JOM

DOI: 10.1007/s11837-017-2608-z Ó 2017 The Minerals, Metals & Materials Society

Modeling Early-Stage Processes of U-10 Wt.%Mo Alloy Using Integrated Computational Materials Engineering Concepts XIAOWO WANG,1 ZHIJIE XU ,1,3 AYOUB SOULAMI,2 XIAOHUA HU,1 CURT LAVENDER,2 and VINEET JOSHI2 1.—Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99352, USA. 2.—Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA 99352, USA. 3.—e-mail: [email protected]

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.

INTRODUCTION Initially proposed in 2006, integrated computational materials engineering (ICME) has become an increasingly important approach in the materials science and engineering field.1,2 The work presented herein represents a first attempt to apply ICME to uranium alloyed with 10 wt.% molybdenum (U10Mo), seeking to obtain a better understanding of the microstructure resulting from its thermomechanical processing. Since the 1980s, U-10Mo has been identified as the most promising candidate low-enriched uranium (LEU) fuel.3–5 Fabrication of U-10Mo alloy involves a complex series of materials processing steps, including casting, homogenization, multiple passes of hot roll bonding of a zirconium (Zircaloy) diffusion barrier, cold rolling and annealing, and hot isostatic pressing (HIP).6,7 In previous U-10Mo modeling efforts,8–10 materials parameters were obtained from existing literature11–16 or from extensive experiments conducted on U-10Mo samples. However, complete understanding of the effects of those processes, from casting through HIP, on the U-10Mo microstructure

is not feasible using conventional standalone models. An integrated process model for U-10Mo, inspired by the ICME concept, would enable information (model, materials parameters, etc.) to be passed between different process models and provide a generic framework for modeling the evolution of the microstructure of U-10Mo alloy during a given series of thermomechanical processes. Figure 1a depicts a flowchart of key U-10Mo processes, starting from casting, homogenization, multiple passes of hot and cold rolling and annealing, and HIP to the corresponding process models to be integrated using ICME. The output is the microstructural information of interest (e.g., Zircaloy thickness and stress–strain characteristic). The shaded boxes represent the three models implemented, integrated, and presented herein: (1) homogenization, (2) microstructure-based finite element method (FEM) for hot rolling, and (3) carbide distribution analysis. Upon completion of casting, U-10Mo is heated to c phase (above 560°C) for homogenization treatment to obtain a more uniform Mo distribution. During homogenization, the dendritic structure of

Wang, Xu, Soulami, Hu, Lavender, and Joshi

Fig. 1. Flowchart for (a) an integrated model of U-10Mo alloy and (b) model integration schematic for the three model components presented in this paper. TTT time-temperature-transformation.

molybdenum is eliminated and Mo segregation is alleviated. All of these microstructural changes affect the behavior of U-10Mo in subsequent processes.17,18 Recently, Xu et al.19 proposed a homogenization model for U-10Mo as an alternative to time-consuming and labor-intensive experiments for optimizing the homogenization process. The homogenization model reconstructs the Mo concentration field from backscattered electron scanning electron microscopy (BSE-SEM) images in as-cast state. The proposed ICME approach for U-10Mo processes passes the microstructures reconstructed by this homogenization model from BSE-SEM images to an FEM model for modeling the effect of rolling U-10Mo with a Zircaloy-2 diffusion barrier. The resulting integrated model can then be used to predict the variation in the thickness of the Zircaloy-2 barrier as a function of the degree of homogenization, which is not possible without such model integration. Information regarding the Mo concentration, carbide distribution, and grain

morphology, i.e., the homogenization model outputs, is then used as the input for the microstructurebased FEM hot rolling model. To characterize carbide redistribution during rolling, this model can be further integrated with carbide distribution analysis to generate two-point correlation functions and probability distributions of pair angles and particle size during the entire rolling process. The carbide distribution is a critical factor affecting the recrystallization, hardness, and fracture toughness of U-10Mo in subsequent processes.20,21 A fully integrated model with all the necessary component models shown in Fig. 1a remains under active development. Figure 1b shows the relationship and input and output information flow between the homogenization, hot rolling, and carbide distribution components. This paper details the ICME approach for integrating three individual modeling components of U10Mo processes. ‘‘Homogenization Model’’ section provides a brief introduction to the homogenization model (see Ref. 19 for details), followed by a

