Locally enhanced Voronoi cell finite element model (LE‐VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions

Abstract

SUMMARYDuctile heterogeneous materials such as cast aluminum alloys undergo catastrophic failure that initiates with particle fragmentation, which evolves with void growth and coalescence in localized bands of intense plastic deformation and strain softening. The Voronoi cell finite element model (VCFEM), based on the assumed stress hybrid formulation, is unable to account for plastic strain-induced softening. To overcome this shortcoming of material softening due to plastic strain localization, this study introduces a locally enhanced VCFEM (LE-VCFEM) for modeling the very complex phenomenon of ductile failure in heterogeneous metals and alloys. In LE-VCFEM, finite deformation displacement elements are adaptively added to regions of localization in the otherwise assumed stress-based hybrid Voronoi cell finite element to locally enhance modeling capabilities for ductile fracture. Adaptive h-refinement is used for the displacement elements to improve accuracy. Damage initiation by particle cracking is triggered by a Weibull model. The nonlocal Gurson-Tvergaard-Needleman model of porous plasticity is implemented in LE-VCFEM to model matrix cracking. An iterative strain update algorithm is used for the displacement elements. The LE-VCFEM code is validated by comparing with results of conventional FE codes and experiments with real materials. The effect of various microstructural morphological characteristics is also investigated.

Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations

“…Ghosh and coworkers [22,27,36,37] have extensively developed the Voronoi Cell Finite Element Method based on an assumed-stress hybrid finite element method. Idelsohn [31] used natural neighbor coordinates of a Delaunay tessellation of points to develop a "meshless" finite element method.…”

“…Once crack branching and crack coalescence phenomena appear, the prospect of modeling a multitude of arbitrary three-dimensional intersecting cracks quickly becomes untenable. However, great progress in this area has been obtained by Ghosh and coworkers [22,27,36,37] in the development of the Voronoi Cell Finite Element Method (VCFEM) based on an assumedstress hybrid finite element method. The VCFEM has been used extensively to model material microstructure and quasistatic fracture.…”

Adaptive Hierarchical-Concurrent Multiscale Modeling of Ductile Failure in Heterogeneous Metallic Materials

“…The method has been extended to the locally enhanced VCFEM (LE-VCFEM) in Ref. 35, to model stages of ductile fracture from particle fragmentation to matrix cracking due to void nucleation, growth and coalescence. In LE-VCFEM, the stress-based hybrid VCFEM formulation is adaptively altered in regions of localized plastic flow with finite deformation, displacementbased element formulation to accommodate strain softening.…”

“…In LE-VCFEM, the stress-based hybrid VCFEM formulation is adaptively altered in regions of localized plastic flow with finite deformation, displacementbased element formulation to accommodate strain softening. LE-VCFEM has been demonstrated to be very effective for simulating both rate-independent 35 and rate-dependent plasticity. 22,36,37 The particulate phase in each Voronoi cell element is assumed to be isotropic, linear elastic.…”

“…4,26,28 The microscale problem involves identification of a SERVE and subsequent micromechanical analyses with LE-VCFEM). 35,36 Parameters of the HCP model are calibrated from homogenization of evolving variables in the SERVE of Fig. 11.…”