702, 373–387 (1978).
T. Rich and R. Roberts, “Plastic enclave sizes for internal cracks emanating from circular cavities within elastic plates,” Eng. Fract Mech.,1, No. 1 (1968).
V. V. Panasyuk, P. M. Vitvitskii, and S. I. Kuten', “Elastoplastic equilibrium in a plate containing a circular hole and cracks emerging at its edge,” Fiz.-Khim. Mekh. Mater., No. 1, 60–64 (1976).
G. G. Chell and V. Vitek, “Post yield solutions for fracture mechanics analyses of cracks emanating from elliptic holes,” Eng. Fract. Mech.,11, No. 2 (1979).
L. A. Bostrom, “The Dugdale model used for short radial cracks emanating from a circular hole in an infinite sheet,” ibid.,34, No. 4, 823–829 (1909).
V. M. Mirsalimov, “Elastoplastic equilibrium in a thin plate weakened by a periodic system of circular holes containing cracks,” Prikl. Mekh.,14, No. 10, 96–101 (1978).
V. M. Mirsalimov, “Elastoplastic equilibrium in a plate containing a doubly periodic system of circular holes bearing cracks emerging on the hole edges,” Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 2, 118–125 (1979).
I. C. Howard and N. R. Otter, “On the elastoplastic deformation of a sheet containing an edge crack,” J. Mech. Phys. Solids,23, No. 2, 139–149 (1975).
V. V. Panasyuk, P. M. Vitvits'kii, and S. I. Kuten', “Plastic strain and failure in a plate having an edge crack,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 4, 346–351 (1975).
G. G. Chell, “Bilby, Cottrell and Swinden model solutions for centre and edge cracked plates subject to arbitrary mode 1 loading,” Int. J. Fract.,12, No. 1, 135–147 (1976).
V. D. Kuliev, “Plastic strain at the end of an edge crack,” Prikl. Mat. Mekh.,43, No. 1, 160–166 (1979).
H. J. Petroskl, “Dugaale plastic zone sizes for edge cracks,” Int. J. Fract.,15, No. 3, 217–230 (1979).
B. M. Singh, H. T. Danykyuk, and J. Vrbik, “A note on plastic deformation at the tip of an edge crack,” Acta Mech.,55, No. 1–2, 81–86 (1985).
S. Atluri and A. Kobayashi, “Quasistatic failure in elastoplastic bodies,” in: Computational Methods in Failure Mechanics [Russian translation], Mir, Moscow (1990), pp. 49–82.
V. V. Panasyuk, P. M. Vitvitskii, and S. I. Kuten', “Elastoplastic equilibrium for a plate with a crack near the edge,” Prikl. Mekh.,15, No. 1, 43–50 (1979).
P. M. Vitvitskii, S. Ya. Yarema, and S. I. Kuten', “An experimental study on the growth of plastic zones in plates with edge slits,” Fiz. -Khim. Mekh. Mater., No. 2, 77–80 (1976).
F. Erdogan and M. Bakioglu, “Crack opening stretch in a plate of finite width,” Int. J. Fract.,11, No. 6, 1031–1039 (1975).
A. C. Kaya and F. Erdogan, “Stress intensity factors and COD in an orthotropic strip,” ibid.,16, No. 2, 171–190 (1980).
V. V. Panasyuk, I. N. Pan'ko, and I. P. Vas'kiv, “The boundary interpolation method applied in the approximate solution of elastoplastic problems in crack theory,” Fiz.-Khim. Mekh. Mater., No. 2, 61–65 (1984).
V. V. Panasyuk, “Deformation criteria in failure mechanics,” ibid., No. 1, 7–17 (1906).
V. V. Panasyuk, A. E. Andreikiv, and M. P. Savruk, “Some Mathematical Methods of Solving Static Cases in Cracking Theory [in Russian], L'vov (1987), Preprint No. 134, Fiz.-Mekh. Inst., AN Ukr. SSR.
I. M. Pan'ko and N. I. Tim'yak, “Determining crack opening by the equivalent stress state method,” Fiz. Khim. Mekh. Mater., No. 2, 16–19 (1989).
