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Acid fracturing is a crucial stimulation technique to enhance hydrocarbon recovery in carbonate reservoirs. However, the interaction between acid fractures and natural fractures remains complex due to the combined effects of mechanical, chemical, and fluid flow processes. This study extends a previously developed hydro-mechano-reactive flow coupled model to analyze these interactions, focusing on the influence of acid dissolution. The model incorporates reservoir heterogeneity and simulates various scenarios, including different stress differences, approaching angles, injection rates, and acid concentrations. Numerical simulations reveal distinct propagation modes for acid and hydraulic fractures, highlighting the significant influence of acid dissolution on fracture behavior. Results show that hydraulic fractures are more likely to cross natural fractures, whereas acid fractures tend to be arrested due to wormhole formation. Increasing stress differences and approaching angles promote fracture crossing, while lower angles favor diversion into natural fractures. Higher injection rates facilitate fracture crossing by increasing pressure accumulation, but excessive acid concentrations hinder fracture initiation due to enhanced wormhole formation. The study demonstrates the importance of tailoring fracturing treatments to specific reservoir conditions, optimizing parameters to enhance fracture propagation and reservoir stimulation. These findings contribute to a deeper understanding of fracture mechanics in heterogeneous reservoirs and offer practical implications for improving the efficiency of hydraulic fracturing operations in unconventional reservoirs. [ABSTRACT FROM AUTHOR]

Recent years, the polarization response of ferroelectrics has been entirely studied. However, it is found that the polarization may disappear gradually with the continually applied of electric field. In this paper, taking K0.48Na0.52NbO3(KNN) as an example, it was demonstrated that the residual polarization began to decrease when the electric field frequency increased to a certain extent using a phase-field methods. The results showed that the content of out-of-plane domains increased first and then decreased with the increase of applied electric field frequency, the maximum polarization disappeared at high frequencies, and the hysteresis loop became elliptical. In order to further study the abnormal changes of hysteresis loops of ferroelectrics under high electric field frequency, we analyzed the hysteresis loop and dielectric response of solid solution 0.1SrTiO3-0.9K0.48Na0.52NbO3. It was found that the doped hysteresis loop maintained its shape at higher frequency and the dielectric constant increased. This kind of doping has a higher field frequency adaptability, which has a key guiding role in improving the dielectric properties of ferroelectric thin films and expanding the frequency application range of ferroelectric nano memory. [ABSTRACT FROM AUTHOR]

The thermal–mechanical–electrical-diffusion strongly coupled equations are established, and the phase field method is employed to investigate the dynamic simulation of intermetallic compound (IMC) evolution at the Cu/Sn/Cu micro-solder joint interface. By comparing with experimental results on IMC evolution in micro-solder joints, this study explores the evolution law of IMCs under the influence of current, temperature, and applied load coupling. Both simulation and experimental findings indicate that higher current density promotes IMC formation, with the largest average thickness observed at a current density of 5000 A/m2. When the analog current density is 5000 A/m2, the anode IMC has a rapid growth period at 62 h, and the corresponding cathode has a rapid consumption period; when the analog current density is 4000 A/m2, the anode has the same phenomenon in 95 h; when the analog current density is 3000 A/m2, this phenomenon is not evident. The observed phenomena are consistent with the evolutionary trend of IMC from the fourth to the fifth day of the experiment, considering it may be affected by 'electronic wind stress' which makes the cathode IMC migrate to the anode. The average thickness of IMCs with an analog ambient temperature of 323–353 K is the largest, which is most suitable for the growth of IMCs. The experimental results also indicate that IMC growth is the fastest at 353 K. The anode IMC was inhibited by tensile stress and shear stress, but the effect on cathode was not obvious. [ABSTRACT FROM AUTHOR]

The tensile failure of complex branching cracks will cause irreversible damage to the structures. In this paper, the effects of the crack orientations, the local branch lengths, and the different load forms on the crack propagation pattern and the bearing capacity of structures are investigated based on the phase field method and experimental research method. The results show that the bearing capacity and propagation patterns of the specimens change significantly with the change of the orientation of the Y-shaped crack under tensile load. The local branch length of the crack only affects the sequence in which the regional crack reaches the final failure and the bearing capacity of the specimen. Under the dynamic impact load, the bifurcation phenomenon occurs, and with the increase of the dynamic impact load, the number of bifurcations increases. The crack propagation pattern in the numerical simulation is completely consistent with the experiment, and the difference in the maximum reaction force is 2.5%. [ABSTRACT FROM AUTHOR]

The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology. [ABSTRACT FROM AUTHOR]

Water freezing in rock fractures causes volumetric expansion and fracture development through frost heaving. This study introduces a novel analytical model to investigate how uneven freezing force and surrounding rock pressure influence fracture initiation, based on mass conservation, elasticity, and water-ice phase transition principles. A model for rock fracture initiation considering freezing temperature, uneven freezing expansion, in-situ stress, and lateral pressure was proposed based on fracture mechanics. Equations for stress intensity factors were developed and validated using the phase field method. The effects of rock elastic modulus anisotropy and critical fracture energy density on fracture initiation were also discussed. The results show that the values of KI and KII exhibit an upward trend as the freezing temperature, uneven expansion, in-situ stress, and lateral pressure increase. The uneven freezing expansion has the most significant influence on KI and KII values among these parameters. As the uneven freezing expansion coefficient increases to 0.5, the fracture initiation mode shifts from tensile fracture to shear fracture. As the lateral pressure coefficient increases to 1, the fracture initiation mode shifts from tensile fracture to shear fracture. Rock elastic modulus anisotropy causes fractures to propagate in a clockwise direction, forming a 'butterfly' pattern. Critical fracture energy density an isotropy causes counterclockwise deviation in propagation direction, resulting in branching paths and an 'H'-shaped pattern. [ABSTRACT FROM AUTHOR]

