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G. Sfantos, M. Aliabadi (2007)
A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materialsInternational Journal for Numerical Methods in Engineering, 69
T. Nguyen, J. Yvonnet, M. Bornert, C. Chateau (2016)
Initiation and propagation of complex 3D networks of cracks in heterogeneous quasi-brittle materials: Direct comparison between in situ testing-microCT experiments and phase field simulationsJournal of The Mechanics and Physics of Solids, 95
P. Munroe, I. Baker (1991)
Observation of 〈001〉 dislocations and a mechanism for transgranular fracture on {001} in FeAlActa Metallurgica Et Materialia, 39
C. Verhoosel, R. Borst (2013)
A phase‐field model for cohesive fractureInternational Journal for Numerical Methods in Engineering, 96
Cv Verhoosel, M. Gutiérrez (2009)
Modelling inter- and transgranular fracture in piezoelectric polycrystalsEngineering Fracture Mechanics, 76
J. Qian, Shaofan Li (2011)
Application of Multiscale Cohesive Zone Model to Simulate Fracture in Polycrystalline SolidsJournal of Engineering Materials and Technology-transactions of The Asme, 133
Thanh Nguyen, J. Yvonnet, Michel Bornert, C. Chateau, K. Sab, R. Romani, B. Roy (2016)
On the choice of parameters in the phase field method for simulating crack initiation with experimental validationInternational Journal of Fracture, 197
T. Zhai, A. Wilkinson, John Martin (2000)
A crystallographic mechanism for fatigue crack propagation through grain boundariesActa Materialia, 48
G. Francfort, J. Marigo (1998)
Revisiting brittle fracture as an energy minimization problemJournal of The Mechanics and Physics of Solids, 46
M. Mehl (1992)
Pressure dependence of the elastic moduli in aluminum-rich Al-Li compounds.Physical review. B, Condensed matter, 47 5
J. Clayton, J. Knap (2016)
Phase Field Modeling and Simulation of Coupled Fracture and Twinning in Single Crystals and PolycrystalsComputer Methods in Applied Mechanics and Engineering, 312
H. Espinosa, P. Zavattieri (2003)
A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: Theory and numerical implementationMechanics of Materials, 35
Andrea Braides (1998)
Approximation of Free-Discontinuity Problems
G Maso (1993)
An introduction to $$\varGamma $$ Γ -convergence
D. Dugdale (1960)
Yielding of steel sheets containing slitsJournal of The Mechanics and Physics of Solids, 8
M. Akao, H. Aoki, K. Katô (1981)
Mechanical properties of sintered hydroxyapatite for prosthetic applicationsJournal of Materials Science, 16
N. Tung, B. José, R. Julien, Baietto Marie-Christine, M. Frégonèse (2016)
A PHASE FIELD METHOD FOR MODELLING STRESS CORROSION CRACKS PROPAGATION IN A NICKEL BASE ALLOY
DP Braides (2002)
$$\varGamma $$ Γ -Convergence for beginners
N. Moës, J. Dolbow, T. Belytschko (1999)
A finite element method for crack growth without remeshingInternational Journal for Numerical Methods in Engineering, 46
G. Jovicic, M. Zivkovic, N. Jovicic (2008)
Extended Finite Element Method for Two-dimensional Crack Modeling
KT Faber, AG Evans (1983)
Crack deflection processes $$-$$ - I. TheoryActa Metall, 31
Michael Borden (2012)
Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture
Xiaopeng Xu, A. Needleman (1993)
Void nucleation by inclusion debonding in a crystal matrixModelling and Simulation in Materials Science and Engineering, 1
A. Musienko, G. Cailletaud (2009)
Simulation of inter- and transgranular crack propagation in polycrystalline aggregates due to stress corrosion crackingActa Materialia, 57
T. Zhai, X. Jiang, J. Li, M. Garratt, G. Bray (2005)
The grain boundary geometry for optimum resistance to growth of short fatigue cracks in high strength Al-alloysInternational Journal of Fatigue, 27
(1990)
Microstructural effects in the fracture of brittlematerials. In:Anderson MP, Rollett AD (eds) Simulation and theory of evolving microstructures
A. Aguilar-Elguezabal, M. Bocanegra-Bernal (2014)
Fracture behaviour of α-Al2O3 ceramics reinforced with a mixture of single-wall and multi-wall carbon nanotubesComposites Part B-engineering, 60
K. Faber, A. Evans (1983)
Crack deflection processes—I. TheoryActa Metallurgica, 31
Bin Li, C. Peco, Daniel Millán, I. Arias, M. Arroyo (2015)
Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energyInternational Journal for Numerical Methods in Engineering, 102
PR Munroe, I Baker (1991)
Observation of $$< 001>$$ < 001 > dislocations and a mechanism for transgranular fracture on $$\{$$ { 001 $$\}$$ } in FeAlActa Metall Mater, 39
D. Warner, J. Molinari (2006)
Micromechanical finite element modeling of compressive fracture in confined alumina ceramicActa Materialia, 54
Andrea Braides (2002)
Γ-convergence for beginners
C. Miehé, M. Hofacker, F. Welschinger (2010)
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splitsComputer Methods in Applied Mechanics and Engineering, 199
A. Simone, C. Duarte, E. Giessen (2006)
A Generalized Finite Element Method for polycrystals with discontinuous grain boundariesInternational Journal for Numerical Methods in Engineering, 67
A Aguilar-Elguézabal, MH Bocanegra-Bernal (2014)