V. V. Panasyuk, I. M. Pan'ko, and N. I. Tim'yak, “Approximate determination of the state of stress and strain in an elastoplastic body weakened by cracks,” ibid., No. 6, 44–50 (1989).
V. V. Panasyuk, O. E. Andreikiv, M. M. Stadnik, and I. V. Didukh, “Determining crack tip opening for an elastoplastic body,” ibid., No. 6, 53–61 (1990).
Y. M. Tsail “Central ductile crack in an orthotropic strip of infinite width,” J. Compos. Mater.,16, No. 5, 358–370 (1902).
D. Gross, “Dugdale-Model-Naherung fur die Scheibe mit Randriss unter Biegung,” Z. Flugwiss. und Weltraumforsch.,8, No. 6, 387–391 (1984).
L. E. Hulbert, G. T. Hahn, A. R. Rosenfield, and M. F. Kanninen, “Al elastic-plastic analysis of a crack in a plate of finite size,” Applied Mechanics, Springer, Berlin (1969), pp. 221–235.
D. J. Hayes and J. G. Williams, “A practical method for determining Dugdale model solutions for cracked bodies of arbitrary shape,” Int. J. Fract. Mech.,8, No. 3, 239–256 (1972).
M. Ishida, “Effects of specimen geometry and loading conditions on the crack tip plastic zone,” Mechanical Behavior of Materials, Vol. 1, Kyoto (1972), pp. 394–407.
D. N. Fenner, “Dugdale model solutions for a single edge cracked plate,” Int. J. Fract.,10, No. 1, 71–76 (1974).
H. Miyamoto, H. Okamura, K. Kageyama, and H. Morita, “Elastic-plastic analysis of a crack by using continuously distributed dislocations,” Numerical Methods of Fracture Mechanics, Swansea (1900), pp. 261–275.
M. Ishida and H. Tsuru, “Development analysis of Dugdale plastic zone at an edge crack tip in a finite plate,” Trans. Jpn. Soc. Mech. Eng.,A40, No. 432. 1006–1013 (1982) (in Japanese).
Chen Yi Zhou, “A Dugdale problem for a finite internally cracked plate,” Eng. Fract. Mech.,17, No. 6, 579–583 (1903).
S. Ya. Yarema, P. M. Vitvitskii, A. I. Zboromirskii, and O. P. Ostash, “Plastic strain around a crack in a thin disk stretched by localized forces,” Fiz.-Khim. Mekh. Mater., No. 5, 34939 (1974).
S. Ya. Yarema, G. S. Krestin, and A. I. Zboromirskii, “Opening and limiting equilibrium for cracks in an elastoplastic disk,” ibid., No. 1, 31–36 (1975).
L. L. Libatskii and Ya. I. Orishchits, “Plasticity bands near crack tips in a circular plate,” Vestn. l'vov. Politekh. Inst, No. 192, 73–75 (1975).
A. V. Boiko, “Elastoplastic deformation of a circular plate containing a central crack,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 1, 161–167 (1986).
A. I. Zboromirskii, G. S. Ivanits'ka, M. V. Ivanovich, et al., “Elastoplastic equilibrium of a disk containing an edge crack,” Fiz.-Khim. Mekh. Mater., No. 1, 30–46 (1990).
A. V. Boiko, “Some effects in the biaxial elastoplastic strain of a plate containing a crack,” Probl. Prochn., No. 6, 20–27 (1990).
D. J. Cartwright and M. H. Aliabadi, “Boundary element analysis of a strip yield crack at a hole,” Boundary Elements X, Vol. 3, Southampton and Berlin (1988), pp. 177–104.
M. P. Savruk, P. N. Osiv, and I. V. Prokopchuk, Numerical Analysis in Planar Topics in Cracking Theory [in Russian], Naukova Dumka, Kiev (1989).
M. P. Savruk and I. V. Prokopchuk, “State of stress in a plate having plasticity bands at the crack edges,” Prikl. Mekh.,26, No. 3, 55–61 (1990).
H. Terada, “Elastoplastic stress analysis of the standard compact specimen,” Trans. ASME. J. Pressure Vessel Technol.,105, No. 2, 132–137 (1983).
