Journal Articles by Mohsen Asle Zaeem
In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimen... more In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this study the modified two-mode PFC model (presented by E. Asadi and M. Asle Zaeem, Comput. Mater. Sci. 2015) was used, in which the free energy can be exactly minimized in each stable crystal structure allowing calculation of accurate phase diagrams for two-mode PFC models. Different crystal structures, such as square, triangle, body-centered cubic (bcc), face-centered cubic (fcc), and stripe lattice structures as well as their coexistence regions were considered in the calculations. The model parameters were discussed to calculate phase diagrams that can be used as a guideline by other researchers for studying solidification and solid state phase transformation using two-mode PFC model.
This work aims to comprehensively study the anisotropy of the hexagonal close-packed (HCP)-liquid... more This work aims to comprehensively study the anisotropy of the hexagonal close-packed (HCP)-liquid interface free energy using molecular dynamics (MD) simulations based on the modified-embedded atom method (MEAM). As a case study, all the simulations are performed for Magnesium (Mg). The solid–liquid coexisting approach is used to accurately calculate the melting point and melting properties. Then, the capillary fluctuation method (CFM) is used to determine the HCP-liquid interface free energy (γ) and anisotropy parameters. In CFM, a continuous order parameter is employed to accurately locate the HCP-liquid interface location, and the HCP symmetry-adapted spherical harmonics are used to expand γ in terms of its anisotropy parameters (ε20, ε40, ε60 and ε66). Eight slip and twinning planes (basal, two prismatic, two pyramidal, and three twinning planes) are considered as the HCP-liquid interface planes. An average HCP-liquid interface free energy of 122.2 (mJ/m2), non-zero ε20, ε40, and ε66 parameters, and approximately zero ε60 parameter for Mg are predicted. Using these findings, the first preferred dendrite growth direction in solidification of Mg is predicted as [112¯0], which is in agreement with experiments. Also, a second preferred dendrite growth direction for Mg is predicted as [336¯2].
There is a clinical need for synthetic bioactive materials that can reliably repair intercalary s... more 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 ± 5 MPa) that was more than twice the value for the uniform grid-like microstructure (15 ± 5 MPa) and a higher compressive strength (88 ± 20 MPa) than the grid-like microstructure (72 ± 10 MPa). Upon implantation of the scaffolds for 12 weeks 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.
Melt flow patterns and turbulence inside a slide-gate throttled submerged entry nozzle (SEN) were... more 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–e (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–e 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.
An iterative procedure is developed to quantify a PFC model for BCC crystals.Applications in mode... more An iterative procedure is developed to quantify a PFC model for BCC crystals.Applications in modeling solidification, grain growth, and defect nucleation.The solid–liquid properties of Fe are determined as an example application.A recently developed two-mode phase-field crystal (PFC) model (Wu et al., 2010; Asadi and Asle Zaeem, 2015) is applied for quantitative modeling of body centered cubic (BCC) crystals at their melting points. This model incorporates the first two density wave vectors of BCC crystals in its formulation and consists of three model parameters (two independent and one dependent) in its dimensionless form. A systematic study is presented to show that the two independent parameters of the model control the material properties such as solid and liquid densities and the structure factor. An iterative procedure is presented to determine the PFC model parameters for specific BCC materials using their liquid structure factor and the fluctuation amplitude of atoms in their crystalline state. As a case study, the two-mode PFC model parameters are determined for Fe at its melting point. The calculated model parameters and results of the PFC model are validated by comparing the calculated expansion in melting, solid and liquid densities, elastic constants, and bulk modulus of Fe with the available experimental and computational data in the literature. In addition, to show the potential application of this PFC model, the solid–liquid interface free energy and surface anisotropy of Fe are determined and compared with their available counterparts in the literature.
Computational Materials Science, 2014
A multi-phase field model was developed for non-selective oxidation of metals which captures both... more A multi-phase field model was developed for non-selective oxidation of metals which captures both the
oxidation kinetics and stress generation. Phase field formulation involved a non-conserved phase field
variable as the marker for the metallic substrate, oxide scale, and a fluid phase containing oxygen, and
a conserved phase field variable representing the concentration of oxygen. The evolution equations of
the phase field variables were coupled to the mechanical equilibrium equations to investigate the evolution
of stress generation in both the oxide scale and the underlying metal. The governing equations were
solved in a finite element framework. This phase field model predicts the oxygen composition depth and
stress profiles in the oxide layer and at the metal–oxide interface. The model was proven successful in
predicting the observed evolution of oxide thickness and growth stresses for Zircaloy-4 oxidized at
900 C. The results of phase field simulations showed that the generation of stresses upon oxidation tends
to slow down the oxidation kinetics, and this substantially improved the model predictability of experimental
data.
