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#### Effects of elastic contributions on the evolution of nano-structure Al3Sc phase: A phase-field study

, Article Scientia Iranica ; Volume 23, Issue 3 , 2016 , Pages 1539-1547 ; 10263098 (ISSN) ; Ebrahimi, H ; Sharif University of Technology
Sharif University of Technology
2016

Abstract

A micromechanical phase-field model is utilized to study the evolution of nanostructure Al3Sc phase in Al-Sc alloy. We study the formation of Al3Sc precipitates in an Al-Sc alloy by using an elastic phase-field model. Since the precipitates of Al3Sc phase are fully coherent with the Al matrix, the elastic energy will have an inuence on the resulting morphology. We have studied the effects of elastic strain energies on shape evolution of Al3Sc phase, numerically. The simulated nano-structures evolve from spherical to cubic shapes. The equilibrium shape of the coherent Al3Sc phase is found to be determined by minimizing the sum of the elastic and interfacial energies through the phase-field...

#### Phase field modeling of crack growth with double-well potential including surface effects

, Article Continuum Mechanics and Thermodynamics ; 2019 ; 09351175 (ISSN) ; Farrahi, G. H ; Javanbakht, M ; Sharif University of Technology
Springer New York LLC
2019

Abstract

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way...

#### Phase field modeling of crack growth with double-well potential including surface effects

, Article Continuum Mechanics and Thermodynamics ; 2019 ; 09351175 (ISSN) ; Farrahi, G. H ; Javanbakht, M ; Sharif University of Technology
Springer New York LLC
2019

Abstract

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way...

#### Phase field modeling of crack growth with double-well potential including surface effects

, Article Continuum Mechanics and Thermodynamics ; Volume 32, Issue 3 , 2020 , Pages 913-925 ; Farrahi, G. H ; Javanbakht, M ; Sharif University of Technology
Springer
2020

Abstract

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way...

#### Thermodynamically consistent and scale-dependent phase field approach for crack propagation allowing for surface stresses

, Article International Journal of Plasticity ; Volume 111 , 2018 , Pages 1-35 ; 07496419 (ISSN) ; Jafarzadeh, H ; Farrahi, G. H ; Javanbakht, M ; Sharif University of Technology
Elsevier Ltd
2018

Abstract

A thermodynamically-consistent phase field approach for crack propagation which includes the following novel features is presented. (1) Scale dependency was included by relating the length scale to the number of cohesive interatomic planes at the crack tip. Because of this, the developed theory is applicable from the atomistic to the macroscopic scales. (2) The surface stresses (tension) are introduced by employing some geometrical nonlinearities even in small strain theory. They produce multiple contributions to the Ginzburg-Landau equation for crack propagation. (3) Crack propagation in the region with compressive closing stresses is eliminated by employing a stress-state-dependent kinetic...

#### Phase field approach to mode-I fracture by introducing an eigen strain tensor: general theory

, Article Theoretical and Applied Fracture Mechanics ; Volume 108 , August , 2020 ; Mansoori, H ; Sharif University of Technology
Elsevier B.V
2020

Abstract

A thermodynamically consistent phase field theory for fracture is developed. An alternative approach to describe the reduction in the slope of the stress–strain curve and the reduction of the stresses to zero during damage is utilized by introducing transformation strain instead of the degradation function. The main requirements for the thermodynamic potential are presented and used to present the general energy terms. The analysis of the equilibrium solution is formulated which describes the desired stress–strain curves and for which the infinitesimal damage produces an infinitesimal change in the equilibrium elastic modulus. Analytical analysis of the equations is performed to calibrate...

#### Phase field theory for fracture at large strains including surface stresses

, Article International Journal of Engineering Science ; Volume 178 , 2022 ; 00207225 (ISSN) ; Farrahi, G. H ; Levitas, V. I ; Javanbakht, M ; Sharif University of Technology
Elsevier Ltd
2022

Abstract

Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses at nanoscale. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface...

#### Unconditionally energy stable time stepping scheme for Cahn-Morral equation: Application to multi-component spinodal decomposition and optimal space tiling

, Article Journal of Computational Physics ; Volume 304 , 2016 , Pages 441-464 ; 00219991 (ISSN) ; Sharif University of Technology
Academic Press Inc

Abstract

An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre's time stepping scheme and Schur complement approach. Although the presented method is general and independent of the choice of homogeneous free energy density function term, logarithmic and polynomial energy functions are specifically considered in this paper. The method is applied to study the spinodal decomposition in multi-component systems and optimal space tiling problems. A penalization strategy is developed, in the case of later problem, to avoid trivial solutions. Extensive numerical experiments...

