Papers by Sinisa Mesarovic
A comprehensive study of molten alloy capillary flow in the wetting/non-wetting wedge-tee configu... more A comprehensive study of molten alloy capillary flow in the wetting/non-wetting wedge-tee configuration is presented. The horizontal Al 2 O 3 substrate is non-wetting, while the vertical, Al-Mn alloy AA3003, is wetting. The braze alloy is a composite of an aluminum-silicon alloy (Al-10Si) with potassium fluoro-aluminate flux embedded. The purpose for selecting such a wetting/non-wetting configuration is for repair and construction in space by means of brazing. When capillary forces are not opposed by gravity, the spreading of a liquid braze may be controlled by a non-wetting surface. Specifically, we study: (i) the evolution of the free surface shape of a large melt mass in the gravity field, (ii) kinetics of advancing/receding triple lines and dynamic contact angles, and (iii) microstructure of the resolidified molten alloy on the substrates. The receding contact line exhibits a sudden withdrawal towards the corner, then a long-time stagnation before final equilibrium in the corner. In contrast to the typical monotonic evolution of the advancing contact angle, the receding contact angle features an anomalous non-monotonic behavior. The microstructure of the re-solidified sample features a phase macrosegregation.
Nature Communications, 2023
Shape distortion in sintering results from
nonhomogeneous temperature activating a
long-range mas... more Shape distortion in sintering results from
nonhomogeneous temperature activating a
long-range mass transport
Physics of Fluids, 2022
Recent capillary flow experiments, conducted on a combined wetting/non-wetting assemble, consiste... more Recent capillary flow experiments, conducted on a combined wetting/non-wetting assemble, consistently feature an anomalous flow over the nonwetting
substrate: (i) apparent abrupt or gradual recession stages in the motion of the contact line, (ii) non-monotonic abrupt changes in the receding
contact angle, and (iii) contact angle overshoot above the nominal equilibrium contact angle. We find that such behavior of a liquid metal alloy
cannot be explained by the standard capillary flow models. However, a model that includes the ageing of the equilibrium contact angle predicts all
the observed features qualitatively. We use the phase field formulation for capillary flows with a diffusive motion of the triple line to accommodate
the novel diffusive boundary condition with the time-evolving quasi-equilibrium contact angle.We discover that the observed anomalies in capillary
flow are qualitatively explained by two factors: (1) time evolution (ageing) of the quasi-equilibrium contact angle and (2) high viscosity of the partially
molten braze. We also discover that for the given flow geometry, the transition from the initial to the final configuration may follow two distinct
topological paths: one is characterized by a coalescence of liquid–solid contact domains, the other by a contact separation. The selection of the
two paths in the configurational space is dependent on both contact ageing parameters and viscosity.
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2023
Repair and construction in space by means of brazing requires understanding of the effect of grav... more Repair and construction in space by means of brazing requires understanding of the effect of gravity on the
capillary flow of a molten metal. We perform two sets of experiments: (1) spreading of a sessile drop of liquid
aluminum-silicon-flux (Al-Si-KxAlyFz) composite braze on a horizontal alumina (Al2O3) substrate (a non-wetting
surface), and (2) capillary flow of the same braze alloy on an inclined aluminum-manganese (AA3003) substrate
(a wetting surface). We vary the mass of the brazing liquid and the inclination of the substrate (i.e., the relative
direction of gravity).
In the composite metal/flux sessile drop experiments, we observe a secondary liquid flux meniscus forming at
the contact line between the liquid Al-Si and the alumina substrate. We demonstrate that the equilibrium contact
angle appears to be close to 180◦, while the apparent contact angle depends on the mass of the braze. In the
second set of experiments, we study the molten braze alloy on different inclinations of AA3003 in a wedge-T
wetting/non-wetting assembly. As the inclination angle decreases, the wetting distance increases and the surface
profile changes from a non-symmetric bag-like shape to a more symmetric pancake shape. With the mass
decreasing, the surface profile on the vertical substrate approaches a symmetric shape when the wetting distance
is equal or smaller than the capillary length. While the non-homogeneous melting and hence, the nonhomogeneous
microstructure of the melt, may prevent a full symmetry. Computational predictions of equilibrium
shapes are in good agreement with experimental results.