Computational Materials Science, 2011
A phase-field model was used to investigate the simultaneous effects of grain boundary energy ani... more A phase-field model was used to investigate the simultaneous effects of grain boundary energy anisotropy
and the presence of second-phase particles on grain growth in polycrystalline materials. The system
of grains with anisotropic grain boundary energies was constructed by considering models of low and
high misorientation angles between adjacent grains. Systems without particles reached a steady state
grain growth rate, and this rate decreased by including the grain boundary energy anisotropy. In addition,
the presence of particles significantly altered the microstructures during grain growth. This study showed
that for systems including particles, the critical average grain size to stop grain growth depends not only
on the volume fraction and size of particles, but also on the grain boundary energy anisotropy.
Current Applied Physics, 2012
Phase stability, topology and size evolution of precipitates are important factors in determining... more Phase stability, topology and size evolution of precipitates are important factors in determining the
mechanical properties of crystalline materials. In this article, the CahneHilliard type of phase-field model
was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the
coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction,
compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates
in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were
investigated. The results demonstrated the ability of the model to simulate coarsening under the
concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological
coarsening power law, coarsening rates were determined to depend on precipitate size and
volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results
also showed that the necking incubation time between two neighboring precipitates depends inversely
on the precipitate’s initial sizes; however, under fixed volume fraction of precipitates, any increase in the
initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the
growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate
coarsening.
Computational Materials Science, 2015
Acta Materialia, 2015
This paper computationally investigates the effect of martensitic variant strain accommodation on... more This paper computationally investigates the effect of martensitic variant strain accommodation on the formation of microstructural and topological patterning in zirconia. We used the phase-field technique to capture the temporal and spatial evolution of embryonic formation of the monoclinic phase in tetragonal single crystals. The three-dimensional simulations were able to capture the formation of all the possible monoclinic variants. We used the multivariant single embryo as an initial condition to mitigate the lack of nucleation criteria at the mesoscale. Without a priori constraint, the model can select the transformation path and final microstructure. The phase-field model was benchmarked against experimental studies on surface uplift formation in zirconia reported by Deville et al. (Acta Mater 2004;52:5697, Acta Mater 2004;52:5709). The simulations showed the excellent capabilities of the model in predicting the formation of a surface relief induced by the tetragonal to monoclinic martensitic transformation.
Journal of Materials Science & Technology, 2012
A cellular automaton (CA){¯nite element (FE) model and a phase ¯eld (PF){FE model were used to si... more A cellular automaton (CA){¯nite element (FE) model and a phase ¯eld (PF){FE model were used to simulate
equiaxed dendritic growth during the solidi¯cation of hexagonal metals. In the CA{FE model, the conservation
equations of mass and energy were solved in order to calculate the temperature ¯eld, 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 solidi¯cation
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.
Acta Materialia, 2015
The two-phase solid-liquid coexisting structures of Ni, Cu, and Al are studied by molecular dynam... more The two-phase solid-liquid coexisting structures of Ni, Cu, and Al are studied by molecular dynamics (MD) simulations using the second nearest-neighbor (2NN) modified-embedded atom method (MEAM) potential. For this purpose, the existing 2NN-MEAM parameters for Ni and Cu were modified to make them suitable for the MD simulations of the problems related to the two-phase solid-liquid coexistence of these elements. Using these potentials, we compare calculated low-temperature properties of Ni, Cu, and Al, such as elastic constants, structural energy differences, vacancy formation energy, stacking fault energies, surface energies, specific heat and thermal expansion coefficient with experimental data. The solidliquid coexistence approach is utilized to accurately calculate the melting points of Ni, Cu, and Al. The MD calculations of the expansion in melting, latent heat and the liquid structure factor are also compared with experimental data. In addition, the solid-liquid interface free energy and surface anisotropy of the elements are determined from the interface fluctuations, and the predictions are compared to the experimental and computational data in the literature.
Applied Mathematical Modelling, 2013
We compared a cellular automaton (CA)–finite element (FE) model and a phase-field (PF)–
FE model... more We compared a cellular automaton (CA)–finite element (FE) model and a phase-field (PF)–
FE model to simulate equiaxed dendritic growth during the solidification of cubic crystals.
