On the consequences of T-stress in elastic brittle fracture

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 462, Issue 2072, 2006, Pages 2415-2437

  Smith, D J ^a   Ayatollahi, M R ^b   Pavier, M J ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Brittle fracture; Mode I; Mode II; T stress

Indexed keywords

EID: 33845519169     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2005.1639     Document Type: Article

References (60)

1. ABAQUS, V 5.7 1997 User's manual. Providence, RI: Hibbitt, Karlsson and Sorensen.
2. Anderson, T. L. 1995 Fracture mechanics; fundamentals and applications, 2nd edn. Ann Arbor, MI: CRC Press.
3. Atkinson, C., Smelser, R. E. & Sanchez, J. 1982 Combined mode fracture via the cracked Brazilian disc test. Int. J. Fract. 18, 279-291.
4. Awaji, H. & Sato, S. 1978 Combined mode fracture toughness measurement by the disc test. J. Eng. Mater. Technol. 100, 175-182.
5. Ayatollahi, M. R. & Aliha, M. R. M. 2005 Cracked Brazilian disc specimen subjected to mode II deformation. Eng. Fract. Mech. 72, 493-503.
6. Ayatollahi, M. R. & Aliha, M. R. M. In press. On determination of mode II fracture toughness using semi-circular bend specimen. Int. J. Solids Struct. (doi:10.1016/j.ijsolstr.2005.07.049)
7. Ayatollahi, M. R., Pavier, M. J. & Smith, D. J. 1996 On mixed mode loading of a single edge notched specimen. Int. J. Fract. 82, R61-R66. (doi:10.1007/BF00013242)
8. Ayatollahi, M. R., Pavier, M. J. & Smith, D. J. 1998 Determination of T-stress from finite element analysis for mode I and mixed mode I/II loading. Int. J. Fract. 91, 283-298. (doi:10.1023/A:1007581125618)
9. Ayatollahi, M. R., Pavier, M. J. & Smith, D. J. 2002a Mode I cracks subjected to large T-stresses. Int. J. Fract. 117, 159-174. (doi:10.1023/A: 1020973802643)
10. Ayatollahi, M. R., Smith, D. J. & Pavier, M. J. 2002b Crack tip constraint in mode II deformation. Int. J. Fract. 113, 153-173. (doi:10.1023/A:1015504414612)
11. Banks-Sills, L. & Arcan, M. 1986 A compact mode II fracture specimen. In Fracture mechanics (ed. J. H. Underwood, R. Chait, C. W. Smith, D. P. Wilhelm, W. A. Andrews & J. C. Newman), vol. 17, ASTM STP 905, pp. 347-363. Philadelphia, PA: ASTM.
12. Banks-Sills, L. & Bortman, Y. 1986 A mixed-mode fracture specimen: analysis and testing. Int. J. Fract. 30, 181-201. (doi:10.1007/BF00019776)
13. Betegon, C. & Hancock, J. W. 1991 Two-parameter characterization of elastic-plastic crack-tip fields. J. Appl. Mech. 58, 104-110.
14. Bhattacharjee, D. & Knott, J. F. 1995 Effect of mixed mode I and II loading on the fracture surface of polymethyl methacrylate (PMMA). Int. J. Fract. 72, 359-381. (doi:10.1007/BF00040373)
15. Chang, S. H., Lee, C. I. & Jeon, S. 2002 Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Eng. Geol. 66, 79-97. (doi:10.1016/S0013-7952(02)00033-9)
16. Chao, Y. J. & Zhang, X. H. 1997 Constraint effect in brittle fracture. In Fatigue and fracture mechanics: 27th Symposium, ASTM STP 1296 (ed. R. S. Piascik, J. C. Newman & D. E. Dowling), pp. 41-60. Philadelphia, PA: American Society for Testing and Materials.
17. Chao, Y. J., Liu, S. & Broviak, B. J. 2001 Brittle fracture: variation of fracture toughness with constraint and crack curving under mode I conditions. Exp. Mech. 41, 232-241. (doi:10.1007/BF02323139)
18. Cotterell, B. 1966 Notes on the paths and stability of cracks. Int. J. Fract. Mech. 2, 526-533.