Drop impact is common in industrial applications and nature. As in the 3D printing, the drops squeezed out of the nozzle do not have to take on a spherical shape. This paper delves into the role of drop shape in drop impact with solidification under the 3D printing conditions. To track the rapidly evolving liquid-gas interface, the Cahn-Hilliard-based phase field method is employed. The solid-liquid interface is tracked by the liquid fraction. The model is discretized using an explicit finite difference scheme on a half-staggered grid. The code was written in FORTRAN and enhanced with the OpenMP technique. After being validated against experimental data, the model was applied to various cases. Moreover, the paper took into account a number of factors influencing drop impact and solidification dynamics, such as aspect ratio, contact angle, and thermal contact resistance. It was found that the aspect ratio exerts little effect on drop profile for the cases under consideration when solidification is on, but that the contact angle could drastically reduce freezing time, converting the convex solidfication pattern to a concave one. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Synthetic Crystals is the property of Journal of Synthetic Crystals Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In response to the problem that the standard AT2 phase field model cannot effectively model quasi-brittle failure and the existence of length dependence, a new modified phase field model is presented in this paper. By introducing an additional energy, the competing relationship between elastic strain energy and dissipation energy during fracture is changed. A new crack dissipation functional is established using the energy equivalent approach. By introducing a novel rational degradation function, not only can the strength of material failure be effectively utilized, but the model can also reproduce the cohesive softening relationship. A multi-field finite element method is used to discretize the model governing equations, and the equations are solved by an efficient BFGS monolithic algorithm. Finally, some representative numerical examples are used to analyze the effects of parameters in degradation function, length scale and mesh size on the results. The presented numerical simulation results demonstrate length scale and mesh scale independence, and are in good agreement with the experimental results and previous numerical results. At the same time, the numerical results also exhibit cohesive softening properties similar to the current phase field cohesive zone model. These results verify the robustness and effectiveness of the modified phase field model presented in this paper for simulating quasi-brittle failure and brittle fracture. [ABSTRACT FROM AUTHOR]

A framework of the topology optimization incorporated with the phase field method considering the interfacial damage for optimizing the fracture resistance of inclusion-matrix composites is presented. The topology optimization was performed to redistribute the inclusion phase in order to reduce its volume while keeping the fracture resistance value of the initial design unchanged. The phase field method uses two scalar phase field variables: one is for the bulk crack and the other is for the interfacial crack. The decomposition of the strain tensor into compression and tension parts was incorporated into this phase field method to improve the mechanical behaviors of the materials. These compression and tension strain parts are orthogonal in the context of the inner product in which the tensor of elastic stiffness behaves as a metric. Moreover, in the simulation process, an investigation of the effects of the interfacial parameters on the numerical results was discussed. Through the obtained results, the method proposed is demonstrated to be accurate and efficient in eliminating spurious effects and singularity points on the behavior curves in the damage process. [ABSTRACT FROM AUTHOR]

The 6–8 wt% yttria-stabilized zirconia with a tetragonal structure (t′-YSZ) is extensively employed in thermal barrier coatings. The exceptional fracture toughness of t′-YSZ can be attributed to its distinctive ferroelastic toughening mechanism. Micro-structure and interface tension play a critical role in ferroelastic variant switching at the micro- and nano-scale. This paper presents an original thermodynamically consistent phase field (PF) theory for analyzing ferroelastic variant switching at the micro- and nano-scale of t′-YSZ. The theory incorporates strain gradient elasticity using higher-order elastic energy and interface tension tensor via geometric nonlinearity to represent biaxial tension resulting from interface energy. Subsequently, a mixed-type formulation is employed to implement the higher-order theory through the finite element method. For an interface in equilibrium, the effects of strain gradient elasticity result in a more uniform distribution of stresses, whereas the presence of interface tension tensor significantly amplifies the stress magnitude at the interface. The introduction of an interface tension tensor increases the maximum value of stress at the interface by a factor of 4 to 10. The nucleation and evolution of variants at a pre-existing crack tip in a mono-phase t′-YSZ have also been studied. The strain gradient elasticity is capable of capturing the size effect of ferroelastic variant switching associated with microstructures in experiments. Specifically, when the grain size approaches that of the specimen, the critical load required for variant switching at the crack tip increases, resulting in greater dissipation of elastic energy during ferroelastic variant switching. Moreover, the interface tension accelerates the evolution of variants. The presented framework exhibits significant potential in modeling ferroelastic variant switching at the micro- and nano-scale. [ABSTRACT FROM AUTHOR]

Purpose: This study aimed to explore how the microarchitectural features of lacunae and perilacunar zones impact the biomechanics of microdamage accumulation in cortical bone, crucial for understanding bone disorders' pathogenesis and developing preventive measures. Methods: Utilizing the phase field finite element method, the study analyzed three bone unit models with varying microarchitecture: one without lacunae, one with lacunae and one including perilacunar zones, to assess their effects on cortical bone's biomechanical properties. Results: The presence of lacunae was found to increase microcrack initiation risk, acting as nucleation points and accelerating microcrack propagation. Proximity to Haversian canals exacerbated stress concentration, speeding microdamage progression. Conversely, perilacunar zones mitigated both initiation and propagation. An elevated critical energy release rate correlated with slower crack growth and reduced damage severity. Conclusions: The research sheds light on the intricate mechanisms governing microcrack behavior in compact bone, highlighting the significant role of bone's microarchitectural features in its biomechanical response to microdamage. These insights are valuable for the development of strategies to prevent and treat bone-related disorders. [ABSTRACT FROM AUTHOR]

