Coupled Field Research Articles

Rejuvenation of La-based metallic glass by controlling different modes of relaxation

Metallic glasses (MGs) have multiple dynamic relaxation modes, among which α and β relaxations are two typical modes. The rejuvenation of MGs usually refers to the increase in the total enthalpy of structural relaxation. However, the control mechanism of single-mode relaxation and the contributions of different relaxation modes to the total enthalpy are still unclear. We investigated the effects of stress, temperature and their coupling fields on α and β relaxations through experimental and molecular dynamics (MD) simulations. We found that the temperature field activated more sites for β relaxation, while the prolonged stress leads to the aggregations and connections of a quantity of localized atomic clusters and even activates α relaxation. The coupled field integrates the characteristics of stress and temperature fields and results in a clear splitting of α and β relaxations. Our work provides useful insights into the single-mode regulation of α and β relaxations in MGs.

Heat Transport Through an Open Coupled Scalar Field Theory Hosting Stability-to-Instability Transition

Heat Transport Through an Open Coupled Scalar Field Theory Hosting Stability-to-Instability Transition

Coupled field modelling of thermomechanical response in materials using peridynamic heat transport model and non-ordinary state-based peridynamics

Predicting the mechanical response of materials subjected to transient heat processes is crucial in various engineering applications. This paper introduces a novel peridynamic (PD) coupled field model formulated within the framework of Non-Ordinary State-Based Peridynamics (NOSBPD). This model offers the capability to simulate the coupled thermo-mechanical behavior of materials by incorporating both thermal transport and mechanical deformation analyses. To verify the model’s accuracy, a benchmark problem involving a steel plate undergoing transient thermal expansion is investigated. This model presents a valuable tool for various engineering applications involving coupled thermo-mechanical processes.

Coupled crystal plasticity-phase field simulation of twin-twin interaction in magnesium

Twin-twin interactions significantly influence the mechanical properties of magnesium and its alloys. A thorough understanding of the underlying mechanisms governing these interactions is essential for designing Mg alloys with enhanced strength and toughness. In this work, a crystal plasticity-twin coupled phase field (CP-TPF) model incorporating multiple extension twin variants and considering the role of dislocation slipping is proposed to investigate the interactions between/among the same twin variants and those between co-zone twin variants in Mg single crystals. The model incorporates an additional energy term to represent the interaction among different twin variants and couples the CP and TPF models through order parameters and stress tensor. The simulated results show that the interaction between the same twin variants can either promote or inhibit the twin propagation, and multiple twins tend to generate concurrently in Mg single crystal to minimize the free energy associated with the accumulation of elastic strain. During co-zone twin-twin interaction, localized thickening of the recipient twin occurs due to the concentrated stresses induced by the intrusion twin, and the mutual extrusion of the two twins leads to blunting of the intrusion twin tip. Both the coalescence of the same twin variants and the formation of twin-twin boundaries between the co-zone twin variants contribute to the effective mechanism of twinning-induced hardening. Moreover, local dislocation accommodation plays a crucial role in twin-twin interactions. It relaxes the stress concentration near the twin tips and twin-twin boundaries and significantly contributes to the uneven migration of the twin boundary.

Optimum management strategy for improving maize water productivity and partial factor productivity for nitrogen in China: A meta-analysis

