Interfacial Propagation Research Articles

Austenite-martensite interfacial patterns and energy dissipation of phase transformation in Ni-Mn-Ga single crystal

The martensitic phase transformation occurs in Shape Memory Alloys (SMA) via the nucleation/propagation of the Austenite-Martensite interface (A-M interface), which is a transition region (domain) between the two coexisting phases. For providing compatibility, the transition region consists of various martensitic twin structures (laminates), forming different interfacial patterns, such as parallel laminates and branching laminates. Due to the energy accumulation in the interfacial structures (e.g., elastic mismatch and twin-boundary surface energy), the interfacial patterns should be relevant to the driving force (energy dissipation) and the associated kinetics of the phase transformation. In this paper, we adopt a special thermal loading, small-temperature-gradient “heating-cooling-reheating”, to control the A-M interface's forward and reverse propagation to generate different interfacial patterns in a Ni-Mn-Ga single crystal SMA with the observation on the twin structures (by optical microscope and SEM) and the InfraRed measurement on the temperature hysteresis of the interface propagation (for characterizing the thermal driving force). Simple energetic analysis indicates that the thermal driving force (energy dissipation) is directly related to the stored energy in the interfacial structure, particularly the large mismatch elastic energy near the habit plane. This study not only provides the details of the various interfacial patterns and their dependence on the loading path, but also indicates the driving force and the associated mechanism about the pattern evolution to understand the phase transformation process.

Interface stabilization and propagation in phase field models of solidification: resolving the issue of large driving forces

Abstract One of the long-standing problems in the phase field, namely, combining the principles of thermodynamics and capillarity with the numerical aspects of interface propagation in simulations, is re-investigated. Numerical schemes are discussed which allow for stable simulations with arbitrary driving forces, considering or excluding capillarity. We re-investigate a classical stabilization scheme that decouples interface stabilization from curvature evaluation, ensuring stable simulations even under large driving forces. A novel mathematical analysis gives a rigorous estimate for the time stepping and a numerical value of the required stabilization strength. The proposed stabilization scheme is benchmarked for 3-dimensional dendritic growth under directional solidification conditions for different solidification speeds.

Biological invasion with a porous medium type diffusion in a heterogeneous space

The knowledge of traveling wave solutions is the main tool in the study of wave propagation. However, in a spatially heterogeneous environment, traveling wave solutions do not exist, and a different approach is needed. In this paper, we study the generation and the propagation of hyperbolic scale singular limits of a KPP-type reaction–diffusion equation when the carrying capacity is spatially heterogeneous and the diffusion is of a porous medium equation type. We show that the interface propagation speed varies according to the carrying capacity.

A thermodynamically consistent machine learning-based finite element solver for phase-field approach

In this article, a thermodynamics-based data-driven approach utilizing machine learning is proposed to accelerate multiscale phase-field simulations. To obtain training data, the interface propagation kinetics, integrated into a physics-based phase-field model, are monolithically solved using a finite element method-based code developed within the Python-based open-source platform FEniCS. The admissible sets of internal state variables (e.g., stress, strain, order parameter, and its gradient) are extracted from the simulations and then utilized to identify the deformation fields of the microstructure at a given state in a thermodynamics-based artificial neural network. Finally, the high performance of the proposed machine learning-enhanced solver is illustrated through detailed comparisons with nanostructural calculations at the nanoscale. Unlike previous methods, the current analysis is not restricted by specific morphologies and boundary conditions, given the length and time scales required to reproduce these results.