International Journal of Solids and Structures, 2022
The lattice continuum formulation for diffusional creep is implemented into the computational fra... more The lattice continuum formulation for diffusional creep is implemented into the computational framework based on the finite difference method for space and the predictor-corrector algorithm for time discretization, to solve the coupled elasticity-diffusion problem with moving boundaries. The numerical scheme is implemented and tested considering 3D periodic structures without grain boundary sliding. Of primary interest in this paper are the stress non-uniformities resulting from nonuniform composition eigenstrains. We consider two regimes: the one where the rate limiting process is bulk diffusion of vacancies, and the one where the rate is controlled by vacancy nucleation/annihilation at grain boundaries (nucleation-controlled creep). We found that the stress concentration factor for diffusion-controlled creep is independent of the applied stress and grain size. No stress concentrations are present for the nucleation-controlled creep case. Stress and grain size dependence of minimum strain creep rates are determined by the present model for a variety of applied stresses, grain sizes, different driving processes (diffusion and nucleation-controlled creep) and compared with the classical theory for diffusional creep. We found that steady-state creep rates varied linearly with applied stresses for both diffusion and nucleation-controlled creep. The numerical results show good correspondence to analytical predictions for idealized diffusional Nabarro-Herring creep. Significantly lower steadystate strain rates were computed for nucleation-controlled creep. These results demonstrate the ability of the present model to reproduce the stress and grain size dependence of the steady-state strain creep rates.
Physics of Fluids, 2021
The importance of the problem of hole-filling by a molten metal lies in the application of brazin... more The importance of the problem of hole-filling by a molten metal lies in the application of brazing for repairs in space, under microgravity
conditions. The negligible effects of gravity and dominance of capillary forces can be approximated under terrestrial conditions, provided
that the hole and the quantity of liquid are small, as quantified by the Bond number. In this paper, we report experimental results, modeling,
and analysis of the hole-filling problem using the liquid aluminum brazing alloy on aluminum substrate. Depending on the hole size, the
capillary driven flow may result in the hole being either filled or not filled. The equilibrium problem (energy minimization) has multiple
solutions in some regions of the parameter space. Therefore, the experimental outcomes may depend on the availability of sufficiently strong
perturbation, required to dislodge the system from a metastable equilibrium. We report good agreement between experimental results and
theoretical/computational predictions. In general, a deeper and narrower hole favors the filled outcome.
Acta Materialia, 2020
Diffusion bonding of ceramics with a metallic interlayer can give a variety of very complex joint... more Diffusion bonding of ceramics with a metallic interlayer can give a variety of very complex joint microstruc-tures, which are highly influenced by ceramic compositions, the material and thickness of the interlayer, bonding temperature as well as time at the peak bonding temperature. Experiments with a diffusion bonding of ZrC using a Ti interlayer clearly show that under a certain bonding condition, a seamless joint with the total dissolution of the interlayer can be obtained. They also indicate the existence of the critical interlayer thickness, below which the seamless homogeneous joint domain is obtained, and above which the joint does not homogenize. The key process leading to these outcomes is the diffusion of carbon from ZrC into Ti, which, when the critical carbon concentration is reached, initiates the phase transformation of bcc Ti to TiC, while the binary Zr/Ti diffusion is then driven by entropy and results in a seamless Zr(Ti)C joint. We first show that the dependence of ZrC/Ti interfacial energy on the carbon concentration jump across the interface is the main thermodynamic driving force of the diffusion of carbon from ZrC to the Ti interlayer. Then, we show that the characteristic length (critical thickness of the interlayer) arises as the ratio of this driving force (energy/area) and the bulk energy densities, which oppose the carbon diffusion. Finally, we develop a diffuse interface (phase-field) model to simulate the process. The novelty in the phase-field model is the introduction of a dependence of the interfacial energy on the carbon concentrations on the two sides of the interface. The critical thickness of the interlayer is estimated employing both models and good agreement with experimental findings is obtained.
Using the apparatus of traditional differential geometry, the transport theorem is derived for th... more Using the apparatus of traditional differential geometry, the transport theorem is derived for the general case of a M-dimensional domain moving in a N-dimensional space, £ M N . The interesting concepts of curvatures and normals are illustrated with well-known examples of lines, surfaces and volumes. The special cases where either the space or the moving subdomain are material are discussed. Then, the transport at hypersurfaces of discontinuity is considered. Finally, the general local balance equations for continuum of arbitrary dimensions with discontinuities are derived.