China’s agricultural production suffers significant constraints due to low water productivity (WP) and partial factor productivity for nitrogen (PFPN). The pivotal solution to enhance maize yield, WP, and PFPN is through optimizing field management practices. However, previous studies primarily focused on the effects of individual or coupled field management practices on maize yield, WP, or PFPN in an area or land mass, so it is necessary to conduct a comprehensive quantitative analysis of various field management practices on maize yield, WP, and PFPN at the national scale. In this study, we compiled 286 studies encompassing 6959 pairs of experimental data spanning from 1990 to 2023. Meta-analysis was conducted to observe the variations in maize yield, WP, and PFPN across diverse field management practices (straw returning, nitrogen fertilizer application, irrigation practice, and tillage practice) on a national scale. The results showed that nitrogen fertilizer application (215 kg N ha−1) was the most effective in enhancing maize yield and WP by 68.1 % and 54.8 %, respectively. Additionally, irrigation had the most substantial impact on PFPN, enhancing 16.8 %. Straw mulching, application of slow and controlled release fertilizers, drip irrigation, and subsoiling were identified as the most effective practices in increasing maize yield, WP, and PFPN by Random forest model. Maize straw returning could reduce nitrogen fertilizer application by 20 kg ha−1, while increasing WP and PFPN by 4.2 % and 11.6 %, respectively. Moreover, straw returning could reduce water consumption by 23–60 mm, while increasing WP and PFPN by 2.9 % and 6.8 %, respectively. These findings can provide a reference for the formulation of comprehensive management strategies for sustainable maize production in China and globally.

Phase field study on the grain size dependent electrical resistivity-strain response in superelastic nanocrystalline NiTi alloys

The superelastic NiTi alloy's electrical resistivity exhibits significant variations in response to deformation, making it a highly attractive material for sensing applications. However, there exists a lack of comprehensive knowledge of the effects of grain size (GS) on the electrical properties of NiTi alloy. To address this gap, a novel electro-mechanical coupled phase field simulation model is developed, with crucial parameters determined through experimental investigations. The results demonstrate a notable change in the relationship between electrical resistivity and strain, transitioning from a quasi-linear pattern to a piecewise nonlinear one as the GS increases. The observed modification is found to be primarily influenced by the martensitic transformation, characterized by a transition from a uniform mode to a localized mode. As the GS increases, there is an initial drop in the total change of electrical resistivity at peak strain, followed by a subsequent stabilization. This is because the GS, through the stress and the degree of phase transformation, exerts two opposing effects on the variation of electrical resistivity. Furthermore, the combined influence of hysteresis and hysteresis in the martensite fraction contributes to a consistent decrease in resistivity hysteresis as the GS diminishes. This study improves the understanding of how GS affects NiTi alloy's electrical resistivity-strain response and lays the foundation for future sensing performance regulation, expanding its multi-functionality as an intelligent material.

Coupled field modeling of thermoresponsive hydrogels with upper/lower critical solution temperature

An inf–sup stable FE formulation for the thermo-chemo-mechanical simulation of thermoresponsive hydrogels is herein proposed by approximating the displacement field via quadratic shape functions and both the chemical potential (fluid pressure) and the temperature fields by linear functions. The formulation is implemented into a stable thermo-chemo-mechanical user-element subroutine (UEL) in Abaqus, denoted as Q2Q1Q1. The proposed formulation has been validated in relation to thermoresponsive hydrogels to interpret several examples of transient diffusion-driven swelling deformations. First, the upper/lower critical solution temperature behaviors of thermoresponsive hydrogels has been captured, studying several peculiarities comprising the diffusion length influence at the instantaneous loading state and the overlooked influence of the mass flux and the hyperelastic stretching on the temperature field. Subsequently, numerical analysis have been conducted in order to investigate the impact of temperature-dependent swelling ratio on the mechanical behavior of spheres undergoing compression. The accuracy of the proposed formulation has been assessed by numerically replicating the seminal experiments that explore the influence of crosslinking density on the thermally driven swelling of PNIPAAm hydrogels.

New insights on Late Pliensbachian-Early Toarcian seawater chemistry based on belemnite rostra element content

