Multi-scale modeling of microstructure dependent intergranular brittle fracture using a quantitative phase-field based method

Abstract The fracture behavior of brittle materials is strongly influenced by their underlying microstructure that needs explicit consideration for accurate prediction of fracture properties and the associated scatter. In this work, a hierarchical multi-scale approach is pursued to model microstructure sensitive brittle fracture. A quantitative phase-field based fracture model is utilized to capture the complex crack growth behavior in the microstructure and the related parameters are calibrated from lower length scale atomistic simulations instead of engineering scale experimental data. The workability of this approach is demonstrated by performing porosity dependent intergranular fracture simulations in UO2 and comparing the predictions with experiments.

[1]  S. L. Phoenix,et al.  Probability distributions for the strength of composite materials II: A convergent sequence of tight bounds , 1981 .

[2]  Ralf Müller,et al.  A continuum phase field model for fracture , 2010 .

[3]  Derek Gaston,et al.  MOOSE: Multiphysics Object-Oriented Simulation Environment , 2014 .

[4]  Wam Marcel Brekelmans,et al.  Comparison of nonlocal approaches in continuum damage mechanics , 1995 .

[5]  Laura De Lorenzis,et al.  A review on phase-field models of brittle fracture and a new fast hybrid formulation , 2015 .

[6]  Ellad B. Tadmor,et al.  A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods , 2009 .

[7]  Liang Wang,et al.  Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks , 2013 .

[8]  Glaucio H. Paulino,et al.  Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture , 2014, International Journal of Fracture.

[9]  Marc Hou,et al.  Comparison of interatomic potentials for UO2. Part I: Static calculations , 2007 .

[10]  A. Needleman.  Micromechanical modelling of interfacial decohesion , 1992 .

[11]  Herbert Levine,et al.  Dynamic instabilities of fracture under biaxial strain using a phase field model. , 2004, Physical review letters.

[12]  Qingli Dai,et al.  A micromechanical finite element model for linear and damage‐coupled viscoelastic behaviour of asphalt mixture , 2006 .

[13]  Shenyang Y. Hu,et al.  Simulation of damage evolution in composites : A phase-field model , 2009 .

[14]  J. G. Crose,et al.  A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses , 1974 .

[15]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[16]  S. Biner,et al.  Simulation of damage evolution in discontinously reinforced metal matrix composites: a phase-field model , 2009 .

[17]  Christian Miehe,et al.  A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits , 2010 .

[18]  Mary F. Wheeler,et al.  A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach , 2015 .

[19]  Timothy D. Burchell,et al.  A microstructurally based fracture model for polygranular graphites , 1996 .

[20]  Pablo J. Sánchez,et al.  A phase-field/gradient damage model for brittle fracture in elastic–plastic solids , 2015 .

[21]  Mary F. Wheeler,et al.  A Phase-Field Method for Propagating Fluid-Filled Fractures Coupled to a Surrounding Porous Medium , 2015, Multiscale Model. Simul..

[22]  Z. Bažant,et al.  Nonlocal Continuum Damage, Localization Instability and Convergence , 1988 .

[23]  R. Bratton,et al.  Statistical Models of Fracture Relevant to Nuclear-Grade Graphite: Review and Recommendations , 2013 .

[24]  H. L. Heinisch,et al.  Weakest Link Theory Reformulated for Arbitrary Fracture Criterion , 1978 .

[25]  C. Miehe,et al.  Phase Field Modeling of Brittle and Ductile Fracture , 2013 .

[26]  Vincent Hakim,et al.  Laws of crack motion and phase-field models of fracture , 2008, 0806.0593.

[27]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[28]  René de Borst,et al.  A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations , 2015 .

[29]  David L. McDowell,et al.  Non-local separation constitutive laws for interfaces and their relation to nanoscale simulations , 2004 .

[30]  N. Chandrasekaran,et al.  Molecular dynamics (MD) simulation of uniaxial tension of some single-crystal cubic metals at nanolevel , 2001 .

[31]  A. G. Evans,et al.  The strength and fracture of stoichiometric polycrystalline UO2 , 1969 .

