Nonlinear implementation of Finite Fracture Mechanics: A case study on notched Brazilian disk samples

Barenblatt, 1959, The formation of equilibrium cracks during brittle fracture: general ideas and hypotheses, 622 Cornetti, 2016, Short cracks and V-notches: Finite Fracture Mechanics vs. Cohesive Crack Model, Eng. Fract. Mech., 168, 2, 10.1016/j.engfracmech.2015.12.016 Cornetti, 2019, Finite Fracture Mechanics and cohesive crack model: weight functions vs. cohesive laws, Int. J. Sol. Struct., 156–157, 126, 10.1016/j.ijsolstr.2018.08.003 Doitrand, 2019, Comparison between cohesive zone and coupled criterion modeling of crack initiation in rhombus hole specimens under quasi-static compression, Theor. Appl. Fract. Mech., 99, 51, 10.1016/j.tafmec.2018.11.007 Dugdale, 1960, Yielding of steel sheets containing slits, J. Mech. Phys. Sol., 8, 100, 10.1016/0022-5096(60)90013-2 Martin, 2016, Initiation of edge debonding: coupled criterion versus cohesive zone model, Int. J. Fract., 199, 157, 10.1007/s10704-016-0101-2 Tvergaard, 1992, The relation between crack growth resistance and fracture process parameters in elastic–plastic solids, J. Mech. Phys. Solids, 40, 1377, 10.1016/0022-5096(92)90020-3 Bourdin, 2000, Numerical experiments in revisited brittle fracture, J. Mech. Phy. Sol., 48, 797, 10.1016/S0022-5096(99)00028-9 Miehe, 2010, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, Int. J. Numer. Methods Eng., 83, 1273, 10.1002/nme.2861 Molnar, 2017, 2D and 3D Abaqus implementation of a robust staggered phase field solution for modeling brittle fracture, Finite Elem. Anal. Des., 130, 27, 10.1016/j.finel.2017.03.002 Hashin, 1996, Finite thermoelastic fracture criterion with application to laminate cracking analysis, J. Mech. Phys. Solids, 44, 1129, 10.1016/0022-5096(95)00080-1 Nairn, 2000, Exact and variational theorems for fracture mechanics of composites with residual stresses, traction-loaded cracks and imperfect interfaces, Int. J. Fract., 105, 243, 10.1023/A:1007666426275 Leguillon, 2002, Strength or toughness? A criterion for crack onset at a notch, Eur. J. Mech. A Solids, 21, 61, 10.1016/S0997-7538(01)01184-6 Doitrand, 2017, Damage onset modeling in woven composites based on a coupled stress and energy criterion, Eng. Fract. Mech., 169, 189, 10.1016/j.engfracmech.2016.11.021 Doitrand, 2017, Mesoscale analysis of damage growth in woven composites, Compos. Part A, 96, 77, 10.1016/j.compositesa.2017.02.018 García, 2016, A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics, Composites B, 95, 475, 10.1016/j.compositesb.2016.03.023 Martin, 2012, A coupled strength and toughness criterion for the prediction of the open hole tensile strength of a composite plate, Int. J. Solids Struct., 49, 3915, 10.1016/j.ijsolstr.2012.08.020 Leguillon, 2015, Application of the coupled stress–energy criterion to predict the fracture behaviour of layered ceramics designed with internal compressive stresses, Eur. J. Mech. A Solids, 54, 94, 10.1016/j.euromechsol.2015.06.008 Leguillon, 2018, What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation?, Int. J. Fract., 212, 89, 10.1007/s10704-018-0294-7 Martin, 2018, Understanding the tensile strength of ceramics in the presence of small critical flaws, Eng. Fract. Mech., 201, 167, 10.1016/j.engfracmech.2018.06.021 Mantič, 2009, Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion, Int. J. Solids Struct., 46, 1287, 10.1016/j.ijsolstr.2008.10.036 Mantič, 2012, Crack onset and growth at the fibre-matrix interface under a remote biaxial transverse load. Application of a coupled stress and energy criterion, Int. J. Solids Struct., 49, 2273, 10.1016/j.ijsolstr.2012.04.023 