Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. This infinitesimal contour limit is required by the definition of \(J_{2}\) while it is not for \(J_{1}\).

  2. It should be emphasized that for \(J_{2}\), \(J_{2}|_{\varGamma ^{+}} +J_{2}|_{\varGamma ^{-}} =\int _{-\infty }^0 (w^{+}-w^{-})\,\hbox {d}x_{1}\) is not necessarily equal to zero even through it is well known that \(J_{1}\) integral vanishes along \(\varGamma ^{+}\) and \(\varGamma ^{-}\) (Eischen 1987; Herrmann and Herrmann 1981).

  3. It should be noted that the counterpart of \(J_{2}^{C}\) obtained in (Li and Lv 2017) misses one term compared to our results due to possible mistakes in derivation.

References

  • Atkinson C (1972) Interaction between a crack and an inclusion. Int J Eng Sci 10:127–136

    Article  Google Scholar 

  • Barati R, Liang JT (2014) A review of fracturing fluid systems used for hydraulic fracturing of oil and gas wells. J Appl Polym Sci 131:40735

    Article  CAS  Google Scholar 

  • Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45:601–620

    Article  Google Scholar 

  • Bower AF (2010) Applied mechanics of solids. CRC Press, Boca Raton

    Google Scholar 

  • Bush MB (1997) The interaction between a crack and a particle cluster. Int J Fract 88:215–232

    Article  Google Scholar 

  • Chudnovsky A, Chaoui K, Moet A (1987) Curvilinear crack layer propagation. J Mater Sci Lett 6:1033–1038

    Article  Google Scholar 

  • Cotterell B (1966) Notes on paths and stability of cracks. Int J Fract Mech 2:526–533

    Article  Google Scholar 

  • Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fract 16:155–169

    Article  Google Scholar 

  • 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 48:1741–1760

    Article  Google Scholar 

  • Eischen JW (1987) An improved method for computing the J2 integral. Eng Fract Mech 26:691–700

    Article  Google Scholar 

  • Erdogan F, Gupta GD, Ratwani M (1974) Interaction between a circular inclusion and an arbitrarily oriented crack. J Appl Mech 41:1007–1013

    Article  Google Scholar 

  • Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lon Ser A 241:376–396

    Article  Google Scholar 

  • Faber KT, Evans AG (1983a) Crack deflection processes. 1. Theory. Acta Metall Mater 31:565–576

    Article  Google Scholar 

  • Faber KT, Evans AG (1983b) Crack deflection processes. 2. Experiment. Acta Metall Mater 31:577–584

    Article  Google Scholar 

  • Gdoutos EE (1985) Stable growth of a crack interacting with a circular inclusion. Theor Appl Fract Mech 3:141–150

    Article  Google Scholar 

  • 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

  • Gramberg J (1965) The axial cleavage fracture 1 Axial cleavage fracturing, a significant process in mining and geology. Eng Geol 1:31–72

    Article  Google Scholar 

  • Gupta M, Alderliesten RC, Benedictus R (2015) A review of T-stress and its effects in fracture mechanics. Eng Fract Mech 134:218–241

    Article  Google Scholar 

  • Haddi A, Weichert D (1998) Three-dimensional interaction between a crack front and particles. Int J Numer Methods Eng 42:1463–1476

    Article  Google Scholar 

  • Han JJ, Chen YH (2000) T-effect for the interaction problem of an interface macrocrack with a near-tip microvoid. Int J Fract 102:205–222

    Article  CAS  Google Scholar 

  • 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 20:3169–3175

    Article  CAS  Google Scholar 

  • Herrmann AG, Herrmann G (1981) On energy-release rates for a plane crack. J Appl Mech 48:525–528

    Article  Google Scholar 

  • Hwu CB, Liang YK, Yen WJ (1995) Interactions between inclusions and various types of cracks. Int J Fract 73:301–323

    Article  Google Scholar 

  • Kitey R, Tippur HV (2005a) Role of particle size and filler-matrix adhesion on dynamic fracture of glass-filled epoxy. I. Macromeasurements. Acta Mater 53:1153–1165

    Article  CAS  Google Scholar 

  • 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 53:1167–1178

    Article  CAS  Google Scholar 

  • Kitey R, Tippur HV (2008) Dynamic crack growth past a stiff inclusion: optical investigation of inclusion eccentricity and inclusion-matrix adhesion strength. Exp Mech 48:37–53

