Two-parameter model of a mode I crack in an elastoplastic body under plane-strain conditions

International Applied Mechanics

Volumn 41, Issue 6, 2005, Pages 621-630

  Kaminskii, A A ^a   Galatenko, G V ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

Dugdale crack model; Fracture toughness; Generalized model; Plane strain; Plane stress state; Plastic zone; Small scale yielding; T stresses

Indexed keywords

DUGDALE CRACK MODEL; GENERALIZED MODEL; PLANE STRAIN; PLANE STRESS STATE; PLASTIC ZONE; SMALL-SCALE YIELDING; T-STRESSES;

ELASTOPLASTICITY; FRACTURE TOUGHNESS; STRAIN; STRESSES;

CRACKS;

EID: 26444560591     PISSN: 10637095     EISSN: 15738582     Source Type: Journal    
DOI: 10.1007/s10778-005-0130-4     Document Type: Article

References (47)

1. B. D. Annin and G. P. Cherepanov, Elastoplastic Problem [in Russian], Nauka, Novosibirsk (1983).
2. A. N. Guz, "Description and study of some nonclassical problems of fracture mechanics and related mechanisms," Int. Appl. Mech., 36, No. 12, 1537-1564 (2000).
3. G. V. Galatenko, "Generalized model of a Dugdale crack," Int. Appl. Mekh., 25, No. 3, 260-265 (1989).
4. G. V. Galatenko, "Elastoplastic fracture of an isotropic plate with a crack under biaxial loading," Int. Appl. Mech., 25, No. 7, 706-711 (1989).
5. G. V. Galatenko, "Toward an elastoplastic model of a normal-break crack under deformation," Int. Appl. Mech., 28, No. 9, 572-578 (1992).
6. GOST 25-506-85. Strength Design and Testing. Methods for Mechanical Testing of Metals. Determination of Crack Resistance (Fracture Toughness) under Static Loading [in Russian], Moscow (1985).
7. A. A. Kaminskii, G. V. Galatenko, and O. S. Degtyareva, "Elastoplastic fracture of an orthotropic plate with a crack under biaxial loading," Prikl. Mekh., 26, No. 8, 93-98 (1990).
8. A. A. Kaminskii, O. S. Degtyareva, and G. V. Galatenko, "Fracture of orthotropic elastoplastic composites with cracks under biaxial loading," Mekh. Komp. Mater., No. 2, 284-291 (1991).
9. A. A. Kaminskii and O. S. Bogdanova, "Long-term crack resistance of an orthotropic viscoelastic plate with a crack under biaxial loading. Safe loads," Int. Appl. Mech., 31, No. 9, 747-753 (1995).
10. A. A. Kaminskii and O. S. Bogdanova, "Modelling the failure of orthotropic materials subject to biaxial loading," Int. Appl. Mech., 32, No. 10, 813-819 (1996).
11. M. Ya. Leonov, P. M. Vitvitskii, and S. Ya. Yarema, "Plastic bands in plates with a crack-like concentrator under tension," Dokl. AN SSSR, 148, No. 3, 541-544 (1963).
12. N. I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).
13. A. N. Guz, M. Sh. Dyshel', and V. M. Nazarenko, Nonclassical Problems of Fracture Mechanics, Vol. 4 Book 1 of the four-volume series Fracture and Stability of Cracked Materials [in Russian], Naukova Dumka, Kiev (1992).
14. V. V. Panasyuk, Limit Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1968).
15. V. V. Panasyuk and M. P. Savruk, "Model of plastic bands in elastoplastic problems in fracture mechanics," Fiz.-Khim. Mekh. Mater., No. 2, 49-68 (1992).
16. V. Z. Parton and E. M. Morozov, Mechanics of Elastoplastic Fracture [in Russian], Nauka, Moscow (1985).
17. Fracture Toughness Testing and Its Applications, ASTM STP. 381, ASTM, Phila (1965).
18. L. P. Khoroshun, "Nonlinear crack mechanics," Int. Appl. Mech., 30, No. 11, 827-833 (1994).
19. G. P. Cherepanov, "Crack propagation in a continuous medium," Prikl. Mat. Mekh., 31, No. 3, 476-488 (1967).
20. N. J. J. Adams, "Some comments on the effect of biaxial stress on fatigue crack growth and fracture," Eng. Fract. Mech., No. 5, 983-989 (1973).
21. G. Alpa, E. Bozzo, and L. Gambarotta, "Validity limits of the Dugdale model for thin cracked plates under biaxial loading," Eng. Fract. Mech., No. 12, 523-529 (1979).