J. C. Newman and S. Mall, “Dugdale plastic zone size and CTOD equations for the compact specimen,” Int. J. Fract.,24, No. 3, R59-R63 (1984).
S. Mall and J. C. Newman, “The Dugdale model for compact specimen,” Fract. Mech.: Proc. 16th Nat. Symp. (Columbus, 1903). Philadelphia (1905), pp. 113–128.
Wu, X. R. and W. Zhao, “Dugdale model solution for compact specimen,” Mech. Behav. Mater.: Proc. 5th Int. Conf. (Beijing, 1987), Vol. 1. Oxford (1988), pp. 243–248.
B. A. Bilby, A. H. Cottrell, and R. H. Swinden, “The spread of plastic yield from a notch,” Proc. R. Soc.,A272, No. 1350, 304–314 (1963).
J. Weertman, “Rate of growth of fatigue cracks calculated from the theory of infinitesimal dislocations distributed on a plane,” Proc. 1st Int. Conf. Fracture, Vol. 1, Sendai (1966), pp. 153–164.
B. L. Karihaloo, “Spread of plasticity from stacked stress concentrations,” Int. J. Solids Struct.,13, No. 3, 221–220 (1977).
W. Becker and D. Gross, “About the mode II Dugdale crack solution,” Int. J. Fract.,34, No. 1, 65–70 (1987).
W. Becker and D. Gross, “About the Dugdale crack under mixed mode loading,” ibid.,37, No. 3, 163–170 (1900).
W. Becker, “Dugdale-Risse unter Mixed Mole-Belastung bei isotropem und anisotropem Materialverhalten,” Z. Angew. Math. Mech.,70, No. 4, 209–291 (1990).
F. Erdogan and M. Ratwani, “Plasticity and the crack opening displacement in shells,” Int. J. Fract. Mech.,8, No. 4, 413–426 (1972).
E. S. Folias, “Estimating plastic zone sizes,” Int. J. Fract.,10, No. 1, 109–111 (1974).
F. Erdogan, “Plastic strip model for thin shells,” Prospects Fracture Mechanics, Leyden (1974), pp. 609–612.
V. A. Osadchuk, V. I. Kir'yan, and M. M. Nikolishin, “Opening at the tip of a through longitudinal crack in a cylindrical shell under internal pressure,” Probl. Prochn., No. 10, 64–67 (1984).
V. A. Osadchuk, State of Stress and Strain and Limiting Equilibrium in a Shell Containing Slits [in Russian], Naukova Dumka, Kiev (1985).
M. M. Nikolishin and A. G. Shabo, “Interaction in a longitudinal-slit system in a closed cylindrical shell on the basis of plastic strain,” Mat. Metody Fiz.-Mekh. Polya, No. 30, 50–55 (1989).
V. A. Osadchuk, M. M. Nikolishin, A. G. Shabo, and T. E. Maselko, “Limiting equilibrium in a shell weakened by cracks and made of work-hardening material,” Prikl. Mekh.,27, No. 2, 67–72 (1991).
J. L. Sanders, “Dugdale model for circumferential through cracks in pipes loaded by bending,” Int. J. Fract.,34, No. 1, 71–81 (1987).
V. A. Osadchuk, M. M. Nikolishin, and T. E. Maselko, “Limiting equilibrium of a spherical shell weakened by a crack and supported on an elastic base,” Prikl. Mekh.,22, No. 10, 47–52 (1986).
M. B. Civelek and F. Erdogan, “Elastic-plastic problem for a plate with a part-through crack under extension and bending,” Int. J. Fract.,20, No. 1, 33–46 (1982).
M. M. Nikolishin, “Opening of part-through cracks in a plate,” Mat. Metody Fiz. -Mekh. Polya, No. 26, 29–31 (1987).
F. Erdogan and M. Ratwani, “Fracture initiation and propagation in cylindrical shell containing an initial surface flaw,” Nucl. Eng. Des.,27, No. 1, 14–29 (1974).
S. Krenk, “Plasticity around an axial surface crack in a cylindrical shell,” Int. J. Pressure Vessels Pip.,7, No. 1, 1–11 (1979).
