journal article·2007-01-31

Numerical simulation of growth pattern of a fluid-filled subsurface crack under moving hertzian loading

Xiaoqing Jin, Leon M. Keer, Eugene L. Chez

International Journal of Fracture· Volume 142· Issue 3-4
Publisher page

Abstract

Cracking of a fluid-filled subsurface crack is studied by means of the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The Griffith crack was initially opened by the application of hydrostatic pressure of an incompressible fluid within the crack. A moving Hertz line contact load distribution is applied at the surface of the half-plane in the presence of friction. The stress intensity factors at the tips of the fluid-filled crack are analyzed with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume. When the crack starts to propagate/kink, numerical results show that the internal fluid pressure will be relieved, and as the ratio of the branched crack length to main crack length increases, the elastic strain energy release rate decreases. The crack growth is assumed to be arrested when the energy release rate is below a certain value. Based on the energy criterion, predictions are attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed to simulate the growth pattern of the fluid-filled crack under moving Hertzian loading.
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Research context

OpenAlex topics: Numerical methods in engineering · Rock Mechanics and Modeling · Hydraulic Fracturing and Reservoir Analysis

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References (41)

Show source-provided references
1. Abé H, Mura T, Keer LM (1976) growth-rate of a penny-shaped crack in hydraulic fracturing of rocks. J of Geophy Res 81(29):5335–534010.1029/JB081i029p05335 ↗
2. Anderson TL (1995) Fracture mechanics fundamentals and applications. CRC Press, Boca Raton
3. Bogdañski S, Lewicki P, Szymaniak M (2005) Experimental and theoretical investigation of the phenomenon of filling the RCF crack with liquid. Wear 258(7–8):1280–128710.1016/j.wear.2004.03.038 ↗
4. Bower AF (1988) The influence of crack face friction and trapped fluid on surface initiated rolling-contact fatigue cracks. J Tribol Trans ASME 110(4):704–71110.1115/1.3261717 ↗
5. Broek D (1982) Elementary engineering fracture mechanics. Martinus Nijhoff Publishers, Boston10.1007/978-94-011-9055-8 ↗
6. Bueckner HF (1958) The propagation of cracks and the energy of elastic deformation. J Appl Mech 80:1225–1230
7. Chue CH, Chung HH (2000) Pitting formation under rolling contact. Theor Appl Fracture Mech 34(1):1–910.1016/S0167-8442(00)00019-7 ↗
8. Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fracture 16(2):155–16910.1007/BF00012619 ↗
9. Datsyshyn OP, Kalakhan OS, Kadyra VM, Shchur RB (2004) Pitting formation under the conditions of fretting fatigue. Mater Sci 40(2):159–17210.1007/s11003-005-0032-y ↗
10. Datsyshyn OP, Levus AB (2003) Propagation of an edge crack under the pressure of liquid in the vicinity of the crack tip. Mater Sci 39(5):754–75710.1023/B:MASC.0000023518.52991.69 ↗
11. Datsyshyn OP, Panasyuk VV (2001) Pitting of the rolling bodies contact surface. Wear 250:1347–135510.1016/S0043-1648(01)00771-2 ↗
12. Datsyshyn OP, Panasyuk VV, Pryshlyak RE, Terlets’kyi AB (2001) Paths of edge cracks in rolling bodies under the conditions of boundary lubrication. Mater Sci 37(3): 363–37310.1023/A:1013243719026 ↗
13. Davis PJ, Rabinowitz P (1984) Methods of numerical integration. Academic Press, San Diego
14. Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4(1): 35–4510.1061/(ASCE)1532-3641(2004)4:1(35) ↗
15. Dewynne JN, Hills DA, Nowell D (1992) Calculation of the opening displacement of surface-breaking plane cracks. Comput meth Appl Mech Eng 97(3):321–33110.1016/0045-7825(92)90049-P ↗
16. Erdogan F, Gupta GD, Cook TS (1973) Numerical solution of singular integral equations In: Sih GC (ed) Mechanics of fracture, method of analysis and solution of crack problems vol 1. Noordhoff International Publishing, pp 368–42510.1007/978-94-017-2260-5_7 ↗
17. Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85:519–52710.1115/1.3656897 ↗
18. He M, Hutchinson JW (1989) Kinking of a crack out of an interface. J Appl Mech 56:270–27810.1115/1.3176078 ↗
19. Hills DA, Kelly PA, Dai DN, Korsunsky AM (1996) Solution of crack problems: the distributed dislocation technique. Dordrecht, Kluwer Academic Publishers10.1007/978-94-015-8648-1 ↗
20. Jin X (2006) Analysis of some two dimensional problems containing cracks and holes. Ph.D. thesis, Northwestern University, Evanston
21. Jin X, Keer L M (2006) Solution of multiple edge cracks in an elastic half plane. Int J Fracture 137(1–4):121–13710.1007/s10704-005-3063-3 ↗
22. Kaneta M, Yatsuzuka H, Murakami Y (1985) Mechanism of crack-growth in lubricated rolling sliding contact. ASLE Trans 28(3):407–41410.1080/05698198508981637 ↗
23. Kaya AC, Erdogan F (1987) On the solution of integral-equations with strongly singular kernels. Q Appl Math 45(1):105–12210.1090/qam/885173 ↗
24. Keer LM, Bryant MD (1983) A pitting model for rolling- contact fatigue. J Lubric Technol Trans ASME 105(2):198–20510.1115/1.3254565 ↗
25. Krenk S (1975) On the use of interpolation polynomial for solutions of singular integral-equations. Q Appl Math 32(4):479–48410.1090/qam/474919 ↗
26. Kudish II (1995) Surface and subsurface cracks and pores with liquid under action of a contact load in the presence of a lubricant. In: Erdogan F (ed) Fracture mechanics, ASTM STP 1220, vol. 25. Philadelphia, ASTM, pp 606–62110.1520/STP14619S ↗
27. Kudish F, Burris KW (2004) Modeling of surface and subsurface crack behavior under contact load in the presence of lubricant. Int J Fracture 125(1–2):125–14710.1023/B:FRAC.0000021022.48417.a6 ↗
28. Li YZ, Hills DA (1990) Stress intensity factor solutions for kinked surface cracks. J Strain Anal Eng Des 25(1):21–2710.1243/03093247V251021 ↗
29. Lister JR, Kerr RC (1991) Fluid-mechanical models of crack-propagation and their application to magma transport in dykes. J Geophys Res Solid Earth Planets 96(B6):10049–1007710.1029/91JB00600 ↗
30. Lo KK (1978) Analysis of branched cracks. J Appl Mech Trans ASME 45(4):797–80210.1115/1.3424421 ↗
31. Menand T, Tait SR (2002) The propagation of a buoyant liquid-filled fissure from a source under constant pressure: an experimental approach. J Geophys Res Solid Earth 107(B11):ECV 161-1310.1029/2001JB000589 ↗
32. Mukai DJ (2000) An analysis of a near-surface crack branching under a rigid indenter. J Tribol Trans ASME 122(1):23–2910.1115/1.555325 ↗
33. Noda NA, Oda K (1992) Numerical-solutions of the singular integral-equations in the crack analysis using the body force method. Int J Fracture 58(4):285–30410.1007/BF00048950 ↗
34. Santare MH, Keer LM, Lewis JL (1987) Cracks emanating from a fluid filled void loaded in compression—Application to the bone-implant interface. J Biomech Eng Trans ASME 109(1):55–5910.1115/1.3138642 ↗
35. Smith JO, Liu CK (1953) Stresses due to tangential and normal loads on an elastic solid with application to some contact stress problems. J Appl Mech 75:157–16610.1115/1.4010643 ↗
36. Sneddon IN (1951) Fourier transforms. McGraw-Hill, New York
37. Takada A (1990) Experimental-study on propagation of liquid-filled crack in gelatin—shape and velocity in hydrostatic stress condition. J Geophys Res Solid Earth Planets 95(B6):8471–848110.1029/JB095iB06p08471 ↗
38. Watanabe TT, Masuyama T, Nagaoka K, Tahara T (2002) Analog experiments on magma-filled cracks: competition between external stresses and internal pressure. Earth Planets Space 54(12):1247–126110.1186/BF03352453 ↗
39. Way S (1935) Pitting due to rolling contact. ASME J Appl Mech 2:A49–A5810.1115/1.4008607 ↗
40. Weertman J (1971) Velocity at which liquid-filled cracks move in earths crust or in glaciers. J Geophys Res 76(35):8544–855310.1029/JB076i035p08544 ↗
41. Zafošnik B, Ren Z, Flašker J, Mishuris G (2005) Modelling of surface crack growth under lubricated rolling-sliding contact loading. Int J Fracture 134(2):127–14910.1007/s10704-005-8546-8 ↗