Fracture behaviour of $$\alpha $$ α - $${\rm Al}_{2}{\rm O}_{3}$$ Al 2 O 3 ceramics reinforced with a mixture of single-wall and multi-wall carbon nanotubesCompos B Eng, 60
T. Nguyen, J. Réthoré, M. Baietto (2017)
Phase field modelling of anisotropic crack propagationEuropean Journal of Mechanics A-solids, 65
N. Sukumar, D. Srolovitz, Timothy Baker, Jean-Herve Prevost (2003)
Brittle fracture in polycrystalline microstructures with the extended finite element methodInternational Journal for Numerical Methods in Engineering, 56
L Ambrosio, VM Tortorelli (1990)
Approximation of functionals depending on jumps by elliptic functionals via $$\varGamma $$ Γ -convergenceCommun Pure Appl Math, 43
G. Was, V. Rajan (1987)
The mechanism of intergranular cracking of Ni-Cr-Fe alloys in sodium tetrathionateMetallurgical Transactions A, 18
T. Nguyen, J. Yvonnet, Q. Zhu, M. Bornert, C. Chateau (2015)
A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructureEngineering Fracture Mechanics, 139
T. Luther, Carsten Konke (2009)
Polycrystal models for the analysis of intergranular crack growth in metallic materialsEngineering Fracture Mechanics, 76
H. Espinosa, P. Zavattieri (2003)
A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: Numerical examplesMechanics of Materials, 35
G. Barenblatt (1959)
The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracksJournal of Applied Mathematics and Mechanics, 23
M. Herbig, A. King, P. Reischig, H. Proudhon, E. Lauridsen, J. Marrow, J. Buffière, W. Ludwig (2011)
3-D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phase-contrast X-ray tomographyActa Materialia, 59
Hanen Amor, J. Marigo, C. Maurini (2009)
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experimentsJournal of The Mechanics and Physics of Solids, 57
(1990)
Approximation of functionals depending on jumps by elliptic functionals via Γ -convergence
M. Hofacker, C. Miehé (2013)
A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patternsInternational Journal for Numerical Methods in Engineering, 93
T. Nguyen (2015)
Modeling of complex microcracking in cement based materials by combining numerical simulations based on a phase-field method and experimental 3D imaging
D. Mumford, J. Shah (1989)
Optimal approximations by piecewise smooth functions and associated variational problemsCommunications on Pure and Applied Mathematics, 42
A. Karma, D. Kessler, H. Levine (2001)
Phase-field model of mode III dynamic fracture.Physical review letters, 87 4
Yujie Wei, L. Anand (2004)
Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metalsJournal of The Mechanics and Physics of Solids, 52
B. Bourdin, C. Larsen, C. Richardson (2011)
A time-discrete model for dynamic fracture based on crack regularizationInternational Journal of Fracture, 168
D. Farkas, H. Swygenhoven, P. Derlet (2002)
Intergranular fracture in nanocrystalline metalsPhysical Review B, 66
A. King, W. Ludwig, M. Herbig, J. Buffiere, A. Khan, N. Stevens, T. Marrow (2011)
Three-dimensional in situ observations of short fatigue crack growth in magnesiumActa Materialia, 59
(2016)
Neper: software package for polycrystal generation and meshing
Long Wang, N. Limodin, A. Bartali, J. Witz, R. Seghir, J. Buffière, E. Charkaluk (2016)
Influence of pores on crack initiation in monotonic tensile and cyclic loadings in lost foam casting A319 alloy by using 3D in-situ analysisMaterials Science and Engineering A-structural Materials Properties Microstructure and Processing, 673
M. Jamal, S. Asadabadi, I. Ahmad, H. Aliabad (2014)
Elastic constants of cubic crystalsComputational Materials Science, 95
T. Nguyen, J. Yvonnet, Q. Zhu, M. Bornert, C. Chateau (2016)
A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomographyComputer Methods in Applied Mechanics and Engineering, 312
J. Clayton, J. Knap (2015)
Phase Field Modeling of Directional Fracture in Anisotropic PolycrystalsComputational Materials Science, 98
G. Maso (1993)
An Introduction to-convergence
L Ambrosio, VM Tortorelli (1992)
On the approximation of free discontinuity problemsBoll UMI, 6–B
A new multi-phase-field method is developed for modeling the fracture of polycrystals at the microstructural level. Inter and transgranular cracking, as well as anisotropic effects of both elasticity and preferential cleavage directions within each randomly oriented crystal are taken into account. For this purpose, the proposed phase field formulation includes: (a) a smeared description of grain boundaries as cohesive zones avoiding defining an additional phase for grains; (b) an anisotropic phase field model; (c) a multi-phase field formulation where each preferential cleavage direction is associated with a damage (phase field) variable. The obtained framework allows modeling interactions and competition between grains and grain boundary cracks, as well as their effects on the effective response of the material. The proposed model is illustrated through several numerical examples involving a full description of complex crack initiation and propagation within 2D and 3D models of polycrystals.
Computational Mechanics – Springer Journals
Published: Apr 8, 2017
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