Finite size and geometrical non-linear effects during crack pinning by heterogeneities: an analytical and experimental study. (English) Zbl 1478.74006
Summary: Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.
References:
| [1] | Bonamy, D.; Bouchaud, E., Failure of heterogeneous materialsa dynamic phase transition?, Phys. Rep., 498, 1-44 (2011) |
| [2] | Bonamy, D.; Santucci, S.; Ponson, L., Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition, Phys. Rev. Lett., 101, 045501 (2008) |
| [3] | Bower, A. F.; Ortiz, M., A 3-dimensional analysis of crack trapping and bridging by tough particles, J. Mech. Phys. Solids, 39, 815-858 (1991) · Zbl 0761.73083 |
| [4] | Budzik, M. K.; Jumel, J.; Shanahan, M. E.R., Adhesive fracture of heterogeneous interfaces, Philos. Mag., 93, 2413-2427 (2013) |
| [5] | Chopin, J.; Prevost, A.; Boudaoud, A.; Adda-Bedia, M., Crack front dynamics across a single heterogeneity, Phys. Rev. Lett., 107, 144301 (2011) |
| [6] | Dalmas, D.; Barthel, E.; Vandembroucq, D., Crack front pinning by design in planar heterogeneous interfaces, J. Mech. Phys. Solids, 57, 446-457 (2010) |
| [7] | Dalmas, D.; Lelarge, A.; Vandembroucq, D., Crack propagation through phase-separated glasseseffect of the characteristic size of disorder, Phys. Rev. Lett., 101, 255501 (2008) |
| [8] | Delaplace, A.; Schmittbuhl, J.; Måløy, K. J., High resolution description of a crack front in a heterogeneous plexiglas block, Phys. Rev. E, 60, 1337-1343 (1999) |
| [9] | Démery, V.; Rosso, A.; Ponson, L., From microstructural features to effective toughness in disordered brittle solids, Europhys. Lett., 105, 34003 (2014) |
| [10] | Gao, H.; Rice, J. R., A first-order perturbation analysis of crack trapping by arrays of obstacles, ASME J. Appl. Mech., 56, 828-836 (1989) · Zbl 0729.73264 |
| [11] | Kendall, K., Thin film peeling-elastic term, J. Phys. D, 8, 105-117 (1973) |
| [12] | Lazarus, V., Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform tensile loading, Int. J. Fract., 122, 33-46 (2003) |
| [13] | Lazarus, V., Perturbation approaches of a planar crack in linear elastic fracture mechanicsa review, J. Mech. Phys. Solids, 59, 121-144 (2011) · Zbl 1270.74177 |
| [14] | Leblond, J. B.; Patinet, S.; Frelat, J.; Lazarus, V., Second-order coplanar perturbation of a semi-infinite crack in an infinite body, Eng. Fract. Mech., 90, 129-142 (2012) |
| [15] | Legrand, L.; Patinet, S.; Leblond, J. B.; Frelat, J.; Lazarus, V.; Vandembroucq, D., Coplanar perturbation of a crack lying on the mid-plane of a plate, Int. J. Fract., 170, 67-82 (2011) · Zbl 1283.74062 |
| [16] | Patinet, S.; Alzate, L.; Barthel, E.; Dalmas, D.; Vandembroucq, D.; Lazarus, V., Finite size effects on crack front pinning at heterogeneous planar interfacesexperimental, finite elements and perturbation approaches, J. Mech. Phys. Solids, 61, 311-324 (2013) |
| [17] | Patinet, S.; Vandembroucq, D.; Roux, S., Quantitative prediction of effective toughness at random heterogeneous interfaces, Phys. Rev. Lett., 110, 165507 (2013) |
| [18] | Ponson, L.; Bonamy, D., Crack propagation in brittle heterogeneous solidsmaterial disorder and crack dynamics, Int. J. Fract., 162, 21-31 (2010) · Zbl 1425.74425 |
| [20] | Ramanathan, S.; Ertas, D.; Fisher, D. S., Quasistatic crack propagation in heterogeneous media, Phys. Rev. Lett., 79, 873-876 (1997) |
| [21] | Rice, J. R., First-order variation in elastic fields due to variation in location of a planar crack front, ASME J. Appl. Mech., 52, 571-579 (1985) · Zbl 0571.73104 |
| [23] | Rivlin, R. S., The effective work of adhesion, Paint Technol., 9, 215-218 (1944) |
| [24] | Santucci, S.; Grob, M.; Toussaint, R.; Schmittbuhl, J.; Hansen, A.; Måløy, K. J., Fracture roughness scalinga case study on planar cracks, Europhys. Lett., 92, 44001 (2010) |
| [25] | Schmittbuhl, J.; Delaplace, A.; Måløy, K. J.; Perfettini, H.; Vilotte, J. P., Slow crack propagation and slip correlations, Pure Appl. Geophys., 160, 396-976 (2003) |
| [26] | Schmittbuhl, J.; Roux, S.; Vilotte, J. P.; Måløy, K. J., Interfacial crack pinning: effect of nonlocal interactions, Phys. Rev. Lett., 74, 1787-1790 (1995) |
| [27] | Taylor, J. R., An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (1997), University Science Books: University Science Books Sausalito, CA, USA |
| [28] | Vasoya, M.; Leblond, J. B.; Ponson, L., A geometrically nonlinear analysis of coplanar crack propagation in some heterogeneous medium, Int. J. Solids Struct., 50, 371-378 (2013) |
| [29] | Vasoya, M.; Lazarus, V.; Ponson, L., Crack front fingering during planar crack propagation in highly heterogeneous toughness field, Procedia Mater. Sci., 3, 2142-2147 (2014) |
| [30] | Willis, J. R., Crack front perturbations revisited, Int. J. Fract., 184, 17-24 (2013) |
| [31] | Willis, J. R.; Movchan, N. V., Second order in-plane dynamic perturbation of a crack propagating under shear loading, Math. Mech. Solids, 19, 82-92 (2014) · Zbl 07278980 |
| [32] | Xia, S.; Ponson, L.; Ravichandran, G.; Bhattacharya, K., Toughening and asymmetry in peeling of heterogeneous adhesives, Phys. Rev. Lett., 108, 196101 (2012) |
| [33] | Xia, S.; Ponson, L.; Ravichandran, G.; Bhattacharya, K., Adhesion of heterogeneous thin filmsII. Adhesive heterogeneity, J. Mech. Phys. Solids, 83, 88-103 (2015) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
