Mohsen Asle Zaeem

Comparison of Cellular Automaton and Phase Field Models to Simulate Dendrite Growth in Hexagonal Crystals

A cellular automaton (CA){flnite element (FE) model and a phase fleld (PF){FE model were used to simulate equiaxed dendritic growth during the solidiflcation of hexagonal metals. In the CA{FE model, the conservation equations of mass and energy were solved in order to calculate the temperature fleld, solute concentration, and the dendritic growth morphology. CA{FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing (SDAS) vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidiflcation of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton{Glicksman{Kurz (LGK), showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 (approximated with the binary Mg{8.9 wt% Al) illustrates the di‐culty of modeling dendrite growth in hexagonal systems using CA{FE regarding mesh-induced anisotropy and a better performance of PF{FE in modeling multiple arbitrarily-oriented dendrites growth.

Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation

Phase-field models with conserved phase-field variables result in a 4th order evolution partial differential equation (PDE). When coupled with the usual 2nd order thermo-mechanics equations, such problems require special treatment. In the past, the finite element method (FEM) has been successfully applied to non-conserved phase fields, governed by a 2nd order PDE. For higher order equations, the convergence of the standard Galerkin FEM requires that the interpolation functions belong to a higher continuity class. We consider the Cahn-Hilliard phase-field model for diffusion-controlled solid state phase transformation in binary alloys, coupled with elasticity of the solid phases. A Galerkin finite element formulation is developed, with mixed-order interpolation: C^0 interpolation functions for displacements, and C^1 interpolation functions for the phase-field variable. To demonstrate convergence of the mixed interpolation scheme, we first study a one-dimensional problem - nucleation and growth of the intermediate phase in a thin-film diffusion couple with elasticity effects. Then, we study the effects of completeness of C^1 interpolation on parabolic problems in two space dimensions by considering the growth of the intermediate phase in a binary system. Quadratic convergence, expected for conforming elements, is achieved for both one- and two-dimensional systems.

Investigation of Phase Transformation in Thin Film Using Finite Element Method

Cahn-Hilliard type of phase field model coupled with elasticity is used to derive governing equations for the stress-mediated diffusion and phase transformation in thin films. To solve the resulting equations, a finite element (FE) model is presented. The partial differential equations governing diffusion and mechanical equilibrium are of different orders; Mixed-order finite elements, with C0 interpolation functions for displacement, and C1 interpolation functions for concentration are implemented. To validate this new numerical solver for such coupled problems, we test our implementation on thin film diffusion couples.

Effect of vacancy defects on generalized stacking fault energy of fcc metals

Molecular dynamics (MD) and density functional theory (DFT) studies were performed to investigate the influence of vacancy defects on generalized stacking fault (GSF) energy of fcc metals. MEAM and EAM potentials were used for MD simulations, and DFT calculations were performed to test the accuracy of different common parameter sets for MEAM and EAM potentials in predicting GSF with different fractions of vacancy defects. Vacancy defects were placed at the stacking fault plane or at nearby atomic layers. The effect of vacancy defects at the stacking fault plane and the plane directly underneath of it was dominant compared to the effect of vacancies at other adjacent planes. The effects of vacancy fraction, the distance between vacancies, and lateral relaxation of atoms on the GSF curves with vacancy defects were investigated. A very similar variation of normalized SFEs with respect to vacancy fractions were observed for Ni and Cu. MEAM potentials qualitatively captured the effect of vacancies on GSF.

Creation of Bioactive Glass (13–93) Scaffolds for Structural Bone Repair using a Combined Finite Element Modeling and Rapid Prototyping Approach

There is a clinical need for synthetic bioactive materials that can reliably repair intercalary skeletal tissue loss in load-bearing bones. Bioactive glasses have been investigated as one such material but their mechanical response has been a concern. Previously, we created bioactive silicate glass (13-93) scaffolds with a uniform grid-like microstructure which showed a compressive strength comparable to human cortical bone but a much lower flexural strength. In the present study, finite element modeling (FEM) was used to re-design the scaffold microstructure to improve its flexural strength without significantly lowering its compressive strength and ability to support bone infiltration in vivo. Then scaffolds with the requisite microstructures were created by a robotic deposition method and tested in four-point bending and compression to validate the FEM simulations. In general, the data validated the predictions of the FEM simulations. Scaffolds with a porosity gradient, composed of a less porous outer region and a more porous inner region, showed a flexural strength (34±5MPa) that was more than twice the value for the uniform grid-like microstructure (15±5MPa) and a higher compressive strength (88±20MPa) than the grid-like microstructure (72±10MPa). Upon implantation of the scaffolds for 12weeks in rat calvarial defects in vivo, the amount of new bone that infiltrated the pore space of the scaffolds with the porosity gradient (37±16%) was similar to that for the grid-like scaffolds (35±6%). These scaffolds with a porosity gradient that better mimics the microstructure of human long bone could provide more reliable implants for structural bone repair.