#### On the phase field modeling of crack growth and analytical treatment on the parameters

, Article Continuum Mechanics and Thermodynamics ; 2018 , Pages 1-18 ; 09351175 (ISSN) ; Javanbakht, M ; Jafarzadeh, H ; Sharif University of Technology
Springer New York LLC
2018

Abstract

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is...

#### On the phase field modeling of crack growth and analytical treatment on the parameters

, Article Continuum Mechanics and Thermodynamics ; Volume 32, Issue 3 , 2020 , Pages 589-606 ; Javanbakht, M ; Jafarzadeh, H ; Sharif University of Technology
Springer
2020

Abstract

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is...

#### Phase Field Simulation of Microstructure Ternary Eutectic Solidification

, M.Sc. Thesis Sharif University of Technology ; Tavakoli, Rouhollah (Supervisor)
Abstract

Physical and mechanical properties of cast alloys is partly a function of the morphology and volume fraction of phases from freezing. The microstructure of the eutectic solidification is function of physical properties (especially mobility and surface tension) and the volume fraction of phases involved in the evolution. The prediction of solidification microstructures will be very helpful for improving the mechanical properties of casting alloys and designing of new families of alloys. The theoretical study of the formation of eutectic microstructures is very difficult and almost impossible in general cases and empirical studies are expensive. The purpose of this study is to predict the...

#### Simulation of Coarsening in Tin/Lead Solders by Using Phase Field Method

, M.Sc. Thesis Sharif University of Technology ; Davami, Parviz (Supervisor) ; Ashouri, Hossein (Supervisor)
Abstract

Soldering is one of the important methods in joining techniques which has wide applications in industries such as microelectronic. Today, the physical and mechanical properties of solder joints is very important because the dimensions of electronic devices are decreasing that cause to increasing of their current density. One of the important problems of high current density in solder joints is the microstructures of solders in microelectronic components, change over time that is weakened the properties of the solder alloy. This study presents a quantitative model , which is capable to simulation phase separation and coarsening phenomenon in Tin/Lead Solders. This model is based on continuum...

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

, Article Nanoscale ; Volume 11, Issue 46 , 2019 , Pages 22243-22247 ; 20403364 (ISSN) ; Levitas, V. I ; Farrahi, G. H ; Javanbakht, M ; Sharif University of Technology
Royal Society of Chemistry
2019

Abstract

The phase field approach (PFA) for the interaction of fracture and martensitic phase transformation (PT) is developed, which includes the change in surface energy during PT and the effect of unexplored scale parameters proportional to the ratio of the widths of the crack surface and the phase interface, both at the nanometer scale. The variation of these two parameters causes unexpected qualitative and quantitative effects: shift of PT away from the crack tip, "wetting" of the crack surface by martensite, change in the structure and geometry of the transformed region, crack trajectory, and process of interfacial damage evolution, as well as transformation toughening. The results suggest...

#### Numerical investigation of two phase flow in micromodel porous media: effects of wettability, heterogeneity, and viscosity

, Article Canadian Journal of Chemical Engineering ; Volume 95, Issue 6 , 2017 , Pages 1213-1223 ; 00084034 (ISSN) ; Rokhforouz, M. R ; Ayatollahi, S ; Sharif University of Technology
Wiley-Liss Inc
2017

Abstract

The aim of the present work is to assess the effects of wettability, heterogeneity, and viscosity differences on water-oil displacement process in micromodel porous media through numerical modelling. The two-phase flow was simulated by Cahn-Hilliard phase field method (PFM) using a finite element package. The micromodel was initially saturated with oil (wetting phase) and oil was produced through invasion of the displacing phase into the matrix. The computed oil and water saturations were in good agreement with those obtained by the visual flooding experiment. Using the validated model, sensitivity analysis was performed to investigate the effects of different wettability states,...

