Abstract
The first investigation of the review [1] presented an analysis and synthesis of the basic mechanical concept and mathematical methodes used in solving three-dimensional problems of the theory of cracks. On the basic of these mechanical concepts and methodes many investigators have solved a number of spatial problems of the theory of cracks to which the second portion of the review is devoted.
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Literature cited
V. V. Panasyuk, A. E. Andreikiv, and M. M. Stadnik, “Spatial problems of the theory of cracks (a review). Part 1. Basic mechanical concepts and mathematical methods in spatial problems of the theory of cracks,” Fiz.-Khim. Mekh. Mater., No. 4, 39–55 (1979).
R. A. Sack, “Extension of the Griffith theory of rupture to three dimensions,” Proc. Phys. Soc.,58, 729–736 (1946).
V. I. Mossakovskii, “The first basic problem of the theory of elasticity for a space with a flat round slit,” Prikl. Mat. Mekh.,19, No. 4, 441–452 (1955).
V. V. Panasyuk and A. E. Andreikiv, “The question of failure of a brittle body with a penny-shaped round crack,” Prikl. Mekhanika,3, No. 12, 28–33 (1967).
F. W. Smith, A. S. Kobayashi, and A. F. Emory, “Stress intensity factors for penny-shaped cracks,” Trans. ASME, Ser. E, J. Appl. Mech.,34, No. 4, 947–952 (1967).
J. Clarence Bell, “Stresses from variously loaded circular cracks,” J. Struct. Div., Proc. Am. Soc. Civ. Eng.,103, No. 2, 355–376 (1977).
V. I. Zhuravlev and A. D. Alekseev, “The criterion of failure of brittle rocks weakened by a crack with a variable shear load,” Fiz.-Tekh. Probl. Razrabotka Polezn. Iskopaemykh, No. 5, 55–65 (1972).
A. E. Andreikiv, “The shear of an unlimited elastic space weakened by a plane crack,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 7, 601–603 (1977).
J. R. Barber, “The penny-shaped crack in shear and related contact problems,” Int. J. Eng. Sci.,13 No. 9, 815–829 (1975).
L. M. Keer, “A note on shear and combined loading for a penny-shaped crack,” J. Mech. and Phys. Solids,14, No. 1, 1–6 (1966).
V. T. Dovnorovich, “The stressed and deformed state of a brittle half-space under the action of specified tangential displacements of the points of a round area of a boundary plane,” in: Reviews of Papers for the Conference on “Science and Technical Progress in Mechanical Engineering” [in Russian], Gomel', 1974, Minsk (1974), pp. 49–50.
R. A. Westmann, “Asymmetric mixed boundary-value problems of the elastic half-space,” Trans. ASME,E32, No. 2, 411–417 (1965).
A. D. Dement'ev, “The influence of the disposition of external forces on the size of a penny-shaped crack,” Fiz.-Tekh. Probl. Razrabotka Polezn. Iskopaemykh, No. 6, 101–102 (1973).
P. Paris and J. Sih, “An analysis of the stressed state near a crack,” in: Applied Questions of Fracture Toughness [Russian translation], Mir, Moscow (1968), pp. 64–142.
Z. Bilek and F. Semela, “Beitrag zur Ausbreitung eines pfennigformingen Risses im spröden Körper,” Z. Angew Math. Mech.,51, No. 6, 487–489 (1971).
C. Atkinson, “An iterative scheme for solving problems relating to cracks opening under a displacementdependent internal stress,” Int. J. Fract. Mech.,6, No. 2, 193–197 (1970).
A. F. Emery and F. W. Smith, “Some basic properties of penny-shaped cracks,” Mathematika,13, No. 2, 172–180 (1966).
L. M. Keer, “Stress distribution at the edge of an equilibrium crack,” J. Mech. and Phys. Solids,12, No. 3, 149–163 (1964).
L. M. Keer, “Mixed boundary value problems for a penny-shaped cut,” J. Elast.,5, No. 2, 89–98 (1975).
I. N. Sneddon, “A note on the problem of the penny-shaped crack,” Proc. Cambridge Philos. Soc.,61, No. 2, 601–611 (1965).
I. N. Sneddon, “Transform solutions of crack problems in the theory of elasticity,” Z. Angew Math. Mech.,49, No. 1–2, 15–23 (1969).
I. Sneddon and J. Tweed, “The stress intensity factor for a penny-shaped crack in an elastic body under the action of symmetric body forces,” Int. J. Fract. Mech.,3, No. 4, 291–299 (1967).
L. M. Keer, “Nonaxisymmetric punch and crack problems for initially stressed bodies,” Quart. Appl. Math.,23, No. 2, 97–107 (1965).
H. D. Bui, “An integral equations method for solving the problem of a plane crack of arbitrary shape,” J. Mech. and Phys. Solids,25, No. 1, 29–39 (1977).
V. I. Mossakovskii and R. L. Mossakovskaya, “The strength of an elastic space weakened by a plane crack close to round,” Gidroaeromekh. Teoriya Uprugosti, No. 22, 56–74 (1977).
W. S. Blackburn and T. K. Hellen, “Calculation of stress intensity factors in three dimensions by finite element methods,” Int. J. Numer. Meth. Eng.,11, No. 2, 211–229 (1977).
J. T. Guidera and R. W. Lardner, “Penny-shaped cracks,” J. Elast.,5, No. 1, 59–73 (1975).
W. D. Collins, “Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks. II. Cracks in solids under torsion,” Mathematika,9, No. 17, 25–37 (1962).
R. L. Salganik, “Longitudinal shear axially symmetric cracks,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 77–80 (1962).
V. I. Mossakovakii and M. T. Rybka, “Generalizing the Griffith-Sneddon criterion for the case of an inhomogeneous body,” Prikl. Mat. Mekh.,28, No. 6, 1061–1069 (1964).
F. Erdogan and K. Arin, “A penny-shaped interface crack between an elastic layer and a half-space,” Int. J. Eng. Sci.,10, No. 2, 115–125 (1972).
M. Lowengrub and I. N. Sneddon, “The effects of internal pressure on a penny-shaped crack at the interface of two bonded dissimilar elastic half-spaces,” Int. J. Eng. Sci.,12, No. 5, 387–396 (1974).
D. V. Grilitskii and A. P. Poddubnyak, “The torsion of a two-layer elastic medium with a flat slit or a rigid inclusion,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 1, 85–93 (1975).
V. I. Rakitin, “A penny-shaped crack at the interface of a piezoelectric and a solid,” Tr. Mosk. Inst. Khim. Mashinostr., No. 56, 14–22 (1974).