22. C. Betegon and J. W. Hancock, "Two-parameter characterization of elastic-plastic crack-tip fields," Trans. ASME, J. Appl. Mech., 58, 104-110 (1991).
23. British Standards Institution. Methods for Crack Opening Displacement Testing, BS 5762-1979 (1979).
24. Y. Z. Chen, "Closed form solutions of T-stress in plane elasticity crack problems," Int. J. Solids Struct., 37, 1629-1637 (2000).
25. D. S. Dugdale, "Yielding of steel sheets containing slits," J. Mech. Phys. Solids, 8, No. 2, 100-108 (1960).
26. T. Fett, "T-stresses in rectangular plates and circular disks," Eng. Fract. Mech., 60, No. 5, 631-652 (1998).
27. G. P. Cherepanov (ed.), Fracture: A Topical Encyclopedia of Current Knowledge, Krieger, Malabor (1998).
28. G. V. Galatenko, "Model of plastic deformation at the front of a circular crack under nonaxisymmetric loading," Int. Appl. Mech., 39, No. 1, 105-109 (2003).
29. G. V. Galatenko, "The stress intensity factor for an elliptic crack under a piecewise-constant load," Int. Appl. Mech., 38, No. 7, 854-860 (2002).
30. G. V. Galatenko, "A ring-shaped plastic zone at an elliptic crack under triaxial axisymmtric loading," Int. Appl. Mech., 40, No. 2, 218-225 (2004).
31. A. A. Griffith, "The phenomena of rupture and flow in solids," Phyl. Trans. Roy. Soc., Ser. A, 221, No. 1, 163-198 (1921).
32. J. W. Hutchinson, "Singular behavior at the end of a tensile crack in a hardening material," J. Mech. Phys. Solids, 16, 13-31 (1968).
33. G. R. Irwin, "Analysis of stresses and strain near end of a crack traversing a plate," J. Appl. Mech., 24, No. 3, 361-364 (1957).
34. A. A. Kaminskii, L. A. Kipnis, and M. V. Dudik, "Initial development of the prefracture zone near the tip of a crack reaching the interface between dissimilar media," Int. Appl. Mech., 40, No. 2, 176-182 (2004).
35. A. A. Kaminsky, L. A. Kipnis, and M. V. Dudyk, "Modeling of the crack tip plastic zone by two slip lines and the order of stress singularity," Int. J. Fracture, 126, No. 4, L89-L93 (2004).
36. S. G. Larsson and A. J. Carlsson, "Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic plastic materials," J. Mech. Phys. Solids, 21, 17-26 (1973).
37. P. S. Leevers and J. Radon, "Inherent stress biaxiality in various fracture specimen geometries," Int. J. Fracture, 19, 311-325 (1982).
38. G.P. Nikishkov, A. Bruckner-Foit, and D. Munz, "Calculation of the second fracture parameter for finite cracked bodies using a three-term elastic-plastic asymptotic expansion," Eng. Fract. Mech., 52, 685-701 (1995).
39. N. P. O'Dowd and C. F. Shih, "Family of crack-tip fields characterized by a triaxiality parameter. I. Structure of fields," J. Mech. Phys. Solids, 39, 989-1015 (1991).
40. E. Orowan, "Fracture and strength of solids," Rep. Prog. Phys., 12, 185-232 (1949).
41. J. R. Rice and G. F. Rosengren, "Plane strain deformation near a crack tip in a power-law hardening material," J. Mech. Phys. Solids, 16, 1-12 (1968).
42. S. M. Sharma and N. Aravas, "Determination of higher-order terms in asymptotic elastoplastic crack tip solutions," J. Mech. Phys. Solids, 39, 1043-1072 (1991).
43. P. M. Vitvitskii, V. V. Panasyuk, and S. Ya. Yarema, "Plastic deformation around crack and fracture criteria," Eng. Fract. Mech., No. 7, 305-319 (1975).
44. A. A. Wells, "Critical tip opening displacement as fracture criteria," in: Proc. Crack Propagation Symp., Granfield, 1 (1961), pp. 210-221.
45. M. L. Williams, "On the stress distribution at the base of a stationary crack," ASME, J. Appl. Mech., 24, 111-114 (1957).
46. L. Xia, T. C. Wang, and C. F. Shih, "Higher-order analysis of a crack tip in power-law hardening material," J. Mech. Phys. Solids, 41, 665-687 (1993).
47. S. Yang, Y. J. Chao, and N. A. Sutton, "Higher order asymptotic fields in a power-law hardening material," Eng. Fract. Mech., 45, 1-20 (1993).