Mathematics, 2020
Using the apparatus of traditional differential geometry, the transport theorem is derived for th... more Using the apparatus of traditional differential geometry, the transport theorem is derived for the general case of a M-dimensional domain moving in a N-dimensional space, £ M N. The interesting concepts of curvatures and normals are illustrated with well-known examples of lines, surfaces and volumes. The special cases where either the space or the moving subdomain are material are discussed. Then, the transport at hypersurfaces of discontinuity is considered. Finally, the general local balance equations for continuum of arbitrary dimensions with discontinuities are derived.
Mesoscale Models: From Micro-Physics to Macro-Interpretation, 2019
Assume that the physics on the microscale (interactions between atoms,
molecules, defects in crys... more Assume that the physics on the microscale (interactions between atoms,
molecules, defects in crystals . . . ) is understood.What is the appropriate mesoscale
continuum theory for the problem? What are the assumptions involved and how do
they define the limitations of the continuum model? To answer these questions, we
begin with the definition of mesoscale continuum kinematics from the microscale
kinematics. The geometry of micro-structure (e.g., order vs. disorder) has a decisive
role in defining the continuum kinematics. We thus arrive at three kinematic
formulations: mass continuum, lattice continuum and granular continuum. Then,
upon formulating the power balance, we use the principle of virtual power to
arrive at a variety of mathematical formulations: simple continuum with moving
boundaries, phase field formulation, and, a higher order, size-dependent continuum.
The problems considered include: mixing of fluids and capillary flows, granular
flow/deformation, and, polycrystalline diffusional/dislocation creep accompanied
by dislocation plasticity.
In the light of recent progress in coarsening the
discrete dislocation mechanics, we consider tw... more In the light of recent progress in coarsening the
discrete dislocation mechanics, we consider two
questions relevant for the development of a
mesoscale, size-dependent plasticity: (i) can the
phenomenological expression for size-dependent
energy, as quadratic form of Nye’s dislocation
density tensor, be justified from the point of view of
dislocation mechanics and under what conditions?
(ii) how can physical or phenomenological
expressions for size-dependent energy be computed
from dislocation mechanics in the general case of
elastically anisotropic crystal? The analysis based
on material and slip system symmetries implies the
negative answer to the first question. However,
the coarsening method developed in response to
the second question, and based on the physical
interpretation of the size-dependent energy as the
coarsening error in dislocation interaction energy,
introduces additional symmetries. The result is that
the equivalence between the phenomenological and
the physical expressions is possible, but only if the
multiplicity of characteristic lengths associated with
different slip systems, is sacrificed. Finally, we discuss
the consequences of the assumption that a single
length scale governs the plasticity of a crystal, and
note that the plastic dissipation at interfaces has a
strong dependence on the length scale embedded in
the energy expression.
Theoretical and Applied Mechanics, 2017
Phase field (diffuse interface) models accommodate diffusive triple line motion with variable con... more Phase field (diffuse interface) models accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. We consider two commonly used classes of phase field models: the compositionally compressible (CC) model with compressibility limited to the fluid mix within the diffuse interface, and the incompressible (IC) model. First, we show that the CC model applied to fluids with dissimilar mass densities exhibits the computational instability leading to the breakup of the triple line. We provide a qualitative physical explanation of this instability and argue that the compositional compressibil-ity within the diffuse interface is inconsistent with the global incompressible flow. Second, we derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. Third, we benchmark the IC model against sharp interface theory and experimental ki-netics. The triple line kinetics is well represented by the triple line mobility parameter. Finally, we investigate the effects of the bulk phase field diffusional mobility parameter on the kinetics of the wetting process and find that within a wide range of magnitudes the bulk mobility does not affect the flow.
Kinetics of liquid-metal spreading over a substrate
is of fundamental importance for applications... more Kinetics of liquid-metal spreading over a substrate
is of fundamental importance for applications of a
number of high-temperature capillary-driven phenomena in
technological processes, e.g., bonding by soldering or
brazing. The sharp interface model combined with the
Navier–Stokes equations and no-slip condition at the solid–
fluid interface, results in unphysical stress singularities.
Moreover, molecular dynamics studies indicate that the
motion of the triple line proceeds by uncorrelated movement
of fluid atoms on the solid surface, i.e., diffusion.
Hence, diffuse interface (phase field) models are the natural
framework for modeling such physical phenomena,
whereby the triple line movement is described in terms of a
local surface diffusion of fluid. Moreover, they are the only
computational models that can describe topological changes
associated with capillary flows (breaking up and coalescence
of fluid domain). This paper offers comprehensive
experimental evidence involving spreading over substrates,
and associated phase-field modeling. A 2-D wedge-tee
joint configuration was considered. The phase-field model
parameters are related to the physical parameters (density,
viscosity interface energies, kinetic barrier for surface
diffusion), and the computational parameters. The latter are
chosen so that neither kinetics nor equilibrium is affected.
