Abstract
This paper investigates the T-stress at crack tips in the periodic crack problem. Remote tension in the y-direction is applied to cracks with an arbitrary inclined angle. The original stress field can be considered a superposition of a uniform stress field and a perturbation stress field. The problem of evaluating the stresses in the perturbation field can be considered a superposition of many single crack problems. A Fredholm integral equation is suggested for the solution of the perturbation stress field. In the equation, the loading on the crack face is chosen as unknown quantity. Once the integral equation is solved, the stress intensity factors and the T-stress at the crack tip can be evaluated immediately. For solving the integral equation and evaluating stresses in the perturbation field, the remainder estimation technique is suggested for evaluating the influences on the central crack from infinite cracks. The technique can considerably improve convergence in computation. Many results for the stress intensity factors and the T-stresses in periodic cracks are presented. It is shown that the interaction is significant for the closer cracks.
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References
Betegon C, Hancock JW (1991) Two parameter characterization of elastic–plastic crack-tip fields. ASME J Appl Mech 58: 104–110
Broberg KB (2005) A note on T-stress determination using dislocation arrays. Int J Fract 131: 1–14. doi:10.1007/s10704-004-3637-5
Chen YZ (1994) T-stress in multiple crack problem for an infinite plate. Eng Fract Mech 48: 641–647. doi:10.1016/0013-7944(94)90171-6
Chen YZ (1997) Novel weight function approach for evaluating T-stress in plane elasticity crack problem. Int J Fract 85: L35–L40. doi:10.1023/A:1007397402482
Chen YZ (2007) Integral equation methods for multiple crack problems and related topics. Appl Mech Rev 60: 172–194. doi:10.1115/1.2750671
Chen YZ, Lin XY (2008) Eigenfunction expansion variational method for stress intensity factor and T-stress evaluation of a circular cracked plate. Acta Mech 196: 55–74. doi:10.1007/s00707-007-0500-6
Chen YZ, Hasebe N, Lee KY (2003) Multiple crack problems in elasticity. WIT Press, Southampton
Chen YZ, Lin XY, Wang ZX (2005) Solution of periodic group crack problems by using the Fredholm integral equation. Acta Mech 178: 41–51. doi:10.1007/s00707-005-0233-3
Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fract 6: 155–169. doi:10.1007/BF00012619
Fett T (2001) Stress intensity factors and T-stress for internally cracked circular disks under various conditions. Eng Fract Mech 68: 1119–1136. doi:10.1016/S0013-7944(01)00025-X
Fett T, Rizzi G (2005) Weight functions for stress intensity factors and T-stress for oblique cracks in a half-space. Int J Fract 132: L9–L16. doi:10.1007/s10704-005-0024-9
Larsson SG, Carlsson AJ (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: 447–473. doi:10.1016/0022-5096(73)90024-0
Li XF, Xu LR (2007) T-stresses across static crack kinking. ASME J Appl Mech 74: 181–190
Melin S (2002) The influence of the T-stress on the directional stability of cracks. Int J Fract 114: 259–265. doi:10.1023/A:1015521629898
Muskhelishvili NI (1953) Some basic problems of mathematical theory of elasticity. Noordhoff, Groningen
Rice JR (1974) Limitations to the small scale yielding approximation of elastic–plastic crack-tip fields. J Mech Phys Solids 22: 17–26. doi:10.1016/0022-5096(74)90010-6
Savruk MP (1981). Two-dimensional problems of elasticity for body with crack. Naukoya Dumka, Kiev (in Russian)
Sham TL (1991) The determination of the elastic T-term using higher order weight functions. Int J Fract 48: 81–102. doi:10.1007/BF00018392
Tsang DKL, Oyadiji SO (2008) Super singular element method for two-dimensional crack analysis. Proc Roy Soc A 464: 2629–2648
Tsang DKL, Oyadiji SO, Leung AYT (2003) Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor. Eng Fract Mech 70: 2199–2214. doi:10.1016/S0013-7944(02)00206-0
Wang X (2002) Determination of weight functions for elastic T-stress from reference T-stress solutions. Fatigue Fract Eng Mater Struct 25: 965–973. doi:10.1046/j.1460-2695.2002.00557.x
Williams ML (1957) On the stress distribution at the base of a stationary crack. ASME J Appl Mech 24: 111–114
Xiao QZ, Karihaloo BL (2004) Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element. Int J Fract 125: 207–225. doi:10.1023/B:FRAC.0000022229.54422.13
Xiao QZ, Karihaloo BL (2007) An overview of a hybrid crack element and determination of its complete displacement field. Eng Fract Mech 74: 1107–1117. doi:10.1016/j.engfracmech.2006.12.022
Yang B, Ravi-Chandar K (1999) Evaluation of elastic T-stress by stress difference method. Eng Fract Mech 64: 589–605. doi:10.1016/S0013-7944(99)00082-X
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Chen, Y.Z., Lin, X.Y. & Wang, Z.X. Evaluation of the stress intensity factors and the T-stress in periodic crack problem. Int J Fract 156, 203–216 (2009). https://doi.org/10.1007/s10704-009-9360-5
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DOI: https://doi.org/10.1007/s10704-009-9360-5