journal article·2020-03Open access

Tuning crack-inclusion interaction with an applied $$\varvec{T}$$-stress

Kai Guo, Bo Ni, Huajian Gao

International Journal of Fracture· Volume 222· Issue 1-2

Abstract

The interaction between cracks and inclusions plays an important role in the fracture behavior of particulate composites. It is commonly recognized that an inclusion stiffer than the matrix tends to deflect an approaching crack away while a softer inclusion attracts the crack. Here, we demonstrate by analytical modeling and numerical simulations that the crack-inclusion interaction can be tuned by an applied T-stress. Under a sufficiently large compressive applied T-stress, cracks can be attracted to stiffer inclusions while repelled by softer ones, thus reversing the conventional trend. Potential applications of this work include composite electrodes in lithium-ion batteries and hydraulic fracturing.
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Research context

OpenAlex topics: Numerical methods in engineering · Fatigue and fracture mechanics · Rock Mechanics and Modeling

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References (55)

Show source-provided references
1. Atkinson C (1972) Interaction between a crack and an inclusion. Int J Eng Sci 10:127–13610.1016/0020-7225(72)90011-0 ↗
2. Barati R, Liang JT (2014) A review of fracturing fluid systems used for hydraulic fracturing of oil and gas wells. J Appl Polym Sci 131:4073510.1002/app.40735 ↗
3. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45:601–62010.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S ↗
4. Bower AF (2010) Applied mechanics of solids. CRC Press, Boca Raton
5. Bush MB (1997) The interaction between a crack and a particle cluster. Int J Fract 88:215–23210.1023/A:1007469631883 ↗
6. Chudnovsky A, Chaoui K, Moet A (1987) Curvilinear crack layer propagation. J Mater Sci Lett 6:1033–103810.1007/BF01729123 ↗
7. Cotterell B (1966) Notes on paths and stability of cracks. Int J Fract Mech 2:526–53310.1007/BF00193691 ↗
8. Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fract 16:155–16910.1007/BF00012619 ↗
9. 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 Methods Eng 48:1741–176010.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L ↗
10. Eischen JW (1987) An improved method for computing the J2 integral. Eng Fract Mech 26:691–70010.1016/0013-7944(87)90134-2 ↗
11. Erdogan F, Gupta GD, Ratwani M (1974) Interaction between a circular inclusion and an arbitrarily oriented crack. J Appl Mech 41:1007–101310.1115/1.3423424 ↗
12. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lon Ser A 241:376–39610.1098/rspa.1957.0133 ↗
13. Faber KT, Evans AG (1983a) Crack deflection processes. 1. Theory. Acta Metall Mater 31:565–57610.1016/0001-6160(83)90046-9 ↗
14. Faber KT, Evans AG (1983b) Crack deflection processes. 2. Experiment. Acta Metall Mater 31:577–58410.1016/0001-6160(83)90047-0 ↗
15. Gdoutos EE (1985) Stable growth of a crack interacting with a circular inclusion. Theor Appl Fract Mech 3:141–15010.1016/0167-8442(85)90025-4 ↗
16. Gomez S, He W (2006) Laboratory method to evaluate fracture development in hard shale formations exposed to drilling fluids. In: Paper presented at the AADE 2006 fluids conference, Houston, April 11–12
17. Gramberg J (1965) The axial cleavage fracture 1 Axial cleavage fracturing, a significant process in mining and geology. Eng Geol 1:31–7210.1016/0013-7952(65)90006-2 ↗
18. Gupta M, Alderliesten RC, Benedictus R (2015) A review of T-stress and its effects in fracture mechanics. Eng Fract Mech 134:218–24110.1016/j.engfracmech.2014.10.013 ↗
19. Haddi A, Weichert D (1998) Three-dimensional interaction between a crack front and particles. Int J Numer Methods Eng 42:1463–147610.1002/(SICI)1097-0207(19980830)42:8<1463::AID-NME429>3.0.CO;2-1 ↗
20. Han JJ, Chen YH (2000) T-effect for the interaction problem of an interface macrocrack with a near-tip microvoid. Int J Fract 102:205–22210.1023/A:1007533120851 ↗
21. Hassoun J, Derrien G, Panero S, Scrosati B (2008) A nanostructured Sn–C composite lithium battery electrode with unique stability and high electrochemical performance. Adv Mater 20:3169–317510.1002/adma.200702928 ↗
22. Herrmann AG, Herrmann G (1981) On energy-release rates for a plane crack. J Appl Mech 48:525–52810.1115/1.3157667 ↗
23. Hwu CB, Liang YK, Yen WJ (1995) Interactions between inclusions and various types of cracks. Int J Fract 73:301–32310.1007/BF00027272 ↗
24. Kitey R, Tippur HV (2005a) Role of particle size and filler-matrix adhesion on dynamic fracture of glass-filled epoxy. I. Macromeasurements. Acta Mater 53:1153–116510.1016/j.actamat.2004.11.012 ↗
25. Kitey R, Tippur HV (2005b) Role of particle size and filler-matrix adhesion on dynamic fracture of glass-filled epoxy. II. Linkage between macro- and micro-measurements. Acta Mater 53:1167–117810.1016/j.actamat.2004.11.011 ↗
26. Kitey R, Tippur HV (2008) Dynamic crack growth past a stiff inclusion: optical investigation of inclusion eccentricity and inclusion-matrix adhesion strength. Exp Mech 48:37–5310.1007/s11340-007-9050-z ↗