V. I. Mossakovakii, P. Yu. Berkovich, and V. M. Rybka, “The composite axially symmetric problem of the theory of elasticity for a piece-by-piece homogeneous space with a round slit in the plane of the interface,” Dop. Akad. Nauk UkrSSR, Ser. A, No. 9, 812–816 (1978).
F. Erdogan, “Stress distribution in loaded dissimilar materials containing circular or ring-shaped cavities,” Trans. ASME,E32, No. 4, 829–836 (1965).
M. K. Kassir and A. M. Bregman, “The stress intensity factor for a penny-shaped crack between two dissimilar materials,” Trans. ASME,E39, No. 1, 308–310 (1972).
V. M. Vainshel'baum and R. V. Gol'dshtein, One Class of Composite Axially Symmetric Problems of the Theory of Elasticity for a Multilayer Medium [in Russian], Preprint No. 61, Inst. Probl. Mekh. Akad. Nauk SSSR, Moscow (1975).
V. M. Vainshel'baum and R. V. Gol'dshtein, “The axially symmetric problem of a crack on the interface of the layers in a multilayer medium,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 130–143 (1976).
Bohuslav Novotný, “Some aspects of numerical analysis of a multilayer halfspace,” Acta Techn. C SAV,20, No. 4, 382–396 (1975).
K. Arin and F. Erdogan, “A penny-shaped crack in an elastic layer bonded to a dissimilar half space,” Int. J. Eng. Sci.,9, No. 2, 213–232 (1971).
V. M. Vainshel'baum, R. V. Gol'dshtein, and V. M. Entov, The Influence of a Penny-Shaped Cavity on the Stressed State of an Inhomogeneous Elastic Medium with a Plane Interface [in Russian], Preprint No. 44, Inst. Probl. Mekh. Akad. Nauk SSSR, Moscow (1974).
F. Erdogan, “Fracture problems in composite materials,” Eng. Fract. Mech., No. 4, 811–840 (1972).
L. M. Smelyanskaya and A. S. Tokar', “The strength of a composite layer weakened by a flat round crack,” Prikl. Mekh.,7, No. 10, 73–80 (1971).
M. Lowengrub and I. Sneddon, “The effect of a shear on a penny-shaped crack at the interface of an elastic half-space and a rigid foundation,” Int. J. Eng. Sci., No. 10, 899–913 (1972).
L. M. Keer, S. H. Chen, and Maria Comminou, “The interface penny-shaped crack reconsidered,” Int. J. Eng. Sci.,16, No. 10, 765–772 (1978).
Vladimir Weiss, “Vznik trhlin v disperzne viztuženém betonu a v přibuzných materiálech,” Stavebn. čas ČCSSR,19, No. 3–4, 289–304 (1971).
F. Erdogan and A. H. Pacella, “A penny-shaped crack in a filament-reinforced matrix. Part I. The filament model” Int. J. Solids Struct.,10, No. 7, 785–805 (1974).74).
A. H. Pacella and F. A. Erdogan, “A penny-shaped crack in a filament-reinforced matrix. Part II. The crack problem,” Int. J. Solids Struct.,10, No. 7, 807–819 (1974).
T. V. Narayanan and F. Erdogan, “A penny-shaped crack in a fiber-reinforced matrix,” Int. J. Solids Struct.,11, No. 12, 1315–1327 (1975).
N. V. Pal'tsun and A. K. Privarnikov, “The stressed state near a slit in a space with a variable modulus of elasticity,” Prikl. Mekh.,3, No. 9, 138–141 (1967).
V. I. Zhuravlev, “The contact problem of the theory of elasticity for an inhomogeneous medium and its application to the failure of solids,” in: Theoretical and Applied Mechanics. The Republic Inderdepartmental Subject Scientific and Technical Conference [in Russian], No. 6 (1975), pp. 40–50.
E. Deutsch, “The axially symmetric crack problem for an infinite elastic medium with transverse isotropy,” Arch. mech. stosowanej,16, No. 1, 65–80 (1964).
G. P. Zaitsev, “The question of the limit equilibrium of plates and bodies of brittle orthotropic materials with cracks,” Probl. Prochn., No. 8, 74–79 (1977).
W. T. Chen and R. P. Soni, “On a circular crack in a transversely isotropic elastic material under prescribed shear stress,” IBMJ Res. Developm.,9, No. 3, 192–195 (1965).
R, W. Lardner and G. E. Tupholme, “A note on arbitrarily loaded penny-shaped cracks in hexagonal crystals,” J. Elast.,6, No. 2, 221–224 (1976).
R. Ya. Suncheleev, “Elastic equilibrium of an unlimited transversely isotropic body weakened by an internal plane round notch,” Prikl. Mat. Mekh.,30, No. 3, 579–583 (1966).
E. Smith, “A note on the growth of a penny-shaped crack in a general uniform applied stress field,” Int. J. Fract. Mech.,7, No. 3, 339–342 (1971).
A. E. Andreikiv, “Determining the limiting loads for an unlimited body with an external round crack,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 141–144 (1969).
V. V. Panasyuk, The Limit Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1968).
Ya. S. Uflyand, “The elastic equilibrium of an unlimited body weakened by an external round notch,” Prikl. Mat. Mekh.,23, No. 1, 101–108 (1959).
V. V. Panasyuk, “Determining the failure load for a body weakened by an external round crack,” in: Questions of the Mechanics of a Real Solid [in Russian], No. 1, Naukova Dumka, Kiev (1962), pp. 63–66.
M. Lowengrub and I. N. Sneddon, “The distribution of stress in the vicinity of an external crack in an infinite elastic solid,” Int. J. Eng. Sci.,3, No. 4, 451–460 (1965).
R. Ya. Suncheleev, “The deformation of an unlimited transversely isotropic body weakened by an external round slit,” Inzh. Zh. Mekh. Tverd. Tela, No. 3, 116–118 (1966).
V. V. Panasyuk, “One spatial problem of the theory of elasticity for an isotropic body with an elliptical crack,” Prikl. Mekh.,8, No. 3, 248–257 (1962).
G. R. Irwin, “The crack-extension force for a part-through crack in a plate,” Trans. ASME,E29, No. 4, 651–654 (1962).
R. C. Shah and A. S. Kobayashi, “The stress intensity factor for an elliptical crack under arbitrary normal loading,” Eng. Fract. Mech.,3, No. 1, 71–96 (1971).
M. K. Kassir and G. C. Sih, “Three-dimensional stress distribution around an elliptical crack under arbitrary loadings,” Trans. ASME,E33, No. 3, 601–611 (1966).
F. W. Smith and D. R. Sorensen, “The elliptical crack subjected to nonuniform shear loading,” Trans. ASME,E41, No. 2, 502–506 (1974).