Investigation on the fatigue crack propagation of rock-concrete interface under fatigue loading below the initial cracking load

The fatigue crack propagation of the composite rock-concrete interface under constant-amplitude flexural fatigue loading below the initial cracking load was investigated in the present study. Fatigue pre-crack initiation and propagation tests were first conducted on three types of rock-concrete interfaces under three-point bend loading. It was shown that for the rock-concrete interface, the damage evolution throughout the fatigue loading process can be divided into deceleration and acceleration stages according to the rate curves of flexural stiffness, deformation and crack propagation. The crack propagation rate exhibited two distinct regions when plotted on a log scale, namely the small-crack growth region and the long-crack growth region. The small-crack growth region for the studied rock-concrete interfaces was not particularly pronounced. The long-crack growth region was the Paris’ law region and included both the acceleration and part of the deceleration stages. Based on the experimental results, the fatigue crack propagation rate in the Paris’ law region was then described using the empirical Paris’ law. The exponent m1 in the Paris’ law was found to be approximately constant, with a value of m1 ≈ 21 for the rock-concrete interface. The pre-factor C1 was found to be dependent on both the load ratio R and the type of the rock-concrete interface (represented by an elastic mismatch parameter α). By introducing R and α into the empirical Paris’ law, an adjusted Paris’ law was proposed. The adjusted Paris’ law can describe the fatigue crack propagation rate in a unified way for the same rock-concrete interface of different R and different interfaces in the scope of this research. Based on the adjusted Paris’ law, the fatigue cycles during the crack propagation and fatigue lifetimes of all tested rock-concrete interface specimens were reasonably predicted. For practical applications, an approach was suggested involving a combination of the adjusted Paris’ law and a material coefficient β (approximately β ≈ 0.143 in this study) to estimate the fatigue lifetimes of structures or specimens with existing pre-cracks at the rock-concrete interface.

Control of Interface Migration in Nonequilibrium Crystallization of Li2SiO3 from Li2O-SiO2 Melt by Spatiotemporal Temperature and Concentration Fields.

During liquid-solid transformation, bulk mass and thermal diffusion, along with the evolved interfacial latent heat, work in tandem to generate interfacial thermodynamic and kinetic forces, the interplay of which decides the solidification velocity and consequently the solidified phase attributes. Hence, access to interface dynamics information in dependence of bulk transfer processes is pivotal to tailor the desired quantity of solid phases of unique compositions. It finds particular application for engineering concentrated Lithium (Li) phases out of Li-ion battery slags, thus generating a high value-added product from a conventional waste process stream. However, considerable challenge exists to predict the impact of the diverse external cooling rates on the evolving internal transfer processes and thus tuning solidification routes for achieving phases of interest. Hence, in this work, a thermodynamically consistent nonequilibrium model, by considering spatiotemporal temperature and concentration fields, is developed and applied to study solidification of Li2SiO3 from a Li2O-SiO2 melt that constitutes an important subsystem of the Li containing battery-recycling slags. The approach treats the sharp solid/liquid interface as a moving heat source. In the presence of different heat extraction profiles, it evaluates the spatial temperature heterogeneity and its implicit correlation to internal material fluxes resulting from maximization of dissipation and consequently the interrelation to interface velocities. Model calculations revealed that irrespective of the external cooling rate, for an initial short time duration, the magnitude of which increased with decreasing cooling rates, the interface velocities show a reducing trajectory directly relatable to the reducing thermodynamic forces due to localized interfacial temperature rise from the generated latent heat of fusion from the initial solidification. This is followed by a thermodynamically controlled regime, whereby for each cooling rate, the interface velocities increase until a maxima, the magnitude of which decreases with decreasing cooling rates. Finally, the interface propagation speeds decrease as controlled by the kinetic regime.

Investigation of stress-wave-induced crack penetration behavior at the rock-Ultra-High-Performance Concrete (UHPC) interface