#### Pore-level influence of micro-fracture parameters on visco-capillary behavior of two-phase displacements in porous media

, Article Advances in Water Resources ; Volume 113 , 2018 , Pages 260-271 ; 03091708 (ISSN) ; Akhlaghi Amiri, H. A ; Sharif University of Technology
Elsevier Ltd
2018

Abstract

In this work, coupled Cahn–Hilliard phase field and Navier–Stokes equations were solved using finite element method to address the effects of micro-fracture and its characterizations on water-oil displacements in a heterogeneous porous medium. Sensitivity studies at a wide range of viscosity ratios (M) and capillary numbers (Ca), and the resultant log Ca–log M stability phase diagram, revealed that in both media, with/without fracture, the three regimes of viscous fingering, capillary fingering and stable displacement similarly occur. However, presence of the fracture caused water channeling phenomenon which resulted in reduction of the number of active fingers and hence the final oil...

#### Magnetic field-induced control of a compound ferrofluid droplet deformation and breakup in shear flow using a hybrid lattice Boltzmann-finite difference method

, Article International Journal of Multiphase Flow ; Volume 146 , 2022 ; 03019322 (ISSN) ; Bijarchi, M. A ; Ghorbanpour Arani, A ; Rahimian, M. H ; Shafii, M. B ; Sharif University of Technology
Elsevier Ltd
2022

Abstract

The deformation and breakup dynamics of a compound ferrofluid droplet under shear flow and uniform magnetic field are numerically studied in this paper. Utilizing magnetic field provides the possibility to obtain better control over the compound droplet morphology and breakup in a simple shear flow. To solve the governing equations for interfaces motion and hydrodynamics, the conservative phase field lattice Boltzmann model is employed, and a finite difference approach is applied for calculating the magnetic field. To verify the accuracy of present simulations, the results are validated with those of four relevant benchmarks including liquid lens between two stratified fluids, three-phase...

#### Optimal Design of Parting Line in the Shape Casting Processes

, M.Sc. Thesis Sharif University of Technology ; Tavakkoli, Rouhollah (Supervisor)
Abstract

More than 70 weight percentage of using parts in diverse industries (such as military, civil, automobile productions and etc.) are produceed by the casting processes. For each one of the casting procceses, mold cavity is requisite for arrived molten metal in the mold cavity to get eventuated as a solidified part. Based on mold ilk, if the mold is permanent, the cast part must be capable to be remoeved from the the mold inside. For the non-permanent mold (asssuming multi-piece and non-monolithic), if the model requires to be removed from the mold inside after molding and before casting, only model (no cast part) has to be moldable (why for removing the solidified cast part from the...

#### Simulation of Nickel Electrodeposition

, M.Sc. Thesis Sharif University of Technology ; Dolati, Abolghasem (Supervisor)
Abstract

In this research project, Ni electrodeposition process has been modeled by a 3D coupled continuum-kinetic Monte Carlo simulation. Kinetic Monte Carlo module processes surface reactions along the substrate using electrochemical equations for the relating events. Continuum model also determines concentration of the whole system according to a 3D interpretation of diffusion law in solutions. After running each module, exchange of data between two codes is done and boundary conditions are updated. In fact, the whole simulation time is divided by small time steps relating to time fastest reactions need to proceed. Present model will generate three outputs: current-time curve, surface morphology...

#### Thermodynamically Consistent Phase Field Modeling of Interaction Between Crack Propagation and Phase Transformation

, Ph.D. Dissertation Sharif University of Technology ; Farrahi, Gholam Hossein (Supervisor) ; Javanbakht, Mahdi (Co-Supervisor)
Abstract

According to the widespread application of shape memory alloys, their study in the presence of cracks has received lots of attention in the last two decades. The phase transformation ahead of the crack tip may change the stress field and the fracture behavior, especially at the nanoscale. Thus, modeling this phenomenon helps to recognize the affecting factors on crack propagation and prediction of material behavior when cracks exist. In the first step of this thesis, a phase field approach for crack propagation was presented, first by considering fracture as phase transformation and then as bond breaking. According to the scaling-up strategy, the developed theory is applicable from the...

#### A Phase-Field Model for Inhomogeneous Multiferroic Materials

, M.Sc. Thesis Sharif University of Technology ; Tavakoli, Rouhollah (Supervisor)
Abstract

In this thesis, by deliberately embedding “emplacements” in the system to locally break the inversion and the time reversal symmetries, the manifold of all possible microstructures is navigated in pursuit of the one that can give rise to maximal magnetoelectric effect mediated by elastic energy of piezoelectric-piezomagnetic phases via their interface --- needless to mention the low intensity of such an effect in single-phase multiferroics. The configuration with the maximal coupling is sought within the context of phase-field modeling. In order to numerically track the conserved dissipative dynamics of the interface (namely, the Cahn-Hilliard equation) --- that is nonlocal by the nature of...