Machine learning for metallurgy V: A neural-network potential for zirconium

The mechanical performance-including deformation, fracture and radiation damage-of zirconium is determined at the atomic scale. With Zr and its alloys extensively used in the nuclear industry, understanding that atomic scale behavior is crucial. The defects controlling that performance are at size scales far larger than accessible by first principles methods, necessitating the use of semiempirical interatomic potentials. Existing potentials for Zr are not sufficiently quantitative, nor easily extendable to alloys, oxides, or hydrides. To overcome these issues, a neural network machine learning potential (NNP) is developed here within the Behler-Parrinello framework for Zr. With a careful choice of descriptors of the atomic environments and the creation of a first-principles training dataset that includes a wide spectrum of configurations of metallurgical relevance, a very accurate NNP is demonstrated. Specifically, the Zr NNP yields a good description of dislocation structures and their relative energies and fracture behavior, along with bulk, surface, and point-defect properties and structures, and significantly outperforms the best available traditional potentials. Results here will enable large-scale simulations of complex processes and provide the basis for future extensions to alloys, oxides, and hydrides.

Embrittlement induced by the synergistic effects of radiation damage and helium in structural steels

Kun Wang

Ferritic/martensitic steels are candidate materials for fusion reactor structural components, liquid metal containers of spallation neutron sources, and accelerator driven systems, with good radiation resistance and thermo-mechanical properties. However, embrittlement resulting from the combined effects of radiation induced displacement damage (measured in dpa = displacement per atom) and transmutation products, especially helium gas, is one of the key issues. Four different steels were selected for mechanical and microstructural studies to understand the mechanisms of embrittlement induced by the combined effects of displacement damage and helium after irradiation in SINQ, the Swiss spallation source. The irradiations conditions were in the range: 10.7 ¿ 20.4 dpa with 850-1750 appm He at 160-300 °C. The evolution of the mechanical properties after irradiation was investigated by tensile and hardness tests. Radiation-induced defect clusters and helium bubbles were quantified by transmission electron microscopy (TEM). Emphasis was put on the deformation mechanisms under the different observed fracture mode, (ductile, quasi-cleavage and intergranular), whose occurrence depends on the irradiation conditions (dpa, He content and irradiation temperature). The tensile stress-strain curves and the scanning electron microscopy images of fracture surfaces showed distinct fracture mechanisms under different irradiation and test conditions. The tensile tests showed a yielding stress increase and loss of ductility of irradiated specimens. Hardness was measured on the specimens before tensile testing. The hardness results demonstrated an increasing trend with irradiation dose and helium content. TEM observations were done for all irradiated fractured specimens. Small defect clusters were observed in the 12.3 dpa specimen, but large defect clusters with loop-shape were very few. In the specimens of 17.2, 17.7 and 20.4 dpa, many large dislocation loops were detected besides small clusters. In addition, helium bubbles were observed in all specimens. The average size of defect clusters increased from 4.2 nm to 11.8 nm with dose increasing from 12.3 dpa to 20.4 dpa, whereas the number density did not change significantly. Meanwhile, the average size of visible helium bubbles increased from 1.03 nm to 1.93 nm. The microstructures in deformed area of irradiated specimens were observed and defect free channels with {110} and {112} slip planes were found in some specimens, indicating plastic flow localization. The average width of the channels is about 100 nm. Regarding the brittle samples, the TEM-lamella were extracted directly below intergranular fracture surfaces or cleavage surfaces by focused ion beam. Strikingly, deformation twinning was observed as the main feature in three irradiated specimens at high dose. Only twins with {112} planes were observed in all of these samples. The average thickness of twins is about 34 nm. Twins started from a fracture surface became gradually thinner with distance away from the fracture surface and stopped in the matrix finally. Features such as twin-precipitates interaction, twin-grain boundary and/or lath boundary interaction were observed. Twinning bands were seen to be arrested by grain boundaries or large precipitates, but could penetrate martensitic lath boundaries. Unlike the case of defect free channels, inside twins small defect-clusters, dislocation loops and dense small helium bubbles were observed.