Copyright of Inorganic Chemicals Industry is the property of Editorial Office of Inorganic Chemicals Industry and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We investigate the dynamics of turbulence and interfacial waves in an oil–water channel flow. We consider a stratified configuration, in which a thin layer of oil flows on top of a thick layer of water. The oil–water interface that separates the two layers mutually interacts with the surrounding flow field, and is characterized by the formation and propagation of interfacial waves. We perform direct numerical simulation of the Navier-Stokes equations coupled with a phase field method to describe the interface dynamics. For a given shear Reynolds number, R e τ = 300 , and Weber number, W e = 0.5 , we consider three different types of oils, characterized by different viscosities, and thus different oil-to-water viscosity ratios μ r = μ o / μ w (being μ o and μ w oil and water viscosities). Starting from a matched viscosity case, μ r = 1 , we increase the oil-to-water viscosity ratio up to μ r = 100 . By increasing μ r , we observe significant changes both in turbulence and in the dynamics of the oil–water interface. In particular, the large viscosity of oil controls the flow regime in the thin oil layer, as well as the turbulence activity in the thick water layer, with direct consequences on the overall channel flow rate, which decreases when the oil viscosity is increased. Correspondingly, we observe remarkable changes in the dynamics of waves that propagate at the oil–water interface. In particular, increasing the viscosity ratio from μ r = 1 to μ r = 100 , waves change from a two-dimensional, nearly-isotropic pattern, to an almost monochromatic one. [ABSTRACT FROM AUTHOR]

In this article, we consider a gradient flow stemming from a problem in two-scale topology optimization. We use the phase-field method, where a Ginzburg–Landau term with obstacle potential is added to the cost functional, which contains the usual compliance but also an additional contribution including a local volume constraint in a penalty term. The minimization of such an energy by its gradient-flow is analyzed in this paper. We use an regularization and discretization of the associated state-variable to show the existence of weak solutions to the considered system. [ABSTRACT FROM AUTHOR]

Copyright of Petroleum Geology & Recovery Efficiency is the property of Petroleum Geology & Recovery Efficiency and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Stiffness degradation resulting from matrix cracking has a great impact on the vibrational behaviors of composite laminates. However, the vibration frequencies of functionally graded graphene-reinforced composite (FG-GRC) plates with crack defects remain largely unexplored. In this paper, the variational phase field theory is implemented to investigate the vibration characteristics of cracked FG-GRC plates subjected to thermal conditions. The effective elastic constants depending on the temperature of FG-GRC plates are characterized by the extended Halpin-Tsai model. The first-order shear deformation theory (FSDT) is employed to describe the displacement fields of the cracked FG-GRC plates. The meshfree kernel particle method is engaged to discretize governing equations over the computational domain and then the obtained governing eigen-equations are calculated using the Ritz methodology. The numerical results illustrate the influences of crack length, crack number, the strength of foundations, graphene distribution, temperature variation and geometric values on the vibration fundamental frequencies of the FG-GRC plates. The present work not only provides an alternative and feasible approach for solving the interaction problems between cracking and vibration, but also makes significant advances to characterize the vibrational behaviors of cracked functionally graded materials for engineering applications. [ABSTRACT FROM AUTHOR]

Topology optimization of eigenfrequencies has significant applications in science, engineering, and industry. Eigenvalue problems as constraints of optimization with partial differential equations are solved repeatedly during optimization and design process. The nonlinearity of the eigenvalue problem leads to expensive numerical solvers and thus requires huge computational costs for the whole optimization process. In this paper, we propose a simple yet efficient linearization approach and use a phase field method for topology optimization of eigenvalue problems with applications in two models: vibrating structures and photonic crystals. More specifically, the eigenvalue problem is replaced by a linear source problem every few optimization steps for saving computational costs. Numerical evidence suggests first-order accuracy of approximate eigenvalues and eigenfunctions with respect to the time step and mesh size. Numerical examples are presented to illustrate the effectiveness and efficiency of the algorithms. [ABSTRACT FROM AUTHOR]

Laser cladding is a new additive manufacturing technology that has emerged in recent years. It offers the advantages of a dense cladding layer structure and good bonding with the substrate, making it suitable for repairing parts surfaces and with broad application prospects. Mechanical properties are key performance indicators of the cladding layer. However, the small size and inhomogeneous structure of the cladding layer make it difficult to prepare mechanical properties tests. The microstructure is a key factor affecting the mechanical properties of the cladding layer. Therefore, it is urgent to carry out research on microstructure simulation of the laser cladding layer in order to obtain its mechanical properties. This paper provides a summary of the commonly used microstructure simulation methods, including the research achievements of phase field method, Monte Carlo (MC) method, and cellular automaton (CA) method in the microstructural simulation of laser cladding and metal solidification. The existing problems are analyzed, and the future development direction of this field is forecasted. The phase field method has high accuracy in its simulation results and does not require complex solid–liquid interface tracking, but its solution is complex, and its calculation efficiency is low due to the large calculation amount. The MC method is relatively simple to calculate and does not assume specific grains, but lacks physical basis for the quantitative analysis of the impact of various physical phenomena. The CA method is a commonly used microstructure simulation method with clear physical significance, high computational efficiency, and low cost and has broad prospects for development. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Xi'an Polytechnic University is the property of Editorial Department of Journal of Xi'an Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The growth of lithium dendrite in solid electrolytes has become a major obstacle to the development of solid-state lithium batteries. Lithium dendrite can cause problems such as reduced Coulombic efficiency and shortened lifespan of the battery, and may even cause short circuits that lead to battery failure. The phase field method is used to establish a coupled electro-thermo-mechanical model to study the growth of lithium dendrite, and the plastic behavior of lithium dendrite is also considered. Based on the theory of heat transfer models, the influence of temperature changes on the morphology of lithium dendrite and von Mises stress are analyzed. Using the theory of plastic work, the influence of temperature changes and external pressure changes on the plastic strain of lithium dendrite are analyzed. The results show that the inhibition effect on lithium dendrite is more significant with increasing external pressure and temperature values, and von Mises stress also increases. Lithium dendrite may fracture due to excessive von Mises stress and form dead lithium. The equivalent plastic strain of lithium dendrite increases with the increase of temperature and external pressure values. [ABSTRACT FROM AUTHOR]