Computational Fluid Dynamics Study of Molten Steel Flow Patterns and Particle-Wall Interactions Inside a Slide-Gate Nozzle by a Hybrid Turbulent Model

Melt flow patterns and turbulence inside a slide-gate throttled submerged entry nozzle (SEN) were studied using Detached–Eddy Simulation (DES) model, which is a combination of Reynolds–Averaged Navier–Stokes (RANS) and Large–Eddy Simulation (LES) models. The DES switching criterion between RANS and LES was investigated to closely reproduce the flow structures of low and high turbulence regions similar to RANS and LES simulations, respectively. The melt flow patterns inside the nozzle were determined by k–ε (a RANS model), LES, and DES turbulent models, and convergence studies were performed to ensure reliability of the results. Results showed that the DES model has significant advantages over the standard k–ε model in transient simulations and in regions containing flow separation from the nozzle surface. Moreover, due to applying a hybrid approach, DES uses a RANS model at wall boundaries which resolves the extremely fine mesh requirement of LES simulations, and therefore it is computationally more efficient. Investigation of particle distribution inside the nozzle and particle adhesion to the nozzle wall also reveals that the DES model simulations predict more particle–wall interactions compared to LES model.

Effective Mechanical Properties of Multilayer Nano-Heterostructures

Two-dimensional and quasi-two-dimensional materials are important nanostructures because of their exciting electronic, optical, thermal, chemical and mechanical properties. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. For example, transition metal dichalcogenides such as MoS2 show promising electronic and piezoelectric properties, but their low mechanical strength is a constraint for practical applications. This barrier can be mitigated by considering graphene-MoS2 heterostructure, as graphene possesses strong mechanical properties. We have developed efficient closed-form expressions for the equivalent elastic properties of such multi-layer hexagonal nano-hetrostructures. Based on these physics-based analytical formulae, mechanical properties are investigated for different heterostructures such as graphene-MoS2, graphene-hBN, graphene-stanene and stanene-MoS2. The proposed formulae will enable efficient characterization of mechanical properties in developing a wide range of application-specific nano-heterostructures.

Competing mechanisms between dislocation and phase transformation in plastic deformation of single crystalline yttria-stabilized tetragonal zirconia nanopillars

Abstract Molecular dynamics (MD) is employed to investigate the plastic deformation mechanisms of single crystalline yttria-stabilized tetragonal zirconia (YSTZ) nanopillars under uniaxial compression. Simulation results show that the nanoscale plastic deformation of YSTZ is strongly dependent on the crystallographic orientation of zirconia nanopillars. For the first time, the experimental explored tetragonal to monoclinic phase transformation is reproduced by MD simulations in some particular loading directions. Three distinct mechanisms of dislocation, phase transformation, and a combination of dislocation and phase transformation are identified when applying compressive loading along different directions. The strength of zirconia nanopillars exhibits a sensitive behavior depending on the failure mechanisms, such that the dislocation-mediated deformation leads to the lowest strength, while the phase transformation-dominated deformation results in the highest strength.

Comparison of CFD Simulations with Experimental Measurements of Nozzle Clogging in Continuous Casting of Steels

Abstract Measurements of clog deposit thickness on the interior surfaces of a commercial continuous casting nozzle are compared with computational fluid dynamics (CFD) predictions of melt flow patterns and particle–wall interactions to identify the mechanisms of nozzle clogging. A submerged entry nozzle received from industry was encased in epoxy and carefully sectioned to allow measurement of the deposit thickness on the internal surfaces of the nozzle. CFD simulations of melt flow patterns and particle behavior inside the nozzle were performed by combining the Eulerian-Lagrangian approach and detached eddy simulation turbulent model, matching the geometry and operating conditions of the industrial test. The CFD results indicated that convergent areas of the interior cross section of the nozzle increased the velocity and turbulence of the flowing steel inside the nozzle and decreased the clog deposit thickness locally in these areas. CFD simulations also predicted a higher rate of attachment of particles in the divergent area between two convergent sections of the nozzle, which matched the observations made in the industrial nozzle measurements.

The Role of Compositional Strain in the Instability of Solid-Fluid Thin Film Interfaces

Consider a binary substitutional solid solution not in equilibrium with a fluid rich in either solid component. At the interface, depending on the chemical energy, the solid may selectively lose or gain atoms from the fluid. Any atom exchange upsets the nominal composition; thereby stresses are generated in the solid by simultaneous action of lattice dilation and interdiffusion. As stresses build up, the local changing volume tends to split up into islands in an effort to escape from stresses, while curvature tends to amalgamate the islands in an effort to minimize surface energy. This competition could lead to substantial corrugations of the solid-fluid interface. These corrugations and the thresholds for noticeable competition between stresses and curvatures had an old tradition in chemo-mechanical models of sharp interfaces beginning with Srolovitz (1989). However, stresses were generally considered as a mere cause of external loads, so a pure solid was tacitly asserted. This paper couples elasticity with a conserved-phase field model to mainly investigate the effect of compositional strain on the interface instability process between a binary solid selectively interacting with a fluid. The chemical energy barrier is considered, however, uncoupled from stress, and the mobility quadratically dependent on the gradient of composition. Under initial enforced sinusoidal perturbations, results of simulations showed that the compositional strain parameter can dramatically alter the effect of the chemical energy barrier on the critical wavelength of perturbations that trigger interface instability.