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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Development of an Electrochemical Impedance Instrument for Monitoring Corrosion Formation (Oxide and Hydride) on Cladding Materials

The objective of this work package is to develop electrochemical impedance spectroscopic (EIS) techniques for the in pile measurement of changes in cladding materials in coupling with model simulation and material characterization. This work package will involve the initial development of electrochemical sensing technologies for measuring spatial and time resolved changes in cladding chemistry. Specific attention will be paid to monitoring changes in monitor cladding corrosion including oxide and hydride formation and deformation. The planned work during this period was focused on cladding material zirconium alloy corrosion, oxide and hydride development, and to characterize samples using EIS under controlled gas atmosphere, atom probe tomography (APT), Raman Spectroscopy, and Synchrotron X-ray diffraction (XRD). The corrosion, including oxide and hydride of zirconium alloy samples, was tested in this study. The samples were treated at a gas environment containing 3% H2 (vol%) balanced with N2 gas at various temperatures (100 – 500°C) and different times (up to 60 hours) and were characterized by in situ EIS. After treatment, various characterization techniques were applied to measure the samples, including TGA, Ramen, XRD, and APT. This study found that impedance spectra can be affected significantly with (furnace/environment) temperature. Higher temperature resulted in higher overall impedance, and longer exposure time exerted similar effects. Proof of concept characterization of oxidized samples, including TGA, Raman, XRD, and APT, were accomplished on samples exposed to 700 oC gas environment containing 20% O2 and 80% N2. TGA provides observable breakaway and bulk oxide growth measurements. High-temperature, in-situ Raman provides observation of oxidation stress at the surface of the oxide. Additionally, a transition from tetragonal to monoclinic zirconia can be seen early in the oxidation experiment. Specifically, tetragonal-rich zirconia is seen at the metal/oxide interface, where a transition to monoclinic-rich zirconia is seen in the bulk of the oxide. It has also been confirmed that highly compressive residual stresses are seen near the metal/oxide interface. It is concluded that the transition from tetragonal to monoclinic zirconia is induced by massive shifts in stress as the oxide grows. APT has supplied evident differences in the distribution of zirconium and oxygen at the metal/oxide interface. On the pre-breakaway sample, the metastable Zr(O) region at the boundary is relatively thin, interfaced by Zr-rich (i.e., metal) and O-rich (i.e., ZrO2) on either side. In contrast, it has been seen on a post-breakaway sample that the Zr(O) metastable region is much greater in thickness, with evidence of four “zones” showing slightly contrasting composition between 49-54% Zr. In addition, it can be seen from the Zr-2.65Nb post-breakaway sample that secondary element concentrations are considerably different than bulk composition measurements show. Specifically, Nb concentration is much lower than expected, whereas Fe concentration is much higher than expected. These differences could play a role in each element’s contribution to oxide growth mechanisms, as well as causation for breakaway. Future work is focused on analyzing EIS spectra of hydride and its correlation with characterization features, finite element (FE) modeling of cladding materials, electrochemical sensor development, targeting cladding oxides/hydrides under thermodynamic equilibria, during transients and under irradiation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

Understanding the Lithium Storage Mechanism of Ti 3 C 2 T x MXene

MXenes, as an emerging family of conductive two-dimensional materials, hold promise for late-model electrode materials in Li-ion batteries. A primary challenge hindering the development of MXenes as electrode materials is that a complete understanding of the intrinsic storage mechanism underlying the charge/discharge behavior remains elusive. This article presents two key discoveries: first, the characteristics of the Ti 3 C 2 T x structure can be modified systematically by calcination in various atmospheres, and second, these structural changes greatly affect Li-ion storage behavior, which reveals the mechanism for lithium storage in Ti 3 C 2 T x MXene. Specifically, via ammonization, the interlayer spacing gets dilated and uniform, giving rise to only one redox couple. In stark contrast, there are two well-recognized redox couples corresponding to two interlayer spacings in pristine Ti 3 C 2 T x MXene, in which Li-ion (de)intercalation occurs between interlayers in a sequential manner as evidenced by ex situ X-ray diffraction (XRD). Notably, the XRD diffraction peaks shift hardly in the whole range of charge/discharge voltage, indicating a zero-strain feature upon Li-ion (de)intercalation. Moreover, the diffusion-controlled contribution percentage to capacity inversely depends on the scan rate. The understanding suggests a new design principle of the MXene anode: reduced lateral size to shorten the diffusion path and dilated interlayer spacing.