Numerical solution of the model indicates excellent
agreement with the ultimately reached equilibrium state,
and follows fully an empirically established trend of the
triple line kinetics. Model is tested by using additional
benchmark processes of spreading water and silicon oil
over non-reactive substrates before implementing it to a
high temperature non-reactive approximation of the liquid metal (Al–Si over aluminum) wetting.
A continuum theory for high temperature creep of polycrystalline solids is developed. It includes... more A continuum theory for high temperature creep of polycrystalline solids is developed. It includes the relevant deformation mechanisms for diffusional and dislocation creep: elasticity with eigenstrains resulting from vacancy diffusion, dislocation climb and glide, and the lattice growth/loss at the boundaries enabled by diffusion. All the deformation mechanisms are described with respect to the crystalline lattice, so that the continuum formulation with lattice motion as the basis is necessary. However, dislocation climb serves as the source sink of lattice sites, so that the resulting continuum has a sink/source of its fundamental component, which is reflected in the continuity equation. Climb as a sink/source also affects the diffusion part of the problem, but the most interesting discovery is the climb-glide interaction. The loss/creation of lattice planes through climb affects the geometric definition of crystallographic slip and necessitates the definition of two slip fields: the true slip and the effective slip. The former is the variable on which the dissipative power is expanded during dislocation glide and is thus, the one that must enter the glide constitutive equations. The latter describes the geometry of the slip affected by climb, and is necessary for kinematic analysis.
Diffusional creep is characterized by growth/ disappearance of lattice planes at the crystal boun... more Diffusional creep is characterized by growth/ disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro– Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro–Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.
We investigate the mechanisms of incipient plasticity at low angle twist and asymmetric tilt boun... more We investigate the mechanisms of incipient plasticity at low angle twist and asymmetric tilt boundaries in fcc metals. To observe plasticity of grain boundaries independently of the bulk plasticity, we simulate nanoindentation of bicrystals. On the low angle twist boundaries, the intrinsic grain boundary (GB) dislocation network deforms under load until a dislocation segment compatible with glide on a lattice slip plane is created. The half loops are then emitted into the bulk of the crystal. Asymmetric twist boundaries considered here did not produce bulk dislocations under load. Instead, the boundary with a low excess volume nucleated a mobile GB dislocation and additional GB defects. The GB sliding proceeded by motion of the mobile GB dislocation. The boundary with a high excess volume sheared elastically, while bulk-nucleated dislocations produced plastic relaxation.
Consolidation phenomena are of fundamental importance for additive manufacturing since the qualit... more Consolidation phenomena are of fundamental importance for additive manufacturing since the quality of metal parts produced by selective laser melting (SLM) is greatly dependent on residual porosity. The most recent studies use the lattice Boltzmann method (LBM) to analyze conjugated multiphase flow, heat transport, and phase transitions in the molten zone. A phase-field approach suggested in this paper retains all advantages of LBM and provides an alternative tool for theoretical analysis of SLM. In case of consolidation of composite powders where wetting phenomena are crucial at the matrix-inclusion interfaces , the phase-field method is more suitable. In this paper, the problem of metallic powder consolidation is numerically studied and the dynamics of pore and gas bubbles evolution in the molten zone is described. A two-step mechanism of consolidation is proposed which differs from a single-step mechanism typical for additive manufacturing of polymer powders. The consolidation time for different particle orderings is studied and an algorithm for the parameter selection in the widely used viscoplastic model is derived.
2Si-B-3C-N ceramic was successfully vacuum brazed to Nb. Brazing was executed at 850 °C for 10 mi... more 2Si-B-3C-N ceramic was successfully vacuum brazed to Nb. Brazing was executed at 850 °C for 10 min using Ag-Cu-Ti/Mo/Ag-Cu-Ti composite interlayer. Effects of the Mo interlayer thickness within the composite interlayer on the microstructure of the joint and its shear strength were investigated. In joints brazed without Mo and with 50 μm Mo interlayer a continuous through cracks propagated within the ceramic during cooling. However, no cracks were found in joints when Mo interlayers thicker than 100 μm were used. The improvement of the shear strength with an increase in the thickness of Mo interlayer within the composite interlayer was achieved. To explain the effects of the Mo layer thickness, detailed FEM simulations of the cooling process were performed. The analysis of the residual stress is consistent with the observed joint strengthening and crack propagation.