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

description of the microstructure-based FEM model (see Ref. 22 for details) in ‘‘Microstructure-Based FEM for U-Mo/Zircaloy-2 Interface Prediction’’ section. These two individual models reported elseare re-presented briefly in where19,22 ‘‘Homogenization Model’’ and ‘‘MicrostructureBased FEM for U-Mo/Zircaloy-2 Interface Prediction’’ sections for the reader’s convenience. Details can be found in the original publications. The novelty of this work is integration of the otherwise standalone models to enable integrated computational study of the early-stage processing of U10Mo. Such integrated study enables investigation of the effect of homogenization on the Zr thickness variation (‘‘Microstructure-Based FEM for U-Mo/ Zircaloy-2 Interface Prediction’’ section) and carbide distribution analysis (‘‘Carbide Particle Distribution Analysis’’ section), as two examples. HOMOGENIZATION MODEL The initial inputs of the integrated model are digital microstructures obtained from BSE-SEM images of as-cast U-10Mo samples (see Fig. 2 in Ref. 19). Detailed description of this image can be found in the Electronic Supplementary Material (ESM). Reconstruction of Mo Concentration Field The Mo concentration over the entire domain can be constructed pixel by pixel based on the nonlinear relationship between the grayscale values in the BSE-SEM image and energy dispersive spectroscopy (EDS) line data. Details about this technique can be found in Ref. 19. Notably, because the operator and machine settings can differ in each case, the correlation between the Mo concentration and EDS line data can vary. To carry out this process, grayscale data are extracted and plotted against the Mo concentration obtained from EDS. The relationship between the grayscale value and Mo concentration is then established between the two series of data, yielding a one-to-one nonlinear relationship between them. Using this relation constructed for EDS images, Fig. 8 in Ref. 19 illustrates the Mo concentration of a sample. Carbide particles are represented by blue regions with very low Mo concentration. Repeating the same procedure, the sample’s Mo concentration after various homogenization durations (4, 8, 16, 24, and 48 h) at 800°C can be reconstructed, respectively. MICROSTRUCTURE-BASED FEM FOR U-MO/ ZIRCALOY-2 INTERFACE PREDICTION As the second component of the integrated model, the microstructures generated from the homogenization model (as described in ‘‘Homogenization Model’’ section) are used to build a microstructurebased FEM for compression and rolling simulations.

Mo-rich and Mo-poor regions with different mechanical properties are incorporated. The effect of homogenization time on the variation of the U10Mo/Zircaloy-2 thickness in as-rolled fuel foils was investigated. One of the defects observed in U-10Mo fuels is nonuniform Zircaloy-2 layer thickness. Edwards et al.23 observed Zircaloy thinning in fullsized plate fuel (Fig. 3-2 in Ref. 23). The Zircaloy layers were found to have significantly nonuniform thickness. In some cases, regions could be as thick as 35–40 lm with localized regions that tapered down to as low as 4–10 lm. Recently, Joshi et al.18 demonstrated that homogenization can lead to uniform Mo concentration and elimination of abnormally coarse grains, which can decrease the roughness of the U-10Mo/Zircaloy-2 interface. This FEM model uses reconstructed microstructures from the described homogenization model (‘‘Homogenization Model’’ section) as input. Actual microstructures from samples in three conditions are considered: (1) as-cast, (2) homogenized at 800°C for 4 h, and (3) homogenized at 800°C for 48 h. Model Description To build the microstructure-based FEM, the Mo concentration must be correlated with mechanical properties. The ultimate tensile strength (UTS) of U-10Mo was defined as a function of Mo concentration using data from Burkes et al.24 and Hills et al.15 for room temperature and data from Beghi25 and Waldron et al.12 for 600°C (Fig. S1 in ESM). Before reaching the UTS, the material over the domain is described by rate-independent plasticity with linear hardening. The yield strength of U-10Mo at 600°C from Joshi et al.18 was used as a reference point to obtain the yield strength for all other Mo concentrations present in the microstructure. In fact, the yield strength differential follows the same trend as the UTS for various Mo concentrations, resulting in parallel stress–strain curves. A 25-lm-thick Zircaloy-2 layer is added on top of the U-10Mo representative volume element (RVE). Zircaloy-2 is considered to be a uniform isotropic material, having the mechanical properties summarized in Table I. Compressive load corresponding to 7% thickness reduction is applied on the top of the Zircaloy-2 layer to simulate rolling conditions and investigate the effect of deformation on the Zircaloy-2 layer variation at 600°C. A plane-strain two-dimensional FEM was created using a fine mesh with 1 lm 9 1 lm element size. The RVE contained 22,500 elements with size of 150 lm 9 150 lm. Each element was assigned mechanical properties based on its Mo concentration using the correlation functions obtained from Ref. 22 (Fig. S1 in ESM). After testing various meshes, the presented mesh showed results similar to those with finer meshes but longer computation

Wang, Xu, Soulami, Hu, Lavender, and Joshi

Table I. Mechanical properties of Zircaloy-2 and U-10Mo alloys8,26,27 Zircaloy-2 Young’s modulus Poisson’s ratio Density Thermal conductivity Yield strength UTS Heat capacity Coefficient of thermal expansion U-10Mo Young’s modulus Poisson’s ratio Density Thermal conductivity Heat capacity Coefficient of thermal expansion

96,526 MPa 0.4 6530 kg/m3 21.5 W/m °C 210 MPa 340 MPa 285 J/kg °C 6.5 9 10 6 m/m °C 65,000 MPa 0.35 16,060 kg/m3 35.5 W/m °C 167 J/kg °C 16.4 9 10 6 m/m °C