25 ENERGY STORAGE↗
DOE OSTI2018

High-throughput computational X-ray absorption spectroscopy

X-ray absorption spectroscopy (XAS) is a widely-used materials characterization technique. In this work we present a database of computed XAS spectra, using the Green's formulation of the multiple scattering theory implemented in the FEFF code. With more than 500,000 K-edge X-ray absorption near edge (XANES) spectra for more than 40,000 unique materials, this database constitutes the largest existing collection of computed XAS spectra to date. The data is openly distributed via the Materials Project, enabling researchers across the world to access it for free and use it for comparisons with experiments and further analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Modeling Mesoscale Processes of Scalable Synthesis

Brown University is part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), led by PNNL. The Collaboratory focuses on developing rigorous mathematical foundations for understanding and controlling fundamental mechanisms in mesoscale processes to enable scalable synthesis of complex materials, through the design of efficient modeling methods and corresponding scalable algorithms.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

Winter wheat: A model for the simulation of growth and yield in winter wheat

The basic ideas and constructs for a general physical/physiological process level winter wheat simulation model are documented. It is a materials balance model which calculates daily increments of photosynthate production and respiratory losses in the crop canopy. The partitioning of the resulting dry matter to the active growing tissues in the plant each day, transpiration and the uptake of nitrogen from the soil profile are simulated. It incorporates the RHIZOS model which simulates, in two dimensions, the movement of water, roots, and soluble nutrients through the soil profile. It records the time of initiation of each of the plant organs. These phenological events are calculated from temperature functions with delays resulting from physiological stress. Stress is defined mathematically as an imbalance in the metabolite supply; demand ratio. Physiological stress is also the basis for the calculation of rates of tiller and floret abortion. Thus, tillering and head differentiation are modeled as the resulants of the two processes, morphogenesis and abortion, which may be occurring simulaneously.

Baker, D. N.↗
NASA NTRS1992

Coupled multi-disciplinary simulation of composite engine structures in propulsion environment

A computational simulation procedure is described for the coupled response of multi-layered multi-material composite engine structural components which are subjected to simultaneous multi-disciplinary thermal, structural, vibration, and acoustic loadings including the effect of hostile environments. The simulation is based on a three dimensional finite element analysis technique in conjunction with structural mechanics codes and with acoustic analysis methods. The composite material behavior is assessed at the various composite scales, i.e., the laminate/ply/constituents (fiber/matrix), via a nonlinear material characterization model. Sample cases exhibiting nonlinear geometrical, material, loading, and environmental behavior of aircraft engine fan blades, are presented. Results for deformed shape, vibration frequency, mode shapes, and acoustic noise emitted from the fan blade, are discussed for their coupled effect in hot and humid environments. Results such as acoustic noise for coupled composite-mechanics/heat transfer/structural/vibration/acoustic analyses demonstrate the effectiveness of coupled multi-disciplinary computational simulation and the various advantages of composite materials compared to metals.

Chamis, Christos C.↗
NASA NTRS1992

Coupled multi-disciplinary simulation of composite engine structures in propulsion environment

A computational simulation procedure is described for the coupled response of multi-layered multi-material composite engine structural components which are subjected to simultaneous multi-disciplinary thermal, structural, vibration, and acoustic loadings including the effect of hostile environments. The simulation is based on a three dimensional finite element analysis technique in conjunction with structural mechanics codes and with acoustic analysis methods. The composite material behavior is assessed at the various composite scales, i.e., the laminate/ply/constituents (fiber/matrix), via nonlinear material characterization model. Sample cases exhibiting nonlinear geometrical, material, loading, and environmental behavior of aircraft engine fan blades, are presented. Results for deformed shape, vibration frequency mode shapes, and acoustic noise emitted from the fan blade, are discussed for their coupled effect in hot and humid environments. Results such as acoustic noise for coupled composite-mechanics/heat transfer/structural/vibration/acoustic analyses demonstrate the effectiveness of coupled multi-disciplinary computational simulation the various advantages of composite materials compared to metals.

