Machine learning for metallurgy IV: A neural network potential for Al-Cu-Mg and Al-Cu-Mg-Zn

Most metallurgical properties, e.g., dislocation propagation, precipitate formation, can only be fully understood atomistically but most phenomena and quantities of interest cannot be measured experimentally. Accurate simulation methods are essential but first-principles density functional theory (DFT) is prohibitively expensive while empirical interatomic potentials are rarely sufficiently accurate for alloys. Machine learning (ML) is emerging as an approach to create computationally-efficient atomistic potentials achieving near-DFT accuracy. Building on recent work on binary Al-Cu and ternary Al-Mg-Si, here a family of neural network potentials (NNPs) for Al alloys of Al-Cu-Mg and Al-Cu-Mg-Zn is developed and assessed using the Behler-Parinello formulation. Training of the potentials uses a robust set of metallurgically-relevant structures including intermetallic phases, stacking faults, solute/solute and solute/stacking fault interactions, solute clusters, and matrix/precipitate interfaces. The accuracy of these NNPs is then demonstrated across a comprehensive set of properties derived from the training set structures and, moreover, many important structures not represented in the training set such as the generalized stacking fault energy (GSFE) surface of the critical S-phase precipitate in Al-Mg-Cu, and antisite and vacancy formation energies for Al-Cu-Mg intermetallics. The broader Al-Cu-Mg-Zn NNPs also have high accuracy for subtle properties such as Cu substitutional energies in the n' and T phases and formation energies of small Al-Zn-Mg clusters. Together with earlier results, this paper shows how increasingly complex multicomponent alloy potentials can be systematically developed by expanding a training database, leading to a comprehensive set of potentials for a broad alloy family, demonstrated here for the technological Al-2xxx, Al-5xxx, and Al-7xxx Al alloys.

Multiscale Modelling of Irradiation Induced Effects on the Plasticity of Fe and Fe-Cr

Seyed Masood Hafez Haghighat

Degradation of mechanical properties due to nanometric irradiation induced defects is one of the challenging issues in designing ferritic materials for future nuclear fusion reactors. Various types of defects, namely dislocation loops, voids, He bubbles and Cr precipitates may be produced in ferritic materials due to high doses of irradiation with the 14 MeV neutrons stemming from the deuterium-tritium fusion reaction. Multiscale modelling methods, namely molecular dynamics (MD) and dislocation dynamics (DD) methods, are used here to study the impact of radiation-induced defects on the mechanical properties of model ferritic material. MD simulation is used to study the state of a nanometric helium bubble in α-Fe as a function of temperature, 10 to 700 K, and He content, 1 to 5 He atoms per vacancy. It appears that up to moderate temperatures the Fe lattice can confine He to solid state, in good agreement with known solid-liquid transition diagram of pure He. However, while for a given temperature and He density range where an fcc structure is expected, He in the bubble forms an amorphous phase. He bubble forms a polyhedron whose morphology depends on either the surface energy or elastic-plastic properties of Fe at either low or high pressure, respectively. At high He contents the bubble surface breaks down at the mechanical stability limit of the Fe crystal, leading to a pressure decrease in the bubble. The basic mechanisms of the interaction in α-Fe between a moving dislocation and a nanometric defect, as a function of temperature, interatomic potentials, interaction geometry and size are investigated using MD simulation. The stress-strain responses are obtained under imposed strain rate and using different interatomic potentials for Fe-Fe and Fe-He interactions. It appears that voids and He bubbles are strong obstacles to dislocation, which induce hardening and loss of ductility. A nanometric void is a stronger obstacle than a He bubble at low He contents, whereas at high He contents, the He bubble becomes a stronger obstacle. It also appears that different potentials give different strengths and rates of decrease of obstacle strength with increasing temperature. Temperature eases the dislocation release, due to the increased mobility of the screw segments appearing on the dislocation line upon bowing from the void or He bubble. Concerning the obstacle size at low content He bubble, where it is penetrable defect, size increase from 1 to 5 nm make them harder in agreement with the elasticity of continuum. At high He contents a size dependent loop punching is observed, which at larger bubble sizes leads to a multistep dislocation-defect interaction. Atomistic simulations reveal that the He bubble induces an inhomogeneous stress field in its surroundings, which strongly influences the dislocation passage depending on the geometry of the interaction. Fe-Cr alloys are also studied using MD simulations as model alloys for the ferritic base steels. Studying the flow stress of a moving edge dislocation in Fe(Cr) shows that the flow stress is not sensitive to temperature and strain rate, while it increases with Cr concentration. The flow stress of a screw dislocation is temperature dependant and its value is much higher than that of edge dislocation. Interaction in a pure Fe matrix of an edge dislocation with a nanometric Cr precipitate having various Cr content inside (Cr/Fe ratio) indicates that with the Cr/Fe ratio the obstacle strength increases, with a strong sensitivity to the short-range order. Temperature induces a monotonous decrease of the strength for all studied Cr/Fe ratios. DD calculation coupled to finite element method (FEM) is used to simulate the interaction of an edge dislocation with a void. DD calculations present a good match to the MD simulation results for the impact of image forces on the dislocation due to the free internal surface of the void. Using DD simulation, hardening due to the presence of nanometric defects, as immobile dislocation segments and spherical defect, are considered. The results of MD simulations for the strength of different defects are introduced in DD simulation. It appears that the presence of both immobile dislocation segments and nanometric defects may lead to the hardening of α-Fe. However, the defect density has more significant importance on the DD simulation, obtained here, than the strength of a single defect. TEM in-situ straining is used to validate simulations, in particular on the dislocation interaction mechanisms. Experiments were performed in ultra high purity Fe specimens. It appears that the microstructure of the material consists mainly in elongated screw dislocations. The in-situ straining tests led to the observation of the formation of screw dislocation dipoles in consistency with the MD simulation results. The interaction between a dislocation and an obstacle, as nanometric defect or immobile dislocations, leading to their shear or to Orowan loop formation were successfully observed. This work shows that using of different simulation methods can assist in the understanding of nano- and meso-scale phenomena occurring due to the presence of irradiation induced defects upon deformation of α-Fe. The information obtained from various microstructure mechanisms at lower scale simulations can be passed to higher scale simulation methods in order to realize the simulated phenomena. Experimental observations may validate what is observed in simulations provided the simulation scale is reachable in experimental observations.