A phase field method based on the Cahn‐Hilliard equation was used to establish a numerical model for the motion and coalescence of multiple droplets under an electric field. The influencing factors of the droplet coalescence rate, velocity field and pressure field distributions, and droplet cluster motion and coalescence were investigated. The observations showed that the dynamic behaviors of droplets under the action of the electric field can be characterized as not coming together, coalescence, and breakup after coalescence. High‐speed (low‐speed) and high‐pressure (low‐pressure) regions are generated inside the droplet or near the interface under the action of the electric field, and the size, number, and location of these regions change over time. The results of this study offer an essential guide for developing new electrostatic coalescers. [ABSTRACT FROM AUTHOR]

The phase field method (PFM) has been proposed and incorporated into the finite element method (FEM) for complex crack evolution problems. However, explicit cracks cannot be obtained in the phase field FEM (PFFEM). In the field of rock engineering, explicit cracks are indispensable for hydraulic fracturing problem in which crack opening displacement should be known, and compression-shear crack problems in which contact region should be determined. In this paper, the recently proposed phase field numerical manifold method (PFNMM) is developed to model rock fracturing processes. In PFNMM, PFM is regarded as a fracturing criterion, which deals with crack initiation, propagation, bifurcation and coalescence in a unified form; then crack paths are reconstructed and reproduced from smearing cracks; finally, the physical patches and manifold elements are cut with the reconstructed paths to obtain explicit cracks. The numerical results for several typical examples indicate that rock fracturing processes, including crack initiation without any preset cracks, crack propagation and crack merging, can be explicitly predicted. Besides, the results are in good agreement with the literature. Compared with PFFEM, explicit cracks and jump displacement fields across rock crack faces can be easily obtained by PFNMM. Highlights: The combination of PFM and NMM can reproduce the explicit fracture process in rock. The proposed method is capable of simulating the free opening and closing of cracks. The PFNMM can predict the evolution mechanism of multi-cracks and merging crack. [ABSTRACT FROM AUTHOR]

Natural crack structures significantly affect coal damage, and are a critical problem in mining engineering. In this paper, we introduced the fluorescent epoxy impregnation method (FEIM) to coal failure research, which can obtain cracks with an accuracy of 1 μm by a much lower experimental cost compared with CT scanning. Then we proposed a way to combine FEIM method and the phase-field finite element method (FEM), and established the tensor characterization theory of crack propagation to fully explore the effects of fracture structures on coal failure properties. The results demonstrated that the distribution of initial cracks in coal significantly affected the subsequent failure path at the micro level. Initiation of cracks occurred at the tips of inflection points of existing cracks. The cracks mainly propagated along or perpendicular to existing cracks. The cracks were tightly connected, forming larger crack networks and developing new cracks. The crack tensor theory can describe the crack initiation and propagation process well. The trace of the crack fabric tensor is equal to the total length of all cracks, while the crack orientation tensor describes the direction characteristics of the crack field. Natural cracks in coal greatly affected the initiation location, but the ultimate failure pattern was always shear failure. The proposed method combined experiments and numerical simulations can provide a basic reference for mining engineering. [ABSTRACT FROM AUTHOR]

A novel explicit phase field material point method (ex‐PFMPM) is proposed for modeling dynamic fracture problems. The rate‐dependent phase field governing equation is discretized by a set of particles, and the phase field is updated by the explicit forward‐difference time integration. Furthermore, the stability of the ex‐PFMPM is studied. A novel explicit critical time step formula is obtained based on the system eigenvalues in one dimension and then extended to two and three dimensions. The critical time step formula takes the effect of particle position and neighboring cell interaction into consideration, and can also be used in an explicit phase field finite element method. Several numerical examples, including a dynamic crack branching, a plate with pre‐existing crack under velocity boundary conditions and a three point bending problem are studied to verify the proposed ex‐PFMPM. The use of the history field in the explicit method is studied, which shows that it will lead to fake phase field update and overestimation of the fracture energy in the unloading case. All of the numerical results show that the proposed ex‐PFMPM has the capacity of modeling the crack initiation and propagation problems with both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

A radial well has a unique wellbore configuration. Fracture propagation in radial well deflagration fracturing is studied rarely. The mechanism of interaction between deflagration fractures, natural fractures, and micro-fractures is still unknown. Based on continuum mechanics, damage mechanics, and variational principles, a numerical model of fracture propagation in deflagration fracturing is established with the Hamilton principle and phase-field fracture theory. The effects of horizontal principal stress difference, natural fracture distribution, and micro-fractures around the wellbore on fracture propagation in deflagration fracturing are studied. First, when no natural fractures are developed around the radial well, fractures are initiated at both ends of the radial well. Second, when there are three natural fractures around the radial well, the created fractures have the morphology of shorter fractures in the middle and longer fractures on both sides under stress interference mechanisms. Third, a larger density of natural fractures causes obvious stress superposition, changes the initiation points of radial wells and fracture morphology, and increases fracture width and reservoir stimulation volume. Fourth, as the micro-fractures increase, their interference and induction effects on deflagration fractures are enhanced gradually, and the deflection angle of fractures increases by 38.7%. The study provides a reference for optimizing deflagration fracturing in a radial well. [ABSTRACT FROM AUTHOR]