The propagation behaviour of initial cracks in concrete penetrating the rock-concrete interface is still unclear. This study investigated the behaviour of stress wave-induced crack penetration through the Ultra-High-Performance Concrete (UHPC)-granite interface and crack propagation speed (CPS) using a combination of the crack propagation gauge (CPG) system and a split Hopkinson pressure bar. The influence of loading rate and UHPC strength grade on the dynamic fracture toughness of the penetration crack entire process was analyzed by experimental–numerical method. The results indicate that the Rock-UHPC interface can suppress the crack opening displacement in UHPC, thereby limiting the CPS. The loading rate significantly enhances the dynamic fracture toughness of the penetration crack's entire process. The interface is the boundary point, and the dynamic fracture toughness at the crack tip shows a trend of first increasing and then decreasing. The increase in concrete strength grade can improve the interface dynamic fracture toughness. Compared to the interface roughness, the enhancement effect of concrete grade on the interface dynamic fracture toughness is one order of magnitude higher. For concrete engineering on rock foundations, increasing the concrete strength grade can effectively prevent the inherent crack defects inside the concrete from expanding into the interior of the rock foundation.

Characterization on thermal hysteresis of shape memory alloys via macroscopic interface propagation

A specimen of Shape Memory Alloy (SMA) starts martensitic phase transformation normally by the nucleation of a macroscopic austenite-martensite interface at the specimen's boundary (i.e., the nucleation is sensitive to boundary conditions). By contrast, the interface propagation only needs to overcome the energy barrier of the incompatibility between the austenite and martensite phases (i.e., the interface-propagation driving force reflects material's intrinsic properties). In this paper, we observe the thermally induced forward and reverse quasi-static propagation of the macroscopic austenite-martensite interface in a Ni-Mn-Ga single-crystal bar. It is found that the temperature difference between the forward and reverse propagation is only 2.8 °C, which is obviously less than the thermal hysteresis evaluated from Differential Scanning Calorimetry measurement (6.3 °C) on the same material. This result not only gives a better characterization of the thermal hysteresis of the phase transformation, but also helps deeply understand the relation between the phase-transformation kinetics and the microstructures of the macroscopic austenite-martensite interface.

Microscopic Cutoff Dependence of an Entropic Force in Interface Propagation of Stochastic Order Parameter Dynamics.

The steady propagation of a (d-1)-dimensional planer interface in d-dimensional space is studied by analyzing mesoscopic nonconserved order parameter dynamics with two local minima under the influence of thermal noise. In this analysis, an entropic force generating interface propagation is formulated using a perturbation method. It is found that the entropic force singularly depends on an ultraviolet cutoff when d≥2. The theoretical calculation is confirmed by numerical simulations with d=2. The result means that an experimental measurement of the entropic force provides an estimation of the microscopic cutoff of the mesoscopic description.

How does the heterogeneous interface influence hydraulic fracturing?

Under the influence of the nonlinear fluid-solid coupling, hydraulic fracture exhibits various propagation modes (such as toughness- or viscosity-dominated), which stem from the competition between the solid deformation and fluid flow. Based on the homogeneous assumption, the basic theoretical analysis has divided toughness and viscosity scales in the tip region. However, regarding more realistic and complex geological conditions, like layered heterogeneity, knowledge of fluid-driven fracture propagation is still unclear. This work establishes a theoretical model and solving approach to reveal the multiscale asymptotic behavior during hydraulic fracture passing through the heterogeneous interface (i.e., discontinuous elastic properties). The influence of material discontinuity, regarded as the remote force, in the near-tip, intermediate, and far-field scales is analyzed by the asymptotic analysis and validated by the numerical solutions. Notably, solutions at the intermediate scale manifest as individual feature owing to the heterogeneity: as the crack in front of the interface, just a specific transition solution governed by the property and position of the interface appears; once the crack tip passes the interface, the interface-governed transition solution and interface solution occur simultaneously and interact as the crack tip moves away from the interface. Such multiscale property results in the interface-governed fluid-solid interaction in the tip region, and finally leads to changes in interface failure and propagation mode. On the one hand, the criterion for interface failure should be modified by simultaneously incorporating the heterogeneity of solid domain and multiscale nature of tip solution, especially for viscosity- or interface-dominated propagation regimes. On the other hand, the propagation mode in a heterogeneous domain is controlled by two characteristics: traditional l/lmk for toughness-viscosity competition associated with c/Lμ for material discontinuity effect proposed in the present work. These insights provide the theoretical foundation for modeling hydraulic fracture propagation in layered heterogeneous domains.