Belemnites were a type of cephalopod abundant in the Jurassic and Cretaceous, whose fossils have been extensively used for paleo-oceanographic studies. For this study, we analyzed 69 elements by Inductively Coupled Plasma-Sector Field Mass Spectrometry (ICP-SFMS) in 15 belemnite rostra from the West Rodiles section in the Asturian Basin, Northern Spain. We aim to determine if belemnite rostra carbonate chemistry reflects changes in seawater chemistry during the Late Pliensbachian–Early Toarcian time interval and examine how belemnites can be used to trace known drivers of the Early Toarcian Oceanic Anoxic Event (T-OAE) and associated oceanographic processes.Discarding drastic intra-species effects and assuming a similar influence of growth rates, diet, and other physiological processes for all analyzed belemnite specimens and taking into consideration the sizeable analytical uncertainty, we assess if determined belemnite rostra element chemistry reflects broad and relative changes in paleo-seawater chemistry. Many determined elements are present in only ppb amounts, and their interpretation is uncertain. We found that Mg, Mn, and P increase in the interval chronocorrelative to the T-OAE. This is interpreted to have resulted from an increase in these elements' inventory in seawater due to an increase in continental weathering and fluvial runoff associated with this global event. Iron, K, and Na contents decrease upwards in the section, potentially indicating that these elements became limited and likely hampered oceanic productivity. Our study also found a correspondence between a change in the behaviour of several elements, warming, the T-OAE negative CIE, and a reduction in the diversity and size of both calcareous nannofossils and belemnites in the study area.

Linear relaxation method with regularized energy reformulation for phase field models

In this paper, we establish a novel linear relaxation method with regularized energy reformulation for phase field models, which we name the RRER method. We employ the molecular beam epitaxy (MBE) model and the phase-field crystal (PFC) model as test beds, along with several coupled phase field models, to illustrate the concept. Our proposed RRER strategy is applicable to a broad class of phase field models that can be derived through energy variation. The RRER method consists of two major steps. First, we introduce regularized auxiliary variables to reformulate the original phase field models into equivalent forms where the free energy is transformed under the auxiliary variables. Then, we discretize the reformulated PDE model under these variables on a staggered time mesh for the phase field models. We incorporate the energy reformulation idea in the first step and the linear relaxation concept in the second step to derive a general numerical algorithm for phase field models that is linear and second-order accurate. Our approach differs from the classical invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches, as we don't need to take time derivatives for the auxiliary variables. The resulting schemes are linear, i.e., only linear algebraic systems need to be solved at each time step. Rigorous theoretical analysis demonstrates that these resulting schemes satisfy the modified discrete energy dissipation laws and preserve the discrete mass conservation for the PFC and MBE models. Furthermore, we present numerical results to demonstrate the effectiveness of our method in solving phase field models.

Numerical Study on Rotor–Building Coupled Flow Field and Its Influence on Rotor Aerodynamic Performance under an Atmospheric Boundary Layer

In urban settings, buildings create complex turbulent conditions, affecting helicopter flight performance during missions and increasing safety risks during takeoff and landing. A numerical study on rotor–building coupled flow field is carried out to address rotor aerodynamic performance under building interferences in natural atmospheric conditions. A high-fidelity atmospheric boundary layer (ABL) model described by an exponential law is established herein. The solution of the coupled flow field is based on the Reynolds-averaged Navier–Stokes (RANS) equations, with the rotor’s rotation achieved through the overset grid method. Based on the dominant wind features, the building flow field is distributed into four regions, where the updraft along the headwind side impacts the rotor, bringing about a 76% increase in pitching moment. On the lateral side of the building, distorted rotor wake squeezed upward into the rotor disk, leading to severe blade–vortex interaction (BVI). During low-altitude hovering over rooftops, the mixing of building shed vortices with forward flow wakes causes the formation of a circulation region on the rotor’s windward side, resulting in a thrust loss of approximately 7.8%. Meanwhile, the flow environment on the leeward side of the buildings is more stable. Therefore, it is recommended that helicopters adopt a headwind approach during rooftop operations. However, an 11.4% loss in the average hover figure of merit is observed due to consistent thrust losses caused by the recirculation region.