EPFL2010

Analysis of nano-sized irradiation-induced defects in Fe-base materials by means of small angle neutron scattering and molecular dynamics simulations

Gang Yu

Thermonuclear fusion of light atoms is considered since decades as an unlimited, safe and reliable source of energy that could eventually replace classical sources based on fossile fuel or nuclear fuel. Fusion reactor technology and materials studies are important parts of the fusion energy development program. For the time being, the most promising materials for structural applications in the future fusion power reactors are the Reduced Activation Ferritic/Martensitic (RAFM) steels for which the greatest technology maturity has been achieved, i.e., qualified fabrication routes, welding technology and a general industrial experience are almost available. The most important issues concerning the future use of RAFM steels in fusion power reactors are derived from their irradiation by 14 MeV neutrons that are the product, together with 3.5 MeV helium ions, of the envisaged fusion reactions between deuterium and tritium nuclei. Indeed, exposure of metallic materials to intense fluxes of 14 MeV neutrons will result in the formation of severe displacement damage (about 20-30 dpa per year) and high amounts of helium, which are at the origin of significant changes in the physical and mechanical of materials, such as hardening and embrittlement effects, for instance. This PhD Thesis work was aimed at investigating how far the Small Angle Neutron Scattering (SANS) technique could be used for detecting and characterizing nano-sized irradiation-induced defects in RAFM steels. Indeed, the resolution limit of Transmission Electron Microscopy (TEM) is about 1 nm in weak beam TEM imaging, and it is usually thought that a large number of irradiation-induced effects have a size below 1 nm in RAFM steels and that these very small defects actually contribute to the irradiation-induced hardening and embrittlement of RAFM steels occurring at irradiation temperatures below about 400°C. The aim of this work was achieved by combing SANS experiments on unirradiated and irradiated specimens of RAFM steels with Molecular Dynamics (MD) simulations of main expected nano-sized defects in irradiated pure Fe and Fe-He alloys, as model materials for RAFM steels, and simulations of their corresponding TEM images and SANS signals. In particular, the SANS signal of various types of defects was simulated for the first time. The methodology used in this work was the following: SANS experiments were performed by applying a strong saturating magnetic field to unirradiated and irradiated specimens of three types of RAFM steels, namely the European EUROFER 97, the Japanese F82H and the Swiss OPTIMAX A steels. The available irradiated specimens included specimens which had been irradiated with 590 MeV protons in the Proton IRradiation EXperiment (PIREX) facility at the Paul Scherrer Institute (PSI) at temperatures in the range of 50-350°C to doses in the range of 0.3-2.0 dpa. SANS spectra as well as values of the so-called A ratio, which represents the ratio of the total scattered intensity to the nuclear scattered intensity, were obtained for the various irradiation doses and temperatures investigated. MD simulations of atomic displacement cascades in pure Fe and in Fe-He alloys were performed using Embedded Atom Method (EAM) many-body interatomic potentials. The main nano-sized defects that should be produced in RAFM steels under irradiation were created by means of MD in pure Fe. These included dislocation loops of various types, voids, helium bubbles with various He concentration and Cr precipitates. TEM images of cascade damage and all the defects created by MD were simulated in the dark field/weak beam imaging modes by using the Electron Microscopy Software (EMS) developed by P.A. Stadelmann (EPFL) and analyzed in terms of variations of contrast intensities versus depth inside the specimen. The SANS signal provided by cascade damage and all the defects created by MD was simulated by using a slightly modified version of EMS, accounting for neutrons instead of electrons. The SANS technique has been proven in this work to be a very powerful tool for detecting nano-sized irradiation-induced defects and a tool well complementary to TEM for characterizing such very small irradiation-induced defects. Indeed, TEM appears most adapted to investigate structural defects, such as dislocation loops and helium bubbles with high helium concentration, which yield significant lattice deformation of the surrounding matrix, while SANS is most adapted to investigate phase defects, such as voids, helium bubbles with low helium concentration and Cr precipitates. By combining the results of SANS experiments with those of MD simulations, TEM image simulations and SANS signal simulations, the nano-sized irradiation-induced defects were tentatively identified as small helium bubbles. While the radiation hardening measured for RAFM steels cannot be explained by accounting only for the defects observed in TEM, it could be successfully modeled by accounting also for a reasonable number density of the nano-sized defects evidenced using the SANS technique.

