A Multi-Scale Approach for Phase Field Modeling of Ultra-Hard Ceramic Composites.

J D Clayton,J P Ligda,J Knap,R B Leavy,M Guziewski

doi:10.3390/ma14061408

Abstract

Diamond-silicon carbide (SiC) polycrystalline composite blends are studied using a computational approach combining molecular dynamics (MD) simulations for obtaining grain boundary (GB) fracture properties and phase field mechanics for capturing polycrystalline deformation and failure. An authentic microstructure, reconstructed from experimental lattice diffraction data with locally refined discretization in GB regions, is used to probe effects of local heterogeneities on material response in phase field simulations. The nominal microstructure consists of larger diamond and SiC (cubic polytype) grains, a matrix of smaller diamond grains and nanocrystalline SiC, and GB layers encasing the larger grains. These layers may consist of nanocrystalline SiC, diamond, or graphite, where volume fractions of each phase are varied within physically reasonable limits in parametric studies. Distributions of fracture energies from MD tension simulations are used in the phase field energy functional for SiC-SiC and SiC-diamond interfaces, where grain boundary geometries are obtained from statistical analysis of lattice orientation data on the real microstructure. An elastic homogenization method is used to account for distributions of second-phase graphitic inclusions as well as initial voids too small to be resolved individually in the continuum field discretization. In phase field simulations, SiC single crystals may twin, and all phases may fracture. The results of MD calculations show mean strengths of diamond-SiC interfaces are much lower than those of SiC-SiC GBs. In phase field simulations, effects on peak aggregate stress and ductility from different GB fracture energy realizations with the same mean fracture energy and from different random microstructure orientations are modest. Results of phase field simulations show unconfined compressive strength is compromised by diamond-SiC GBs, graphitic layers, graphitic inclusions, and initial porosity. Explored ranges of porosity and graphite fraction are informed by physical observations and constrained by accuracy limits of elastic homogenization. Modest reductions in strength and energy absorption are witnessed for microstructures with 4% porosity or 4% graphite distributed uniformly among intergranular matrix regions. Further reductions are much more severe when porosity is increased to 8% relative to when graphite is increased to 8%.

Highlights

Fractures initiate in the silicon carbide (SiC) matrix and grain boundary (GB) layer phases in Figure 13, in regions where baseline diamond-SiC interfacial strengths from molecular dynamics (MD) distributions are low and are further degraded due to graphitic lamellae and voids
A phase field theory has been informed by characterization experiments, MD simulations, and micromechanics-based homogenization
The material consists of diamond and SiC, with a range of grain sizes and initial defects in the form of graphitic layers, graphite inclusions, and voids

Summary

Introduction

Simpler by construction, sequential approaches address the system’s response at different length and/or time scales consecutively, where most often, the fine-scale solution is used to provide properties or conditions invoked subsequently to establish or solve the coarse-scale problem. References encompassing both classes of approaches include [1,2,3]. A sequential multi-scale approach is used for modeling fracture, whereby failure properties of grain boundaries (GBs) are obtained at the fine scale via molecular dynamics (MD) simulations. Prior works that have invoked atomistic simulations (e.g, MD or density functional theory (DFT)) to inform phase field models, via prescription of properties or functional forms of phase field energy potentials, include [5,6,7,8,9]

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Conclusion