27. Kitey R, Phan AV, Tippur HV, Kaplan T (2006) Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method. Int J Fract 141:11–2510.1007/s10704-006-0047-x ↗
28. Knight MG, Wrobel LC, Henshall JL, De Lacerda LA (2002) A study of the interaction between a propagating crack and an uncoated/coated elastic inclusion using the BE technique. Int J Fract 114:47–6110.1023/A:1014837509347 ↗
29. Kumar R, Woo JH, Xiao XC, Sheldon BW (2017) Internal microstructural changes and stress evolution in silicon nanoparticle based composite electrodes. J Electrochem Soc 164:A3750–A376510.1149/2.0951714jes ↗
30. Lei J, Wang YS, Gross D (2005) Analysis of dynamic interaction between an inclusion and a nearby moving crack by BEM. Eng Anal Bound Elem 29:802–81310.1016/j.enganabound.2005.04.002 ↗
31. Li RS, Chudnovsky A (1993a) Energy analysis of crack interaction with an elastic inclusion. Int J Fract 63:247–26110.1007/BF00012471 ↗
32. Li RS, Chudnovsky A (1993b) Variation of the energy-release rate as a crack approaches and passes through an elastic inclusion. Int J Fract 59:R69–R7410.1007/BF00034570 ↗
33. Li Q, Lv JN (2017) Invariant integrals of crack interaction with an inhomogeneity. Eng Fract Mech 171:76–8410.1016/j.engfracmech.2016.12.013 ↗
34. Li ZH, Yang LH (2004) The near-tip stress intensity factor for a crack partially penetrating an inclusion. J Appl Mech 71:465–46910.1115/1.1651539 ↗
35. Lipetzky P, Knesl Z (1995) Crack-particle interaction in a two-phase composite. 2. Crack deflection. Int J Fract 73:81–9210.1007/BF00039853 ↗
36. Lipetzky P, Schmauder S (1994) Crack-particle interaction in 2-phase composites. 1. Particle-shape effects. Int J Fract 65:345–35810.1007/BF00012373 ↗
37. Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–15010.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J ↗
38. Mura T (1987) Micromechanics of defects in solids, 2nd edn. Martinus Nijho Publishers, Dordrecht10.1007/978-94-009-3489-4 ↗
39. Muthu N, Falzon BG, Maiti SK, Khoddam S (2013) Modelling crack propagation in particle-reinforced composites using the element-free Galerkin method. In: Paper presented at the 19th international conference on composite materials, Montreal, July 28–August 2
40. Muthu N, Maiti SK, Falzon BG, Yan WY (2016) Crack propagation in non-homogenous materials: evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG method. Eng Anal Bound Elem 72:11–2610.1016/j.enganabound.2016.07.017 ↗
41. Nielsen CV, Legarth BN, Niordson CF (2012) Extended FEM modeling of crack paths near inclusions. Int J Numer Methods Eng 89:786–80410.1002/nme.3268 ↗
42. Obrovac MN, Chevrier VL (2015) Alloy negative electrodes for Li-ion batteries (vol 114, pg 11444, 2014). Chem Rev 115:2043–204310.1021/acs.chemrev.5b00061 ↗
43. Ponnusami SA, Turteltaub S, van der Zwaag S (2015) Cohesive-zone modelling of crack nucleation and propagation in particulate composites. Eng Fract Mech 149:170–19010.1016/j.engfracmech.2015.09.050 ↗
44. Rubinstein AA (1991) Mechanics of the crack path formation. Int J Fract 47:291–30510.1007/BF00012948 ↗
45. Sendeckyj GP (1974) Interaction of cracks with rigid inclusions in longitudinal shear deformation. Int J Fract 10:45–5210.1007/BF00955078 ↗
46. Sherry AH, France CC, Goldthorpe MR (1995) Compendium of T-Stress solutions for 2 and 3-dimensional cracked geometries. Fatigue Fract Eng Mater Struct 18:141–15510.1111/j.1460-2695.1995.tb00148.x ↗
47. Tamate O (1968) The effect of a circular inclusion on the stresses around a line crack in a sheet under tension. Int J Fract Mech 4:257–26610.1007/BF00185261 ↗
48. Wang YB, Chau KT (2001) A new boundary element method for mixed boundary value problems involving cracks and holes: interactions between rigid inclusions and cracks. Int J Fract 110:387–40610.1023/A:1010853804657 ↗
49. Wang C, Libardi W, Baldo JB (1998) Analysis of crack extension paths and toughening in a two phase brittle particulate composite by the boundary element method. Int J Fract 94:177–18810.1023/A:1007591216796 ↗
50. Wang ZY, Ma L, Wu LZ, Yu HJ (2012) Numerical simulation of crack growth in brittle matrix of particle reinforced composites using the XFEM technique. Acta Mech Solida Sin 25:9–2110.1016/S0894-9166(12)60002-0 ↗
51. Wang ZY, Yu HJ, Wang ZH (2015) A local mesh replacement method for modeling near-interfacial crack growth in 2D composite structures. Theor Appl Fract Mech 75:70–7710.1016/j.tafmec.2014.10.009 ↗
52. Wang ZY, Gu J, Hou C, Song M (2018) Numerical simulation of the interaction between a crack and an inclusion: the role of T-stress for 2D composite materials. Multidiscip Model Mater Struct 14:339–35910.1108/MMMS-03-2017-0014 ↗
53. Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24:109–11410.1115/1.4011454 ↗
54. Zhou C, Li ZH (2007) The effect of T-stress on crack-inclusion interaction under mode I loading. Mech Res Commun 34:283–28810.1016/j.mechrescom.2006.10.001 ↗
55. Zhou R, Li Z, Sun J (2011) Crack deflection and interface debonding in composite materials elucidated by the configuration force theory. Compos Part B Eng 42:1999–200310.1016/j.compositesb.2011.05.024 ↗