EPFL2008

Numerical simulation of solid state phase transformations in gamma-TiAl alloys

Amin Rostamian

Gamma titanium aluminide (γ-TiAl) based alloys are very interesting materials for structural applications at elevated temperatures owing to the combination of high specific strength, good oxidation, creep and fatigue resistance. However, their relatively poor ductility and fracture toughness remain important obstacles for their industrial applications in engineering components. The mechanical properties of these alloys, namely the poor room temperature ductility, as well as the yield stress, creep and fracture resistance, can be significantly improved by controlling the microstructure. These alloys undergo solid state phase transformations upon cooling from the high temperature α phase, which results in formation of different types of microstructures depending on the cooling conditions and the alloy composition. Low and moderate cooling rates lead to the precipitation of the γ phase as parallel plates within the α matrix, followed by the α → α2 ordering reaction. As a result of this transformation, the characteristic lamellar structure of TiAl is produced. Rapid cooling leads to a massive transformation from α to γ. It has been shown that the massive microstructure can be used as a precursor to obtain a refined microstructure through a subsequent tempering in the α + γ phase field. However, obtaining a fully massive microstructure at all depths in a component can be difficult to achieve. Numerical simulation of microstructure formation can be used as a tool to anticipate the microstructure distribution in a component depending on the local chemistry and cooling conditions. The main objective of this work was to develop microstructure models describing the formation of the massive and lamellar microstructures. Two distinct modeling approaches have been used. The first approach is a deterministic model having for objective to predict the microstructure distribution in a cast and heat treated component. The model was designed to be integrated into a FEM or FDM heat flow solver in order to calculate microstructural quantities such as the proportion of phases and lamellar spacings at each nodal point of the mesh. The modeling approach is based on a combination of nucleation and growth laws which take into account the specific mechanisms of each phase transformation. Nucleation of massive and lamellar γ is described with classical nucleation theory, accounting for the fact that nuclei are formed predominantly at α/α grain boundaries. Growth of the massive γ grains is based on theory for interface-controlled reactions. A modified Zener model is used to calculate the thickening rate of the lamellar γ precipitates. The model incorporates the effect of particle impingement and coverage of the nucleation sites by the growing phases. The driving pressures of the phase transformations are obtained from Thermo-Calc based on the actual temperature and matrix composition. The deterministic approach was used to calculate CCT diagrams and lamellar spacings, which showed to be in good agreement with experimental data obtained from dedicated heat treatment experiments and from the literature. The model permitted investigating the influence of cooling rate, alloy chemistry and average α grain size upon the amount of massive γ and the average thickness and spacing of the lamellae. In particular, it indicated that the Al depletion of the α phase during lamellar precipitation seems to play an important role in the suppression of the massive transformation at moderate cooling rate and in the large lamellar spacings observed at low cooling rate. It was also found that Nb additions enhance the formation of massive γ by lowering the lamellar transformation temperature, increasing the T0 temperature and slowing down the lamellar growth due to the low diffusivity of Nb. The second approach was a cellular automaton (CA) model, which was used to describe the formation of the lamellar microstructure on the scale of a few microns. The objective of this approach was to make a direct description of the growth of a precipitate by an interfacial ledge mechanism, and then to evaluate whether the simplifications made in the deterministic model regarding this mechanism are appropriate. The modelling approach is based on the resolution of the diffusion equations in the α and γ phases. The ledge structure at the α/γ interface is described by introducing different types of cells in the CA grid. The CA model was used to describe the formation of the lamellar microstructure at isothermal conditions and at various cooling rates. The thickening kinetics of the lamellae, the lamellar spacings and the overall kinetics of the transformation were calculated with this approach and were compared with the results obtained with the deterministic model. It was found first that the thickening kinetics of the lamellae calculated with the deterministic model are slower than those calculated with the CA model. It was established that the method used in the deterministic model to account for the growth by a ledge mechanism always leads to a growth exponent of 0.5, which is characteristic of diffusion controlled reactions. In contrast, the CA approach yields growth exponents that are comprised between 0.5 and 1, as it is expected for growth in a mixed diffusion/interface controlled mode. The incorporation of a kinetic undercooling term into the deterministic model was found to be an appropriate correction. A good agreement was finally obtained in terms of lamellar spacings and overall kinetics. The underestimated thickening kinetics of the deterministic model was observed to be partly compensated by a higher nucleation rate at the beginning of the transformation. The overall kinetics of the lamellar transformation calculated with the deterministic model was found to be sufficiently accurate to correctly predict the competition between the lamellar and massive microstructures.

EPFL2009