Convective Drying of Porous Media: Comparison of Phase-Field Simulations with Microfluidic Experiments

Convective drying of porous media is central to many engineering applications, ranging from spray drying over water management in fuel cells to food drying. To improve these processes, a deep understanding of drying phenomena in porous media is crucial. Therefore, detailed simulation of multiphase flows with phase change is of great importance to investigate the complex processes involved in drying porous media. While many studies aim to access the phenomena solely by simulations, here we succeed to compare comprehensively simulations with an experimental methodology based on microfluidic multiphase flow studies in engineered porous media. In this contribution, we propose a Navier–Stokes Cahn–Hilliard model coupled with balance equations for heat and moisture to simulate the two-phase flow with phase change. The phase distribution of the two fluids air and water is modeled by the Phase-Field equation. Comparisons with experiments are rare in the literature and usually involve very simple cases. We compare our simulation with convective drying experiments of porous media. Experimentally, the interface propagation of the water–air interface was visualized in detail during drying in a structured microfluidic cell made from PDMS. The drying pattern and the drying time in the experiment are very well reproduced by our simulation. This validation will enable the application for the presented Navier–Stokes Cahn–Hilliard model in more complex cases focused more on applications, e.g., in the field of fibrous materials.

Mesoscale analysis of aging mechanical behaviors of 3D woven composites

3D orthogonal woven composites (3DOWCs) are inevitably subjected to the severe cyclic hygrothermal aging environment in the application of supersonic aircraft structures and their durability should be proven. However, most current works relating to the hygrothermal aging of 3DOWCs rely on the experimental methods which are of high cost. To address this issue, a matrix-yarn mesoscale model of 3DOWCs was established to investigate the cyclic hygrothermal aging mechanical behaviors in this paper. High-fidelity mesoscale representative volume element (RVE) was constructed with realistic geometric configuration of the reinforcement. Only the aging properties of pure resin were needed in the mesoscale model. The aging properties of fiber yarns were calculated with Chamis formulas accounting for resin aging. Tension-compression asymmetry behavior of resin matrix was accounted in the constitutive model. The damage initiation and propagation of resin matrix, yarn and cohesive interface were modeled by the progressive 3D damage model. The mechanical properties of 3DOWCs before and after aging were predicted by the mesoscale model and validated with experiment. This work can provide effective tool for the design of 3DOWCs applied in harsh environments.

Numerical simulation of a non-classical moving boundary problem with control function and generalized latent heat as a function of moving interface

Abstract In this paper, the work is concerned with the study of moving boundary based on non-classical heat equation that includes a time dependent heat flux and convection. The latent heat is represented as a function of the moving interface. Mathematical model accounts for a control function varying with heat flux. We have obtained the explicit solution of the given mathematical model in the presence of convection and a control function. The Legendre wavelet Galerkin approach (LWGA) is used to solve the mathematical problem. In a particular case, our numerical results were compared with previous results and found to be in excellent agreement. Moreover, the current numerical technique is more efficient and accurate in comparison to the previous available method. An extensive analysis of the problem parameters is presented. It is found that the control function offers a significant contribution during the melting or freezing of a PCM. A greater value of the heat flux accelerates the rate of propagation of interface. Convection heat transfer increases the speed of the interface. Results obtained from the current study are expected to improve the fundamental understanding of heat transfer and aid in sublimation and desorption like physical phenomena.

