Phase field approach for nanoscale interactions between crack propagation and phase transformation

Multiscale modeling of nanoindentation and nanoscratching by generalized particle method

Most concurrent multiscale methods that expand atomistic region by continuum domain suffer from inconsistent material constitutive properties, which affect the integrity of model in the interface of atomistic and continuum domains. In this paper, the Generalized Particle (GP) method is employed to simulate nanoindentation and nanoscratching of a single-crystal aluminum sample. The main advantage of the GP method lies in its ability to extend the simulation model while maintaining consistent atomic properties across all scales. Coarsening of the atomic domain has been conducted through two-scale and three-scale GP model. The results showed a strong consistency between the results of full atomic simulations and those achieved through the GP method for both nanoindentation and nanoscratch simulations. Also, wave reflections were not seen at the interfaces. The study revealed that an increase in the number of distinct particle domains led to a reduction in the accuracy of multiscale simulations.

Interplay of Fracture and Martensite Transformation in Microstructures: A Coupled Problem

We are witnessing a tremendous transition towards a society powered by net-zero carbon emission energy, with a corresponding escalating reliance on functional materials (FM). In recent years, the application of FM in multiphysics environments has brought new challenges to the mechanics and materials research communities. The underlying mechanism in FM, which governs several fundamental characteristics, is known as martensitic phase transformation (MPT). When it comes to the application of FM in the multiphysics context, a thorough understanding of the interplay between MPT and fracture plays a crucial role in FM design and application. In the present work, a coupled problem of crack nucleation and propagation and multivariant stress-induced MPT in elastic materials is presented using a finite element method based on Khachaturyan's microelasticity theory. The problem is established based on a phase-field (PF) approach, which includes the Ginzburg-Landau equations with advanced thermodynamic potential and the variational formulation of Griffith's theory. Therefore, the model consists of a coupled system of the Ginzburg-Landau equations and the static elasticity equation, and it characterizes evolution of distributions of austenite and two martensitic variants as well as crack growth in terms of corresponding order parameters. The numerical results show that crack growth does not begin until MPT has grown almost completely through the microstructure. Subsequent to the initial formation of the martensite variants, the initial crack propagates in such a way that its path mainly depends on the feature of martensite variant formations, the orientation and direction upon which the martensite plates are aligned, and the stress concentration between martensite plates. In addition, crack propagation behavior and martensite variant evaluations for different lattice orientation angles are presented and discussed in-detail.

Phase-field approach to evolution and interaction of twins in single crystal magnesium

Crack initiation and propagation as well as abrupt occurrence of twinning are challenging fracture problems where the transient phase-field approach is proven to be useful. Early-stage twinning growth and interactions are in focus herein for a magnesium single crystal at the nanometer length-scale. We demonstrate a basic methodology in order to determine the mobility parameter that steers the kinetics of phase-field propagation. The concept is to use already existing molecular dynamics simulations and analytical solutions in order to set the mobility parameter correctly. In this way, we exercise the model for gaining new insights into growth of twin morphologies, temporally-evolving spatial distribution of the shear stress field in the vicinity of the nanotwin, multi-twin, and twin-defect interactions. Overall, this research addresses gaps in our fundamental understanding of twin growth, while providing motivation for future discoveries in twin evolution and their effect on next-generation material performance and design.

Remarkable toughness of a nanostructured medium-entropy nitride compound

A novel medium-entropy nitride (MEN) - CrCoNiN doped with Al and Ti was prepared using magnetron sputtering. The new MEN possesses a single-phase face-centered cubic (FCC) structure, offering a superior combination of hardness (∼21.2 GPa) and fracture toughness (∼4.53 MPa m^1/2) that surpasses those of most of the conventional and high-entropy ceramics. The ultrahigh hardness value is attributed to a combined effect of lattice friction, solid solution, nanograin structure and compressive residual stress. The exceptional damage tolerance of the new nitride is underlain by the formation and operation of multiple steady shear bands and amorphization mediated by dislocation accumulations. The discovery of the deformation-induced amorphization and extensive shear banding in the MEN, in conjunction with the mechanistic understanding of the critical roles of high dislocation density and large lattice resistance in dislocation-mediated solid-state amorphization, opens up a new frontier for the development of damage-tolerant MPENs for application under extreme loading conditions.

Transformation toughness induced by surface tension of the crack-tip process zone interface: A field-theoretical approach

We study a crystal with a motionless crack exhibiting the transformational process zone at its tip within the field-theoretical approach. The latter enables us to describe the transformation toughness phenomenon and relate it to the solid's location on its phase diagram. We demonstrate that the zone extends backward beyond the crack tip due to the zone boundary surface tension. This setback engenders the crack-tip shielding, thus forming the transformation toughness. We obtain a quadrature expression for the effective fracture toughness using two independent approaches-(i) with the help of the elastic Green function and, alternatively, (ii) using the weight functions-and calculate it numerically applying the results of our simulations. Based on these findings, we derive an accurate analytical approximation that describes the transformation toughness. We further express it in terms of the experimentally accessible parameters of the phase diagram: the hysteresis width, the phase transition line slope, and the transformation strain.

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

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%.