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At least 505 records · Page 28

Ordering effects on deformation substructures and strain hardening behavior of a CrCoNi based medium entropy alloy

Here, a CrCoNi based medium entropy alloy with small additions of Ti, Al and Nb (denoted as (CrCoNi) 93 Al 4 Ti 2 Nb) in the as-quenched condition, exhibits tensile properties comparable to those of the equiatomic CrCoNi alloy at room temperature. Dark field transmission electron microscopy (TEM), atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) together with atom probe tomography (APT) show that spatially-localized long range ordering (LRO) L1 2 domains exist in this alloy. The evolution of deformation substructure with plastic deformation in this alloy was characterized using electron backscatter diffraction (EBSD), electron channeling contrast imaging (ECCI) and STEM based techniques including the recently developed weak beam dark field STEM imaging. Plastic deformation occurs by the slip of a/2<110>dislocations, which are narrowly dissociated into Shockley partial dislocations on {111} slip planes. Their dissociation distances in the (CrCoNi) 93 Al 4 Ti 2 Nb alloy are much smaller than the widths of the corresponding partials in the equiatomic CrCoNi alloy due to one or more of the minor alloying elements (Al, Ti, Nb). Dislocation slip in this alloy has a pronounced planar character. The leading dislocations in slip bands glide as pairs due to the existence of LRO domains. Multipoles were formed through the slip of dislocations with opposite signs on adjacent {111} slip planes. Those multipoles serve as building blocks for the formation of subgrain structures consisting of fine slip bands. The distances between slip bands were continuously refined during plastic deformation and dynamic refinement of slip bands plays a crucial role in strain hardening. The effects of LRO domains on planar dislocation slip, the deactivation of deformation twinning and strain hardening of this alloy are discussed.

36 MATERIALS SCIENCE↗

On the 3D printing of polypropylene and post-processing optimization of thermomechanical properties

Polypropylene (PP) is a highly desirable polyolefin in various plastic industries due to its outstanding thermomechanical properties and chemical resistance. Therefore, the 3D printing of PP is an interesting avenue to explore in digitized manufacturing, where more freedom in structural designs is available for new and extended applications, such as high-performance engineering parts. Here, in this work, we 3D printed PP and studied the effect of printing parameters and post-processing conditions on the printed polymer’s thermomechanical behavior. Results showed that nozzle and bed temperatures of 220 and 100°C produced a high printing quality. Infill percentages between 80 and 90%, coupled with a 4-h annealing at 110ºC, also resulted in optimal printed properties. It is thought that PP can be potentially blended with polyethylene or other vinyl polymers for a more extended 3D printing utility and practical applications in rapid tooling and prototyping.

36 MATERIALS SCIENCE↗

Effect of non-uniform void distributions on the yielding of metals

High-throughput (several thousand) calculations have been carried out to investigate the yield behavior of porous materials with randomly distributed pores, porosity levels over four orders of magnitude and up to a hundred pores per simulation box. To this end, a Galerkin based fast Fourier transform (FFT) formulation was enhanced to deal with high phase contrast materials. In addition, GPU parallelization was employed in solving the governing equation for strain fluctuations using a Krylov iterative solver. Emphasis is laid on the conditions under which percolation of plastically non-deforming zones through the porous network emerge, a regime termed unhomogeneous yielding. By way of contrast, the regime where the plastic strain fluctuations (associated with the heterogeneous void-matrix aggregate) fall below the percolation threshold is defined as homogeneous yielding. Here, we find that nonuniform pore distributions only affect unhomogeneous yielding and have a universal softening effect. The extent of this distribution softening is analyzed as a function of porosity, cell size and number of realizations. Whether the uncovered universal distribution softening has direct implications on failure resistance of porous materials is discussed.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Atomistic processes of surface-diffusion-induced abnormal softening in nanoscale metallic crystals