Coupled quintessence scalar field model in light of observational datasets

We do a detailed analysis of a well-theoretically motivated interacting dark energy scalar field model with a time-varying interaction term. Using current cosmological datasets from CMB, BAO, Type Ia Supernova, H(z) measurements from cosmic chronometers, angular diameter measurements from Megamasers, growth measurements, and local SH0ES measurements, we found that dark energy component may act differently than a cosmological constant at early times. The observational data also does not disfavor a small interaction between dark energy and dark matter at late times.When using all these datasets in combination, our value of H 0 agrees well with SH0ES results but in 2.5σ tension with Planck results. We also did AIC and BIC analysis, and we found that the cosmological data prefer coupled quintessence model over ΛCDM, although the chi-square per number of degrees of freedom test prefers the latter.

Insulation Degradation Characteristics and Phase-Field Simulation of Epoxy Resin for Valve-Side Bushing Under Strongly Coupled Electrothermal Field

Insulation Degradation Characteristics and Phase-Field Simulation of Epoxy Resin for Valve-Side Bushing Under Strongly Coupled Electrothermal Field

Online Magneto-Thermal Coupled Model of PMECCs Using Measured Boundaries

Online modeling of the magneto-thermal coupled field (MCF) in permanent magnet eddy current couplings (PMECCs) has long been challenging since it exists in the copper layer and cannot be directly measured. This article proposes an online magneto-thermal coupled model (OMCM) to reconstruct the MCF using measured boundaries. The magnetic field (MF), eddy current field (ECF), and temperature field (TF) in the MCF are coupled in an identical space-time united discretization system. Virtual boundary nodes are added to the system, which can adapt to different boundary conditions in electromagnetic and thermal analysis. The measured data of single-point sensors are spanned to continuous boundary conditions. An approximate solution of the MCF is derived based on the measured boundaries and the general solutions of Laplace's equation and Poisson's equation in magneto-thermal analysis. The three-dimensional distribution of the MF, ECF, and TF at each spatial node and time segment can be simultaneously calculated in matrix form by the OMCM. Furthermore, the output torque is estimated and compared with the conventional methods. A verification process is carried out to assess the reconstructed results, showing that the OMCM can yield results close to the verification sensors for various slips and air gaps.

Coupled thermo-mechanical phase field modeling for shear ductile fracture at high strain rate and temperature

The objective of the current study is to introduce a coupled thermo-mechanical phase field model to elucidate shear ductile fracture under varying strain rates and temperatures. Both the plastic work threshold and fracture energy exhibit dependence on the strain rate and temperature. To explore this in detail, hat-shaped specimens are adopted to systematically investigate shear ductile fracture under distinct strain rates and temperatures by the split Hopkinson pressure bar apparatus. The simulated and experimental strain waveforms are then compared to calibrate and validate the damage parameters of the presented phase field model. The results demonstrate that the numerical simulations are in agreement with the experiments. Moreover, the fracture process of the hat-shaped specimen is also examined. The numerical results furnish a reliable description of the hat-shaped specimen from damage initiation to complete fracture. It's found that the influences of strain rate on shear stress and fracture initiation are less pronounced than that of temperature for U75V steel. In summary, the developed phase field model can reproduce shear ductile failure of the hat-shaped specimen under diverse strain rates and temperatures.

The Coupled Temperature Field Model of Difficult-to-Deform Mg Alloy Foil High-Efficiency Electro-Rolling and Experimental Study

In response to the challenging difficult-to-deform of magnesium foils, a high-efficiency and high-precision electro-rolling temperature field coupled model is established. This model is designed to simulate the non-annealing electric rolling (NAER) process of Mg foils under conditions of high current density, rapid temperature rise rates, and large temperature gradients. Firstly, a coupled temperature field difference model for the guide roller, roll, and Mg foil is established, based on the equipment for NAER and the electrification conditions. The Joule heat, distortion heat, and friction heat in the electric rolling process were precisely considered. Secondly, considering the peculiarity of the heat source and the heat transfer mechanism during NAER, the influence of the dynamic boundary conditions on the instantaneous temperature of the Mg foil was analyzed, which was closer to the actual situation. The experimental results show that the original model can accurately simulate the transient temperature change in Mg foils during NAER, and the error between the predicted value and the measured value is within 7.1%. According to the calculation of the model, the microstructure of completely recrystallized magnesium foil with a grain size of 4.61 μm and a texture strength of 11.3 can be obtained at an inlet temperature of 250 °C.