V. A. Osadchuk, M. M. Nikolishin, and V. I. Kir'yan, “Use of aδ k model analog for determining the opening of a part-through crack in a closed cylindrical shell,” Fiz.-Khim. Mekh. Mater., No. 1, 88–92 (1986).
F. Erdogan and F. Delale, “Ductile fracture of pipes and cylindrical containers with a circumferential flaw,” Trans. ASME. J. Pressure Vessel Technol.,103, No. 2, 160–168 (1981).
M. M. Nikolishin and A. G. Shabo, “Limiting equilibrium of a closed cylindrical shell containing P transverse surface crack,” Teor. Prikl. Mekh., No. 21, 83–86 (1990).
M. M. Nikolishin and T. E. Maselko, “Opening of a part-through crack in a spherical shell on the basis of plastic strain,” Mat. Metody Fiz.-Mekh. Polya, No. 28, 74–78 (1900).
I. M. Mikhovski, “Extension of the Dugdale model to bending of a plate containing a crack,” in: Researches on Elasticity and Plasticity [in Russian], No. 10 (1974), pp. 174–102.
W. Becker, “The problem of a Dugdale crack in a plate under normal bending,” Eng. Fract. Mech.,34, No. 5/6, 1063–1067 (1909).
S. Ya. Yarema and Z. M. Manyuk, “Plastic strain in an annular crack in a cylindrical specimen for various temperatures and loading rates,” Fiz.-Khim. Mekh. Mater., No. 2, 15–18 (1971).
Y. M. Mirsalimov, “Plastic-strain structure at a crack tip,” Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 6, 24–29 (1970).
J. R. Rice, “Limitations to the small scale yielding approximation for crack tip plasticity,” J. Mech. Phys. Solids,22, No. 1, 17–26 (1974).
G. P. Cherepanov, “Plastic discontinuity lines at the end of a crack,” Prikl. Mat. Mekh.,40, No. 4, 720–720 (1976).
L. A. Kipnis and G. P. Cherepanov, “Slip lines at the tip of a wedge crack,” ibid.,48, No. 1, 160–163 (1984).
K. K. Lo, “Modeling of plastic yielding at a crack tip by inclined slip planes,” Int. J. Fract.,15, No. 6, 583–589 (1979).
H. Riedel, “Plastic yielding on inclined slip planes at a crack tip,” J. Mech. Phys. Solids,24, No. 5, 277–289 (1976).
V. Vitek, “Yielding on inclined planes at the tip of a crack loaded in uniform tension,” ibid..
J. T. Evans, “Reverse shear on inclined planes at the tip of a sharp crack,” ibid.,27, No. 1, 73–88 (1979).
C. Atkinson and M. F. Kanninen, “A simple representation of crack tip plasticity: the inclined strip yield superdislocation model,” Int. J. Fract.,13, No. 2, 151–163 (1977).
L. M. Keer and T. Mura, “Stationary crack and continuous distributions of dislocations,” Proc. 1st Int. Conf. Fracture, Vol. 1, Sendai (1966), pp. 99–115.
F. A. Field, “Fluidity in a plate containing a crack in longitudinal shear,” J. ASME, Ser. E, No. 4, 162–163 (1963).
B. V. Kostrov and L. V. Nikitin, “A longitudinal-shear crack with an infinitely narrow plastic zone,” Prikl. Mat. Mekh.,31, No. 2, 334–336 (1967).
P. F. Arthur and W. S. Blackburn, “Antiplane strain around two equal collinear cracks and a crack containing dislocations in non-work-hardening elastic-plastic material loaded uniformly at infinity,” Int. J. Eng. Sci., No. 12, 975–988 (1970).
P. M. Vitvitskli and V. A. Kriven', “Growth of layer-type plastic zones in longitudinal shear in a body containing a periodic crack system,” Fiz.-Khim. Mekh. Mater., No. 3, 77–82 (1977).
P. M. Vitvitskii and V. A. Kriven', “Plastic-zone structure at the tip of a crack in antiplanar deformation,” Dokl. Akad. Nauk Ukr. SSR, No. 4, 32–36 (1981).
V. A. Kriven', “Continuous and discontinuous solutions to an elastoplastic problem on antiplanar deformation in a body containing a crack,” Fiz.-Khim. Mekh. Mater., No. 6, 10–16 (1985).