Chamis, Christos C.↗
NASA NTRS1994

Transfer function modeling of damping mechanisms in distributed parameter models

This work formulates a method for the modeling of material damping characteristics in distributed parameter models which may be easily applied to models such as rod, plate, and beam equations. The general linear boundary value vibration equation is modified to incorporate hysteresis effects represented by complex stiffness using the transfer function approach proposed by Golla and Hughes. The governing characteristic equations are decoupled through separation of variables yielding solutions similar to those of undamped classical theory, allowing solution of the steady state as well as transient response. Example problems and solutions are provided demonstrating the similarity of the solutions to those of the classical theories and transient responses of nonviscous systems.

Slater, J. C.↗
NASA NTRS2018

Implementation of J-A Methodology Elastic-Plastic Crack Instability Analysis Capability into the WARP-3D Code

Characterization of the near crack-tip stress/strain fields is the foundation of fracture mechanics. The description of the near tip stress field and the prediction of when fracture occurs is well established for brittle materials that exhibit linear elastic behavior. However, in ductile materials or conditions that violate linear elastic assumptions (Aluminum alloys, Al 2024-T3, Al 2024- T351 etc.), the elastic-plastic crack-tip stress fields are characterized by the Hutchison-Rice-Rosengren (HRR) field. The J-integral is commonly used to characterize amplitude of the HRR field under elastic-plastic conditions. The J-integral has been demonstrated for crack-tip fields that are under high constraint conditions (i.e., small-scale plasticity where the J-dominance is maintained). However, as the external load increases, yielding changes from small- to largescale plasticity and usually a loss of constraint (i.e., reduction in the triaxial stress field along the crack front). The loss of constraint leads to the deviation of the crack-tip stress fields from that given by the HRR field. Hence, the J-dominance will be gradually lost and additional parameter(s) are required to quantify the crack-tip stress fields and predict fracture behavior. The assessment objectives were to: 1) implement a two-parameter (i.e., J-A) fracture criterion into an elastic-plastic three-dimensional (3D) finite element analysis (FEA), 2) validate the implementation by comparison with the A parameter from literature data, 3) conduct material characterization tests to quantify the material behavior and provide fracture data for validation of the J-A fracture criteria, and (4) perform evaluations to establish if the J-A criteria can be used to predict fracture in a ductile metallic material (e.g., aluminum alloys). The A parameter in these criteria is the second parameter in a three-term elastic-plastic asymptotic expansion of the neartip stress behavior. A series of extensive FEAs were performed using WARP3D software package to obtain solutions for the A parameter for different specimen configurations. The methodology needed for the estimation of the A parameter in the asymptotic expansion was developed and implemented using Matlab®. A user material (UMAT) routine was used to model the material stress-strain response using a Ramberg-Osgood power law with a hardening exponent (n) and a material coefficient (alpha). This UMAT routine was successfully implemented in WARP3D software and validated through comparison with the experimental data. Three configurations were extracted from published results: 1) center cracked plate (CCP), 2) single edge-cracked plate (SECP), and 3) double edge-cracked plate (DECP). These configurations and four other configurations (three-hole tension (THT)), three-point bend (3PTB), three-hole compact tension (3PCT), and compact tension (CT)) were analyzed to verify the methodology that was developed and implemented into WARP3D. Solutions of the A parameter were obtained for remote tension loading conditions that started with small-scale yielding and continued into the large-scale plasticity regime. The results indicate that the methodology developed can be used to calculate the elastic-plastic J-A parameters for test specimens with a range of crack geometries, material strain hardening behaviors, and loading conditions. The J-A parameters were implemented as fracture criteria and used to predict the test results. For comparison, other fracture criteria were used to predict the same test results. Major findings include: The A constraint parameter A varies with specimen type and applied load thus accurate determination is crucial in predicting the failure load, and the A parameter is asymptotic as the failure load is approached, making an accurate determination difficult (i.e., small differences in the A parameter can cause large variations in failure load) for materials exhibiting elastic-plastic behavior. The failure predictions from J-A methodology were more accurate than the traditionally used KC and J methods, and have comparable scatter to that observed when using the crack-tip opening angle (CTOA) method. However, the J-A methodology requires considerable effort (expertise level and labor) to implement and to evaluate the A parameter for different specimen types and materials, or to apply this methodology to part-through crack (e.g., 3D problems) structural applications.

