Evaluation of the T-stress in branch crack problem
Source abstract
Abstract
This paper investigates the T-stress in the branch crack problem. The problem is modeled by a continuous distribution of dislocation along branches, and the relevant singular integral equation is obtained accordingly. After discretization of the singular integral equation, the balance for the number of equations and unknowns is well designed. After the singular integral equation is solved, the equation for evaluating the T-stress is derived. The merit of present study is to provide necessary equation for evaluating T-stress, rather than to provide the integral equation. Many computed results for T-stress under different conditions for branch crack are presented. It is found from the computed results that the interaction for T-stress among branches is complicated.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Fatigue and fracture mechanics · Numerical methods in engineering · Geotechnical Engineering and Underground Structures
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (27)
Show source-provided references
1. Ayatollahi MR, Pavier MJ, Smith DJ (1998) Determination of T-stress from finite element analysis for mode I and mixed mode I/II loading. Inter J Fract 91: 283–29810.1023/A:1007581125618 ↗
2. Boiko AV, Karpenko LN (1981) On some numerical methods for the solution of the plane elasticity problem for bodies with cracks by means of singular integral equation. Int J Fract 17: 381–38810.1007/BF00036190 ↗
3. Bourton JK, Phoenix SL (2000) Superposition method for calculating singular stress fields at kinks, branches and tips in multiple crack arrays. Int J Fract 102: 99–13910.1023/A:1007558018808 ↗
4. Broberg KB (2005) A note on T-stress determination using dislocation arrays. Int J Fract 131: 1–1410.1007/s10704-004-3637-5 ↗
5. Chen YZ, Hasebe N (1995) New integration scheme for the branch crack problem. Eng Fract Mech 52: 791–80110.1016/0013-7944(95)00052-W ↗
6. Chen YZ, Hasebe N, Lee KY (2003) Multiple crack problems in elasticity. WIT Press, Southampton
7. Chen YZ, Lin XY (2008) Comments on “Approximate Green’s functions for singular and higher order terms of an edge crack in a finite plate” by Xiao and Karihaloo [Eng Fract Mech 2002;69:959–981]. Eng Fract Mech 75:4844–484810.1016/j.engfracmech.2008.06.001 ↗
8. Chen YZ, Wang ZX, Lin XY (2008) Crack front position and crack back position techniques for evaluating the T-stress at crack tip using functions of a complex variable. J Mech Mater Struct 3: 1659–167310.2140/jomms.2008.3.1659 ↗
9. Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Inter J Fract 16: 155–16910.1007/BF00012619 ↗
10. Daux C, Moes N, Dolbow J, Sukumar N, Belytschko T (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Meth Eng 48: 1741–176010.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L ↗
11. Dutta BK, Kakodkar A, Maiti SK (1991) Two singular points finite elements in the analysis of kinked cracks. Comp Mech 7: 329–33910.1007/BF00350162 ↗
12. Englund J (2006) Stable algorithm for the stress field around a multiply branched crack. Int J Numer Meth Eng 63: 926–94610.1002/nme.1311 ↗
13. Fett T (1999) A Green’s function for T-stresses in an edge cracked rectangular plate. Eng Fract Mech 57: 365–37310.1016/S0013-7944(97)00034-9 ↗
14. Fett T (2001) Stress intensity factors and T-stress for internally cracked circular disks under various conditions. Eng Fract Mech 68: 1119–113610.1016/S0013-7944(01)00025-X ↗
15. Fett T, Rizzi G, Bahr HA (2006) Green’s functions for the T-stress of small kink and fork cracks. Eng Fract Mech 73: 1426–143510.1016/j.engfracmech.2005.12.007 ↗
16. Karihaloo BL, Xiao QZ (2001) Higher order terms at the crack tip asymptotic field for a notched three-point bend beam. Int J Fract 112: 111–12810.1023/A:1013392324585 ↗
17. Li XF, Xu LR (2007) T-stresses across static crack kinking. ASME J Appl Mech 74: 181–19010.1115/1.2188016 ↗
18. Lo KK (1978) Analysis of kinked crack. ASME J Appl Mech 45: 797–80210.1115/1.3424421 ↗
19. Melin S (1986) On singular integral equations for kinked cracks. Inter J Fract 30: 57–6510.1007/BF00034579 ↗
20. Melin S (1994) Accurate data for stress intensity factors at infinitesimal kinks. ASME J Appl Mech 61: 467–47010.1115/1.2901468 ↗
21. Muskhelishvili NI (1953) Some basic problems of mathematical theory of elasticity. Noordhoff, Groningen
22. Rice JR (1974) Limitations to the small scale yielding approximation of elastic–plastic crack-tip fields. J Mech Phys Solids 22: 17–2610.1016/0022-5096(74)90010-6 ↗
23. Savruk MP (1981) Two-dimensional problems of elasticity for body with crack. Naukoya Dumka, Kiev (in Russian)
24. Theocaris PS (1977) A symmetric branching of cracks. ASME J Appl Mech 44: 611–61810.1115/1.3424145 ↗
25. Yang B, Ravi-Chandar K (1999) Evaluation of elastic T-stress by stress difference method. Eng Fract Mech 64: 589–60510.1016/S0013-7944(99)00082-X ↗
26. Yavuz AK, Phoenix SL, TerMaath SC (2006) An accurate and fast analysis for strongly interacting multiple crack configurations including kinked (V) and branched (Y) cracks. Inter J Solids Struct 43: 6727–675010.1016/j.ijsolstr.2006.02.005 ↗
27. Williams ML (1957) On the stress distribution at the base of a stationary crack. ASME J Appl Mech 24: 111–11410.1115/1.4011454 ↗