Here, two initial microstructures generated from the homogenization model described in ‘‘Homogenization Model’’ section are considered to analyze the carbide particle distribution resulting from the rolling deformation: an as-cast sample, and another homogenized at 800°C for 4 h. The two initial microstructures were directly mapped into the FEM plane-strain compression model (presented in ‘‘Microstructure-Based FEM for U-Mo/Zircaloy-2 Interface Prediction’’ section) and deformed to 20%, 40%, and 60% reduction of the original height. The properties of the c-U-based material were correlated with the Mo concentration as described in ‘‘Microstructure-Based FEM for U-Mo/Zircaloy-2 Interface Prediction’’ section. The deformed microstructures generated from the FEM model were then used as input for carbide particle analysis. Two-Point Correlation Functions

times. A MATLAB script was written to generate the FEM input file. Commercial FEM code LSDYNA was used to conduct the simulations using an explicit formulation with the FEM mesh shown in Fig. S2 in the ESM. Elements with Mo concentration below 0.1% were considered to be carbides with elastic behavior. Results and Discussion for MicrostructureBased FEM Model A closer look at the Zircaloy-2 layer reveals that the model predicted nonuniform thickness in the case of as-cast U-10Mo. Waviness is observed for the as-cast sample shown in the top image of Fig. 2, which is due to segregation of Mo concentration, corresponding to stresses in the RVE. In the line plot in Fig. 2, the nonuniformity of the Zircaloy-2 layer is quantified by plotting its thickness along the longitudinal cross-section of the rolled RVE. The Mo concentrations and von Mises stresses for ascast and homogenized samples are shown in Fig. S3 in the ESM. For the as-cast model, the Zircaloy-2 layer varied by up to 4 lm, while the model subjected to 800°C for 48 h varied by less than 1 lm, indicating that homogenization reduces the variability of the Zircaloy-2 layer thickness. CARBIDE PARTICLE DISTRIBUTION ANALYSIS Uranium carbide is preferred as fuel material because of its superior uranium density and thermal conductivity. U-10Mo material contains about 2% volume fraction of uranium carbide particles. With progressive rolling reduction, these carbides redistribute and tend to align as stringers along the rolling direction. Such redistribution of carbides may influence recrystallization during annealing treatment.

The two-point correlation function method is one of the most important statistical descriptors of the microstructure of heterogeneous materials. A detailed description (Fig. S4) of the two-point correlation function can be found in the ESM. In the current work, the two-point correlation functions of the two microstructures were calculated only in the vertical direction. To obtain sufficient data, the vertical direction was defined as a range of +15° and 15° around h = 90°. Results and Discussion for Carbide Distribution Analysis Figure 3 summarizes the location of the first and second peak in the vertical direction for the as-cast and homogenized cases. A mild decrease in the first peak and a more prominent decrease in the second peak became apparent with the thickness reduction. The first peaks represent the most possible nearest distance d1 between particles, whereas the second peaks (triangle markers) represent the most possible second nearest distance d2. As carbide particles usually appear in the form of clusters, the first peaks mostly form because of the distances between particles inside each cluster, while the second peaks primarily represent the distances between particles from different clusters. It is expected that the changes in d1 will be quite small with thickness reduction compared with the changes in d2 during deformation. During rolling, the sheet will extend along the rolling direction while contracting along the thickness direction. This will make the interparticle spacing smaller along the thickness direction but larger along the rolling direction. Therefore, the dependence of the vertical (throughthickness) interparticle spacing shown in Fig. 3 on rolling reduction is expected. More results for the two-point correlation and carbide particle size

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

Fig. 2. Zircaloy thickness variation along the longitudinal cross-section (reprinted from Ref. 22). Thickness variation indicates nonuniform thickness for as-cast U-10Mo, in contrast to the homogenized samples.

CONCLUSION AND FUTURE WORK

Fig. 3. The location of the first (d1) and second (d2) peaks from twopoint correlation analysis along vertical direction varying with rolling reductions for two different samples (as cast and homogenized for 4 h). The distance between carbide clusters decreases with deformation.

distribution of the as-cast and homogenized microstructures can be found in Figs. S5–S9 in the ESM.

This paper presents an integrated model using the ICME concept to enable investigation of the effect of homogenization on the thickness of the Zircaloy-2 barrier and carbide particle distribution. It integrates standalone models, i.e., a homogenization model, a microstructure-based FEM model, and carbide distribution analysis, for improved understanding of U-10Mo thermomechanical processes. This first step demonstrates the application of ICME concepts to the modeling and simulation of U-10Mo alloy. This multiprocess model enables investigation of the evolution of the microstructure after various processes, including phase stability, microstructure texture, grain growth, carbide morphology and fracture, porosity morphology, and eutectoid transformation.

ELECTRONIC SUPPLEMENTARY MATERIAL The online version of this article (doi:10.1007/ s11837-017-2608-z) contains supplementary material, which is available to authorized users.

Wang, Xu, Soulami, Hu, Lavender, and Joshi

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