[32]  J. C. D. César de Sá,et al.  Damage driven crack initiation and propagation in ductile metals using XFEM , 2013 .

[33]  Cv Clemens Verhoosel,et al.  A phase‐field model for cohesive fracture , 2013 .

[34]  Christian Miehe,et al.  Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations , 2010 .

[35]  Somnath Ghosh,et al.  A Voronoi Cell finite element model for particle cracking in elastic-plastic composite materials , 1998 .

[36]  Aranson,et al.  Continuum field description of crack propagation , 2000, Physical review letters.

[37]  L. Stainier,et al.  A two-scale model predicting the mechanical behavior of nanocrystalline solids , 2013 .

[38]  Edward H. Glaessgen,et al.  Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum , 2006 .

[39]  Somnath Ghosh,et al.  Multiple cohesive crack growth in brittle materials by the extended Voronoi cell finite element model , 2006 .

[40]  L. J. Sluys,et al.  A new method for modelling cohesive cracks using finite elements , 2001 .

[41]  John W. Cahn,et al.  On Spinodal Decomposition , 1961 .

[42]  M. Anvari,et al.  Simulation of dynamic ductile crack growth using strain-rate and triaxiality-dependent cohesive elements , 2006 .

[43]  Zdeněk P. Bažant,et al.  Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture , 2007 .

[44]  Jean-Jacques Marigo,et al.  Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments , 2009 .

[45]  Mark F. Horstemeyer,et al.  Atomistic simulations on the tensile debonding of an aluminum-silicon interface , 2000 .

[46]  Masaomi Oguma,et al.  Microstructure effects on fracture strength of UO2 fuel pellets. , 1982 .

[47]  Jean-Louis Chaboche,et al.  CONTINUUM DAMAGE MECHANICS :PRESENT STATE AND FUTURE TRENDS , 1987 .

[48]  C. Jiang,et al.  A micromechanics-based strain gradient damage model for fracture prediction of brittle materials - Part II: Damage modeling and numerical simulations , 2011 .

[49]  Wolfgang Bleck,et al.  A micromechanical damage simulation of dual phase steels using XFEM , 2012 .

[50]  Gilles A. Francfort,et al.  Revisiting brittle fracture as an energy minimization problem , 1998 .

[51]  P. Dondeti.  Rate-Dependent Homogenization Based Continuum Plasticity Damage Model for Dendritic Cast Aluminum Alloys , 2012 .

[52]  Michael R. Tonks,et al.  Molecular dynamics simulations of intergranular fracture in UO2 with nine empirical interatomic potentials , 2014 .

[53]  T. Baker,et al.  Brittle fracture in polycrystalline microstructures with the extended finite element method , 2003 .

[54]  K. Trustrum,et al.  Statistical approach to brittle fracture , 1977 .

[55]  M. Ortiz,et al.  FINITE-DEFORMATION IRREVERSIBLE COHESIVE ELEMENTS FOR THREE-DIMENSIONAL CRACK-PROPAGATION ANALYSIS , 1999 .

[56]  Cv Clemens Verhoosel,et al.  A phase-field description of dynamic brittle fracture , 2012 .

[57]  B. Bourdin,et al.  Numerical experiments in revisited brittle fracture , 2000 .

[58]  S. B. Biner,et al.  A unified cohesive zone approach to model the ductile to brittle transition of fracture toughness in reactor pressure vessel steels , 2014 .

[59]  A. Abdollahi,et al.  Phase-field simulation of anisotropic crack propagation in ferroelectric single crystals: effect of microstructure on the fracture process , 2011 .

[60]  Ted Belytschko,et al.  Cracking node method for dynamic fracture with finite elements , 2009 .

[61]  G. Bellettini,et al.  Discrete approximation of a free discontinuity problem , 1994 .

[62]  A. Chambolle.  An approximation result for special functions with bounded deformation , 2004 .

[63]  Zdenek P. Bazant,et al.  Modulus of Rupture: Size Effect due to Fracture Initiation in Boundary Layer , 1995 .