Abstract Ultrahigh surface-to-volume ratio in nanoscale materials, could dramatically facilitate mass transport, leading to surface-mediated diffusion similar to Coble-type creep in polycrystalline materials. Unfortunately, the Coble creep is just a conceptual model, and the associated physical mechanisms of mass transport have never been revealed at atomic scale. Akin to the ambiguities in Coble creep, atomic surface diffusion in nanoscale crystals remains largely unclear, especially when mediating yielding and plastic flow. Here, by using in situ nanomechanical testing under high-resolution transmission electron microscope, we find that the diffusion-assisted dislocation nucleation induces the transition from a normal to an inverse Hall-Petch-like relation of the strength-size dependence and the surface-creep leads to the abnormal softening in flow stress with the reduction in size of nanoscale silver, contrary to the classical “alternating dislocation starvation” behavior in nanoscale platinum. This work provides insights into the atomic-scale mechanisms of diffusion-mediated deformation in nanoscale materials, and impact on the design for ultrasmall-sized nanomechanical devices.

36 MATERIALS SCIENCE↗

Low viscosity of solid MgO at high pressures and strain rates measured using the laser-driven Richtmyer-Meshkov instability

Solids are often assumed to behave as viscous fluids under high-strain rates. This behavior has been studied experimentally in metals but largely unexplored in brittle ceramic materials. Here, in this study, we present a technique for measuring the viscosity of MgO using time-resolved velocimetry to track the growth rate of a perturbation caused by the Richtmyer-Meshkov instability at the OMEGA EP laser facility. To interpret the results, we use an in-house Eulerian hydrocode to simulate our experiments and model the plastic deformation of solid MgO as a viscous fluid. Results indicate that MgO has a surprisingly low upper bound to its effective viscosity of ∼10 2 ⁢ Pa s at 175 ± 15⁢ GPa, ∼3500⁢K, and 10 6 −10 7 s −1 strain rate.

Perez, Tyler M. [Johns Hopkins Univ., Baltimore, M↗

The influence of thermomechanical treatment pathways on texture and mechanical properties in ARB Cu/Nb nanolaminates

Accumulative roll-bonded Cu/Nb nanolaminates (ARB Cu/Nb) possess high strength, thermal stability, and radiation tolerance arising from a high content of heterophase interfaces at fine layer thicknesses. These properties can be tailored by processing parameters used in the ARB Cu/Nb fabrication process, in which layer thickness, thermal history, and strain pathway determine the interface types and resultant properties found in the material. In this work, we subject ARB Cu/Nb to annealing, and then two different rolling pathways – one where rolling direction is held constant (longitudinal rolling, or LR), and one where rolling direction is rotated by 90º and held constant thereafter (cross rolling, or CR). Rolling is performed on ARB Cu/Nb over a targeted range of layer thicknesses from 193 to 25 nm and resultant bulk textures measured by neutron diffraction are correlated with mechanical properties measured by miniaturized tensile tests. The annealing procedure sharpens texture in both phases. We find that Cu mostly develops the same texture in LR and CR. In contrast, Nb develops a distinct texture along the CR pathway that is distinct from the LR texture. The composite texture of Cu/Nb is thus distinct between LR and CR pathways. This difference in texture development between Cu and Nb as a function of strain after change in rolling direction demonstrates the viability for deliberate pairing of Cu LR and Nb CR textures at a desired layer thickness. For mechanical properties, we find that differences in texture do not result in yield or flow stress differences above a layer thickness of 25 nm. Below a layer thickness of 25 nm, despite similar Taylor factors, yield and flow stress and are significantly different. In conclusion, this indicates texture only influences mechanical behavior at low layer thickness, where interface structure dominates mechanical properties.