We discuss the interaction of the strongly nonlinear fluid motion induced by the collapse of a vapor microbubble over a planar surface and the elastic dynamics of the underlying solid. The fluid is described using an extension of the Navier-Stokes equations endowed with distributed capillary stresses in the context of a diffuse interface approach. The collapse of the bubble is triggered by overpressure in the liquid and leads to an intense jet that pierces the bubble, changing the bubble topology from spheroidal to toroidal, and impinges the solid wall inducing an intense and strongly localized load. Moreover, at bubble collapse, a compression wave is launched into the liquid surrounding the bubble. By propagating along the solid surface, the compression wave combined with the liquid jet excites the dynamics of the elastic solid, producing a complex system of waves, including, longitudinal, transversal, and Rayleigh waves, propagating in the solid. It is conjectured that the intense deformation of the solid induced by the strongly localized liquid jet may lead to the plastic deformation of the solid producing the surface pitting observed in many applications subject to cavitation-induced material damage. [ABSTRACT FROM AUTHOR]

The dynamic growth process of intermetallic compounds (IMCs) at the interface of copper–tin coating and the process of microvoid formation were studied using the phase field method combined with thermal–mechanical–electrical diffusion coupling theory. Numerical results show that the thickness of IMCs in the copper–tin coating increased rapidly and then slowly. Current density had a significant effect on the growth of IMCs at the interface. Under the action of electromigration, the thickness of IMCs at the anode was much greater than that at the cathode, which was consistent with the experimental results. The thickness of IMCs increased with the increase in current density. The influence of a rough interface on IMCs was also studied. Uneven diffusion occurred in the rough interface, resulting in microvoids, and the electromigration effect was one of the reasons for the unbalanced diffusion. [ABSTRACT FROM AUTHOR]

Primary dendrite arm spacing (PDAS) is a crucial microstructural feature in nickel-based superalloys produced by laser cladding. In order to investigate the effects of process parameters on PDAS, a multi-scale model that integrates a 3D transient heat and mass transfer model with a quantitative phase-field model was proposed to simulate the dendritic growth behavior in the molten pool for laser cladding Inconel 718. The values of temperature gradient (G) and solidification rate (R) at the S/L interface of the molten pool under different process conditions were obtained by multi-scale simulation and used as input for the quantitative phase field model. The influence of process parameters on microstructure morphology in the deposition layer was analyzed. The result shows that the dendrite morphology is in good agreement with the experimental result under varying laser power (P) and scanning velocity (V). PDAS was found to be more sensitive to changes in laser scanning velocity, and as the scanning velocity decreased from 12 mm/s to 4 mm/s, the PDAS increased by 197% when the laser power was 1500 W. Furthermore, smaller PDAS can be achieved by combining higher scanning velocity with lower laser power. [ABSTRACT FROM AUTHOR]

Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, a phase field method based on the Cahn–Hilliard equation was used to simulate the spinodal decomposition in Zr-Nb-Ti alloys, and the effects of Ti concentration and aging temperature (800–925 K) on the spinodal structure of the alloys for 1000 min were investigated. It was found that the spinodal decomposition occurred in the Zr-40Nb-20Ti, Zr-40Nb-25Ti and Zr-33Nb-29Ti alloys aged at 900 K with the formation of the Ti-rich phases and Ti-poor phases. The spinodal phases in the Zr-40Nb-20Ti, Zr-40Nb-25Ti and Zr-33Nb-29Ti alloys aged at 900 K were in an interconnected non-oriented maze-like shape, a discrete droplet-like shape and a clustering sheet-like shape in the early aging period, respectively. With the increase in Ti concentration of the Zr-Nb-Ti alloys, the wavelength of the concentration modulation increased but amplitude decreased. The aging temperature had an important influence on the spinodal decomposition of the Zr-Nb-Ti alloy system. For the Zr-40Nb-25Ti alloy, with the increase in the aging temperature, the shape of the rich Zr phase changed from an interconnected non-oriented maze-like shape to a discrete droplet-like shape, and the wavelength of the concentration modulate increased quickly to a stable value, but the amplitude decreased in the alloy. As the aging temperature increased to 925 K, the spinodal decomposition did not occur in the Zr-40Nb-25Ti alloy. [ABSTRACT FROM AUTHOR]

Copyright of Natural Gas Industry is the property of Natural Gas Industry Journal Agency and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A critical issue in simulating the evolution of a crack using the phase field approach resides in the ability of the model to predict crack nucleation. In this work, we study the impact of the Ambrosio–Tortorelli regularized crack formulation on the phase field model's ability to represent the phenomena of nucleation and early crack propagation in two-dimensional domains under generic boundary conditions. Through numerical experiments we study the nature of the errors introduced by the crack's regularization at the early stages of crack propagation and its critical effects on the predictability of the nucleation phenomenon. We also show that the errors introduced through the regularization of the crack are systematic and can be predicted for a broad range of boundary conditions. Both external and internal crack cases are analyzed and the scalability of the error is verified. We then investigate the nature of the error and identify its localization with reference to the crack geometry. We conclude that the classical formulation of phase field is not designed to predict nucleation without affecting the early propagation of the crack. [ABSTRACT FROM AUTHOR]