19. Cotterell, B. & Rice, J. R. 1980 Slightly curved or kinked cracks. Int. J. Fract. 16, 155-169. (doi:10.1007/BF00012619)
20. Davenport, J. C. W. & Smith, D. J. 1993 A study of superimposed fracture modes I, II, III on PMMA. Fatigue Fract. Eng. Mater. Struct. 16, 1125-1133.
21. Doll, W. 1989 Fractography and failure mechanisms of amorphous thermoplastics. In Fractography and failure mechanisms of polymers and composites (ed. A. C. Roulin-Moloney). Essex, England: Elsevier, pp. 387-436.
22. Erdogan, F. & Sih, G. C. 1963 On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. Trans. ASME 85, 519-527.
23. Ewing, P. D. & Williams, J. G. 1974 Further observations on the angled crack problem. Int. J. Fract. 10, 135. (doi:10.1007/BF00955093)
24. Finnie, I. & Saith, A. 1973 A note on the angled crack problem and the directional stability of cracks. Int. J. Fract. 9, 484-486.
25. Fowler, H., Smith, D. J. & Bell, K. 1997 Scatter in cleavage fracture toughness following proof loading. Advances in fracture research, Proc. 9th Int. Conf. on Fracture, ICF 9, vol. 5, pp. 2519-2526.
26. Hadidimoud, S., Sisan, A. M., Truman, C. E. & Smith, D. J. 2002 Predicting how crack tip residual stresses influence brittle fracture, PVP 2002, vol. 434, pp. 111-116.
27. Hussain, M. A., Pu, S. L. & Underwood, J. 1974 Strain energy release rate for a crack under combined mode I and mode II. Fracture analysis, ASTM STP 560 pp. 2-28. Philadelphia, PA: American Society for Testing and Materials.
28. Khan, K. & Al-Shayea, N. A. 2000 Effect of specimen geometry and testing method on mixed I-II fracture toughness of a limestone rock from Saudi Arabia. Rock Mech. Rock Eng. 33, 179-206. (doi:10.1007/s006030070006)
29. Kosai, M., Shimamoto, A., Yu, C. T., Kobayashi, A. S. & Tan, P. W. 1996 A biaxial test specimen for crack arrest studies. Exp. Mech. 36, 277-283. (doi:10.1007/BF02318019)
30. Kosai, M., Shimamoto, A., Yu, C. T., Kobayashi, A. S. & Tan, P. W. 1999 Axial crack propagation and arrest in a pressurised cylinder: an experimental-numerical analysis. Exp. Mech. 39, 256-264. (doi:10.1007/ BF02329802)
31. Krishnan, G. R., Zhao, X. L., Zaman, M. & Roegiers, J. C. 1998 Fracture toughness of a soft sandstone. Int. J. Rock Mech. Min. Sci. 35, 695-710. (doi:10.1016/S0148-9062(97)00324-0)
32. Larsson, S. G. & Carlsson, A. J. 1973 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, 263-277. (doi:10.1016/0022-5096(73)90024-0)
33. Leevers, P. S. & Radon, J. C. 1982 Inherent stress biaxiality in various fracture specimen geometries. Int. J. Fract. 19, 311-325. (doi:10.1007/BF00012486)
34. Leevers, P. S., Radon, J. C. & Culver, L. E. 1976 Frature trajectories in a biaxially stressed plate. J. Mech. Phys. Solids 24, 381-395. (doi:10.1016/0022-5096(76)90010-7)
35. Li, F. Z., Shih, C. F. & Needleman, A. 1985 A comparison of methods for calculating energy release rate. Eng. Fract. Mech. 21, 405-421. (doi:10.1016/0013-7944(85)90029-3)
36. Liu, S. & Chao, Y. 2003 Variation of fracture toughness with constraint. Int. J. Fract. 124, 113-117. (doi:10.1023/B:FRAC.0000018230.97560. ae)
37. Liu, C., Huang, Y. & Stout, M. G. 1998 Enhanced mode-II fracture toughness of an epoxy resin due to shear banding. Acta. Mater. 46, 5647-5661. (doi:10.1016/S1359-6454(98)00253-5)
38. Maccagno, T. M. &: Knott, J. F. 1989 The fracture behaviour of PMMA in mixed modes I and II. Eng. Fract. Mech. 34, 65-86. (doi:10.1016/0013-7944(89) 90243-9)