Toshikazu Shibuya, “An infinite body containing a plane elliptical crack under the action of shear,” Bull. JSME,21, No. 153, 375–380 (1978).
G. C. Sih and B. C. Cha, “A fracture criterion for three-dimensional crack problems,” Eng. Fract.Mech.,6, No. 4, 699–723 (1974).
Yu. N. Podil'chuk, “A plane elliptical crack in an arbitrary uniform field of stresses,” Prikl. Mekh.,4, No. 8, 94–100 (1968).
L. Mirandy and B. Paul, “Stresses at the surface of a flat three-dimensional ellipsoidal cavity,” Trans. ASME, H98, No. 2, 164–172 (1976).
Toshikazu Shibuya, “Some boundary problems for an infinite body containing a flat elliptical crack,” Nihon Kikai Gakkai Rombunsyu, Trans. Jpn. Soc. Mech. Eng.,42, No. 364, 3718–3725 (1976).
V. I. Mossakovskii and L. R. Mossakovskaya, “One relationship in the theory of equilibrium of flat cracks,” in: Hydroaeromechanics and the Theory of Elasticity, Inter-university Scientific Collection [in Russian], No. 14 (1972), pp. 103–108.
M. K. Kassir and G. C. Sih, “Griffith's theory of brittle fracture in three dimensions,” Int. J. Eng. Sci.,5, No. 12, 899–918 (1967).
V. V. Panasyuk and A. E. Andreikiv, “The limit equilibrium condition of an unlimited brittle body with an arbitrarily oriented elliptical crack,” Fiz.-Khim. Mekh. Mater., No. 1, 116–118 (1969).
R. J. Hartranft and G. C. Sih, “Stress singularity for a crack with an arbitrary curved front,” Eng. Fract. Mech.,9, No. 3, 705–718 (1977).
W. T. Chen, “Some aspects of a flat elliptical crack under shear stress,” J. Math. and Phys.,45, No. 2, 213–223 (1966).
M. K. Kassir and G. C. Sih, “Three-dimensional stress around elliptical cracks in transversely isotropic solids,” Eng. Fract. Mech.,1, No. 2, 327–345 (1968).
J. R. Willis, “The stress field around an elliptical crack in an anisotropic elastic medium,” Int. J. Eng. Sci.,6, No. 5, 253–263 (1968).
I. A. Kunin, G. M. Mirenkova, and É. G. Sosnina, “An ellipsoidal crack and a needle in an anisotropic medium,” Prikl. Mat. Mekh.,37, No. 3, 524–533 (1973).
N. Laws, “A note on interaction energies associated with cracks in anisotropic solids,” Phil. Mag.,36, No. 2, 367–372 (1977).
M. K. Kassir, “On the problem of an external elliptical crack in an infinite solid,” Trans. ASME, E,35, No. 2, 422–424 (1968).
M. K. Kassir and G. C. Sih, “An external elliptical crack in an elastic solid,” Int. J. Fract. Mech.,4, No. 4, 347–356 (1968).
V. V. Panasyuk and A. E. Andreikiv, “The limit equilibrium of an unlimited brittle body weakened by an external crack,” Prikl. Mekh.,5, No. 1, 87–91 (1969).
A. E. Andreikiv, “The propagation of an external crack elliptical in plan view,” in: The First Republic Conference of Young Scientists on the Mechanics of a Deformed Solid (1969), Reviews of the Papers [in Russian] Inst. Mekhaniki Akad. Nauk UkrSSR, Kiev (1969), p. 6.
J. R. Willis, “The distribution of stress in an anisotropic elastic body containing an exterior crack,” Int. J. Eng. Sci., No. 7, 559–574 (1970).
M. K. Kassir, “A note on mixed boundary-value problems in nonhomogeneous elasticity,” J. Elast.,4, No. 4, 317–321 (1974).
V. S. Gubenko and I. F. Filimonov, “A plane circular notch in an elastic half-space, “Tr. Dnepropetr. Inst. Inzh. Zh.-d. Transp., No. 50, 165–168 (1964).
V. S. Gubenko, “One type of integral transformations,” Prikl. Mekh.,1, No. 4, 67–72 (1965).
V. T. Grinchenko and A. F. Ulitko, “The tension of an elastic half-space weakened by a ring crack,” Prikl. Mekh.,1, No. 10, 61–64 (1965).
B. I. Smetanin, “The question of tension of an elastic half-space containing a plane ring slit,” Prikl. Mat. Mekh.,32, No. 3, 458–462 (1968).
R. P. Kanwai and M. L. Pasha, “Axially symmetric stress distributions in elastic solids containing ringshaped cracks under torsion,” Trans. ASME,E41, No. 2, 516–517 (1974).
Toshikazu Shibuya, Takashi Koizumi, and Ichiro Nakahara, “The axially symmetric problem of torsion of an infinite body with a plane ring crack,” Nihon Kikai Gakkai Rombunsyu, Trans. Jpn. Soc. Mech. Eng.,41, No. 352, 3391–3397 (1975).
T. Hara, T. Shibuya, T. Koizurami, and I. Nakahara, “Asymmetric distribution of stresses in bending of an elastic solid containing a plane crack,” Nihon Kikai Gakkai Rombunsyu, Trans. Jpn. Soc. Mech. Eng.,44, No. 379, 771–771 (1978).
M. M. Stadnik, “Failure of a three-dimensional brittle solid weakened by an internal plane crack,” Prikl. Mekh.,9, No. 4, 117–120 (1973).
M. Higuchi and Y. Imai, “The circumferential crack extension force in a normal-anisotropic elastic body,” Bull. ISME,15, No. 79, 21–24 (1975).
M. Kumar and A. Atsumi, “A pressurized annular crack in a transversely Isotropic medium,” Lett. Appl. Eng. Set.,4, No. 6, 443–455 (1976).
A. E. Andreikiv, V. V. Panasyuk, and M. M. Stadnik, “The failure of brittle bodies weakened by systems of cracks,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 54–58 (1975).
V. V. Panasyuk and M. D. Dmitrakh, “Before the question of the kinetics of extension of an internal oval crack in a brittle body,” Visn. L'vivsk. Politekh. Inst., No. 66, 27–37 (1972).
N. D. Dmitrakh, “Determining the failure load for a brittle body with a plane oval crack,”Vestn. L'vovsk. Politekh. Inst., Dokl. Nauchn. Soobshch., No. 7, 74–77 (1976).
V. V. Panasyuk, “Some spatial problems of the theory of equilibrium cracks in a brittle body being deformed,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 85–93 (1962).