36 MATERIALS SCIENCE↗

Postirradiation Examination of WIRE-21 Experiment Irradiated in the High Flux Isotope Reactor

Westinghouse Electric Company is developing wireless sensors to monitor the centerline temperature and internal pressure of commercial light-water reactor fuel rods during irradiation. Oak Ridge National Laboratory and Westinghouse Electric Company developed the Wireless Instrumented RB Experiment 2021 (WIRE-21) to test wireless temperature and pressure sensor technologies in a removable beryllium position in the High Flux Isotope Reactor. The experiment was irradiated for a total of 75 days, at temperatures ranging from approximately 150°C to 400°C, resulting in a peak fast (energy > 0.1 MeV) neutron fluence of about 3 × 10 21 n/cm 2 . The temperature was intentionally cycled multiple times to compare the response of the wireless temperature sensor to collocated thermocouples. Similarly, the pressure sensor was actuated in multiple steps to compare the response of the wireless measurement to excore pressure transducers (Petrie et al., 2023). After irradiation, the experiment was disassembled in the Irradiated Fuels Examination Laboratory (IFEL) hot cell at Oak Ridge National Laboratory with the intent to recover sensor and dosimetry components, document the as-irradiated condition of the hardware, and investigate possible causes of the sensor behavior observed during irradiation. The postirradiation examination successfully recovered and preserved key WIRE-21 components. After the housing was removed using a milling machine, the internal experiment sections were examined. All eight fiber-optic sensors were recovered, cut, and stored. The silicon carbide thermometry, temperature sensor, pressure sensor, lower spacer, and selected pressure and temperature cable sections were also removed and stored. The metal bellows of the pressure sensor was found to be plastically deformed, indicating that it had been properly pressurized during irradiation and generally behaved as expected. X-ray diffraction analysis of a section of one of the irradiated inductor cores within the pressure sensor was performed and confirmed the presence of phase-pure alpha ferrite (i.e., no unexpected phase transformations). Inductance testing was performed on the irradiated pressure sensor cores using an unirradiated test coil, and DC resistance measurements of the transceiver coils were also performed. The measurements with irradiated inductor cores assembled inside unirradiated coils showed slightly reduced inductance compared to measurements made with unirradiated cores, but the difference was not sufficient to explain the more significant reductions in inductance that were observed in-pile. Therefore, it is suspected that degradation of the inductor coils (specifically the wire wrapping) is responsible for the reduced inductance observed in-pile.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A constitutive model incorporating grain refinement strengthening on metallic alloys

Surface nano-crystallization techniques have been recently developed as one of the most efficient ways to optimize materials’ structure, and therefore develop the local and global mechanical behavior as to increase strength without compromising ductility. Here, in this work, we present a constitutive model incorporating grain refinement hardening to simulate the nano-crystallization technique, specifically, surface mechanical attrition treatment. The computation is implemented using user-defined VUMAT subroutines. As an example of its application, a geometry model with full coverage of random impacts are employed. The results show that the model has rather precise predictability of grain size evolution during plastic deformation. The readily embedded with a computational code of material dynamics enables this novel model to be a promising tool to study the dynamic evolution of microstructures under plastic deformation.

36 MATERIALS SCIENCE↗

Novel method to control explosive shock sensitivity: Formulations, experiments and modeling

The microstructure of a heterogeneous high explosive (HE) affects its shock initiation sensitivity and detonation performance. Alteration of the void content and/or void structure (i.e., bulk heating or mechanical damage) therefore changes the shock initiation behavior. Controlling and predicting the change in shock sensitivity after an HE has undergone microstructural changes addresses an important and challenging goal for the design and understanding of novel energetic material formulations. In this study, we aimed to develop HE systems to precisely tune shock sensitivity by a thermal treatment prior to use. Specifically, we incorporated a small fraction (1 wt% or less) of thermally expandable microspheres (TEMs) during the formulation process of various plastic-bonded explosives (PBX). TEMs typically consist of a thermoplastic acrylonitrile shell (10-50 µm diameter), which encapsulates an inert low boiling hydrocarbon. Upon heating, the TEMs expand as the shell softens while the hydrocarbon gasifies, increasing the internal pressure and expanding the particle by as much as 120 vol% (irreversibly). Here, we present our progress on shock sensitivity comparisons of HE formulations doped with TEMs after heating and expansion. Experiments, using Composition C-4 thermally cycled to 120°C, showed an increase in shock sensitivity. Additionally, mesoscale modeling revealed that the TEM itself does not act as a hotspot, but instead has a secondary effect on the response of nearby voids. We conclude that TEMs indeed do provide a method to tune shock sensitivity. Further, our results emphasize the non-uniformity of shock waves at the mesoscale, and that upstream defects influence the reactivity of downstream defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Unlocking superplasticity in medium and high-entropy alloys