    Article  Google Scholar 

  • 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 141:11–25

    Article  Google Scholar 

  • 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 114:47–61

    Article  Google Scholar 

  • 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–A3765

    Article  CAS  Google Scholar 

  • 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 29:802–813

    Article  Google Scholar 

  • Li RS, Chudnovsky A (1993a) Energy analysis of crack interaction with an elastic inclusion. Int J Fract 63:247–261

    Article  Google Scholar 

  • 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–R74

    Google Scholar 

  • Li Q, Lv JN (2017) Invariant integrals of crack interaction with an inhomogeneity. Eng Fract Mech 171:76–84

    Article  Google Scholar 

  • Li ZH, Yang LH (2004) The near-tip stress intensity factor for a crack partially penetrating an inclusion. J Appl Mech 71:465–469

    Article  Google Scholar 

  • Lipetzky P, Knesl Z (1995) Crack-particle interaction in a two-phase composite. 2. Crack deflection. Int J Fract 73:81–92

    Article  Google Scholar 

  • Lipetzky P, Schmauder S (1994) Crack-particle interaction in 2-phase composites. 1. Particle-shape effects. Int J Fract 65:345–358

    Article  Google Scholar 

  • Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  Google Scholar 

  • Mura T (1987) Micromechanics of defects in solids, 2nd edn. Martinus Nijho Publishers, Dordrecht

    Book  Google Scholar 

  • 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

  • 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 72:11–26

    Article  Google Scholar 

  • Nielsen CV, Legarth BN, Niordson CF (2012) Extended FEM modeling of crack paths near inclusions. Int J Numer Methods Eng 89:786–804

    Article  Google Scholar 

  • Obrovac MN, Chevrier VL (2015) Alloy negative electrodes for Li-ion batteries (vol 114, pg 11444, 2014). Chem Rev 115:2043–2043

    Article  CAS  Google Scholar 

  • Ponnusami SA, Turteltaub S, van der Zwaag S (2015) Cohesive-zone modelling of crack nucleation and propagation in particulate composites. Eng Fract Mech 149:170–190

    Article  Google Scholar 

  • Rubinstein AA (1991) Mechanics of the crack path formation. Int J Fract 47:291–305

    Article  Google Scholar 

  • Sendeckyj GP (1974) Interaction of cracks with rigid inclusions in longitudinal shear deformation. Int J Fract 10:45–52

    Article  Google Scholar 

  • Sherry AH, France CC, Goldthorpe MR (1995) Compendium of T-Stress solutions for 2 and 3-dimensional cracked geometries. Fatigue Fract Eng Mater Struct 18:141–155

    Article  Google Scholar 

  • 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 4:257–266

    Google Scholar 

  • 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 110:387–406

    Article  Google Scholar 

  • 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 94:177–188

    Article  CAS  Google Scholar 

  • 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 25:9–21

    Article  CAS  Google Scholar 

  • 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 75:70–77

    Article  Google Scholar 

  • 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 14:339–359

    Article  Google Scholar 

  • Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24:109–114

    Google Scholar 

  • Zhou C, Li ZH (2007) The effect of T-stress on crack-inclusion interaction under mode I loading. Mech Res Commun 34:283–288

    Article  Google Scholar 

  • 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 42:1999–2003

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support by the Assistant Secretary for Energy Efficiency and Renewable Energy, Vehicle Technologies Office of the U.S. Department of Energy under Contract No. Award Number DE-EE0007787 under the Battery Material Research (BMR) Program and the National Science Foundation under grant CMMI-1634492.

Author information

Author notes

  1. Kai Guo and Bo Ni contributed equally to this work.

Authors and Affiliations

  1. School of Engineering, Brown University, Providence, RI, 02912, USA

    Kai Guo, Bo Ni & Huajian Gao

  2. Laboratory for Atomistic and Molecular Mechanics (LAMM), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Kai Guo

  3. School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological University, 70 Nanyang Drive, Singapore, 639798, Singapore

    Huajian Gao

Authors
  1. Kai Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huajian Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huajian Gao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (docx 141 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, K., Ni, B. & Gao, H. Tuning crack-inclusion interaction with an applied \(\varvec{T}\)-stress. Int J Fract 222, 13–23 (2020). https://doi.org/10.1007/s10704-020-00423-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-020-00423-9

Keywords

Search

Navigation