Hamm, Kenneth R., Jr.↗
DOE OSTI2015

Minimum critical values for various fissile media with very low content of plutonium mixed in different kinds of matrix - 14340

For materials slightly contaminated by fissile nuclides (such as radioactive sludge), it could be useful to take into account the low fissile density in order to define the nuclear criticality safety limits (mass, volume,...) when this density is lower than the one of the optimally moderated fissile-water mixture (e.g. 30 g/dm{sup 3} for {sup 239}Pu). In such a case, if the material is modelled by the usual fissile-water mixture only, the fissile medium still contains a void fraction when the optimal moderation ratio is reached. Then, the question is to know whether modeling the other elements of the material can impact the nuclear criticality safety limits, in particular when they are good scattering elements. This paper aims at studying the impact of replacing the void fraction in plutonium fissile media, with various apparent densities, by different kinds of matrix containing scattering elements. Minimum critical values (mass, volume, diameter and thickness) have been determined for plutonium media, composed of 100 % {sup 239}Pu, with densities of 2, 5.8 and 7.3 g/dm{sup 3} in different kinds of matrix containing scattering elements (graphite, carbon, alumina, silica, magnesia, fluorite and calcium oxide). Different contents of the aforementioned scattering elements in the fissile media were studied and additional moderation was ensured by water. The results highlight that minimum critical values are lower when considering a fissile medium containing graphite, carbon, silica, alumina and magnesia with additional water moderation, compared to plutonium-water mixture only with the same low fissile apparent density. However, there is still a benefit of crediting density (critical values for a low fissile density are still higher than critical values without a density control). (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Towards replacing physical testing of granular materials with a Topology-based Model

In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The “effective surface area,” the surface area accessible to the airflow, is typically measured using a permeametry apparatus that relates the flow conductance to the permeable surface area via the Carman-Kozeny equation. This equation allows calculating the flow rate of a fluid flowing through the granules packed in the sample for a given pressure drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and flow paths that may not accurately hold in situations where the particles possess a wide distribution in shapes, sizes, and aspect ratios, as is true with many powdered systems of technological and commercial interest. To address this challenge, we replicate these measurements virtually on micro-CT images of the powdered material, introducing a new Pore Network Model based on the skeleton of the Morse-Smale complex. Pores are identified as basins of the complex, their incidence encodes adjacency, and the conductivity of the capillary between them is computed from the cross-section at their interface. We build and solve a resistive network to compute an approximate laminar fluid flow through the pore structure. Here, we provide two means of estimating flow-permeable surface area: (i) by direct computation of conductivity, and (ii) by identifying dead-ends in the flow coupled with isosurface extraction and the application of the Carman-Kozeny equation, with the aim of establishing consistency over a range of particle shapes, sizes, porosity levels, and void distribution patterns.

36 MATERIALS SCIENCE↗
NASA NTRS2014

Electrostatic Levitation for Studies of Additive Manufactured Materials

The electrostatic levitation (ESL) laboratory at NASA's Marshall Space Flight Center is a unique facility for investigators studying high temperature materials. The laboratory boasts two levitators in which samples can be levitated, heated, melted, undercooled, and resolidified. Electrostatic levitation minimizes gravitational effects and allows materials to be studied without contact with a container or instrumentation. The lab also has a high temperature emissivity measurement system, which provides normal spectral and normal total emissivity measurements at use temperature. The ESL lab has been instrumental in many pioneering materials investigations of thermophysical properties, e.g., creep measurements, solidification, triggered nucleation, and emissivity at high temperatures. Research in the ESL lab has already led to the development of advanced high temperature materials for aerospace applications, coatings for rocket nozzles, improved medical and industrial optics, metallic glasses, ablatives for reentry vehicles, and materials with memory. Modeling of additive manufacturing materials processing is necessary for the study of their resulting materials properties. In addition, the modeling of the selective laser melting processes and its materials property predictions are also underway. Unfortunately, there is very little data for the properties of these materials, especially of the materials in the liquid state. Some method to measure thermophysical properties of additive manufacturing materials is necessary. The ESL lab is ideal for these studies. The lab can provide surface tension and viscosity of molten materials, density measurements, emissivity measurements, and even creep strength measurements. The ESL lab can also determine melting temperature, surface temperatures, and phase transition temperatures of additive manufactured materials. This presentation will provide background on the ESL lab and its capabilities, provide an approach to using the ESL in supporting the development and modeling of the selective laser melting process for metals, and provide an overview of the results to date.