G. P. Cherepanov, “An elastoplastic treatment under antiplanar strain conditions,” Prikl. Mat. Mekh.,26, No. 4, 697–700 (1962).
E. Smith, “Strain concentration effect in large structures,” Proc. R. Soc.,A285, No. 1400, 40–59 (1965).
R. W. Lardner, “Plastic yield on inclined slip planes at the tip of a crack deformed in anti-plane strain,” Int. J. Fract. Mech.,4, No. 3, 299–319 (1968).
J. R. Rice, “On the theory of perfectly plastic anti-plane straining,” Mech. Mater.,3, No. 1, 55–80 (1984).
F. Erdogan, “Elastic-plastic antiplane problems for bonded dissimilar media containing cracks and cavities,” Int. J. Solids Struct.,2, No. 3, 447–465 (1966).
M. Ya. Leonov and V. V. Panasyuk, “Growth of a crack of circular form in plan,” Dokl. Akad. Nauk Ukr. SSR, No. 2, 166–168 (1961).
E. Smith, “The stability of a penny-shaped crack in a solid subject to an applied tensile stress,” Int. J. Fract.,24, No. 4, 279–207 (1984).
Z. Olesiak and M. Wnuk, “Plastic deformation around an axisymmetric slit predicted by Dugdale's model,” Rozpr. Inz.,14, No. 1, 125–142 (1966).
Z. Olesiak and M. Wnuk, “Energy dissipation around an elastoplastic longitudinal slit with axial symmetry,” ibid., No. 3, 341–477.
M. Wnuk, “A criterion for reduction in the elastic compliance of a slit with axisymmetric surroundings under hydrostatic pressure,” ibid.,15, No. 4, 595–616 (1967).
Z. Olesiak, “Plastic zone due to thermal stress in an infinite solid containing a penny-shaped crack,” Int. J. Eng. Sci.,6, No. 2, 113–125 (1968).
Z. Olesiak and M. Wnuk, “Plastic energy dissipation due to a penny-shaped crack,” Int. J. Fract. Mech.,4, No. 4, 383–396 (1968).
M. K. Kassir, “Size of thermal plastic zones around an external crack,” ibid.,5, No. 3, 167–177 (1969).
A. Kobayashi and W. Moss, “Coefficients for stress intensity increase on stretching a plate containing a surface defect or a circular rod containing a ring notch,” in: New Methods of Estimating Metal Resistance to Brittle Failure [Russian translation], Mir, Moscow (1972), pp. 127–145.
Z. Olesiak and J. R. Shadley, “Plastic zone in a thick layer with a disc-shaped crack,” Int. J. Fract. Mech.,5, No. 4, 305–313 (1969).
B. M. Singh, A. Cardou, and M. C. Au, “Plastic zone correction in a stretched thick-walled cylinder with an internal circumferential crack,” Eng. Fract. Mech.,29, No. 4, 503–511 (1908).
C. Mattheck, P. Morawietz, D. Munz, and B. Wolf, “Ligament yielding of a plate with semielliptical surface cracks under uniform tension,” Int. J. Pressure Vessels Pip.,16, No. 2, 131–143 (1984).
C. Mattheck and D. Gross, “A Dugdale model including strain hardening for through wall and surface cracks,” Trans. 8th Int. Conf. Struct. Mech. React. Techn., Brussels, 1985, Vol. G. Amsterdam (1985), pp. 107–194.
A. E. Andreikiv, V. V. Panasyuk, and I. N. Pan'ko, “Theory of the limiting equilibrium for cylindrical specimens with external ring cracks,” Fiz.-Khim. Mekh. Mater., No. 3, 29–39 (1974).
M. M. Stadnik, “The equivalent-state method for the approximate determination of crack opening,” ibid., No. 6, 114–116 (1986).
Author information
Authors and Affiliations
Additional information
Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 28, No. 1, pp. 49–68, January–February, 1992.
Rights and permissions
About this article
Cite this article
Panasyuk, V.V., Savruk, M.P. Model for plasticity bands in elastoplastic failure mechanics. Mater Sci 28, 41–57 (1992). https://doi.org/10.1007/BF00723631
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00723631