Complex structures consisting of intertwined, nominally vertical carbon nanotubes (CNTs) are call... more Complex structures consisting of intertwined, nominally vertical carbon nanotubes (CNTs) are called turfs. Under uniform compression experiments, CNT turfs exhibit irreversible collective buckling of a layer preceded by reorientation of CNT segments. Experimentally observed independence of the buckling stress and the buckling wavelength on the turf width suggests the existence of an intrinsic material length. To investigate the relationship the macroscopic material properties and the statistical parameters describing the nanoscale geometry of the turf (tortuosity, density and connectivity) we develop a nano-scale computational model, based on the representation of CNT segments as elastica finite elements with van der Waals interactions. The virtual turfs are generated by means of a constrained random walk algorithm and subsequent relaxation. The resulting computational model is robust and is capable of modeling the collective behavior of CNTs. We first establish the dependence of statistical parameters on the computational parameters used for turf generation, then establish relationships between post-buckling stress, initial elastic modulus and buckling wavelength on statistical turf parameters. Finally, we analyze the reorientation of buckling planes of individual CNTs during the collective buckling process.
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Papers by Sinisa Mesarovic
nonhomogeneous temperature activating a
long-range mass transport
substrate: (i) apparent abrupt or gradual recession stages in the motion of the contact line, (ii) non-monotonic abrupt changes in the receding
contact angle, and (iii) contact angle overshoot above the nominal equilibrium contact angle. We find that such behavior of a liquid metal alloy
cannot be explained by the standard capillary flow models. However, a model that includes the ageing of the equilibrium contact angle predicts all
the observed features qualitatively. We use the phase field formulation for capillary flows with a diffusive motion of the triple line to accommodate
the novel diffusive boundary condition with the time-evolving quasi-equilibrium contact angle.We discover that the observed anomalies in capillary
flow are qualitatively explained by two factors: (1) time evolution (ageing) of the quasi-equilibrium contact angle and (2) high viscosity of the partially
molten braze. We also discover that for the given flow geometry, the transition from the initial to the final configuration may follow two distinct
topological paths: one is characterized by a coalescence of liquid–solid contact domains, the other by a contact separation. The selection of the
two paths in the configurational space is dependent on both contact ageing parameters and viscosity.
capillary flow of a molten metal. We perform two sets of experiments: (1) spreading of a sessile drop of liquid
aluminum-silicon-flux (Al-Si-KxAlyFz) composite braze on a horizontal alumina (Al2O3) substrate (a non-wetting
surface), and (2) capillary flow of the same braze alloy on an inclined aluminum-manganese (AA3003) substrate
(a wetting surface). We vary the mass of the brazing liquid and the inclination of the substrate (i.e., the relative
direction of gravity).
In the composite metal/flux sessile drop experiments, we observe a secondary liquid flux meniscus forming at
the contact line between the liquid Al-Si and the alumina substrate. We demonstrate that the equilibrium contact
angle appears to be close to 180◦, while the apparent contact angle depends on the mass of the braze. In the
second set of experiments, we study the molten braze alloy on different inclinations of AA3003 in a wedge-T
wetting/non-wetting assembly. As the inclination angle decreases, the wetting distance increases and the surface
profile changes from a non-symmetric bag-like shape to a more symmetric pancake shape. With the mass
decreasing, the surface profile on the vertical substrate approaches a symmetric shape when the wetting distance
is equal or smaller than the capillary length. While the non-homogeneous melting and hence, the nonhomogeneous
microstructure of the melt, may prevent a full symmetry. Computational predictions of equilibrium
shapes are in good agreement with experimental results.
conditions. The negligible effects of gravity and dominance of capillary forces can be approximated under terrestrial conditions, provided
that the hole and the quantity of liquid are small, as quantified by the Bond number. In this paper, we report experimental results, modeling,
and analysis of the hole-filling problem using the liquid aluminum brazing alloy on aluminum substrate. Depending on the hole size, the
capillary driven flow may result in the hole being either filled or not filled. The equilibrium problem (energy minimization) has multiple
solutions in some regions of the parameter space. Therefore, the experimental outcomes may depend on the availability of sufficiently strong
perturbation, required to dislodge the system from a metastable equilibrium. We report good agreement between experimental results and
theoretical/computational predictions. In general, a deeper and narrower hole favors the filled outcome.
molecules, defects in crystals . . . ) is understood.What is the appropriate mesoscale
continuum theory for the problem? What are the assumptions involved and how do
they define the limitations of the continuum model? To answer these questions, we
begin with the definition of mesoscale continuum kinematics from the microscale
kinematics. The geometry of micro-structure (e.g., order vs. disorder) has a decisive
role in defining the continuum kinematics. We thus arrive at three kinematic
formulations: mass continuum, lattice continuum and granular continuum. Then,
upon formulating the power balance, we use the principle of virtual power to
arrive at a variety of mathematical formulations: simple continuum with moving
boundaries, phase field formulation, and, a higher order, size-dependent continuum.