Coupled Field and Circuit Permanent Magnet Model for High-Speed Motor Analysis

Coupled Field and Circuit Permanent Magnet Model for High-Speed Motor Analysis

A study of microstructure and mechanical properties of (CoCrNi)82Al9Ti9 high entropy alloy by electrical-thermal-mechanical coupled rapid post-treatment

In this work, we have creatively used electrical-thermal-mechanical coupled rapid post-treatment to improve the properties of (CoCrNi)82Al9Ti9 high entropy alloy (HEA). The effect of the electrical-thermal-mechanical coupled field on the phase, microstructure, microhardness, fracture toughness, and compression properties of SLM specimens are investigated. The results show that the SLM specimen exhibits face-centered cubic (FCC) and body-centered cubic (BCC) phases and the microstructure is a dendrite structure. The SLM specimens exhibit imperfections, including porosity and cracks, as well as low densification. After electrical-thermal-mechanical coupled rapid post-treatment, the FCC phase decreases while the BCC phase increases in the SLM specimen, and the microstructure changes from dendritic to recrystallized. The created specimens are healed of defects and the densification is increased to 99.6%. It can be attributed to the combination of the electrical (Electron wind) and thermal effects (Joule heat) of pulse current. Electron wind promotes the diffusion of atoms and expansion of the movement of dislocations, providing the material basis for defect healing and recrystallization. Joule heat provides the substance conditions. The (CoCrNi)82Al9Ti9 HEA has a remarkable improvement in strength and ductility.

Effect of homogeneous generalized thermoelasticity on semiconductor layer under magnetic field on Green and Naghdi model without energy dissipation

This paper aims to explore the impact of viscosity and time on the spread of thermoelastic waves within a uniform and isotropic three-dimensional medium subject to a thermal load on its surface. This study utilizes the temperature-rate-dependent thermoelasticity based on the GN model, specifically applying the GN II model of generalized thermoelasticity, which does not account for energy dissipation. The normal mode analysis technique is employed to address the non-dimensional coupled field equations, yielding precise formulas for displacement, stress, temperature distribution, and strain. This issue is further illustrated by graphically depicting the field variables for a material similar to copper alongside the corresponding results. Comparative analyses of numerical data, with and without considering viscosity effects, suggest that the wave propagation speed will be limited.

Effects of Thermal-Moisture Coupled Field on Delamination Behavior of Electronic Packaging

Abstract Delamination failure is one of the most prevalent and serious reliability issues in micro-electronic packaging. To understand this phenomenon further, this study constructs an experimental test system consisting of a double cantilever beam (DCB) fixture, an MTS-Acumen microforce tester, and a temperature and humidity controller. The system is employed to investigate the effects of coupled moisture-thermal loading on the critical strain energy release rate (SERR) at the epoxy molding compound (EMC)/Cu leadframe (LF) interface of a very thin quad flat no-lead package (WQFN) assembly. A three-dimensional computational model with hygro-thermal loading conditions is developed to evaluate the moisture diffusion, thermal stress, and integrated stress of a multichip WQFN package under typical processing conditions and precondition tests. The validated simulation model is then applied with the virtual crack closure technique (VCCT) to investigate the fracture behavior at the EMC/Cu LF interface in the WQFN package. The effects of three design parameters on the SERR performance of the package are identified through a parametric analysis. Finally, a Genetic Algorithm (GA) optimization method is employed to examine the effects of the main structural design parameters of the WQFN package on its delamination reliability. The results are used to determine the optimal packaging design that minimizes the SERR and hence enhances the package reliability.

Numerical Simulation and Optimization of the Gas-Solid Coupled Flow Field and Discharging Performance of Straw Crushers

Numerical Simulation and Optimization of the Gas-Solid Coupled Flow Field and Discharging Performance of Straw Crushers