EPFL2015

Constitutive behavior and fracture properties of tempered martensitic steels for nuclear applications

Raul Alejandro Bonadé

In this study, the tensile and fracture properties and the microstructure of the reduced-activation tempered martensitic steel Eurofer97 have been investigated. This technical alloy is a 9%Cr steel developed within the European fusion material research program. To a lesser extend, the plastic flow properties of a equiaxed ferritic Fe9%Cr model alloy were also studied for comparison with those of the tempered martensitic structure. The main objectives of this work are described hereafter: to correlate the microstructural features with the plastic flow properties measured by the tensile tests for both the Eurofer97 steel and the model alloy. The correlation established should be reflected in a physically-based model of plastic flow. to study the fracture properties of the Eurofer97 steel in details in the lower ductile-to-brittle transition region. to calculate with finite element modeling the stress fields at the crack tip. This information is further used in conjunction with a local approach model for quasi-cleavage to reconstruct the fracture toughness-temperature curve. Tensile tests were carried out at different imposed nominal strain rate at several temperatures from 77K up to 473K, on both the Eurofer97 steel and the Fe9%Cr model alloy. The temperature dependence of the yield stress was precisely determined. As expected for body-centered cubic (BCC) materials, a strong increase of the yield stress by decreasing temperature, below 200 K, was observed. At higher temperatures, the temperature dependence of the yield stress was found much weaker, being associated with the temperature dependence of the shear modulus. Efforts were made to analyze in details the post-yield behavior (strain-hardening) as a function of temperature. The post-yield behavior was modeled using the Kocks phenomenological model based on the competition of storage and annihilation of dislocations. While this model was originally developed for face-centered cubic (FCC) metals where the rate-controlling mechanism of dislocation motion is the dislocation-dislocation interaction, we used is model in the high temperature domain (T>200K) of BCC materials, to model the strain-hardening evolution of the Eurofer97 steel and the model alloy. The values obtained for the key parameters of the model, namely the dislocation mean free path and annihilation coefficient, were found consistent with the microstructural features. The parameters temperature-dependence observed was also consistent with the physics of two basic mechanisms of dislocation storage and annihilation (dynamical recovery). For the low temperature domain, the strain-hardening model was modified to account for the strong Peierls lattice friction, based on an original idea of Rauch. Transmission electron microscopy observations were done to characterize the undeformed microstructures and their evolution with strain. A clear correlation was established between the stress-dependence of the strain-hardening and the microstructures. Fracture toughness tests on the Eurofer97 steel were performed with 0.2T C(T) and 0.4T C(T) specimens in the lower transition. Five temperatures were selected at which many tests were repeated to determine the amplitude of the inherent scatter of quasi-cleavage. The temperature were chosen in such a way that the measure fracture toughness remain below 150 MPa m1/2, which correspond for the 0.4T C(T) at a M value larger than 70 at the highest temperature. Such a M value for 0.4T C(T) specimens is known to ensure enough constraint. An attempt to analyze the experimental data in the framework of the master-curve approach by following the ASTM E-1921 standard was done. It was clearly demonstrated that the assumed shape of the toughness-temperature curve as described in the ASTM E-1921 standard for the reactor pressure vessel steels is not adequate for the tempered martensitic Eurofer97 steel, which present a particularly steep transition. Our Eurofer97 fracture database was then compared to the existing one on another similar steel, the F82H. Differences in the amplitude of the scatter of both steels was found while the lower bound of the toughness-temperature curve, describing the 1% failure probability was shown to be the same. 2D finite element simulations of the compact tension specimens were performed at various temperatures using the constitutive laws determined previously. The stress field around the crack tip were calculated and used to determine a local criterion of quasi-cleavage. The criterion is defined by the attainment of a critical stress encompassing a critical area. The lower bound of the toughness-temperature curve was then successfully reconstructed by using this local criterion. Finally, the relationship between the critical area and the applied stress intensity factor for the C(T) specimen was shown to follow a power law whose coefficients are dependent on the real dimensions of the specimen. Such a relationship allows scaling the C(T) toughness data from one size to another in case of in-plane constraint loss.