V. V. Panasyuk, “The extension of a crack which in plan view has a shape close to round,” Dop. Akad. Nauk UkrSSR, No. 7, 891–895 (1962).
V. V. Panasyuk, “Some spatial problems of the theory of equilibrium of brittle bodies with a crack,” in: Questions of the Mechanics of a Real Solid [in Russian], No. 2, Naukova Dumka, Kiev (1964), pp. 3–26.
V. V. Panasyuk and N. D. Dmitrakh, “The limit equilibrium of a three-dimensional solid with an internal plane crack having in plan view the form of an oval,” Prikl. Mekh.,5, No. 5, 107–111 (1969).
M. D. Dmitrakh, “Determining the critical loads for a body with a macrocrack which in plan view has a form close to round,” Zbirnik Nauk. Robit Aspirantiv L'viv. Politekh. Inst., No. 5, 44–50 (1971).
R. V. Gol'dshtein, Kh. S. Kestenboim, and L. N. Savova, “Calculating the growth of some forms of plane cracks in three-dimensional brittle bodies,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 89–95 (1972).
R. V. Gol'dshtein and V. M. Entov, “Variation determinations for the stress intensity factor on the contour of a normal rupture plane crack,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 59–64 (1975).
Z. Bažant, “Three-dimensional harmonic functions near termination or intersection of gradient singularity lines: A general numerical method,” Int. J. Eng. Sci.,12, 221–243 (1974).
A. E. Andreikiv and M. M. Stadnik, “Propagation of a plane crack with a piece-by-piece smooth contour,” Prikl. Mekh., No. 10, 50–56 (1974).
A. Ya. Aleksandrov and B. M. Zinov'ev, “An approximate method of solution of plane and spatial problems of elasticity for bodies with reinforced elements and notches,” in: The Mechanics of Deformed Bodies and Structures [in Russian], Mashinostroenie, Moscow (1975), pp. 15–25.
John Weaver, “Three-dimensional crack analysis,” Int. J. Solids and Struct.,13, No. 4, 321–330 (1977).
R. V. Gol'dshtein, V. M. Entov, and A. F. Zazovskii, “The solution of composite boundary problems by a direct variation method,” in: Numerical Methods of the Mechanics of a Continuum [in Russian], Vol. 7, No. 5, Novosibirsk (1976), pp. 5–13.
R. C. Shah and A. S. Kobayashi, “On the parabolic crack in an elastic solid,” Eng. Fract. Mech.,1, No. 2, 309–325 (1968).
M. K. Kassir, “The distribution of stress around a flat parabolic crack in an elastic solid,” Eng. Fract. Mech.,2, No. 4, 373–385 (1971).
L. T. Boiko, V. A. Zyuzin, and V. I. Mossakovskii, “A spherical notch in an elastic space,” Dokl. Akad. Nauk SSSR,181, No. 6, 1357–1360 (1968).
N. L. Prokhorova and Yu. I. Solov'ev, “The axially symmetric problem for an elastic space with a spherical notch,” Prikl. Mat. Mekh.,40, No. 4, 692–698 (1976).
L. T. Boiko, “A spherical notch in an elastic space under the action of internal pressure,” Prikl. Mekh.,8, No. 4, 54–61 (1972).
A. A. Kapshivyi and N. V. Nogin, “Solution of the basic problems of the axially symmetric theory of elasticity for a space with a spherical notch,” Mat. Fiz. Resp. Mezhved. Sb., No. 9, 38–47 (1971).
V. A. Zyuzin and S. A. Smirnov, “Solution of the problem of a spherical notch in an elastic space,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 5, 427–430 (1977).
Ya. S. Uflyand and E. S. Melenevskaya, “The torsion of an elastic space weakened by a spherical notch,” Prikl. Mekh.,7, No. 2, 111–114 (1971).
M. A. Martynenko and A. F. Ulitko, “The stressed state close to the tip of a spherical notch in an unlimited elastic medium,” Prikl. Mekh.,14, No. 9, 15–23 (1978).
V. Kh. Sirunyan, “A cylindrical crack in an elastic space,” ïzv. Akad. Nauk ArmSSR, Mekh.,27, No. 4, 3–24 (1974).
Ya. V. Shlyapoberskii, “An asymptotic solution of the spatial problem of equilibrium of an elastic body with a notch,” Prikl. Mat. Mekh.,42, No. 3, 532–539 (1978).
Tadahiko Kawai, “A singular solution of a general surface crack problem,” Seisen Ken Kyn, Mon, J. Inst. Ind. Sci., Univ. Tokyo,28, No. 2, 74–77 (1976).
Tadahiko Kawai and Yoshinobu Fujitani, “Analysis of three-dimensional surface crack problems byboundary in integral method,” Seisen Ken Kyn Mon, J. Inst. Ind. Sci., Univ. Tokyo,28, No. 2, 70–73 (1976).
N. M. Stoyan, “Another basic axially symmetric problem for an elastic space with a hyperbolic notch,” Visn. Kiivsk. Univ., Mat., Mekh., No. 20, 117–123 (1978).
Yu. A. Borshch and A. V. Stezhko, “The compression of a space weakened by a round axially symmetric slit,” in: The Resistance of Materials and the Theory of Structures. Republic Interdepartmental Scientific and Technical Collection [in Russian], No. 22 (1974), pp. 29–34.
Yu. A. Borshch and N. G. Goncharev, “The compression of a space weakened by an external axially symmetric slit,” in: Mathematical Physics. Republic Interdepartmental Collection [in Russian], No. 18 (1975), pp. 65–69.
N. N. Lebedev and Ya. S. Uflyand, “The spatial problem of the theory of elasticity for an unlimited body weakened by two flat round cracks,” Tr. Leningr. Politekh. Inst., No. 210, 39–49 (1960).
W. D. Collins, “Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks. I. Cracks in an infinite solid and a thick plate,” Proc. Roy. Soc.,A266, No. 1326, 359–386 (1962).
Yu. N. Kuz'min, “The elastic equilibrium of a space containing periodically distributed round slits,” Inzh. Zh. Mekh. Tverd. Tela, No. 2, 140–143 (1966).
Yu. N. Kuz'min, “The axially symmetric problem of the theory of elasticity for an unlimited body having two coaxial slits of different radiuses,” Inzh. Zh. Mekh. Tverd. Tela, No. 6, 129–135 (1966).
M. L. Pasha, “Axially symmetric stress distributions in elastic solids containing penny-shaped cracks under torsion,” Trans. ASME,E42, No. 4, 896–897 (1975).
A. A. Kapshivyi and N. P. Kopystyra, “Axially symmetric problems for an elastic space with a system of coaxial round notches,” Prikl. Mekh.,10, No. 10, 113–119 (1974).