Martin, 2008, Competition between deflection and penetration at an interface in the vicinity of a main crack, Int. J. Fract., 151, 247, 10.1007/s10704-008-9228-0 Stein, 2015, A model for brittle failure in adhesive lap joints of arbitrary joint configuration, Compos. Struct., 133, 707, 10.1016/j.compstruct.2015.07.100 Leguillon, 2007, Size effects for crack initiation at blunt notches or cavities, Eng. Fract. Mech., 74, 2420, 10.1016/j.engfracmech.2006.11.008 Leguillon, 2017, Failure initiation at V-notch tips in quasi-brittle materials, Int. J. Solids Struct., 122–123, 1, 10.1016/j.ijsolstr.2017.05.036 A. Doitrand, D. Leguillon, Numerical modeling of the nucleation of facets ahead of a primary crack under mode I+III loading. Int. J. Fract. 213, 37-50. Sapora, 2014, Carpinteri V-notched elements under mode II loading conditions, Struct. Eng. Mech., 49, 499, 10.12989/sem.2014.49.4.499 Weißgraeber, 2016, A review of Finite Fracture Mechanics: crack initiation at singular and non-singular stress raisers, Arch. Appl. Mech., 86, 375, 10.1007/s00419-015-1091-7 Doitrand, 2018, 3D application of the coupled criterion to crack initiation prediction in epoxy/aluminum specimens under four point bending, Int. J. Sol. Struct., 143, 175, 10.1016/j.ijsolstr.2018.03.005 Doitrand, 2018, Comparison between 2D and 3D applications of the coupled criterion to crack initiation prediction in scarf adhesive joints, Int. J. Adhes., 85, 69, 10.1016/j.ijadhadh.2018.05.022 Leite, 2014, Application of finite fracture mechanics to composites: crack onset in a stretched open hole polymer plate with nonlinear behaviour, 22 Rosendahl, 2018, Crack nucleation in hyperelastic adhesive bonds, Ce/Papers, 2, 409, 10.1002/cepa.941 Li, 2019, Numerical implementation of the coupled criterion for damaged materials, Int. J. Sol. A/Struct., 165, 93, 10.1016/j.ijsolstr.2019.01.025 Rosendahl, 2019, Nonlinear elastic finite fracture mechanics: modeling mixed-mode crack nucleation in structural glazing silicone sealants, Materials and Design, 10.1016/j.matdes.2019.108057 Talmon l’Armée, 2017, Nonlinear crack opening integral : Mode mixity for finite cracks, Eng. Fract. Mech., 186, 283, 10.1016/j.engfracmech.2017.10.006 Li, 2006, A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials, Eng. Fract. Mech., 73, 505, 10.1016/j.engfracmech.2005.09.001 Torabi, 2017, Size effects on brittle fracture of Brazilian disk samples containing a circular hole, Eng. Fract. Mech., 186, 496, 10.1016/j.engfracmech.2017.11.008 P. Cornetti, N. Pugno, A. Carpinteri, D. Taylor, Finite fracture mechanics: a coupled stress and energy failure criterion, Engng. Fract. Mech. 73(14), 2021-2033. Sapora, 2015, An improved Finite Fracture Mechanics approach to blunt V-notch brittle fracture mechanics: Experimental verification on ceramic, metallic, and plastic materials, Theor. Appl. Fract. Mech., 78, 20, 10.1016/j.tafmec.2015.04.004 Sapora, 2018, Crack onset and propagation stability from a circular hole under biaxial loading, Int. J. Fract., 214, 97, 10.1007/s10704-018-0315-6 W. Ramberg, W.R. Osgood, Description of stress–strain curves by three parameters. Technical Note No. 902, National Advisory Committee For Aeronautics, Washington DC. Doitrand, 2019, Experimental characterization and numerical modeling of crack initiation in rhombus hole PMMA specimens under compression, Eur. J. Mech. A/Sol., 76, 290, 10.1016/j.euromechsol.2019.04.013 Sapora, 2017, Symmetric vs. asymmetric crack initiation from a circular hole Hobbs, 1965, An assessment of a technique for determining the tensile strength of rock, Br. J. Appl. Phys., 16, 259, 10.1088/0508-3443/16/2/319