Superplasticity, the capacity of materials to sustain extraordinary tensile elongations at elevated temperatures, underpins a range of advanced metal-forming technologies. Conventionally, it is achieved in fine-grained alloys where deformation is dominated by grain-boundary sliding, accommodated by diffusion and dislocation activity. The advent of medium- and high-entropy alloys (M/HEAs), with their high chemical complexity and unconventional phase stability, offers new pathways to superplastic behavior beyond traditional alloy systems. Although investigated only recently, several M/HEAs already exhibit elongations that rival or exceed those of classical superplastic materials, particularly when ultrafine or metastable microstructures are engineered. Here, we review progress in understanding superplastic deformation in M/HEAs, emphasizing the interplay among composition, initial microstructure, thermomechanical processing, and microstructural evolution during high-temperature deformation. We discuss approaches to generating the fine-grained structures necessary for grain-boundary sliding, including severe plastic deformation and tailored heat treatments. We further highlight dynamic phenomena such as phase transformations, evolving grain-boundary chemistry, and deformation-induced grain refinement that can enhance plasticity in these systems. These mechanisms often shift the balance of deformation processes, enabling large elongations even outside classical criteria. Finally, we outline key challenges for application, including cost, scalability, recyclability, and microstructural stability.

klenam, Desmond [University of the Witwatersrand, ↗

FY20 Verification of BISON Using Analytic and Manufactured Solutions

In 2010, the U.S. Department of Energy created its first Energy Innovation Hub, which is focused on developing high-fidelity and high-resolution Modeling and Simulation (M&S) tools for modeling of Light Water Reactors (LWRs). This hub, Consortium for Advanced Simulation of LWRs (CASL), has developed an LWR simulation tool called Virtual Environment for Reactor Applications (VERA). The multi-physics capability of VERA is achieved through the coupling of single-physics codes, including BISON, CTF, MPACT, and MAMBA. BISON is a fuel performance code which models the thermo-mechanical behavior of nuclear fuel using high performance M&S. It is capable of modeling traditional LWR fuel rods, fuel plates, and TRi-structural ISOtropic (TRISO) fuel particles. It can employ three-dimensional Cartesian, two-dimensional axisymmetric cylindrical, or one-dimensional radial spherical geometry. It includes empirical models for a large variety of fuel physics: temperature- and burnup-dependent thermal properties, fuel swelling and densification, fission gas production, cladding creep, fracture, cladding plasticity, and gap/plenum models. This document details a series of code verification test problems that are used to test BISON. These problems add confidence that the BISON code is a faithful representation of its underlying mathematical model. The suite of verification tests are mapped to the underlying conservation equations solved by the code: heat conduction, mechanics, and species conservation. Twenty-two problems are added for the heat conduction solution, two for the mechanics solution, and none for species conservation. Method of Manufactured Solutions (MMS) capability is demonstrated with three problems, and temperature drops across the fuel gap are tested.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Pure- and mixed-gas transport properties of a microporous Tröger's Base polymer (PIM-EA-TB)