The equations of mass and heat transports were solved in the CA–FE model to calculate the
temperature field, solute concentration, and the dendritic growth morphology. In the PF–
FE model, a PF variable was used to identify solid and liquid phases and another PF variable
was considered to determine the evolution of solute concentration. Application to Al–
3.0 wt.% Cu alloy illustrates the capability of both CA–FE and PF–FE models in modeling
multiple arbitrarily-oriented dendrites in growth of cubic crystals. Simulation results from
both models showed quantitatively good agreement with the analytical model developed
by Lipton–Glicksman–Kurz (LGK) in the tip growth velocity and the tip equilibrium liquid
concentration at a given melt undercooling. The dendrite morphology and computational
time obtained from the CA–FE model are compared to those of the PF–FE model and the
distinct advantages of both methods are discussed.
International Journal of Plasticity, 2014
Martensitic tetragonal-to-monoclinic transformation in zirconia is a ''double-edged sword'', enab... more Martensitic tetragonal-to-monoclinic transformation in zirconia is a ''double-edged sword'', enabling transformation toughening or shape memory effects in favorable cases, but also cracks and phase degradation in undesirable scenarios. In stressed polycrystals, the transformation can burst from grain to grain, enabling stress field shielding and toughening in an autocatalysis fashion. This transformation strain can be recovered by an adequate thermal cycle at low temperatures (when monoclinic is stable) to provide a shape memory effect, or by unloading at higher temperatures (when tetragonal is stable) to provide pseudoelasticity.
Acta Materialia, 2013
The allotropic phase transformation in zirconia from the tetragonal to monoclinic double lattices... more The allotropic phase transformation in zirconia from the tetragonal to monoclinic double lattices is known to occur by a martensitic twinning mechanism which shows a complex dependence on temperature, stress and environment. This paper is concerned with the development of a phase field model which accounts for the main metallurgical mechanisms governing this martensitic transition. The symmetry reduction and orientation relationship between the parent and product phases were simulated using several non-conserved order parameters representing different transformation paths. Inhomogeneous and anisotropic elastic properties were considered to determine the resultant elastic stresses. Governing equations of the tetragonal-to-monoclinic transformation were solved in a finite element framework under a variety of initial and boundary conditions. It was shown that applying different initial conditions, such as seed embryo or random, did not change the twinning patterns or the final volume fractions of the parent and product phases after the relaxation period. On the other hand, enforcing different boundary conditions resulted in completely different twinning patterns and phase volume fractions. The model was able to predict both the "V" shape morphology of twinning and the surface stress relief with "gable roof" patterns, which were observed by transmission electron microscopy and atomic force microscopy to be characteristic of the tetragonal-to-monoclinic transition.
Journal of Nuclear Materials, 2015
Nucleation and formation of hydride precipitates in zirconium alloys have been an important facto... more Nucleation and formation of hydride precipitates in zirconium alloys have been an important factor in limiting the lifetime of nuclear fuel cladding for over 50 years. This review provides a concise summary of experimental and computational studies performed on hydride precipitation in zirconium alloys since the 1960's. Different computational models, including density functional theory, molecular dynamics, phase field, and finite element models applied to study hydride precipitation are reviewed, with specific consideration given to the phase field model, which has become a popular and powerful computational tool for modeling microstructure evolution. The strengths and weaknesses of these models are discussed in detail. An outline of potential future work in this area is discussed as well.
JOM, 2014
Phase-field crystal (PFC) is a model with atomistic-scale details acting on diffusive time scales... more Phase-field crystal (PFC) is a model with atomistic-scale details acting on diffusive time scales. PFC uses the density field as its order parameter, which takes a constant value in the liquid phase and a periodic function in the solid phase. PFC naturally takes into account elasticity, solid-liquid interface free energy, surface anisotropy, and grain boundary free energy by using this single-order parameter in modeling of coexisting solid-liquid structures. In this article, the recent advancements in PFC modeling of materials nanostructures are reviewed, which includes an overview of different PFC models and their applications, and the numerical algorithms developed for solving the PFC governing equations. A special focus is given to PFC models that simulate coexisting solid-liquid structures. The quantitative PFC models for solidliquid structures are reviewed, and the methods for determining PFC model parameters for specific materials are described in detail. The accuracy of different PFC models in calculating the solid-liquid interface properties is discussed.
Computational Materials Science, Jan 1, 2010
"We consider morphological instabilities in binary multilayers and the post-instability evolution... more "We consider morphological instabilities in binary multilayers and the post-instability evolution of the system. The alloys with and without intermediate phase are considered, as well as the cases with stable and meta-stable intermediate phase. Using the Galerkin finite element formulation for coupled Cahn–Hilliard – elasticity problem, maps of different evolution paths are developed in the parameter space of relative thicknesses of initial phases. We consider the relative importance of elastic and chemical energy of the system and develop maps for different cases.