EPFL2006

Two-phase modelling of hot tearing in aluminium alloys using a semi-coupled method

Vincent Mathier

Hot tearing is one of the most severe defects observed in castings, e.g. in billets or sheet ingots of aluminum alloys produced by DC casting. It is due to both tensile strains and a lack of interdendritic feeding in the mushy zone. In order to predict this phenomenon at the scale of an entire casting, the two-phase averaged conservation equations for mass and momentum must be solved in the mushy (i.e. mixed solid and liquid) region of the material. In recent contributions, M'Hamdi et al [1] proposed a strongly coupled resolution scheme for this set of equations. The solution of the problem was obtained using a rheological model established by Ludwig et al [2] and that captures the partially cohesive nature of the mushy alloy. In the present contribution, the problem is addressed using a slightly different approach. The same rheological model (i.e. saturated porous media treatment) is used, but the influence of the liquid pressure is neglected at this stage. This assumption allows for a weakly coupled resolution scheme in which the mechanical problem is first solved alone using ABAQUS™ and user subroutines. Then the pressure in the liquid phase is calculated separately accounting for the viscoplastic deformation of the porous solid skeleton and solidification shrinkage. This is done with a code previously developed for porosity calculations, and that uses a refined mesh in the mushy zone [3]. This semi-coupled method was implemented and its numerical convergence studied from the point of view of both time step and mesh size. Guidelines for selecting these numerical parameters as well as the conditions under which the semi-coupled method may be applied are provided. The model was then applied to three cases, i.e. two tensile tests conducted on mushy alloys [4, 5] and the casting of an entire billet [6]. Experimental data was indeed available concerning these problems prior to the present work. This information was used for the validation of the thermal and mechanical models that were setup to describe these different cases. The results of the semi-coupled approach were also used to describe in more details these different castings. First of all, the numerical study of the mushy zone tearing test [5] proved helpful for distinguishing different fracture modes. The role of the high strain rate applied to the mushy alloy in this case was also outlined. Another tensile test, referred to as the rig test [4], was successfully modeled in the present framework. The numerical results could be used to quantify the redistribution of strain in the mushy sample. As a consequence, intrinsic properties of the material, such as its ductility, could be extracted from the results. This study also gave further insight about the conditions under which tearing occurs in the samples. Finally, the semi-coupled method was used to study the DC casting process. In this case, a real process performed under realistic conditions for the production of an industrial scale billet was modeled. As it is more complex and difficult to characterize experimentally, the conditions for hot tearing formation are less accessible. However, the isotherm velocity, the strain, the strain rate and the liquid pressure could be described reasonably accurately. It was thus possible to correlate experimental observations of the hot tear with various calculated indicators of hot tearing susceptibility. Even with this information, it remains difficult to formulate new hot tearing criteria because all the indicators follow a similar trend during the casting and their respective contributions can thus not be distinguished. The present work showed that the level of accuracy and detail that can be reached using two-phase models with appropriate materials properties and boundary conditions is satisfactory. It is indeed possible to model the relevant phenomena (heat flow, solid deformation and liquid feeding) at the scale of an entire casting. The variation of the different simulated fields can be described down to a scale of the order of a few millimeters. In that sense, this approach is one important aspect required to build a multiscale model for the problem of hot tearing. It is expected that coupling such a method with granular models (which cover length scales from a few microns to a few centimeters [7]) will allow for a more complete description of the phenomena at hand. In the future, the development of such a multiscale numerical tool may prove to be the most efficient way towards quantitative predictions of hot tearing formation in real solidification processes.

EPFL2007