39. Mahajan, R. V. & Ravi-Chandar, K. 1989 An experimental investigation of mixed-mode fracture. Int. J. Fract. 41, 235-252. (doi:10.1007/BF00018856)
40. O'Dowd, N. P. & Shih, F. C. 1991 Family of crack-tip fields characterized by a triaxiality parameter-I. Structure of field. J. Mech. Phys. Solids 39, 989-1015. (doi:10.1016/0022-5096(91)90049-T)
41. O'Dowd, N. P. & Shih, F. C. 1992 Family of crack-tip fields characterized by a triaxiality parameter-II. Fracture applications. J. Mech. Phys. Solids 40, 939-963. (doi:10.1016/0022-5096(92)90057-9)
42. Richard, H. A. 1981 A new shear specimen. Int. J. Fract. 17, R105-R107.
43. Ritchie, R. O., Knott, J. F. & Rice, J. R. 1973 On the relationship between critical stress and fracture toughness in mild steel. J. Mech. Phys. Solids 21, 395-410. (doi:10.1016/0022-5096(73)90008-2)
44. Royer, J. 1986 A specimen geometry for plane mixed modes. Eng. Fract. Mech. 23, 363-375.
45. Royer, J. 1988 Study of pure and mixed-mode fracture of a brittle material. Exp. Mech. 45, 382-387. (doi:10.1007/BF02325180)
46. Scherre, S. S., Botsis, J., Studer, M., Pini, M., Wiskott, H. W. A. & Belser, U. C. 2000 Fracture toughness of aged dental composites in combined mode I and mode II loading. J. Biomed. Mater. Res. (Appl. Biomater.) 53, 362-370. (doi:10.1002/1097-4636(2000)53:4 〈362::AID-JBM10〉 3.0.CO;2-S)
47. Selvarathinam, A. S. & Goree, J. G. 1998 T-stress based fracture model for cracks in isotropic materials. Eng. Fract. Mech. 60, 543-561. (doi:10.1016/S0013-7944(98)00032-0)
48. Shetty, D. K., Rosenfield, A. R. & Duckworth, W. H. 1987 Mixed-mode fracture in biaxial stress state: application of the diametral-compression (Brazilian disk) test. Eng. Fract. Mech. 20, 825-840. (doi:10.1016/0013-7944(87) 90032-4)
49. Sih, G. C. 1973 Methods of analysis and solutions of crack problems. In Mechanics of fracture vol. 1 (ed. G. C. Sih). Leiden: Noordhoff.
50. Smith, D. J., Ayatollahi, M. R. & Pavier, M. J. 2001 The role of T-stress in brittle fracture for linear elastic materials under mixed mode loading. Fatigue Fract. Eng. Mater. Struct. 24, 137-150. (doi:10.1046/j.1460- 2695.2001.00377.x)
51. Streit, R. & Finnie, I. 1980 An experimental investigation of crack-path directional stability. Exp. Mech. 20, 17-23. (doi:10.1007/BF02324422)
52. Suresh, S., Shih, C. F., Morrone, A. & O'Dowd, N. P. 1990 Mixed-mode fracture toughness of ceramic materials. J. Am. Ceram. Soc. 73, 1257-1267. (doi:10.1111/j.1151-2916.1990.tb05189.x)
53. Tada, H., Paris, P. C. & Irwin, G. R. 1985 The stress analysis of cracks handbook, 2nd edn. St Louis, MO: Paris Publications.
54. Ueda, Y., Ikeda, K., Yao, T. & Aoki, M. 1983 Characteristics of brittle fracture under general combined modes including those under bi-axial tensile loads. Eng. Fract. Mech. 18, 1131-1158. (doi:10.1016/0013-7944(83)90007- 3)
55. Ic-results. Eng. Fract. Mech. 19, 1085-1093.
56. Weibull, W. 1951 A statistical distribution function of wide applicability. J. Appl. Mech. 18, 293-297.
57. Williams, M. L. 1957 On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24, 109-114.
58. Williams, J. G. 1983 Fracture mechanics of polymers. Chichester, England: Ellis Honvood.
59. Williams, J. G. & Birch, M. W. 1976 Mixed mode fracture in anisotropic media, pp. 125-137, ASTM STP 601. Philadelphia, PA: American Society for Testing and Materials.
60. Williams, J. G. & Ewing, P. D. 1972 Fracture under complex stress-the angled crack problem. Int. J. Fract. 8, 441-446.