Graphyne-based membrane as a promising candidate for Li-Battery electrodes protection: Insight from atomistic simulations

All-solid electrolytes could lead to a technological breakthrough in the performance of all-solid-state batteries when combined with a lithium-metal anode. However, the use of a lithium-metal anode presents several challenges, such as dendrite growth, interface electrochemical stability, formation and propagation of cracks, and delamination of the electrode/electrolyte interfaces. This work aims to explore the effectiveness of using newly synthesized 2D graphyne-based membranes (namely graphyne, graphdiyne, and graphtriyne) for electrode protection in a solid polymer electrolyte battery through first-principle calculations, nudged elastic band method, and classical molecular dynamics simulation. Specifically, we aim to investigate the effectiveness of these membranes in mitigating the aforementioned challenges. A high external electric field of up to 0.5 V/Å, 0.75 V/Å, and 1 V/Å was applied to accelerate the ions diffusion process. The adsorption energies, charge transfer, and in-plane/out-plane diffusion of single lithium on graphyne-based surfaces were investigated. Afterward, we calculated and compared the Li+ permeability, the electrolyte molecules’ rejection efficiency, and the intrinsic properties of graphyne-based nanoporous membranes. Our findings show that both graphyne and graphdiyne surfaces effectively permit Li+ intercalation while preventing other electrolyte molecules from reaching the electrodes.

Combustion behavior and mechanism of TC25 alloy

The combustion behavior and mechanism of TC25 alloy were investigated by titanium fire melt liquid droplet tests. Moreover, the microstructure and element distribution after combustion were analyzed. Results showed that the combustion reaction zone was composed of the oxide zone, melting zone and heat affected zone. The enrichment of alloying elements, such as Si, Zr, Mo, Sn and W at the melting zone/heat affected zone interface played a pivotal role in regulating the interface propagation rate. The diffusion of Al element was the rate-determining step in the initial stable combustion stage, whereas the diffusion of O element became the rate-determining step in the subsequent combustion stage.

A robust high-resolution discrete-equations method for compressible multi-phase flow with accurate interface capturing

The discrete-equations method (DEM) [1] provides a universal approach to solve multi-phase-flow equations as it combines the solutions of pairwise Riemann problems. Although very robust, the original DEM with piecewise-constant volume fractions suffers from strong diffusion preventing accurate interface capturing. High-order interface reconstruction, however, introduces a restrictive time-step limit.This paper presents RDEMIC, a robust extension of DEM for accurate interface capturing on Cartesian meshes. By a modified partitioning of the Riemann solutions and a specific combination of fluxes and non-conservative terms, the time-step restriction is effectively prevented, which is critical for making the method practically applicable. Moreover, the accuracy of interface and shock-wave propagation is maintained. RDEMIC is not limited to two-phase flow but defined for an arbitrary number of phases.The method is combined with a THINC scheme [2] to reconstruct volume fractions. The reconstruction is enhanced by a positivity-preserving averaging procedure, which is consistent with the underlying multi-stage Runge–Kutta scheme of the flow solver.The resulting scheme consisting of RDEMIC and the positivity-preserving THINC reconstruction is very robust and captures the interface with high accuracy. We demonstrate its performance for various cases of shock-interface interactions, which show very good agreement with reference results from literature.

Numerical investigation into the composite behaviour of over-deformed segmental tunnel linings strengthened by bonding steel plates

Bonding steel plate has been used as a strengthening approach to repair disrupted segmental lining of operational tunnels. This paper introduces numerical investigation into the composite behaviour of the initially deformed segmental tunnel linings strengthened by bonding steel plates using finite element modelling. Cohesive zone modelling was used to simulate the interface bonding behaviour between the segmental linings and steel plates. The full history of the tunnel behaviour before and after strengthening were simulated, where the segmental tunnel lining is initially loaded to create some deformation, then after bonding steel plate, the strengthened tunnel is reloaded until failure occurs. By comparing the results with experimental data from the literature, the proposed model was proved to be capable of simulating the strengthened lining behaviour and able to capture the strengthening failure process in terms of the interface debonding. Subsequently, the segmental lining response and interface shear stress distribution and propagation were analysed to interpret the interaction and failure mechanism of the steel plate strengthened segmental linings. The influence of the initial deformation and the steel plate thickness were investigated and discussed in terms of the strengthened stiffness and capacity. It has been found that the interface shear stress concentration occurred at the positions of the segment joints, where bond damage first initiated. The ultimate failure of the steel plate strengthening happened suddenly once a local debonding zone close to the segmental joint was formed. In addition, the predicted results indicate that a delay in strengthening would result in an increase in strengthened capacity but a decrease in strengthened stiffness. By using thicker steel plates, the strengthened stiffness was improved, while the strengthened capacity could be improved only if the thickness was relatively thin.