SanSoucie, Michael P.↗
NASA NTRS2003

High-Fidelity Micromechanics Model Enhanced for Multiphase Particulate Materials

This 3-year effort involves the development of a comprehensive micromechanics model and a related computer code, capable of accurately estimating both the average response and the local stress and strain fields in the individual phases, assuming both elastic and inelastic behavior. During the first year (fiscal year 2001) of the investigation, a version of the model called the High-Fidelity Generalized Method of Cells (HFGMC) was successfully completed for the thermo-inelastic response of continuously reinforced multiphased materials with arbitrary periodic microstructures (refs. 1 and 2). The model s excellent predictive capability for both the macroscopic response and the microlevel stress and strain fields was demonstrated through comparison with exact analytical and finite element solutions. This year, HFGMC was further extended in two technologically significant ways. The first enhancement entailed the incorporation of fiber/matrix debonding capability into the two-dimensional version of HFGMC for modeling the response of unidirectionally reinforced composites such as titanium matrix composites, which exhibit poor fiber/matrix bond. Comparison with experimental data validated the model s predictive capability. The second enhancement entailed further generalization of HFGMC to three dimensions to enable modeling the response of particulate-reinforced (discontinuous) composites in the elastic material behavior domain. Next year, the three-dimensional version will be generalized to encompass inelastic effects due to plasticity, viscoplasticity, and damage, as well as coupled electromagnetothermomechanical (including piezoelectric) effects.

Pindera, Marek-Jerzy↗
DOE OSTI2015

Relating Synthesis Parameters to the Morphology of the Photoactive Layer in Organic Photovoltaic Solar Cells Using Molecular Dynamics Simulations. In: Organic Solar Cells. Materials, Devices, Interfaces, and Modeling

Photovoltaic solar cells, which utilize incidental solar radiation to generate electrical energy, are widely considered as potential renewable energy devices capable of meeting the increasing energy demand. Photovoltaic solar cells are often classified based on the materials employed to achieve energy conversion, which include both inorganic and organic carbon-based materials. Despite the dominant use of inorganic materials in solar cell technology, organic photovoltaic (OPV) solar cells have generated significant scientific interest, owing to the inexpensive fabrication process, light weight, ease of manufacturing, flexible structure, and low operating temperature. Although state-of-the-art OPV solar cells lack the efficiency for large-scale applications and have stability issues, their low production costs have resulted in significant research efforts to improve their efficiency. Such efforts have led to a substantial increase in the power conversion efficiency (PCE) over the past decade with a maximum efficiency of 12% reported recently.

Mortuza, S. M.↗
DOE OSTI2019

MODELING THE DYNAMICS OF MATERIALS PROCESSING AND ELECTROCHEMICAL SYSTEMS FOR ENERGY STORAGE APPLICATIONS

To realize the promise of electric vehicles, personal electronics, and renewable energy sources, improvements in energy storage technology are crucial. However, avenues for improvement such as designing superior electrode materials or modifying the battery electrolyte and separator are difficult without sufficient understanding of the materials and processes used to produce them. One such process is electrospinning, which uses high voltage to produce polymer nanofibers cheaply and continuously. To examine the effect of electrospinning on material morphology, the placement of nanoparticles within lamella-forming polymer blends and block copolymers is simulated using molecular dynamics under planar elongational flow. Then, extensional flow is combined with cylindrical confinement to simulate a block copolymer-filled cylinder with a constantly shrinking diameter, which is a better model for electrospinning. The appearance of ordered or disordered morphologies is found to be connected to a Weissenberg number relating the deformation and self-assembly time scales. A second approach towards understanding energy storage systems is to simulate the battery’s electrochemical performance. Of particular interest is the lithium-sulfur (Li-S) battery, which aims to replace lithium-ion batteries due to its higher specific capacity and cheaper material costs. However, well-known challenges such as polysulfide crossover, large volume changes during cycling, and deposition of insulating lithium sulfide limit the capacity and capacity retention of Li-S batteries. Using a continuum-level numerical simulation which includes reaction, mass transport, adsorption, and nucleation, these challenges are investigated in order to explain the mechanisms underlying Li-S discharge behavior. The model is used to explain the end-of-discharge failure behavior of liquid and gel electrolyte systems, finding that insufficient mass transport of polysulfides is the cause. In addition, the effects of adsorptive materials, cathode passivation with insulating lithium sulfide, and spherical carbon cathode particle geometry is investigated. It is found that adsorptive materials can greatly improve battery performance when the location of lithium sulfide deposition is considered in the model. Finally, the model suggests that different cathode processing techniques in experiment can lead to different end-of-discharge failure mechanisms.

25 ENERGY STORAGE↗
DOE OSTI2016

Final Report

This is the final report for the work conducted at the University of Minnesota (during the period 12/01/12-09/18/14) by PI Panos Stinis as part of the "Collaboratory on Mathematics for Mesoscopic Modeling of Materials" (CM4). CM4 is a multi-institution DOE-funded project whose aim is to conduct basic and applied research in the emerging field of mesoscopic modeling of materials.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Material Response Analysis of PICA-NuSil at the Hypersonic Materials Environmental Test System

Phenolic impregnated carbon ablator (PICA) is a thermal protection system (TPS) that gained heritage during the Stardust mission and is the baseline TPS material for expeditions to Mars (e.g., Mars Science Laboratory and Mars 2020).1 PICA is friable; therefore, a polysiloxane resin (NuSil CV-1144-0) is deposited onto the surface of flight hardware before assembly, test, and launch operations (ATLO) to mitigate particle shedding. Furthermore, the Mars Science Laboratory (MSL) and Mars 2020 heatshields were instrumented with an array of thermocouple plugs (MEDLI Integrated Sensor Plugs or MISP) designed to measure the in-depth thermal response of PICA during flight. Post-flight analysis of MISP data suggests that recession was lower than predicted, and NuSil is suspected as a reasonable cause. NuSil primarily consists of a copolymer blend of dimethyl and diphenyl-substituted polysiloxane resin. Four decades of research in the field of polymer-derived ceramics demonstrate that polysiloxane resins form oxidation-resistant silicon oxycarbide materials at pyrolysis temperatures as low as 800 °C. -2 Furthermore, silicon oxycarbide materials exhibit excellent thermal stability at relatively high-temperatures (< 1200 °C) but eventually decompose via carbothermal reduction. -3 Therefore, it is reasonable to suggest that NuSil forms an oxidation-resistant thermal barrier coating on the TPS surface and influences the material response during atmospheric entry. Evidence for this notion was observed during prior arc-jet testing at both the Aerodynamic Heating Facility (AHF) and the Panel Test Facility (PTF) at the NASA Ames Research Center. Articles of PICA were subjected to testing in airflow, and a temperature discontinuity was recorded at the surface of coupons coated with NuSil. A glassy coating was observed to form at the surface in shear flow configurations (wedge and panel) under moderate heat fluxes. Furthermore, state-of-the-art material response models have yet to account for the underlying physics and chemistry of the temperature discontinuity. To this end, a pathfinder test campaign was executed at the Hypersonic Materials Environmental Test System (HyMETS) to enhance the fundamental understanding of PICA-NuSil ablation phenomena and provide a preliminary data set to aid in the development of material response models.

PICA↗
NASA NTRS1989

A numerical model for the thermo-elasto-plastic behaviour of a material

This paper presents a numerical model for the thermo-elasto-plastic behavior of an isotropic material. The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening. This unique model can be used both for isothermal and non-isothermal cases. The original formulation for the non-isothermal three-dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided. The finite element implementation of this model is also outlined.

Ray, Sujit K.↗

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