The problems considered include: mixing of fluids and capillary flows, granular
flow/deformation, and, polycrystalline diffusional/dislocation creep accompanied
by dislocation plasticity.
discrete dislocation mechanics, we consider two
questions relevant for the development of a
mesoscale, size-dependent plasticity: (i) can the
phenomenological expression for size-dependent
energy, as quadratic form of Nye’s dislocation
density tensor, be justified from the point of view of
dislocation mechanics and under what conditions?
(ii) how can physical or phenomenological
expressions for size-dependent energy be computed
from dislocation mechanics in the general case of
elastically anisotropic crystal? The analysis based
on material and slip system symmetries implies the
negative answer to the first question. However,
the coarsening method developed in response to
the second question, and based on the physical
interpretation of the size-dependent energy as the
coarsening error in dislocation interaction energy,
introduces additional symmetries. The result is that
the equivalence between the phenomenological and
the physical expressions is possible, but only if the
multiplicity of characteristic lengths associated with
different slip systems, is sacrificed. Finally, we discuss
the consequences of the assumption that a single
length scale governs the plasticity of a crystal, and
note that the plastic dissipation at interfaces has a
strong dependence on the length scale embedded in
the energy expression.
is of fundamental importance for applications of a
number of high-temperature capillary-driven phenomena in
technological processes, e.g., bonding by soldering or
brazing. The sharp interface model combined with the
Navier–Stokes equations and no-slip condition at the solid–
fluid interface, results in unphysical stress singularities.
Moreover, molecular dynamics studies indicate that the
motion of the triple line proceeds by uncorrelated movement
of fluid atoms on the solid surface, i.e., diffusion.
Hence, diffuse interface (phase field) models are the natural
framework for modeling such physical phenomena,
whereby the triple line movement is described in terms of a
local surface diffusion of fluid. Moreover, they are the only
computational models that can describe topological changes
associated with capillary flows (breaking up and coalescence
of fluid domain). This paper offers comprehensive
experimental evidence involving spreading over substrates,
and associated phase-field modeling. A 2-D wedge-tee
joint configuration was considered. The phase-field model
parameters are related to the physical parameters (density,
viscosity interface energies, kinetic barrier for surface
diffusion), and the computational parameters. The latter are
chosen so that neither kinetics nor equilibrium is affected.
Numerical solution of the model indicates excellent
agreement with the ultimately reached equilibrium state,
and follows fully an empirically established trend of the
triple line kinetics. Model is tested by using additional
benchmark processes of spreading water and silicon oil
over non-reactive substrates before implementing it to a
high temperature non-reactive approximation of the liquid metal (Al–Si over aluminum) wetting.
nonhomogeneous temperature activating a
long-range mass transport
substrate: (i) apparent abrupt or gradual recession stages in the motion of the contact line, (ii) non-monotonic abrupt changes in the receding
contact angle, and (iii) contact angle overshoot above the nominal equilibrium contact angle. We find that such behavior of a liquid metal alloy
cannot be explained by the standard capillary flow models. However, a model that includes the ageing of the equilibrium contact angle predicts all
the observed features qualitatively. We use the phase field formulation for capillary flows with a diffusive motion of the triple line to accommodate
the novel diffusive boundary condition with the time-evolving quasi-equilibrium contact angle.We discover that the observed anomalies in capillary
flow are qualitatively explained by two factors: (1) time evolution (ageing) of the quasi-equilibrium contact angle and (2) high viscosity of the partially
molten braze. We also discover that for the given flow geometry, the transition from the initial to the final configuration may follow two distinct
topological paths: one is characterized by a coalescence of liquid–solid contact domains, the other by a contact separation. The selection of the
two paths in the configurational space is dependent on both contact ageing parameters and viscosity.
capillary flow of a molten metal. We perform two sets of experiments: (1) spreading of a sessile drop of liquid
aluminum-silicon-flux (Al-Si-KxAlyFz) composite braze on a horizontal alumina (Al2O3) substrate (a non-wetting
surface), and (2) capillary flow of the same braze alloy on an inclined aluminum-manganese (AA3003) substrate
(a wetting surface). We vary the mass of the brazing liquid and the inclination of the substrate (i.e., the relative
direction of gravity).