Interphase mass transfer is an important solute transport process in two-phase flow in porous media. During two-phase flow, hydrodynamically stagnant and flowing zones are formed, with the stagnant ones being adjacent to the interfaces through which the interphase mass transfer happens. Due to the existence of these stagnant zones in the vicinity of the interface, the mass transfer coefficient decreases to a certain extent. There seems to be a phenomenological correlation between the mass transfer coefficient and the extent of the stagnant zone which, however, is not yet fully understood. In this study, the phase-field method-based continuous species transfer model is applied to simulate the interphase mass transfer of a dissolved species from the immobile, residual, non-aqueous phase liquid (NAPL) to the flowing aqueous phase. Both scenarios, this of a simple cavity and this of a porous medium, are investigated. The effects of flow rates on the mass transfer coefficient are significantly reduced when the stagnant zone and the diffusion length are larger. It is found that the stagnant zone saturation can be a proxy of the overall diffusion length of the terminal menisci in the porous medium system. The early-stage mass transfer coefficient continuously decreases due to the depletion of the solute in the small NAPL clusters that are in direct contact with the flowing water. The long-term mass transfer mainly happens on the interfaces associated with large NAPL clusters with larger diffusion lengths, and the mass transfer coefficient is mainly determined by the stagnant zone saturation. Article highlights: Flow rates can hardly affect the mass transfer coefficient when the stagnant zone and the diffusion length are large. The stagnant zone saturation can be a proxy of the overall diffusion length of the menisci in the porous media system. The correlations between the mass transfer coefficient and the stagnant zone saturations are built, based on simulations at different flow rates. [ABSTRACT FROM AUTHOR]

The phase field method uses a length scale parameter to regularize the discrete crack to a diffuse crack, which removes the numerical tracking of the discontinuities in the displacement. The displacement field is coupled with the phase field and both are solved as a sequentially coupled systems using staggered method. The phase field ϕ varies between zero and unity (i.e., ϕ = 0 for intact region and ϕ = 1 for fully broken region), and it is a scalar. In this study, a new way of implementation is done using ABAQUS software to solve for the two fields. User defined element subroutine (UEL) is used to solve for the phase field variable and user defined material subroutine (UMAT) for the displacement field variable. Phase field model can simulate any complex crack paths and branching even without previously defined cracks. Some benchmark examples of quasi-static brittle fracture and dynamic brittle fracture are solved and verified with the existing numerical results. To account for the rate-dependent effect under high-rate loading, micro-inertia is incorporated into the phase-field model for dynamic fracture as proposed in the literature and verified with one example. [ABSTRACT FROM AUTHOR]

In this paper, a thermomechanical coupled phase field method is developed to model cracks with frictional contact. Compared to discrete methods, the phase field method can represent arbitrary crack geometry without an explicit representation of the crack surface. The two distinguishable features of the proposed phase field method are: (1) for the mechanical phase, no specific algorithm is needed for imposing contact constraints on the fracture surfaces; (2) for the thermal phase, formulations are proposed for incorporating the phase field damage parameter so that different thermal conductance conditions are accommodated. While the stress is updated explicitly in the regularized interface regions under different contact conditions, the thermal conductivity is determined under different conductance conditions. In particular, we consider a pressure-dependent thermal conductance model (PDM) that is fully coupled with the mechanical phase, along with the other three thermal conductance models, i.e., the fully conductive model (FCM), the adiabatic model (ACM), and the uncoupled model (UCM). The potential of this formulation is showcased by several benchmark problems. We gain insights into the role of the temperature field affecting the mechanical field. Several 2D boundary value problems are addressed, demonstrating the model's ability to capture cracking phenomena with the effect of the thermal field. We compare our results with the discrete methods as well as other phase field methods, and a very good agreement is achieved. [ABSTRACT FROM AUTHOR]

Unlike the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS) is free from the limitation of uniform meshes, coupled time step and mesh spacing, and high memory cost. Specifically, the existing interface LBFS (LBFS-CH0) is reconstructed by locally applying the Cahn–Hilliard-based (CH-based) LBM with additional artificial terms. In the framework of LBM, the influence of the additional artificial terms has been assessed. Besides, the comparative study of the CH-based and the Allen–Cahn-based (AC-based) LBM shows that the latter has higher accuracy and stability. Though the LBFS is originated from the LBM, their performances may not be exactly the same. In this study, the AC-based and CH-based LBFS (LBFS-AC and LBFS-CH1) models which can accurately recover the phase field equations are developed from the interface LBM models without any additional terms. The gradient term in the LBFS-AC is discretized by the second-order central difference method. Compared with the LBFS-CH0, the LBFS-CH1 can eliminate the additional terms and recover the true CH equation. Then these interface LBFS models are compared to evaluate their performance and the influence of the additional terms. Different from the LBM, it is found that the CH-based LBFS is superior to the AC-based one in terms of the numerical accuracy and stability. In addition, numerical results show that the additional terms have minor effect on the ability to model the phase interface. This study can provide guidance to ensure the accuracy and stability of interface modeling. Taking into account the accuracy, stability and simplicity, we can conclude that the LBFS-CH0 model could be the first choice to simulate the phase interface in the framework of LBFS. [ABSTRACT FROM AUTHOR]