A. A. Kapshivyi and N. P. Kopystyra, “The first basic axially symmetric problem for an elastic space with two round coaxial notches,” in: Calculation and Applied Mathematics. Inderdepartment Scientific Collection [in Russian], No. 33 (1977), pp. 3–10.
A. E. Andreikiv and V. V. Panasyuk, “The limit equilibrium of a brittle body weakened by a system of axially symmetric external cracks,” Fiz.-Khim. Mekh. Mater., No. 3, 338–344 (1969).
V. V. Panasyuk and O. É. Andreikiv, “The boundary equilibrium of a brittle body weakened by two external cracks,” Dop. Akad. Nauk UkrRSR, Ser. A, No. 9, 823–827 (1969).
I. V. Kim, “The elastic equilibrium of an unlimited orthotropic space weakened by two elliptical notches,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 74–80 (1971).
Ya. S. Uflyand, Integral Transformations in Problems of the Theory of Elasticity [in Russian], Nauka, Moscow-Leningrad (1968).
Ya. S. Uflyand, “The torsion of a brittle body containing spherical notches,” in: Successes in the Mechanics of Media Being Deformed [in Russian], Nauka, Moscow (1975), pp. 545–550.
A. E. Andreikiv and V. V. Panasyuk, “The elastic equilibrium of a body weakened by a system of round cracks located in a single plane,” Dokl. Akad. Nauk SSSR,197, No. 2, 312–314 (1971).
A. E. Andreikiv and V. V. Panasyuk, “The composition problem of the theory of elasticity for a halfspace with round interfaces of the boundary conditions,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 26–32 (1972).
A. E. Andreikiv, V. V. Panasyuk, and M. M. Stadnik, “The failure of brittle prismatic beams weakened by round internal cracks,” Probl. Prochn., No. 10, 37–41 (1972).
M. M. Stadnik and V. P. Silovanyuk, “The tension of prismatic beams with round cracks,” Fiz.-Khim. Mekh. Mater., No. 6, 84–88 (1978).
A. E. Andreikiv and M. M. Stadnik, “The bending of a rectangular brittle beam weakened by a round internal crack,” Fiz.-Khim. Mekh.Mater., No. 4, 77–79 (1972).
F. W. Smith and M. J. Alavi, “Stress intensity factors for a penny-shaped crack in a half-space,” Eng. Fract. Mech.,3, No. 3, 241–254 (1971).
A. E. Atidreikiv, V. V. Panasyuk, and M. M. Stadnik, “The question of determining the stress intensity factors in solids with cracks,” Probl. Prochn., No. 3, 45–50 (1974).
M. M. Stadnik, “Determining the stress intensity factor in bending of a beam with a round crack,” Fiz.-Khim. Mekh. Mater., No. 3, 114–115 (1979).
G. N. Savin, Yu. N. Podil'chuk, and A. P. Zhurba, “Bending of an elastic beam with a crack elliptical in plan view,” Prikl. Mekh.,7, No. 8, 44–52 (1971).
W. D. Collins, “Some complanar punch and crack problems in three-dimensional elastostatics,” Proc. Roy. Soc.,A274, No. 1359, 507–528 (1963).
A. F. Ulitko, “The tension of an elastic space weakened by two round cracks lying in a single plane,” in: Stress Concentration [in Russian], Naukova Dumka, Kiev (1968), pp. 201–208.
W. S. Fu and L. M. Keer, “Complanar circular cracks under shear loading,” Int. J, Eng. Sci.,7, No. 4, 361–372 (1969).
V. V. Panasyuk, O. E. Andreikiv, and M. M. Stadnik, “Determining the boundary equilibrium of a brittle tody weakened by a system of cracks close tn plan view to round,” Dop. Akad. Nauk UrkRSR, Ser A., No. 6, 541–544 (1973).
L. R. Hall and A. S. Kobayashi, On the Correction of Stress Intensity Factors for Two Embedded Cracks, Boeing Structural Development Research Memorandum, No. 9, May, 1964.
O. E. Andreikiv, “One spatial problem of the theory of cracks,” Dop. Akad. Nauk UkrRSR, Ser. A, No. 4, 313–316 (1969).
V. V. Panasyuk and A. E. Andreikiv, “One problem of limit equilibrium for an unlimited brittle body with a crack,” Prikl. Mekh.,6, No. 6, 25–29 (1970).
A. A. Kapshivyi and G. F. Maslyuk, “A solution of the first basic axially symmetric problem of thetheory of elasticity for a space with plane cracks by the method of p-analytical functions,” in: Computer and Applied Mathematics Interdepartmental Scientific Collection [in Russian], No. 8 (1969), pp. 65–79.
A. E. Andreikiv and V. V. Panasyuk, “The elastic equilibrium of an unlimited body weakened by a system of concentric cracks,” Prikl. Mekh.,6, No. 4, 124–128 (1970).
G. M. Valov, “The deformation of an elastic space having concentric circular slits,” in; Elasticity and Inelasticity [in Russian], No. 4, Mosk. Univ., Moscow (1975), pp. 36–49.
V. V. Panasyuk, O. E. Andreikiv, and M. M. Stadnik, “The failure of a brittle body weakened by a system of circular cracks,” Dop. Akad. Nauk UkrRSR, Ser. A, No. 9, 807–900 (1971).
A. E. Andreikiv, “Three-dimensional problems of the theory of cracks for quasibrittle bodies,” Fiz.-Khim. Mekh. Mater., No. 3, 54–60 (1976).
G. S. Kit, M. V. Khai, and I. P. Lauishnik, “The first basic problem of the theory of elasticity for a body with penny-shaped cracks,” Mat. Metody Fiz.-Mekh. Polya, No. 7, 26–32 (1978).
A. E. Andreikiv, “The elastic equilibrium of an unlimited body weakened by a system of arbitrarily oriented round cracks,” Fiz.-Khim. Mekh. Mater., No. 1, 76–78 (1979).
G. S. Kit, “A general method of solving spatial problems of thermal conductivity and thermal elasticity for a body with penny-shaped cracks,” Prikl. Mekh.,13, No. 12, 18–24 (1977).
Bernard Budiansky and Richard J. O'Connell, “Elastic moduli of a cracked solid,” Int. J. Solids Struct.,12, No. 2, 81–97 (1976).
Yu. N. Kuz'min, and Ya. S. Uflyand, “The axially symmetric problem of the theory of elasticity for a half-space weakened by a plane round slit,” Prikl. Mat. Mekh.,29, No. 6, 1132–1137 (1965).