The systems exhibit rich evolution behavior. Depending on the initial configuration (which determines the mass conservation condition), the final equilibrium varies, but even greater variety is observed in evolution paths. The paths may consist of multiple evolution steps, which may proceed at different rates. Except for few special circumstances, the instabilities are to perturbations non-homogeneous in the film plane. Post-instability evolution is essentially two-dimensional, and cannot be reduced to the one-dimensional model."
Materials Letters, 2015
A combination of severe plastic deformation by equal channel angular pressing (ECAP) and bake har... more A combination of severe plastic deformation by equal channel angular pressing (ECAP) and bake hardening (BH) was used to produce high strength ultrafine-grained AA6061 aluminum alloy. 2, 4 and 8 passes of ECAP were performed, and the bake hardenability of samples was tested by 6% pre-straining followed by baking at 200 1C for 20 min. The microstructures obtained for various passes of ECAP were characterized by XRD, EBSD, and TEM techniques. The microstructures were refined from an average grain size of 20 mm to 212 nm after 8 passes of ECAP. Maximum bake hardenability of 110 MPa, and final yield stress of 330 MPa were obtained in the specimens processed by 8 passes of ECAP.
Materials Letters, 2012
A cyclic forward-backward extrusion (CFBE) process was used as a severe plastic deformation (SPD)... more A cyclic forward-backward extrusion (CFBE) process was used as a severe plastic deformation (SPD) technique to
produce ultrafine-grained aluminum rods. Yield strength and tensile strength of the specimens increased by increasing
the number of CFBE cycles,while elongation to break decreased due to an increase in the grain refinement
and microhardness. According to transmission electron microscopy (TEM) and electron backscatter diffraction
(EBSD) results, the average grain size was reduced from 120 μm to 315 nm after only 3 cycles of CFBE.
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Journal Articles by Mohsen Asle Zaeem
oxidation kinetics and stress generation. Phase field formulation involved a non-conserved phase field
variable as the marker for the metallic substrate, oxide scale, and a fluid phase containing oxygen, and
a conserved phase field variable representing the concentration of oxygen. The evolution equations of
the phase field variables were coupled to the mechanical equilibrium equations to investigate the evolution
of stress generation in both the oxide scale and the underlying metal. The governing equations were
solved in a finite element framework. This phase field model predicts the oxygen composition depth and
stress profiles in the oxide layer and at the metal–oxide interface. The model was proven successful in
predicting the observed evolution of oxide thickness and growth stresses for Zircaloy-4 oxidized at
900 C. The results of phase field simulations showed that the generation of stresses upon oxidation tends
to slow down the oxidation kinetics, and this substantially improved the model predictability of experimental
data.
and the presence of second-phase particles on grain growth in polycrystalline materials. The system
of grains with anisotropic grain boundary energies was constructed by considering models of low and
high misorientation angles between adjacent grains. Systems without particles reached a steady state
grain growth rate, and this rate decreased by including the grain boundary energy anisotropy. In addition,
the presence of particles significantly altered the microstructures during grain growth. This study showed
that for systems including particles, the critical average grain size to stop grain growth depends not only
on the volume fraction and size of particles, but also on the grain boundary energy anisotropy.
mechanical properties of crystalline materials. In this article, the CahneHilliard type of phase-field model
was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the
coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction,
compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates
in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were
investigated. The results demonstrated the ability of the model to simulate coarsening under the
concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological
coarsening power law, coarsening rates were determined to depend on precipitate size and
volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results
also showed that the necking incubation time between two neighboring precipitates depends inversely
on the precipitate’s initial sizes; however, under fixed volume fraction of precipitates, any increase in the
initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the
growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate
coarsening.
equiaxed dendritic growth during the solidi¯cation of hexagonal metals. In the CA{FE model, the conservation
equations of mass and energy were solved in order to calculate the temperature ¯eld, 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 solidi¯cation
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.
FE model to simulate equiaxed dendritic growth during the solidification of cubic crystals.
The equations of mass and heat transports were solved in the CA–FE model to calculate the
temperature field, solute concentration, and the dendritic growth morphology. In the PF–
FE model, a PF variable was used to identify solid and liquid phases and another PF variable
was considered to determine the evolution of solute concentration. Application to Al–
3.0 wt.% Cu alloy illustrates the capability of both CA–FE and PF–FE models in modeling
multiple arbitrarily-oriented dendrites in growth of cubic crystals. Simulation results from
both models showed quantitatively good agreement with the analytical model developed
by Lipton–Glicksman–Kurz (LGK) in the tip growth velocity and the tip equilibrium liquid
concentration at a given melt undercooling. The dendrite morphology and computational
time obtained from the CA–FE model are compared to those of the PF–FE model and the
distinct advantages of both methods are discussed.
