Engineering Transactions, 14, 1, pp. 125–142, 1966

Deformacja plastyczna wokół osiowo-symetrycznej szczeliny przedstawionej modelem Dugdale'a

Zbigniew OLESIAK
Instytut Podstawowych Problemów Techniki PAN

Miłosz WNUK
Politechnika Krakowska

Plastic strain around an axially symmetric crack represented by the Dugdale model

The introduction contains a brief discussion of a number of works of other authors concerning non-propagating cracks. Next, the method for determining the plastic region (according to Dugdale) is described in the case of the two-dimensional problem. The subsequent part of the paper is devoted to the determination of the range of plastic strain for an axially symmetric crack in a perfect elastic-plastic body.

The paper contains a table of the extent of plastic zone in function of the load and a diagram confronting the curves of the distributions of plastic strain zones computed by means of four formulae.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


Г. И. Баренблатт, О равновесмых трещинах, образующихся при хрупком разрушении, Прикл. Мат. Мех., 3, 4, 5, 23 (1959).

Г. И. Баренблатт, Математическая теория раыновесных трещин, образующихся при хрупком разрушении, ПМТФ, 4, 1961, 3.

B.A. Bilby, A.H. Cottrell, K.H. Swinden, The spread of plastic yield from a notch, Proc. Roy. Soc., A, No 1350, 272 (1960), 304.

F.P. Bowden, D. Tabor, Friction and Lubrication of Solids, Oxford University Press, Oxford 1962.

H.F. Bueckner, The propagation of cracks and the energy of elastic deformation, Trans. ASME, 6, 80 (1958).

W.D. Collins, On the solution of some axisymmetric boundary value problems by means of integral equations, Quart. J. Mech. Appl. Math., 1, 14 (1961), 101.

J. Cook, J.E. Gordon, А mechanisт for the control of crack propagation in all-brittle systems, Proc. Roy. Soc. A, No. 1391, 282 (1964), 508.

J. Dixon, W. Visser, An investigation of the elastic-plastic strain distribution around cracks in various sheet materials, Proc. Internat. Symp. Photoelasticity, Chicago 1961, Pergamon Press 1963.

L.H. Donnell, Stress concentrations due to elliptical discontinuities in plates under edge forces, Calif. Inst. Tech., T. von Karman Anniv., 1941, 293.

D.S. Dugdale, Yielding of steel sheets containing slits, J. Mech. Phys. Sol., 8 (1960), 100.

Я.И. Френкель, Теория обратимых и необратимых трещин в твердых телах, Ж. Тех. Физ. 11, 22 (1952), 1857.

N.E. Frost, Non-propagating cracks in vee-notched specimens subject to fatigue loading, The Aeronaut. Quart., 8 (1957), 1.

N.E. Frost, D.S. Dugdale, The propagation fatigue cracks in sheet specimens, J. Mech. Phys. Solids, 6 (1958), 92.

N.E. Frost, C.E. Phillips, Some observations on the spread fatigue cracks, Proc. Roy. Soc., A. 242 (1957), 216.

W. W. Gerberich, Plastic strains and energy density in cracked plates l . Experimental technique and results, Proc. SESA 2, 21 (1964), 335.

J.N. Goodier, F.A. Field, Plastic energy dissipation in crack propagation, Fracture or Solids, edited by D.C. Drucker and J.J. Gilman, New York 1963, 103.

A.E. Green, On Boussinesq's problem and penny-shaped cracks, Proc. Cambridge Phil. Soc., 45 (1949), 251.

A.A. Griffith, The phenomena of rupture and flow in solids, Phil. Trans., A, 221 (1921), 163.

A.K. Head, The growth of fatigue cracks, Phil. Mag., 44 (1953), 925.

A.K. Head, The propagation of fatigue cracks, J. Appl. Mech., 23 (1956), 407.

J. Hult, Experimental studies of fatigue crack propagation in torsion, Trans. Roy. Inst. Tech., Nr. 119, Stockholm 1958.

J. Hult, McClintock, Elastic-plastic stress and strain distributions around sharp notches under repeated shear, IX Int. Congr. Appl. Mech., Brussels 1956, Proceedings VIII, 51.

C.E. Innglis, Stresses in a plate due to the presence of cracks and sharp corners, Trans. Inst. Naval Archit., 55 (1913), 219.

G.R. Irwin, Analysis olstresses and strains near Ihe end ola crack traversing a plate, J. AppI. Mech., 3, 24 (1957).

G.R. Irwin, Fracture Mechanics, Pergamon Press, New York 1960.

J.A. Jacobs, Relaxation methods applied to problems of plastic flow I. Notched bar under tension, Phil. Mag., 41 (1950), 349.

С.Я. Ярема, Исследовагисе полос пластичности при растяжении пластин г концен¬тратором, Вопросы Мех. Реального Твердого Тела, 2, Изд. «Наукова Думка», Киев 1964, 177.

I. Kobayashi, Darstellung eines Potentiales in Zylinderschen Koordinaten das sich aus einer Ebene innerhalb und ausserhalb einer Kreisbegrenzung verschiedene Grenzbedingung unterwurft, Sci. Rep. Tohoku Imp. Univ., 20 (1931), 197.

Г.И. Корнилов, С.Я. Ярема, Плоские ообразуы с трек:иновидным кон центратором для экспериментального исследования полос пластичности, Вопросы мех. реального твердого тела, Изд. АН УССР, 7, Киев 1962.

М.Я. Леонов, Элементы теории хрупкого разрушения ПМТФ, 3 (1961), 85.

М.Я. Леонов, Н.Я. IDвайко, Упруго-пластическая деформация при кручении стержня с мелким гголуцылиндрическим разам на поверхности, Вопросы мех. реального твердого тела, Изд. АН УССР, 1, Киев 1962.

N.F. Mott, Fracture of metals theoretical consideration, Engineering 4275, 165 (1948), 4276.

S.A.F. Murrell, The theory of the propagation of elliptical Griffith cracks under various conditions of plane strain or р1апе stress, Brit. J. Арр1. Phys., 15 (1964), part. I, 1195, part. II and III, 1211.