In the composite metal/flux sessile drop experiments, we observe a secondary liquid flux meniscus forming at
the contact line between the liquid Al-Si and the alumina substrate. We demonstrate that the equilibrium contact
angle appears to be close to 180◦, while the apparent contact angle depends on the mass of the braze. In the
second set of experiments, we study the molten braze alloy on different inclinations of AA3003 in a wedge-T
wetting/non-wetting assembly. As the inclination angle decreases, the wetting distance increases and the surface
profile changes from a non-symmetric bag-like shape to a more symmetric pancake shape. With the mass
decreasing, the surface profile on the vertical substrate approaches a symmetric shape when the wetting distance
is equal or smaller than the capillary length. While the non-homogeneous melting and hence, the nonhomogeneous
microstructure of the melt, may prevent a full symmetry. Computational predictions of equilibrium
shapes are in good agreement with experimental results.
conditions. The negligible effects of gravity and dominance of capillary forces can be approximated under terrestrial conditions, provided
that the hole and the quantity of liquid are small, as quantified by the Bond number. In this paper, we report experimental results, modeling,
and analysis of the hole-filling problem using the liquid aluminum brazing alloy on aluminum substrate. Depending on the hole size, the
capillary driven flow may result in the hole being either filled or not filled. The equilibrium problem (energy minimization) has multiple
solutions in some regions of the parameter space. Therefore, the experimental outcomes may depend on the availability of sufficiently strong
perturbation, required to dislodge the system from a metastable equilibrium. We report good agreement between experimental results and
theoretical/computational predictions. In general, a deeper and narrower hole favors the filled outcome.
molecules, defects in crystals . . . ) is understood.What is the appropriate mesoscale
continuum theory for the problem? What are the assumptions involved and how do
they define the limitations of the continuum model? To answer these questions, we
begin with the definition of mesoscale continuum kinematics from the microscale
kinematics. The geometry of micro-structure (e.g., order vs. disorder) has a decisive
role in defining the continuum kinematics. We thus arrive at three kinematic
formulations: mass continuum, lattice continuum and granular continuum. Then,
upon formulating the power balance, we use the principle of virtual power to
arrive at a variety of mathematical formulations: simple continuum with moving
boundaries, phase field formulation, and, a higher order, size-dependent continuum.
The problems considered include: mixing of fluids and capillary flows, granular
flow/deformation, and, polycrystalline diffusional/dislocation creep accompanied
by dislocation plasticity.
discrete dislocation mechanics, we consider two
questions relevant for the development of a
mesoscale, size-dependent plasticity: (i) can the
phenomenological expression for size-dependent
energy, as quadratic form of Nye’s dislocation
density tensor, be justified from the point of view of
dislocation mechanics and under what conditions?
(ii) how can physical or phenomenological
expressions for size-dependent energy be computed
from dislocation mechanics in the general case of
elastically anisotropic crystal? The analysis based
on material and slip system symmetries implies the
negative answer to the first question. However,
the coarsening method developed in response to
the second question, and based on the physical
interpretation of the size-dependent energy as the
coarsening error in dislocation interaction energy,
introduces additional symmetries. The result is that
the equivalence between the phenomenological and
the physical expressions is possible, but only if the
multiplicity of characteristic lengths associated with
different slip systems, is sacrificed. Finally, we discuss
the consequences of the assumption that a single
length scale governs the plasticity of a crystal, and
note that the plastic dissipation at interfaces has a
strong dependence on the length scale embedded in
the energy expression.
is of fundamental importance for applications of a
number of high-temperature capillary-driven phenomena in
technological processes, e.g., bonding by soldering or
brazing. The sharp interface model combined with the
Navier–Stokes equations and no-slip condition at the solid–
fluid interface, results in unphysical stress singularities.
Moreover, molecular dynamics studies indicate that the
motion of the triple line proceeds by uncorrelated movement
of fluid atoms on the solid surface, i.e., diffusion.