Polymers of intrinsic microporosity (PIMs) offer tantalizing combinations of high selectivity and permeability in initial gas permeation measurements. Here, we report characterization of pure- and mixed-gas permeation properties of a thick (~80 μm) PIM consisting of Tröger's Base (TB) and Ethanoanthracene (EA) films. The effects of feed pressure and temperature on pure-gas permeabilities of CH 4 , N 2 , O 2 , H 2 , and CO 2 were investigated. The physical aging behavior of the thick film was tracked via pure-gas O 2 , N 2 , and CH 4 permeability at 35 °C. Gas permeability decreased noticeably and selectivity increased as aging time increased. Particular attention was given to mixed-gas measurements of CO 2 and CH 4 (50/50) permeabilities at 35 °C and fugacities ranging from 2 to 18 atm to explore whether the rigid, bridged, bicyclic TB and EA units could resist CO 2 -induced plasticization. These results are presented along with pure-gas CO 2 and CH 4 results for membrane samples aged at different times. PIM-EA-TB aged for ~24 h did not show signs of plasticization across the fugacity range considered. Furthermore, dual-mode competitive sorption presumably caused the CO 2 /CH 4 mixed-gas selectivity to be slightly higher than its corresponding pure-gas selectivity. However, as aging time increased, aged films underwent progressively more rapid and extensive CO 2 -induced plasticization with increasing fugacity, suggesting a systematic relationship between physical aging and plasticization in PIMs. Consequently, physical aging caused less improvement in mixed-gas CO 2 /CH 4 selectivity than it did in pure-gas selectivity, due mainly to plasticization effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Rheological Properties of Enzymatically Hydrolyzed Corn Stover Pretreated via Deacetylation and Mechanical Refining

Lignocellulosic biomass is a feedstock for fuels and chemicals that does not compete with food resources and has less contaminants than refuse-derived biomass feedstocks. To convert lignocellulosics to biofuels or value-added products, multiple processing steps are typically necessary. One method of producing biofuels from lignocellulosic biomass utilizes a deacetylation and mechanical refining pretreatment and an enzymatic hydrolysis reaction to produce fermentable sugars from cellulose and hemicellulose. The rheological properties of biomass, such as yield stress and plastic viscosity, change during enzymatic hydrolysis and alter the energy requirements for pumping and mixing, an important consideration for the design of processing equipment. The dynamic changes in rheological properties that occur in a corn stover feedstock undergoing enzymatic hydrolysis are characterized in this work, and the influence on pressure losses in piping systems is estimated. Two rheometer geometries were fabricated with stereolithography 3D printing to reduce wall slip and sample ejection. The slurries have complex rheological behaviors that include shear-thinning behavior. Shear stress ramps were performed on samples at 20 and 50 degrees C using the custom geometries, and the Herschel-Bulkley model was fit to the data. The dynamic nature of the rheological properties is correlated with changes in the average fiber length at various extents of reaction, and the influence of solids concentration on the observed rheology and piping pressure losses is discussed.

09 BIOMASS FUELS↗

Unveiling the Fatigue Behavior of 2D Hybrid Organic–Inorganic Perovskites: Insights for Long-Term Durability

2D hybrid organic–inorganic perovskites (HOIPs) are commonly found under subcritical cyclic stresses and suffer from fatigue issues during device operation. However, their fatigue properties remain unknown. Here, the fatigue behavior of (C 4 H 9 -NH 3 ) 2 (CH 3 NH 3 ) 2 Pb 3 I 10 , the archetype 2D HOIP, is systematically investigated by atomic force microscopy (AFM). It is found that 2D HOIPs are much more fatigue resilient than polymers and can survive over 1 billion cycles. 2D HOIPs tend to exhibit brittle failure at high mean stress levels, but behave as ductile materials at low mean stress levels. These results suggest the presence of a plastic deformation mechanism in these ionic 2D HOIPs at low mean stress levels, which may contribute to the long fatigue lifetime, but is inhibited at higher mean stresses. The stiffness and strength of 2D HOIPs are gradually weakened under subcritical loading, potentially as a result of stress-induced defect nucleation and accumulation. The cyclic loading component can further accelerate this process. The fatigue lifetime of 2D HOIPs can be extended by reducing the mean stress, stress amplitude, or increasing the thickness. These results can provide indispensable insights into designing and engineering 2D HOIPs and other hybrid organic–inorganic materials for long-term mechanical durability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Athermal glass work at the nanoscale: Engineered electron-beam-induced viscoplasticity for mechanical shaping of brittle amorphous silica