Fracture initiation, propagation, merging and branching in rocks are considerably complicated and commonly exhibit a great variety of patterns. How to characterize and capture the complicated fracturing process is still a challenging task for recent studies. In this study, a new double phase field model (DPFM) for mixed-mode fractures in rocks modified from triple shear energy criterion is proposed. We introduce two independent phase field variables to describe the tensile fractures and shear fractures individually. In the proposed DPFM, a new fracture driving force based on triple shear energy criterion is proposed and a hybrid formulation is adopted for constructing the new fracture governing equations. Differently from the existing phase field models, our new model can comprehensively consider the influence of cohesion, internal friction angles and intermediate principal stress. Uniaxial compression tests on rock specimens with an inclined flaw and double flaws are performed to validate our DPFM. We also test the fracture patterns of rocks with intermittent fissures in 3D compressive-shear tests. It is observed that the proposed new DPFM can capture the complicated fracturing processes and fracture coalescence types, which are in good agreement with the existing experimental and numerical results. [ABSTRACT FROM AUTHOR]

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In this paper, melting of long Al nanowires is studied using a phase field model in which deviatoric transformation strain described by a kinetic equation produces a promoting driving force for both melting and solidification and consequently, a lower melting temperature is resolved. The coupled system of the Ginzburgâ€"Landau equation for solidification/melting transformation, the kinetic equation for the deviatoric transformation strain and elasticity equations are solved using the COMSOL finite element code to obtain the evolution of melt solution. A deviatoric strain kinetic coefficient is used which results in the same pressure as that calculated with the Laplace equation in a solid neglecting elastic stresses. The surface and bulk melting temperatures are calculated for different nanowire diameters without mechanical loading which shows a good agreement with existing MD and analytical results. For radii R > 5 nm, a complete surface solid-melt interface is created which propagates to the center. For smaller radii, premelting occurs everywhere starting from the surface and the nanowire melts without creating the interface. The melting rate shows an inverse power relationship with radius for R < 15 nm. For melting under pressure, the model with constant bulk modulus results in an unphysical parabolic variation versus pressure in contrast to the almost linear increase of the melting temperature versus pressure from known MD simulations. Such drawback is resolved by considering the pressure dependence of the bulk modulus through the Murnaghan’s equation due to which an almost linear increase of the melting temperature versus pressure is obtained. Also, a reduction of the interface width and a significant increase of the melting rate versus pressure are found. The presented model and results allow for a better understanding of the premelting and melting of different metallic nanowires with various loading conditions and structural defects. [ABSTRACT FROM AUTHOR]

In comparison to Pb-based solders which have a toxic effect, the tin-silver-copper (SAC) family of alloys have relatively strong reliability and are widely used in the electronics industry. Phase separation and coarsening phenomenon on the surface of 96.5 wt. % Sn-3.0 wt. % Ag-0.5 wt. % Cu (SAC305) solder products exhibit special microstructural features and offer opportunities for the microstructure control of microelectronic interconnects. However, the formation mechanism of such morphological patterns is still unknown. Here, we applied a combination of experimental and phase field methods to study how such patterns form. It was observed that the pattern was Sn-rich and exhibited the characteristic morphology of spinodal decomposition. Contrary to earlier findings that only binary systems like Sn-Pb and Sn-Bi experienced such phenomena, spinodal decomposition was firstly observed in ternary solder system Sn-Ag-Cu. Morphology of Sn-rich patterns depended on whether the spinodal decomposition reacted completely. SAC305 solder alloy was easily decomposed by Sn component after being heated to roughly 260 °C. The above conclusions could offer theoretical support for quantitatively controlling the microstructure of solder alloys and would enhance the quality of related products. [ABSTRACT FROM AUTHOR]

This work simulates the morphological evolution process of the solidification interface of silicon crystal. Based on the phase field model of single dendrite growth of pure material in a single-phase system, the control equation of the phase field is re-optimized, and an interface free energy anisotropy equation that can simulate the competitive growth of multiple crystal grains is established. The competitive growth of polysilicon is then simulated and analyzed. The results show that when the degree of undercooling exceeds a certain value, the non-facet crystals are transformed into facet crystals. The main branches in each direction are relatively thick when the anisotropy is small. With increasing anisotropy, the main branches in each direction show gradual thinning, and edges and corners appear on the interface. The dendrites are no longer smooth, and they transform from non-facet crystals to facet crystals. The main branches of different grains inhibit each other when multiple crystal grains compete for growth. The growth of the main branches is curved, which is different from existing branches. The experimental results can more realistically simulate the evolution process of single-crystal silicon and polycrystalline silicon crystal micromorphology. [ABSTRACT FROM AUTHOR]

As an environmentally friendly and efficient separation technology, electrostatic dehydration is widely used in oil-water separation in water-in-oil emulsions. To investigate droplet coalescence behavior under different electric field parameters, the coalescence of two water droplets in water-in-oil emulsions was numerically analyzed with the proprietary software Comsol Multiphysics. The motion of the interface was captured by the phase field method and microscopic mechanism of electrostatic coalescence in water-in-oil emulsions was determined. According to force simulation, the difference between electrostatic attraction and interfacial tension of two droplets' proximal-end and distal-end promoted their approach and fusion process. Furthermore, approach time, fusion time, coalescence time, and distal-end distance S were defined to describe the coalescence characteristics under different electric field frequencies, intensities, and waveforms. The drop-drop coalescence effect was more obvious under an electric field frequency of 20–40 Hz, a higher electric field intensity, as well as DC pulse and half-sinusoidal wave. The deformation degree and electric field intensity at the beginning of droplet coalescence had a significant influence on the coalescence velocity. The results obtained provide much knowledge and a theoretical basis for the technology of compact electrostatic coalescers, which is of great guiding significance for performance prediction and structure optimization. [ABSTRACT FROM AUTHOR]