The systems exhibit rich evolution behavior. Depending on the initial configuration (which determines the mass conservation condition), the final equilibrium varies, but even greater variety is observed in evolution paths. The paths may consist of multiple evolution steps, which may proceed at different rates. Except for few special circumstances, the instabilities are to perturbations non-homogeneous in the film plane. Post-instability evolution is essentially two-dimensional, and cannot be reduced to the one-dimensional model."
produce ultrafine-grained aluminum rods. Yield strength and tensile strength of the specimens increased by increasing
the number of CFBE cycles,while elongation to break decreased due to an increase in the grain refinement
and microhardness. According to transmission electron microscopy (TEM) and electron backscatter diffraction
(EBSD) results, the average grain size was reduced from 120 μm to 315 nm after only 3 cycles of CFBE.
oxidation kinetics and stress generation. Phase field formulation involved a non-conserved phase field
variable as the marker for the metallic substrate, oxide scale, and a fluid phase containing oxygen, and
a conserved phase field variable representing the concentration of oxygen. The evolution equations of
the phase field variables were coupled to the mechanical equilibrium equations to investigate the evolution
of stress generation in both the oxide scale and the underlying metal. The governing equations were
solved in a finite element framework. This phase field model predicts the oxygen composition depth and
stress profiles in the oxide layer and at the metal–oxide interface. The model was proven successful in
predicting the observed evolution of oxide thickness and growth stresses for Zircaloy-4 oxidized at
900 C. The results of phase field simulations showed that the generation of stresses upon oxidation tends
to slow down the oxidation kinetics, and this substantially improved the model predictability of experimental
data.
and the presence of second-phase particles on grain growth in polycrystalline materials. The system
of grains with anisotropic grain boundary energies was constructed by considering models of low and
high misorientation angles between adjacent grains. Systems without particles reached a steady state
grain growth rate, and this rate decreased by including the grain boundary energy anisotropy. In addition,
the presence of particles significantly altered the microstructures during grain growth. This study showed
that for systems including particles, the critical average grain size to stop grain growth depends not only
on the volume fraction and size of particles, but also on the grain boundary energy anisotropy.
mechanical properties of crystalline materials. In this article, the CahneHilliard type of phase-field model
was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the
coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction,
compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates
in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were
investigated. The results demonstrated the ability of the model to simulate coarsening under the
concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological
coarsening power law, coarsening rates were determined to depend on precipitate size and
volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results
also showed that the necking incubation time between two neighboring precipitates depends inversely
on the precipitate’s initial sizes; however, under fixed volume fraction of precipitates, any increase in the
initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the
growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate
coarsening.
equiaxed dendritic growth during the solidi¯cation of hexagonal metals. In the CA{FE model, the conservation
equations of mass and energy were solved in order to calculate the temperature ¯eld, 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 solidi¯cation
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.
FE model to simulate equiaxed dendritic growth during the solidification of cubic crystals.
The equations of mass and heat transports were solved in the CA–FE model to calculate the
temperature field, solute concentration, and the dendritic growth morphology. In the PF–
FE model, a PF variable was used to identify solid and liquid phases and another PF variable
was considered to determine the evolution of solute concentration. Application to Al–
3.0 wt.% Cu alloy illustrates the capability of both CA–FE and PF–FE models in modeling
multiple arbitrarily-oriented dendrites in growth of cubic crystals. Simulation results from
both models showed quantitatively good agreement with the analytical model developed
by Lipton–Glicksman–Kurz (LGK) in the tip growth velocity and the tip equilibrium liquid
concentration at a given melt undercooling. The dendrite morphology and computational
time obtained from the CA–FE model are compared to those of the PF–FE model and the
distinct advantages of both methods are discussed.
The systems exhibit rich evolution behavior. Depending on the initial configuration (which determines the mass conservation condition), the final equilibrium varies, but even greater variety is observed in evolution paths. The paths may consist of multiple evolution steps, which may proceed at different rates. Except for few special circumstances, the instabilities are to perturbations non-homogeneous in the film plane. Post-instability evolution is essentially two-dimensional, and cannot be reduced to the one-dimensional model."
produce ultrafine-grained aluminum rods. Yield strength and tensile strength of the specimens increased by increasing
the number of CFBE cycles,while elongation to break decreased due to an increase in the grain refinement
and microhardness. According to transmission electron microscopy (TEM) and electron backscatter diffraction
(EBSD) results, the average grain size was reduced from 120 μm to 315 nm after only 3 cycles of CFBE.