Hence, diffuse interface (phase field) models are the natural
framework for modeling such physical phenomena,
whereby the triple line movement is described in terms of a
local surface diffusion of fluid. Moreover, they are the only
computational models that can describe topological changes
associated with capillary flows (breaking up and coalescence
of fluid domain). This paper offers comprehensive
experimental evidence involving spreading over substrates,
and associated phase-field modeling. A 2-D wedge-tee
joint configuration was considered. The phase-field model
parameters are related to the physical parameters (density,
viscosity interface energies, kinetic barrier for surface
diffusion), and the computational parameters. The latter are
chosen so that neither kinetics nor equilibrium is affected.
Numerical solution of the model indicates excellent
agreement with the ultimately reached equilibrium state,
and follows fully an empirically established trend of the
triple line kinetics. Model is tested by using additional
benchmark processes of spreading water and silicon oil
over non-reactive substrates before implementing it to a
high temperature non-reactive approximation of the liquid metal (Al–Si over aluminum) wetting.
of materials on multiple length and time scales. In particular, the finest scale (ab
initio, atomistic level) and coarsest (classic continua) are well understood and are
now fine-tuned for numerous applications. From numerous studies, the realization
has emerged that most macroscopic properties of materials depend critically on
the mesoscale: the evolving microstructure and interactions which occur on the
length and time scales much larger than atomic, yet much smaller than macroscopic
observables. These lecture notes follow the 1-week advanced course presented in
the International Centre for Mechanical Sciences (CISM), Udine, in May 2017.
The topics of the course are chosen with the following criteria in mind:
• Significant progress has been made in the past decades
• Some outstanding problems remain as a challenge for future researchers.
• The past efforts have been multidisciplinary, and future efforts are expected to
remain such, involving researchers in engineering, physics and mathematics.
Three broad areas representative of the field are selected: dislocation plasticity
and creep of crystals and polycrystals, interfaces in solids and fluids, and granular
deformation and flow.
Geometrical complexity of dislocation assemblies—a mixture of order and
disorder arising from highly constrained, yet rich, kinematics, combined with
the long-range interactions (inherent non-locality)—results in a very challenging
problem. Experimentally observed size effects indicate a size-dependent mesoscale
model, but the consensus about the correct formulation has not been reached.
The structure of crystalline interfaces, mechanisms of their motion, and their
role in the overall deformation of polycrystalline assemblies have been the subject
of intense research but many questions remain open, among which are dislocationinterface
interactions. Fluid interfaces in capillary flows exhibit topological discontinuities
(breaking and coalescence of subdomains). These are effectively handled
with the phase field formulations, so that questions arise regarding the appropriate
phase field model.
Depending on the packing density, the mechanical behavior of granular materials
may resemble that of solids or fluids, but also exhibits unique features (dilatancy,
critical state, shear localization with a characteristic width, vortex flow). Microscopically,
the geometry is strongly disordered and interparticle forces strongly
inhomogeneous. A continuum theory capable of describing all the salient features
is yet to be formulated.
The lecture notes are intended to provide answer to the following general
questions. How far have the understanding and mesoscale modeling advanced in
recent decades?What are the key open questions that require further research?What
are the mathematical and physical requirements for a mesoscale model intended to
provide either insight or a predictive engineering tool?
The book begins and ends with two perspectives on continuum theory. In chapter
“Physical Foundations of Mesoscale Continua” (Mesarovic), the relationship
between microscale physics and mesoscale continua is examined, with a goal of
providing a method for deriving the latter from the former. Chapter “Generalized
Continua and Phase-Field Models: Application to Crystal Plasticity” (Forest)
presents a comprehensive overviewof higher order continua and phase field models.
Chapters “Multiscale Dislocation-Based Plasticity” and “Statistical Theory
of Dislocation” are dedicated to dislocation plasticity. In chapter “Multiscale
Dislocation-Based Plasticity” (Zbib), computational discrete dislocation mechanics
and its relationship to continuum computational models are reviewed. In
chapter “Statistical Theory of Dislocation”, Istvan Groma brings the power of
modern statistical mechanics to bear on discrete dislocation dynamics, with the aim
of formulating a continuum model.
In chapter “Granular Materials: Micromechanical Approaches of Model Systems”,
Jean-Noël Roux gives a comprehensive review of computational experiments
on granular materials (discrete element method) and the advances in understanding
of granular deformation/flow that follows from such experiments.
In chapter “Multiscale Modeling of Interfaces, Dislocations, and Dislocation
Field Plasticity”, David McDowell provides a tour de force through the variety of
length and time scales from first principle models to macroscale continua, with a
broad scope of applications.
The editors are indebted to the CISM for funding and organizing the lectures and
to the guest lecturers for their contributions.