An atomistic-based interphase zone model for crystalline solids

Abstract In this paper, we present an atomistic-based interphase zone model (AIZM), discuss its physical foundation, and apply it to simulate fractures at small scales. The main technical ingredients of the atomistic-based multiscale finite element method are: (1) a colloidal crystal model to describe material interface degradation including slip planes, grain boundaries, cracks, and inhomogeneities; (2) implementation of the reduced integration and hour-glass model control technique to avoid locking inside the interphase element, and (3) introduction of a novel concept of “element stacking fault energy”, which can be utilized in simulations to distinguish ductile and brittle failures at small scales. In particular, AIZM provides an interface description that is consistent with the bulk material properties, and it can capture microstructure-based mixed-mode interfacial fracture automatically. The method may provide a mesoscale solution for polycrystalline solids by bridging the gap between fine scale molecular dynamics and macroscale continum dynamics.

[1]  Shaofan Li,et al.  Application of Multiscale Cohesive Zone Model to Simulate Fracture in Polycrystalline Solids , 2011 .

[2]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[3]  M. Baskes,et al.  Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals , 1984 .

[4]  Shaofan Li,et al.  A cohesive finite element for quasi-continua , 2008 .

[5]  O. T. Nguyen,et al.  Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior , 2002 .

[6]  James R. Rice,et al.  Dislocation Nucleation from a Crack Tip" an Analysis Based on the Peierls Concept , 1991 .

[7]  Gregory J. Tallents,et al.  Temporal resolution of a transient pumping X-ray laser , 2001 .

[8]  David A. Weitz,et al.  Visualizing dislocation nucleation by indenting colloidal crystals , 2006, Nature.

[9]  Efthimios Kaxiras,et al.  From Electrons to Finite Elements: A Concurrent Multiscale Approach for Metals , 2005, cond-mat/0506006.

[10]  R. Peierls.  The size of a dislocation , 1940 .

[11]  Mark F. Horstemeyer,et al.  A multiscale analysis of fixed-end simple shear using molecular dynamics, crystal plasticity, and a macroscopic internal state variable theory , 2003 .

[12]  S. Suresh.  Colloid model for atoms , 2006, Nature materials.

[13]  Huajian Gao,et al.  Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds , 1998 .

[14]  Youping Chen,et al.  Atomistic formulation of a multiscale field theory for nano/micro solids , 2005 .

[15]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[16]  Frank Reginald Nunes Nabarro,et al.  Mathematical theory of stationary dislocations , 1952 .

[17]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[18]  P. Serena,et al.  A comparison between EAM interatomic potentials for Al and Ni: from bulk systems to nanowires , 2006 .

[19]  R. Hill.  On constitutive macro-variables for heterogeneous solids at finite strain , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[20]  M. Ortiz,et al.  Effective Cohesive Behavior of Layers of Interatomic Planes , 2006 .

[21]  Shaofan Li,et al.  Perfectly matched multiscale simulations for discrete lattice systems: Extension to multiple dimensions , 2006 .

[22]  D. Malkus,et al.  Mixed finite element methods—reduced and selective integration techniques: a unification of concepts , 1990 .

[23]  Huajian Gao,et al.  Hyperelasticity governs dynamic fracture at a critical length scale , 2003, Nature.

[24]  Gregory J. Wagner,et al.  Coupling of atomistic and continuum simulations using a bridging scale decomposition , 2003 .

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

[26]  T. Belytschko,et al.  Extended finite element method for cohesive crack growth , 2002 .

[27]  J. M. Kennedy,et al.  Hourglass control in linear and nonlinear problems , 1983 .

[28]  Harold S. Park,et al.  The bridging scale for two-dimensional atomistic/continuum coupling , 2005 .

[29]  Rong Tian,et al.  A multiresolution continuum simulation of the ductile fracture process , 2010 .

[30]  John R. Rice,et al.  The activation energy for dislocation nucleation at a crack , 1994 .

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

[32]  Shaofan Li,et al.  Introduction To Micromechanics And Nanomechanics , 2008 .

[33]  A. Curnier,et al.  A finite element method for a class of contact-impact problems , 1976 .

[34]  Shaofan Li,et al.  An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method , 2012 .

[35]  J. Clayton.  Modeling Dynamic Plasticity and Spall Fracture in High Density Polycrystalline Alloys , 2005 .

[36]  John R. Rice,et al.  A Critical Evaluation of Cohesive Zone Models of Dynamic Fracture , 2001 .

[37]  James D. Lee,et al.  Multiscale modeling of dynamic crack propagation , 2010 .

[38]  Shaofan Li,et al.  A multiscale cohesive zone model and simulations of fractures , 2010 .

[39]  Roger A. Sauer,et al.  A contact mechanics model for quasi‐continua , 2007 .

[40]  James R. Rice,et al.  Ductile versus brittle behaviour of crystals , 1974 .

[41]  Glaucio H. Paulino,et al.  A unified potential-based cohesive model of mixed-mode fracture , 2009 .

[42]  Youping Chen,et al.  Multiscale material modeling and its application to a dynamic crack propagation problem , 2009 .

[43]  Weixuan Yang,et al.  A temperature‐related homogenization technique and its implementation in the meshfree particle method for nanoscale simulations , 2007 .

[44]  J. Rice,et al.  Crack front waves , 1998 .

[45]  G. I. Barenblatt.  THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .