Microstructure-based Finite Element Method Research Articles

Dynamic data-driven multiscale modeling for predicting the degradation of a 316L stainless steel nuclear cladding material

We have developed a long short-term memory stacked ensemble (LSTM-SE) surrogate modeling approach that can provide rapid predictions of microstructural evolution and the resultant mechanical properties of American Iron and Steel Institute (AISI) 316L series stainless steel (SS316L) fuel cladding under conditions of varying temperature and radiation dose rate. To acquire training data, we developed and implemented a kinetic Monte Carlo (KMC) model to simulate precipitation kinetics of M23C6, γ’, and G phases within SS316L cladding. Experimentally reported precipitation kinetics of SS316L in literature were linked to the kinetic parameters of the simulated precipitation in our KMC model. The model was then used to simulate microstructure evolution under synthetically generated treatments of varying temperature and radiation dose rate for periods of up to 3000 h. Changes in volume fraction, number density, and particle size of precipitates were recorded, and particle area fractions were correlated using statistical methods to develop the surrogate model. Simultaneously, the mechanical properties of the simulated microstructures were evaluated using microstructure-based finite element method (FEM) analysis to determine the elastic modulus, yield stress, ultimate tensile strength, and elongation to failure of the aged microstructures. Using this approach, our surrogate model can predict precipitation behavior within 0.25 % volume fraction and mechanical properties within 6 % relative error from the values predicted by the KMC and FEM models using 50 training simulations as input. The trained recurrent neural network-based model can return estimations of precipitation kinetics and mechanical properties ∼1000 times faster than the physics-based codes. This work demonstrates, as a proof of concept, that microstructural evolution under variable conditions can be predicted using a statistics-based model informed by a practicably obtainable dataset. The potential applications of this type of modeling framework are discussed.

Minimizing thickness variation in monolithic U-10Mo fuel foil and Zr interlayer during hot rolling: A microstructure-based finite element method analysis

Low-enriched uranium alloyed with 10 wt. % molybdenum (U-10Mo) has been identified as a promising alternative to highly enriched uranium fuel for the United States’ high performance research reactors. The monolithic U-10Mo fuel plate consists of a metallic U-10Mo fuel foil with a 25 µm Zr interlayer and a relatively thick cladding of aluminum alloy 6061. The Zr interlayer is typically applied during the hot co-rolling process, and this process dictates the uniformity of the Zr interlayer. Thickness variation observed in the U-10Mo and Zr interlayer has been attributed to several sources: the initial grain size of the U-10Mo castings, can materials, rolling temperature, inhomogeneous molybdenum content, and porosity in the cast U-10Mo. This thickness variation limits the ability to meet the dimensional specification; thus, a better understanding of the factors causing the nonuniform thickness is needed. In this work, we used a novel, microstructure-based finite element method to model the hot rolling process to address these concerns. Grain microstructures in U-10Mo were tessellated and explicitly considered in the finite element model. Each grain was assigned a random material property to mimic the grain strength variations induced by different grain orientations. Simulations were performed using six steel can thicknesses, four grain sizes, and with or without a Zr interlayer to investigate the influences of those variables on the thickness nonuniformity. The simulation results showed that a thinner steel can and finer U-10Mo grain size reduce thickness variations in both the U-10Mo fuel foil and Zr interlayer. The direct findings from the simulations and analysis can be used to optimize the hot rolling schedule, reduce fabrication defects, and meet the dimensional specifications. The proposed microstructure-based finite element model can be also coupled with experimental microstructure characterization data, images, and models to simulate multi-pass hot rolling.

A framework for predicting the local stress-strain behaviors of additively manufactured multiphase alloys in the sequential layers

The additive manufacturing (AM) process often results in non-uniform microstructure and different mechanical properties in sequential layers, impacting the overall performance of the AM-ed component. However, it is extremely challenging to evaluate the local stress-strain behavior of each individual layer, owing to the limited size of the AM-ed layered structure. To this end, a framework for characterizing and predicting the mechanical evolution of AM-ed multiphase alloys by combing nanoindentation and microstructure-based finite element method (FEM) was proposed. The sample used in this study was superduplex stainless steel (SDSS) manufactured by wire arc additive manufacturing (WAAM), and the microstructure varied from layer to layer. Firstly, the mechanical properties of the two constituent phases in each layer, including elastic modulus and hardness, were obtained by nanoindentation, and the indentation size effect (ISE) was also evaluated. The yield strength and hardening exponent of each phase were subsequently estimated by reverse analysis method, and therefore the constitutive behaviors of the individual phase, which served as input parameters for FEM, were acquired. By aid of real microstructure-based FEM under uniaxial tension, the overall stress-strain behaviors of each layer and the distributions of the stress and strain during the deformation process were investigated. This work provides a new avenue for the characterization of the multiphase alloys in AM industry, beneficial to the understanding of the mechanical evolution in AM-ed materials.

Micromechanical simulation of plastic deformation behavior and failure commencement in high silicon bainitic steel after austempering

The plastic deformation and failure initiation of super bainitic steels containing different amount of bainite were analyzed using a real microstructure-based micromechanical finite element method (FEM). Real micrograph of such phase steels obtained by microscope were utilized as the representative volume elements (RVEs) in the micromechanical approach. Ductile mode of failure throughout selected RVE was simulated in term of strain localization for the duration of deformation. Calculations were carried out on the representative volume to numerically analyze the effects of characteristics of every individual constituents phase on the macroscopic mechanical properties of steels regarding their quantitative volumetric amount. The results obtained from simulation were assessed against experimental records and it was determined that the real microstructure-based FEM can predict strength and also ductility of the studied bainitic steels. Furthermore, shear failure mode occurs in all heat treated state of the studied steel which correlate quite well with experimental findings.

Behavior of vibration energy harvesters composed of polymer fibers and piezoelectric ceramic particles

Flexible piezoelectric composites of polymer fiber and ceramic particles are promising candidates for ambient vibration energy harvesters. However, observations of stress transfer behavior between polymer fiber and ceramic particle have not been clarified. In this study, the output from two types of composite with ceramic particles inside and outside of the fiber was measured, where the output for ceramic particles inside the fiber was 209 mV and 91 mV for fibers outside. Experimental results were confirmed using a microstructure-based finite element method. A simplified microstructure model that consists of one piezoelectric particle and two polymer fibers was created and loaded with the prescribed strain. Ceramic particle strain inside the fiber was higher than one outside the fiber, which was quantitatively consistent with experimental results. Analysis indicates that stress transfer between the polymer fiber and ceramic particles occurs on the interface and is important for electrical output. This is the first study to clarify the relation between stress transfer and output. Study results will lead to the material design of flexible piezoelectric composites and their application to ambient vibration energy harvesters.

Characterization on stress-strain behavior of ferrite and austenite in a 2205 duplex stainless steel based on nanoindentation and finite element method

Abstract The stress-strain behavior of ferrite and austenite in a commercial 2205 duplex stainless steel was investigated by using nanoindentation test and microstructure-based finite element method (FEM). Results showed that the optimum load range for measuring phase properties in nanoindentation test was from 3000 μN to 7000 μN. The ferrite has slightly higher average elastic modulus than austenite, while austenite has higher average nanohardness than ferrite. Representative stress-strain curves of ferrite and austenite were determined by means of the power-law hardening and empirical relationship. Based on FEM, the differences in distribution and portion of stress-strain in local phases were visualized, and the overall flow curve of the sample 2205 was extracted, which was in good agreement with the obtained results from uniaxial tensile experiment.

Modeling Early-Stage Processes of U-10 Wt.%Mo Alloy Using Integrated Computational Materials Engineering Concepts

Low-enriched uranium alloyed with 10 wt.% molybdenum (U-10Mo) has been identified as a promising alternative to high-enriched uranium. Manufacturing U-10Mo alloy involves multiple complex thermomechanical processes that pose challenges for computational modeling. This paper describes the application of integrated computational materials engineering (ICME) concepts to integrate three individual modeling components, viz. homogenization, microstructure-based finite element method for hot rolling, and carbide particle distribution, to simulate the early-stage processes of U-10Mo alloy manufacture. The resulting integrated model enables information to be passed between different model components and leads to improved understanding of the evolution of the microstructure. This ICME approach is then used to predict the variation in the thickness of the Zircaloy-2 barrier as a function of the degree of homogenization and to analyze the carbide distribution, which can affect the recrystallization, hardness, and fracture properties of U-10Mo in subsequent processes.

Predicting Deformation Limits of Dual-Phase Steels Under Complex Loading Paths

In this study, the deformation limits of various DP980 steels are examined with the deformation instability theory. Under uniaxial tension, overall stress–strain curves of the material are estimated based on a simple rule of mixture (ROM) with both iso-strain and iso-stress assumptions. Under complex loading paths, an actual microstructure-based finite element (FE) method is used to resolve the deformation compatibilities explicitly between the soft ferrite and hard martensite phases. The results show that, for uniaxial tension, the deformation instability theory with iso-strain-based ROM can be used to provide the lower bound estimate of the uniform elongation (UE) for the various DP980 considered. Under complex loading paths, the deformation instability theory with microstructure-based FE method can be used in examining the effects of various microstructural features on the deformation limits of DP980 steels.

Finite Element Simulation of Mechanical Behavior of TRIP800 Steel Under Different Loading Conditions Using an Advanced Microstructure-Based Model

The mechanical behavior of a low alloy multiphase TRIP steel has been predicted by an advanced microstructure-based finite element method. A representative volume element chosen based on the actual microstructure has been utilized for simulating the mechanical behavior of the studied steel. The parameters describing the martensitic transformation kinetics have been estimated using both crystallographic and thermodynamic theories of martensitic transformation. The mechanical behavior of each of the constituent phases required for the prediction of mechanical behavior of the studied material has been extracted from those reported in the literature. Comparison of the predicted mechanical behavior of the investigated TRIP800 steel with those reported in the literature shows that there is good agreement between simulated and experimental results. Therefore, it can be said that, the utilized microstructure-based model can be used for the prediction of both mechanical and transformation behaviors of the TRIP800 steels. It is worth noting that all of the parameters used in the model, except the sensitivity of the martensitic transformation to the stress state, can be estimated theoretically; thus, the number of parameters obtained by correlating the simulated and experimental results reduces to one. This is the unique characteristic of the utilized model, which makes the application of the model for simulation of the mechanical behavior of TRIP steels simpler than that of the similar ones.

Characterization of phase properties and deformation in ferritic-austenitic duplex stainless steels by nanoindentation and finite element method

The phase properties and deformation behavior of the δ–ferrite and γ–austenite phases of CF–3 and CF–8 cast duplex stainless steels were characterized by nanoindentation and microstructure-based finite element method (FEM) models. The elastic modulus of each phase was evaluated and the results indicate that the mean elastic modulus of the δ–ferrite phase is greater than that of the γ–austenite phase, and the mean nanoindentation hardness values of each phase are approximately the same. The elastic FEM model results illustrate that greater von Mises stresses are located within the δ–ferrite phase, while greater von Mises strains are located in the γ–austenite phase in response to elastic deformation. The elastic moduli calculated by FEM agree closely with those measured by tensile testing. The plastically deformed specimens exhibit an increase in misorientation, deformed grains, and subgrain structure formation as measured by electron backscatter diffraction (EBSD).

Comparison of Different Upscaling Methods for Predicting Thermal Conductivity of Complex Heterogeneous Materials System: Application on Nuclear Waste Forms

To develop strategies for determining thermal conductivity based on the prediction of a complex heterogeneous materials system and loaded nuclear waste forms, the computational efficiency and accuracy of different upscaling methods has been evaluated. The effective thermal conductivity, obtained from microstructure information and local thermal conductivity of different components, is critical in predicting the life and performance of waste forms during storage. Several methods, including the Taylor model, Sachs model, self-consistent model, and statistical upscaling method, were developed and implemented. Microstructure-based finite-element method (FEM) prediction results were used to as a benchmark to determine the accuracy of the different upscaling methods. Micrographs from waste forms with varying waste loadings were used in the prediction of thermal conductivity in FEM and homogenization methods. Prediction results demonstrated that in term of efficiency, boundary models (e.g., Taylor model and Sachs model) are stronger than the self-consistent model, statistical upscaling method, and finite-element method. However, when balancing computational efficiency and accuracy, statistical upscaling is a useful method in predicting effective thermal conductivity for nuclear waste forms.

Predicting Fracture Toughness of TRIP 800 Using Phase Properties Characterized by In-Situ High-Energy X-Ray Diffraction

Transformation-induced plasticity (TRIP) steel is a typical representative of first generation advanced high-strength steel, which exhibits a combination of high strength and excellent ductility due to its multiphase microstructure. In this article, we study the crack propagation behavior and fracture resistance of a TRIP 800 steel using a microstructure-based finite element method with the various phase properties characterized by in-situ high-energy X-ray diffraction (HEXRD) technique. Uniaxial tensile tests on the notched TRIP 800 sheet specimens were also conducted, and the experimentally measured tensile properties and R curves (resistance curves) were used to calibrate the modeling parameters and to validate the overall modeling results. The comparison between the simulated and experimentally measured results suggests that the micromechanics based modeling procedure can well capture the overall complex crack propagation behaviors and the fracture resistance of TRIP steels. The methodology adopted here may be used to estimate the fracture resistance of various multiphase materials.

Three-dimensional visualization and microstructure-based modeling of deformation in particle-reinforced composites

Modeling and prediction of the overall elastic–plastic response and local damage mechanisms in composite materials, in particular particle-reinforced composites, is a very complex problem. This is because microstructural aspects of the composite, such as particle size, shape, and distribution, play important roles in deformation behavior. Analytical models and numerical models that simplify the microstructure of the composite do not account for the microstructural factors that influence the mechanical behavior of the material. In this paper we describe a serial sectioning process, followed by finite element method (FEM) simulation, to reproduce, visualize, and model the three-dimensional (3D) microstructure of particle-reinforced metal matrix composites. The 3D microstructure-based FEM accurately represents the alignment, aspect ratio, and distribution of the particles. Comparison with single-particle and multiparticle models of simple shape (spherical and ellipsoidal) shows that the 3D microstructure-based approach is more accurate in simulating and understanding macroscopic and microscopic material behavior.

Effect of particle orientation anisotropy on the tensile behavior of metal matrix composites: experiments and microstructure-based simulation

Abstract Deformation processing of particle reinforced metal matrix composites induces preferential orientation of the reinforcement particles. Thus, the orientation anisotropy of the reinforcement will strongly influence the mechanical behavior of the composite. In this study, the effect of reinforcement orientation anisotropy on the mechanical behavior of extruded 2080 Al matrix composite was examined. Microstructure characterization showed a preferred orientation of the reinforcement particles parallel to the extrusion axis, although the degree of orientation decreased with increasing reinforcement volume fraction. Young's modulus and tensile strength in the longitudinal orientation (parallel to the extrusion axis) were higher than that in the transverse orientation (perpendicular to the extrusion axis). The particle orientation-induced changes in stress–strain behavior were modeled using a microstructure-based finite element method approach, yielding good agreement with experimental results. The relationship between tensile behavior of the composites, especially elastic modulus, to the degree of anisotropy in orientation of the reinforcement particles is discussed.