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

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.

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

On the relationship between the microstructure and the mechanical properties of an ODS ferritic/martensitic steel

Amuthan Ramar

In the quest of materials for the first wall of the future fusion reactor, it has been shown that oxide dispersion strengthened (ODS) ferritic / martensitic (F/M) steels appear to be promising candidates. The inherent good mechanical properties supported by a good thermal conductivity, swelling resistance and low radiation damage accumulation of the base material, such as EUROFER97, are further enhanced by the presence of a fine dispersion of nanometric oxide particles. They would allow in principle for a higher operating temperature of the fusion reactor, above 550°C, which improves its thermal efficiency. In effect, their strength remains higher than the base material at high temperatures. There are however limitations to their application in the reactor, which relate to the intimate link between the microstructure and the mechanical properties. These limitations, such as an increased ductile to brittle transition temperature above room temperature relative to the base material, come directly from the role played by the oxide particles but also from their indirect impact on the overall microstructure, stemming from the procedure of elaboration of these materials. In addition, there is a lack of knowledge on their response to irradiation, which, even though it appears to be promising with a reduced irradiation induced hardening, is not very well understood. In this work we have developed and evaluated ferritic/martensitic steel, EUROFER97, strengthened by a dispersion of yttria particles. (1) The powder metallurgical process used to obtain it was optimized, (2) the basic mechanisms of hardening were identified and (3) the impact of irradiation on its microstructure and mechanical properties were investigated. In order to understand the behaviour of this class of material other oxide dispersion strengthened (ODS) ferritic/martensitic steels based on EUROFER97 and model alloys were also investigated. For the elaboration of the ODS steel the powders of atomized EUROFER97 and yttria are ball milled in a planetary ball mill and the material is compacted by hot isostatic pressing (HIP). The mechanical properties are evaluated by uniaxial tensile test, Charpy test and micro-indentation while the microstructure is investigated by optical microscopy, scanning electron microscopy and transmission electron microscopy. The focused ion beam (FIB) technique is also used. In the study of the ball milling it appears that the optimal time is 20 hours, as the X-ray peak broadening, crystallite size and hardness of the particles remain unchanged at longer times. Yttria nanoparticles clusters are no more detectable by X-ray after 2 hrs of milling, which is attributed here to their incorporation in the matrix, as opposed to dissolution in the matrix as is often suggested in the open literature. HR-TEM performed on the yttria particles before and after incorporation in the steel by ball milling shows that the yttria maintain its bcc equilibrium structure throughout the process. This could suggest that they are not dissolved during ball milling. We have clarified this point by a cross sectional examination of the EUROFER97 ball milled particles with 0.3wt% of yttria in an FIB. By X-ray EDS analysis it shows nanometric regions reach in yttrium and oxygen, which are the yttria particles embedded in the EUROFER97 particles, proving that they are not dissolved by ball milling. The mechanism at the origin of the alloy compaction during HIP was elaborated. The alloy compaction was done through HIPing at 1150°C for 2.5 hrs at a pressure of 190 MPa. This condition is shown to provide the highest bulk density, to a value close to 99.9%. In the optimization process, it is found that temperature plays a larger role than pressure for alloy compaction. The compaction appears to be mainly due to diffusion. Also, it appears that the ball milled particle size plays a major role in the alloy compaction. It is shown that smaller particles size induces better compaction, provided that the densification proceeds through diffusion flow. This further suggests to terminate the ball milling process by 20 hrs as the particles size reaches its minimum. The impact of the ball milling process on the mechanical properties was evaluated. EUROFER97 with and without ball milling, with and without oxide addition presents an average density around 99.8%. In the as received state, casted EUROFER97, atomized EUROFER97, ball milled EUROFER97 and ODS Yttria present microstructure morphology typical of tempered martensite, whereas ODS Ti presents a nano sized grain microstructure with an average grain size of 200 nm. Ball milling and HIPping does have a slight influence up to 400°C, due to the higher dislocation density induced by ball milling relative to casted EUROFER97. It becomes negligible above 400°C, since both casted and ball milled EUROFER97 present similar hardness and microstructure. In ODS Yttria, yttria presents an average particle size of 25 nm. In ODS Ti, Y-Ti-O presents an average particle size of 7 nm. In the following the identification of the hardening mechanisms in ODS F/M steels. A new model was developed to quantify the collective hardening due to different obstacles, assuming that they provide independent hardening mechanisms. The model helped identifying the dominating source of hardening in ODS F/M steels. The base of the model is the dispersion barrier strengthening model, which is given by Δσsparticle or defects = Mαμb(Nd)1/2 for the hardening due small defects or oxide particles and is given by Δσd-d = Mαμb(ρ)1/2 for the hardening due to dislocations. In this approximation, the total hardening is then given by Δσtotal = {(Δσd-d)2 + (Δσparticle or defects)2}1/2 . The model is used to explain the hardening due to oxides, dislocations and irradiation induced defects. It appears that dispersed oxides is dominating hardness up to 800°C, while following a heat treatment at 1000°C it is the dislocations that then dominate the hardness. Deformation mechanisms were investigated using differential strain rate experiments. The activation parameters, i.e. the activation volume and activation energy, were calculated. It appears that there is a decrease in the activation volume from room temperature to 400°C, which is less than 3%. At about 500°C there is a sudden drop in the activation volume that reaches a minimum at 600°C. With further increase in temperature, there is a significant raise in the activation volume. This abrupt decrease between 400°C and 600°C hints at a change in dislocation-rate controlling mechanism, marking two regimes, a low temperature one and a high temperature one. In situ TEM observations show that at low temperature the deformation is mainly due to the formation of the Orowan loops around the particle. At high temperature the activation energy is about 3.4 eV for ODS, whereas it is 1.3 eV for EUROFER97. The calculated activation energy corresponds well to the one of dislocation climb mechanism. This indicates that at high temperature the yttria particles could be overcome by climb, while at low temperature they are overcome by the Orowan mechanism. The peculiar response of the yield stress to irradiation for this class of material was rationalized using the total hardening model we developed. At a dose of 2 dpa, irradiation induced defects are higher in number density than the dispersed yttria particles, which although they are weaker than the yttria particles they can explain the significant hardening observed in the material. Conversely, the shallow impact of irradiation on ODS F/M steels at low doses, relative to base F/M steels, is explained by the fact that the amount of dispersoid is found to be higher than the density of irradiation induced defects.