Amorphous silica deforms viscoplastically at elevated temperatures, which is common for brittle glasses. The key mechanism of viscoplastic deformation involves interatomic bond switching, which is thermally activated. Here, for this study, we precisely control the mechanical shaping of brittle amorphous silica at the nanoscale via engineered electron–matter interactions without heating. We observe a ductile plastic deformation of amorphous silica under a focused scanning electron beam with low acceleration voltages (few to tens of kilovolts) during in-situ compression studies, with unique dependence on the acceleration voltage and beam current. By simulating the electron–matter interaction, we show that the deformation of amorphous silica depends strongly on the volume where inelastic scattering occurs. The electron–matter interaction via e-beam irradiation alters the Si–O interatomic bonds, enabling the high-temperature deformation behavior of amorphous silica to occur athermally. Finally, by systematically controlling the electron–matter interaction volume, it is possible to mechanically shape the brittle amorphous silica on a small scale at room temperature to a level comparable to glass shaping at high temperatures. The findings can be extended to develop new fabrication processes for nano- and microscale brittle glasses.

36 MATERIALS SCIENCE↗

Plasticity in irradiated FeCrAl nanopillars investigated using discrete dislocation dynamics

Here, in this paper, we investigate plasticity in irradiated FeCrAl nanopillars using discrete dislocation dynamics simulations (DDD), with comparisons to transmission electron microscopic (TEM) in situ tensile tests of ion- and neutron-irradiated commercial C35M FeCrAl alloy. The effects of irradiation-induced defects, such as a/2<111> and a<100> type loops and composition fluctuations representative of phase separation in irradiated FeCrAl alloys, are investigated separately as well as superposed together in simulations. We explore the effects of defects on the stress-strain behavior, specifically yield strength and hardening response, of FeCrAl nanopillars. Our simulations confirm the widely accepted fact that irradiated alloys exhibit a stress-strain response with higher yield strength as compared to unirradiated alloys. However, our DDD calculations reveal an atypical superposition of the hardening contributions due to composition inhomogeneity and irradiation loops wherein composition inhomogeneity annihilates the hardening due to irradiation loops at small scales. As a result, we observe that the yield strength in irradiated alloys, after taking into consideration the effects of both composition inhomogeneity and irradiation loops, is smaller than the yield strength of the alloys with only irradiation loops and is approximately same for the alloy with composition inhomogeneity alone. This is referred to as “destructive interference” between the hardening contributions due to composition fluctuations and irradiation loops in the paper. We also identify this destructive interference in the superposition in our parallel TEM in situ tensile tests on unirradiated, ion-irradiated, and neutron-irradiated C35M FeCrAl alloy. This destructive interference in the hardening contributions contrasts with the dispersed barrier hardening (DBH) models widely utilized by the experimental community to model the hardening contributions due to different irradiation induced defects. The effects of the loading orientations on the yield strength and hardening are investigated and the mechanisms for the hardening in irradiated FeCrAl alloys are also reported.

36 MATERIALS SCIENCE↗

3D micromechanical simulation of PBX composites

Previous research studied the constitutive response and interface strength of a bonded bicrystal system containing two HMX explosive grains bound with a HTPB polymer binder by performing FE simulations on real geometry imaged with micro Computed Tomography (µCT). The parameters generated from this past study were successfully applied to 2D mesoscale simulations of µCT imaged HMX-HTPB polycrystal samples. Presently, the mechanical response of PBXs containing a Nitro-Plasticized Estane (NPE) binder with similar microstructural geometry to the HMX-HTPB polycrystal samples were studied. Imaging of a HMX-NPE bicrystal sample allowed for simulation of the new material pairing. However, imaging using µCT techniques on the new polycrystal samples was difficult due to the decrease in contrast between the HMX grains and the NPE binder. Mesoscale polycrystal simulations utilizing a single µCT imaged microstructure were performed on a 3D representative volume element (RVE) comparing the delamination behavior and mechanical response of both HMX-HTPB and HMX-NPE PBXs. Furthermore, this technique shows the ability to virtually explore the mechanical response of a range of hypothetical materials that share common microstructural geometric characteristics in addition to studying numerically altered geometries.

36 MATERIALS SCIENCE↗

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations.

36 MATERIALS SCIENCE↗