Yu. N. Kuz'min, “The axially symmetric deformation of an elastic layer containing coaxial slits,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 121–130 (1972).
K. N. Srivastava and Kripal Singh, “The effect of a penny-shaped crack on the distribution of stress in a semi-infinite solid,” Int. J. Eng. Sci.,7, No. 5, 469–490 (1969).
V. M. Aleksandrov, “The theory of equilibrium cracks in an elastic layer,” in: Stress Concentration [in Russian], No. 1, Naukova Dumka, Kiev (1965), pp. 39–45.
R. C. Shah and A. S. Kobayashi, “Stress intensity factors for an elliptical crack approaching the surface of a semi-infinite solid,” Int. J. Fract.,9, No. 2, 133–146 (1973).
A. Nisitani and Y. Murakami, “Stress intensity factors of an elliptical crack or a semi-elliptical crack subjected to tension,” Int. J. Fract.,10, No. 3, 353–368 (1974).
Ya. S. Uflyand, “Stress concentration in an elastic layer weakened by a round slit,” Nauch.-Tekh. Inform. Byull. Leningr. Politekh. Inst. Fiz.-Mat. Nauki, No. 8, 56–61 (1959).
M. Lowengrub, “Stress in the vicinity of a crack in a thick elastic plate,” Quart. Appl. Math.,19, No. 2, 119–126 (1961).
V. N. Aleksandrov and B. I. Smetanin, “An equilibrium crack in a thin layer,” Prikl. Mat. Mekh.,29, No. 4, 782–785 (1965).
N. V. Pal'tsun, “The critical stresses for a layer weakened by a flat round slit,” in: Materials of the Interuniversity Conference of Young Scientists and Mathematicians [in Russian], Khar'kov (1966), pp. 106–109.
N. V. Pal'tsun, “The axially symmetric problem of the theory of elasticity for a layer weakened,by a flat round slit,” in: Some Questions of Applied Mathematics [in Russian], No. 3, Naukova Dumka, Kiev (1967), pp. 153–164.
B. I. Smetanin, “Some problems of slits in an elastic wedge and a layer,” Tnzh. Zh. Mekh. Tverd. Tela, No. 2, 115–122 (1968).
Y. M. Tsai, “Stress distribution crack shape and energy for a penny-shaped crack in a plate of finite thickness,” Eng. Fract. Mech.,4, No. 1, 155–169 (1972).
R. E. Kalaba and E. A. Zagustin, “Exact solution for the stress concentration in a slot,” Int. J. Eng. Sci.,10, No. 6, 491–502 (1972).
G. K. Dhawan, “The distribution of stress in the vicinity of an external crack in an infinite thick plate,” Acta Mech.,16, No. 3–4, 225–270 (1973).
I. M. Keer, “A class of non-symmetrical punch and crack problems,” Quart. J. Mech. Appl. Math.,17, No. 4, 423–436 (1964).
G. K. Dhawan, “Asymmetric distribution of stress in a thick plate containing a penny-shaped crack,” Indian J. Pure Appl. Math.,3, No. 5, 729–734 (1972).
O. P. Piddubnyak, “The torsion of an elastic sphere weakened by a round slot,” Visn. L'vivs'k. Univ., Ser. Mekh.-Mat., No. 9, 69–74 (1974).
A. S. Kobayashi, M. Ziv, and L. R. Hall, “The approximate stress intensity factor for an embedded elliptical crack near two parallel free surfaces,” Int. J. Fract. Mech.,1, No. 2, 81–95 (1965).
V. S. Gubenko, “The problem of a round punch coupled with a half-space and of a layer weakened by a circular slit,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Mekh. Mashinostr., No. 5, 151–153 (1961).
Takashi Koizumi, Toshkazu Shibuya, Tchiro Nakahara, and Shuno Tanaka, “A crack problem in a slab with an annular crack subjected to pressure,” Bull. JSME,20, No. 139, 17–23 (1977).
M. Kumar and A. Atsumi, “A pressurized annular crack in a transversely Isotropic slab,” Acta Mech.,26, No. 1–4, 321–330 (1977).
V. S. Nikitin and G. S. Shapiro, “Local axially symmetric compression of an elastic layer weakened by a ring or circular slits,” Prikl. Mat. Mekh.,38, No. 1, 139–144 (1974).
N. V. Pal'tsun, “The stresses in an elastic layer weakened by two round slits,” Prikl. Mekh.,3, No. 2, 62–70 (1967).
N. V. Pal'tsun, “The critical stresses for a layer with two cracks,” in: Republic Interdepartment Scientific and Technical Collection [in Russian], No. 7 (1968), pp. 72–78.
A. E. Andreiklv, “The limit equilibrium state of a layer weakened by a system of parallel external cracks which are round in plan view,” Fiz.-Khim. Mekh. Mater.,12, No. 5, 65–70 (1976).
K. N. Srivastava and J. P. Dwivedi, “The effect of a penny-shaped crack on the distribution of stress in an elastic sphere,” Int. J. Eng. Sci.,9, No. 4, 399–420 (1971).
Masanori Abe and Akira Atumi, “The distribution of elastic stresses in a composite sphere containing a penny-shaped crack,” Nihon Kikai Gakkai Rombunsyu, Trans. Jpn. Soc. Mech. Eng.,41, No. 352, 3399–3409 (1975).
F. W. Smith, A. F. Emery, and A. S. Kobayashi, “Stress intensity factors for semicircular cracks,” Trans. ASME,E34, No. 4, 953–959 (1967).
G. P. Cherepanov, “The brittle strength of vessels under pressure,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 90–101 (1969).
J. S. Raju and J. C. Newman, “Improved stress-intensity factors of semi-elliptical surface cracks in finite-thickness plates,” in: Trans. 4th Int. Conf. Struct. Mech in Reactor Technol., San Francisco, Calif., 1977, Vol. 6, G 5.8/1-G 5.8/14, Amsterdam et al., (1977).
Satya N. Atluri and K. Kathiresan, “Stress analysis of typical flaws in aerospace structural components using 3-D hybrid displacement finite element method, “ in: AIAA/ASME 19th Struct. Dyn. and Mater. Conf., Bethesda, Md., 1978, New York (1978), pp. 340–350.
W. S. Blackburn and T. K. Hellen, “Finite element stress intensity evaluations in two and three dimensions,” in: Fract. Mech. Eng. Pract. Pap.Annu. Conf., Stress Anal. Group, Inst. Phys., Sheffield, 1976, London (1977), pp. 97–112.
R. P. Hartranft and G. C. Sih, “An alternating method applied to edge and surface crack problems,” in: Mech. Fracture, Vol. 1, Leyden (1973), pp. 179–238.