Based on the error indicator computed from the scaled boundary equations, a quadtree based adaptive phase-field method is proposed for dynamic brittle fracture problems in isotropic material using the scaled boundary finite element method (SBFEM). The use of SBFEM alleviates the need for additional: (a) constraints to handle hanging nodes resulting from adaptive refinement and (b) post-processing techniques. Three representative examples are solved to demonstrate the efficiency of the proposed approach. From the numerical study, it is opined that the proposed approach requires an order of magnitude fewer degrees of freedom when compared to uniform refinement and can capture the crack morphology under dynamic loading conditions without compromising accuracy. [ABSTRACT FROM AUTHOR]

The spinodal decomposition was studied in the aged Mn-40 at. %Cu, Mn-30 at. %Cu, Mn-20 at. %Cu alloys using a phase-field model based on the Cahn–Hillard equation, considering a subregular solution model and the energy contribution of the magnetic behavior. The simulations were performed at aging temperatures of 300, 400, and 500 °C for times from 1 to 240 min. The growth kinetics of the Mn concentration profiles with time indicated clearly that the phase decomposition of the supersaturated solid solution γ into a mixture of Mn-rich γ′ and Cu-rich γ phases occurred by the spinodal decomposition mechanism. Moreover, the phase decomposition at the early stages of aging exhibited the characteristic morphology of spinodal decomposition, an interconnected and percolated microstructure of the decomposed phases. The most rapid growth kinetics of spinodal decomposition occurred for the aging of Mn-20 and 30 at. %Cu alloys because of the higher driving force. The presence of the phase decomposition is responsible for the increase in hardness, as well as the improvement of the damping capacity of Mn-Cu alloys. [ABSTRACT FROM AUTHOR]

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Drop-on-demand electrohydrodynamic jet (DoD E-Jet) printing is considered a well-known type of fabrication method contemporary since it can be used to print high-resolution microstructures (< 1 μm) on various insulating substrates. This paper presents a numerical study of DoD E-Jet printing using a novel combination of needle and focused electrode ring to print stable and consistent microdroplets on a Polyethylene terephthalate substrate. Primarily, a phase field method was used to generate a stable cone-jet morphology that can allow the production of high-resolution micron/nano structures on PET substrates. The numerical simulation of cone-jet morphology was performed by COMSOL multiphysics software. Further, the impact of key parameters such as flow rate and dc positive pulse voltage was studied on cone-jet morphology through numerical simulation. Subsequently, optimized operating parameters i.e., f = 5.3 × 10–15 m3 s−1, Vn = 1.9 kV and Vr = 0.7 kV were achieved by performing a series of numerical experiments. Then, optimized parameters by simulation were directly used to print arrays of stable droplets on PET substrate using the focused electrode ring in different locations by regulating distance 0.2 mm to 1.3 mm between needles to focused electrode ring. The minimum size of stable microdrop was measured 3 μm on PET substrate (thickness = 0.2 mm) using a 50 μm size quartz capillary maintaining a distance of 0.2 mm between combined needle and focused electrode ring. The experimental results proved that the simulation model is useful for printing different microstructures on insulating substrates and creating a promising production path for micro-electro mechanical system and nano-electro mechanical system (MEMS and NEMS). [ABSTRACT FROM AUTHOR]

Ultra pure metals have various applications, e. g. as electrical conductors. Crystallization from the melt, e. g. via zone melting, using the segregation of impurities at the solidification front is the basic mechanism behind different technical processes for the refining of metals and semi-metals. In this paper, we focus on a crystallization methodology with a gas cooled tube ("cooled finger") dipped into a metallic melt in a rotating crucible. The necessary requirement for purification in a solidification process is a morphologically stable solidification front. This is the only way to enable macroscopic separation of the impurities, e. g. by convection. For cellular or dendritic solidification morphologies, the segregated impurities are trapped into the interdendritic melt and remain as microsegregations in the solidified metal. Morphological stability depends on the temperature gradient G at the solidification front, the solidification front velocity V front and thermodynamic alloy properties like the segregation coefficients of the impurity elements. To quantify the impact of these parameters on the morphological evolution, especially on the planar/cellular transition and thus on microsegregation profiles, phase field simulations coupled to a thermodynamic database are performed for an aluminium melt with three impurities, Si, Mn and Fe. In particular, we have investigated the morphology evolution from the start of solidification at the cooled finger towards a stationary growth regime, because in the technical process a significant fraction of the melt solidifies along the initial transient. To solve the transient long range temperature evolution on an experimental length scale, the temperature field has been calculated using the homoenthalpic approach together with a 1D temperature field approximation. The simulations provide the process window for an energy efficient purification process, i. e. low thermal gradients, and elucidate the benefit of melt convection. [ABSTRACT FROM AUTHOR]

Rapid solidification leads to unique microstructural features, where a less studied topic is the formation of various crystalline defects, including high dislocation densities, as well as gradients and splitting of the crystalline orientation. As these defects critically affect the material's mechanical properties and performance features, it is important to understand the defect formation mechanisms, and how they depend on the solidification conditions and alloying. To illuminate the formation mechanisms of the rapid solidification induced crystalline defects, we conduct a multiscale modelling analysis consisting of bond-order potentialbased molecular dynamics (MD), phase field crystal-based amplitude expansion simulations, and sequentially coupled phase field-crystal plasticity simulations. The resulting dislocation densities are quantified and compared to past experiments. The atomistic approaches (MD, PFC) can be used to calibrate continuum level crystal plasticity models, and the framework adds mechanistic insights arising from the multiscale analysis. [ABSTRACT FROM AUTHOR]

Copyright of Food & Machinery is the property of Food & Machinery Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)