Molecular dynamics study of thermal transport properties across covalently bonded graphite-nanodiamond interfaces

The groundbreaking experiment [Luo et al. Nature 2022, 607 (7919) 486–491] recently led to the development of new ultrastrong Carbon/Carbon composites, in which graphene and nanodiamond are strongly connected via covalent bonding. This covalently bonded interface endows the composites with spectacular high strength and other exceptional properties. Herein, non-equilibrium molecular dynamic simulations are conducted to examine the interfacial thermal conductance of graphite-diamond structures by considering the effects of size, environmental temperature, interfacial atomic structures, and tensile strain. Further insight into the microscopic heat transport mechanism of various effects is obtained by analyzing the phonon vibration modes, structural deformation and atomic stress distribution. The variations of interfacial thermal conductance at various temperatures and interfacial configurations are explained qualitatively by the phonon coupling factor. Interestedly, our findings indicate that the interfacial thermal conductance is nearly independent of the graphene size, while it is dependent on the length of the diamond in the direction of heat transport. Furthermore, our study reveals that the interfacial structure retains its heat transport properties even subject to large tensile strain due to interface propagation. Our research provides valuable insights into the heat transport properties of these newly developed Carbon/Carbon composites.

Mode-III fracture toughness measurements of foam-cored sandwich composites using a constrained Shear-Torsion-Bending specimen

This work presents a constrained version of the Shear-Torsion-Bending (STB) test fixture, specially developed for testing of the mode-III face/core fracture toughness of sandwich specimens. Compared to the traditional STB test fixture, the free end of the specimen is now constrained between two support rollers, restraining the twisting deformation of the specimen resulting from the mode-III shear forces. The constrained STB test fixture was applied for mode-III fracture characterization of sandwich specimens with longitudinal slits and consisting of E-glass/epoxy face sheets and Divinycell PVC foam cores. Three density classes of the foam material were considered and tested, that is, H45, H100, and H160. Furthermore, two core thicknesses were tested for the H160 cored specimens. The experimental results from the constrained STB test method show that stable crack growth is obtained without kinking into the core. However, post-mortem investigations showed that longitudinal 45° tension cracks in the core just below the face/core interface occurred, before interface crack opening. Consequently, an apparent mode-III fracture toughness was computed using a three-dimensional Finite Element (FE) model in conjunction with the Crack Surface Displacement Extrapolation (CSDE) mode-mixity method and an optical Digital Image Correlation (DIC) based crack propagation method. Finally, based on the experimental observations presented in this paper, a general discussion of the existence of pure mode-III face/core interface propagation in foam-cored sandwich composites in relation to core and face/core bond strength is included.

Interface propagation and energy dissipation in Shape Memory Alloys

Recent experiments showed that the macroscopic interface propagation of the martensitic phase transformation in Shape Memory Alloys (SMAs) includes unstable microstructure evolution in the macroscopic diffuse interfacial zone (with nucleation, branching, merging and/or annihilation of numerous small domains), releasing the stored energy of the diffuse interface. In this paper, with a one-dimensional Cahn-Hilliard model, a quantitative relation between the energy dissipation and the interfacial properties (interface energy and interface thickness) is revealed: the energy dissipation is governed by the energy barrier caused by the diffuse interface. The relation is verifiable with existing experiments. It can also help understand the interfacial effect on the material's fatigue failure and provide a hint to search for low-hysteresis SMAs: weak first-order phase transformation implies weak energy dissipation (low hysteresis).