Hiroshi Miyamoto, “Application of the finite element method to failure mechanics, Part I,” Sosei To Kako, J. Jpn. Soc. Technol. Plast.,14, No. 153, 847–854 (1973).
J. R. Rice and N. Levy, The Part-Through Surface Crack in an Elastic Plate, ASME Paper N APM-20 (1971).
R. C. Shah and A. S. Kobayashi, “An elliptical crack in a finite-thickness plate subjected to tensile and bending loading,” Trans. ASME,J96, No. 1, 47–54 (1974).
F. W. Smith and D. R. Sorensen, “The semi-elliptical surface crack. A solution by the alternating method,” Int. J. Fract.,12, No. 1, 47–57 (1976).
G. G. Chell, “The stress intensity factors for part through thickness embedded and surface flaws subjected to a stress gradient,” Eng. Fract. Mech.,8, No. 2, 331–340 (1976).
A. S. Kobayashi, “Crack opening displacement in a surface flawed plate subjected to tension or plate bending,” in: Proc. 2nd Int. Conf. Mech. Behav. Mater., Boston, Mass., 1976, S. 1 (1977), pp. 1073–1077.
T. G. Gray, “Convenient closed form stress intensity factors for common crack configurations,” Int. J. Fract.,13, No. 1, 65–75 (1977).
A. S. Kobayashi, N. Polvanich, A. F. Emery, and W. J. Lowe, “Inner and outer cracks in internally pressurized cylinders,” Trans. ASME,J99, No. 1, 83–89 (1977).
Asao Nishimura, Shigeru Aoki, and Masaru Sokata, “The stress intensity factor for a semielliptical crack in a cylinder under the action of internal pressure,” Nihon Nikai Gakkai Rombunsyu, Trans. Jpn. Soc. Mech. Eng.,43, No. 363, 3192–3199 (1977).
W. T. Fujimoto, “Determination of crack growth and fracture toughness parameters for surface flaws emanating from fastener holes,” Proc. AIAA/ASME/SAE 17th Struct., Struct. Dyn., and Mater. Conf., King of Prussia, Pa., 1976, S. 1, pp. 522–531.
T. E. Kullgren, F. W. Smith, and G. P. Ganong, “Quarter elliptical cracks emanating from holes in plates,” Trans. ASME, J. Eng. Mater. Technol.,100, No. 2, 144–149 (1978).
R. P. Srivastav and P. Narain, “Stress distribution due to a pressurized exterior crack in an infinite Isotropie medium with a coaxial cylinder cavity,” Int. J. Eng. Sci.,4, No. 6, 689–697 (1966).
R. P. Srivastav and D. Lee, “Axisymmetric external crack problems for media with cylindrical cavities,” Int. J. Eng. Sci.,10, No. 3, 217–232 (1972).
L. M. Keer, V. K. Luk, and J. M. Freedman, “A circumferential edge crack in a cylindrical cavity,” Trans. ASME,E44, No. 2, 250–254 (1977).
R. J. Hartranft and G. C. Sih, “An approximate three-dimensional theory of plates with application to crack problems,” Int. J. Eng. Sci.,8, No. 8, 711–729 (1970).
G. C. Sih and R. J. Hartranft, “Variation of strain energy release rate with plate thickness,” Int. J. Fract. Mech.,9, No. 1, 75–82 (1973).
M. Shmuely and Z. S. Alterman, “A three-dimensional numerical analysis of stress distribution in the vicinity of a crack tip,” Isr. J. Technol.,9, No. 5, 523–530 (1971).
E. S. Folias, “On the three-dimensional theory of cracked plates,” Trans. ASME,E42, No. 3, 663–674 (1975).
Yoichi Sumi and Yoshiyuki Yamamoto, “Three-dimensional analysis of the stress intensity factors in problems of a through crack,” Nihon Kakai Gakkai Rombunsyu. Trans. Jpn. Soc. Mech, Eng.,44, No. 378, 413–418 (1978).
D. Ayers, “A numerical procedure for calculating stress and deformation near a slit in a three-dimensional elastic-plastic solid,” Eng. Fract. Mech.,2, 87–106 (1970).
P. P. Voroshko, “Determining the three-dimensional stressed state of a rectangular beam with a center through crack,” Probl. Prochn., No. 4, 9–14 (1979).
J. P. Benthem, “The state of stress at the vertex of a quarter infinite crack in a half-space,” Int. J. Solids Struct.,13, No. 5, 479–492 (1977).
M. K. Kassir and G. C. Sih, “Application of Papkovich-Neuber potentials to a crack problem,” Int. J. Solids Struct.,9, No. 5, 643–654 (1973).
R. J. Hartranft and G. C. Sih, “Three-dimensional growth characteristics of a plane crack subjected to concentrated forces,” Trans. ASME,E41, No. 3, 808–809 (1974).
D. O. Harris, “Slicing procedure for approximate three-dimensional Green's functions for cracks in plates of finite thickness,” Int. J. Fract.,9, No. 1, 21–32 (1973).
H. Neiber, Stress Concentration [in Russian], Obed. Gos. Izd., Moscow (1947).
B. M. Wundt, A Unified Interpretation of Room Temperature Strength of Notch Specimens as Influenced by Size, ASME Paper, N59 (1959), Met-9.
G. R. Irwin, “Fracture mechanics,” in: Structural Mechanics, Proc. 1st Symposium of Naval Structure Mechanics (1960), pp. 557–591.
H. F. Bueckner, Discussion of Reference 4, Fracture Toughness Testing and Its Applications, ASTM Special Technical Publication N 381, Philadelphia, Pa. (1965), pp. 82–83.
D. P. Clausing, “Stress and strain distribution in a tension specimen with a circumferential notch,” J. Mater.,4, No. 3, 566–582 (1969).
A. A. Wells, “Crack opening displacements from elastic-plastic analysis of externally notched tension bars,” Eng. Fract. Mech.,1, No. 3, 399–410 (1969).
S. Ya. Yarema, “Stress intensity factors for cylindrical samples with an external crack of variable depth,” Fiz. Khim. Mekh. Mater., No. 1, 87–89 (1970).
A. E. Andreikiv, V. V. Panasyuk, and I. N. Pan'ko, “The theory of limit equilibrium of cylindrical samples with external circular cracks,” Fiz.-Khim. Mekh. Mater., No. 3, 29–39 (1974).
A. Kobayasi and W. Moss, “Coefficients of the increase in stress intensity in tension of a plate with a surface defect and of a round rod with a circular notch,” in: New Methods of Rating the Resistance of Materials to Brittle Failure [Russian translation], Mir, Moscow (1972), pp. 127–145.
D. O. Harris, “Stress intensity factors for hollow circumferentially notched round bars,” Trans. ASME,D89, No. 1, 49–54 (1967).
D. J. Hayes and J. G. Williams, “A practical method for determining the Dugdale model solution for cracked bodies of arbitrary shape,” Int. J. Fract. Mech.,8, No. 3, 239–256 (1972).
L. M. Keer, J. M. Freedman, and H. A. Watts, “An infinite tensile cylinder with a circumferential edge crack,” Lett. Appl. Eng. Sci.,5, No. 2, 129–139 (1977).
Y. Muzakami and H. Nishitani, “The stress intensity factor in tension of a round rod with a circular crack,” Nihon Kikkai Gakkai Rombunsyu, Trans. Jpn., Soc. Mech. Eng.,41, No. 342, 360–367 (1975).
I. D. Lubahn, “Experimental determination of the energy release rate for notch bending and notch tension,” Proc. ASTM,59, 885–913 (1959).
V. V. Panasyuk, A. E. Andreikiv, and S. E. Kovchik, “Experimental determination of the fracture toughness of structural materials,” Fiz.-Khim. Mekh. Mater., No. 2, 10–17 (1976).
J. N. Sneddon and R. J. Tait, “The effect of a penny-shaped crack on the distribution of stress in a long circular cylinder,” Int. J. Eng. Sci.,1, 391–409 (1963).
W. D. Collins, “Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks,” Proc. Edinburgh Math. Soc.,13, No. 1, 69–78 (1962).
I. N. Pan'ko, “The question of the limit equilibrium state of a quasibrittle cylinder with an internal round crack,” in: Materials of the Seventh Conference of Young Scientists of the Physicomechanical Institute of the Academy of Scientists of the Ukrainian SSR. Section on the Physicochemical Mechanics of Materials (L'vov, 1975) [in Russian], Dep. in the All-Union Institute for Scientific and Technical Information No. 1138–76 (1976), pp. 140–142.
G. C. Sih, “On the crack-tip stress intensity factors for cylindrical bars under torsion,” J. Aerospace Sci.,29, No. 10, 1265–1266 (1962).
G. C. Sih, “Strength of stress singularities at crack tips for flexural and torsional problems,” Trans. ASME,E30, No. 30, 419–425 (1963).
N. B. Romalis, “Failure in torsion of a round bar with a crack on the arc of the circumference,” Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 121–125 (1970).
M. K. Kassir, “A note on the twisting deformation of a nonhomogeneous shaft containing a circular crack,” Int. J. Fract. Mech.,8, No. 3, 325–334 (1972).
B. I. Kudryavtsev and V. Z. Parton, “The torsion and tension of a cylinder with an external circular notch,” Prikl. Mat. Mekh.,37, No. 2, 316–325 (1973).
G. B. Kuzina and N. B. Romalis, “The distribution of radial cracks in a round bar in torsion,” Zh. Prikl. Mekh. Tekh. Fiz., No. 1, 169–171 (1974).
J. Tweed and G. Longmuir, “The torsion problem for a circular cylinder with a radial edge crack,” J. Eng. Math.,9, No. 2, 117–125 (1975).
Paul J. Blatz, “Finite elastic deformation of a plane strain wedge-shaped radial crack in a compressible cylinder,” in: Intern. Sympos. Nonlinear Differential Equations and Nonlinear Mech., Colorado Springs, 1961, Academic Press, New York-London (1963), pp. 193–210.
A. F. Emery and C. M. Segedin, “The evaluation of the stress intensity factors for cracks subjected to tension, torsion, and flexure by an efficient numerical technique,” Trans. ASME,D94, No. 2, 387–393 (1972).
G. P. Nikishkov and E. M. Morozov, “The stress intensity factors for circular cracks in heavy walled tabes intension,” Probl. Prochn., No. 6, 44–48 (1976).
R. Erdol and F. A. Erdogan, “A thick-walled cylinder with an axisymmetric internal or edge crack,” Trans. ASME, J. Appl. Mech.,45, No. 2, 281–286 (1978).
Kazuyoshi Suzuki, Toshikari Shibuya, and Takashi Kiozumi, “The torsion of an infinite hollow cylinder with an external crack,” Int. J. Eng. Sci.,16, No. 10, 707–715 (1978).
J. P. Benthem and W. T. Koiter, “Asymptotic approximations to crack problems,” in: Mechanics of Fracture, Vol. 1, Leyden (1973), pp. 131–178.
V. V. Panasyuk, A. E. Andreikiv, S. E. Kovchik, et al., “Determining the characteristics of KIc by bending of a cylindrical sample with a circular crack,” Fiz.-Khim. Mekh. Mater., No. 2, 3–9 (1976).
V. V. Panasyuk, A. E. Andreikiv, and S. E. Kovchik, Methods of Rating the Crack Resistance of Structural Materials [in Russian], Naukova Dumka, Kiev (1977).
A. E. Andreikiv, The Failure of Quasibrittle Bodies with Cracks in the Complex Stressed State [in Russian], Naukova Dumka, Kiev (1979).
A. N. Zlatin, “The tension of a cylinder containing periodically distributed penny-shaped cracks,” Dokl. Akad. Nauk SSSR,241, No. 6, 1300–1302 (1978).
G. P. Cherepanov, The Mechanics of Brittle Failure [in Russian], Nauka, Moscow (1974).
D. D. Ivlev, “A theory of quasibrittle failure cracks,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 88–128 (1967).
V. Z. Parton and E. M. Morozov, The Mechanics of Elastoplastic Failure [in Russian], Nauka, Moscow (1974).
G. I. Barenblatt, “A mathematical theory of equilibrium cracks formed in brittle failure,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 3–56 (1961).
H. Libowitz, J. Eftis, and D. L. Jones, “Some recent theoretical and experimental developments infracture mechanics,” in: Advances in Research on the Strength and Fracture of Materials, 4th Int. Conf. Fract., Waterloo, 1977, Vol. 1, New York et al. (1978), pp. 695–723.
G. C. Sih, Handbook of Stress Intensity Factors, Vol. 1, Lehigh Univ. Press, Bethelehem (1973).
I. N. Sneddon and M. Lowengrub, Crack Problems in the Classical Theory of Elasticity, John Wiley and Sons, New York (1969).
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Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 15, No. 5, pp. 45–65, September–October, 1979.
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Panasyuk, V.V., Andreikiv, A.E. & Stadnik, M.M. Spatial problems of the theory of cracks (a review). Mater Sci 15, 467–484 (1980). https://doi.org/10.1007/BF00729239
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DOI: https://doi.org/10.1007/BF00729239