EPFL2008

Strengthening due to Cr-rich precipitates in Fe–Cr alloys: Effect of temperature and precipitate composition

Seyed Masood Hafez Haghighat

Molecular dynamics (MD) simulations were carried out to study the interaction between nanometric Cr precipitates and a 1/2 < 111 >>{110} edge dislocation (ED) in pure Fe and Fe-9 at. % Cr (Fe-9Cr) random alloy. The aim of this work is to estimate the variation in the pinning strength of the Cr precipitate as a function of temperature, its chemical composition and the matrix composition in which the precipitate is embedded. The dislocation was observed to shear Cr precipitates rather than by-pass via the formation of the Orowan loop, even though a pronounced screw dipole was emerged in the reactions with the precipitates of size larger than 4.5 nm. The screw arms of the formed dipole were not observed to climb thus no point defects were left inside the sheared precipitates, irrespective of simulation temperature. Both Cr solution and Cr precipitates, embedded in the Fe-9Cr matrix, were seen to contribute to the flow stress. The decrease in the flow stress with temperature in the alloy containing Cr precipitates is, therefore, related to the simultaneous change in the matrix friction stress, precipitate resistance, and dislocation flexibility. Critical stress estimated from MD simulations was seen to have a strong dependence on the precipitate composition. If the latter decreases from 95% down to 80%, the corresponding critical stress decreases almost as twice. The results presented here suggest a significant contribution to the flow stress due to the alpha-alpha(') separation, at least for EDs. The obtained data can be used to validate and to parameterize dislocation dynamics models, where the temperature dependence of the obstacle strength is an essential input data.

American Institute of Physics2010

On the relationship between the microstructure and the mechanical properties of an ODS ferritic/martensitic steel

Amuthan Ramar

EPFL2008

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

Gang Yu

EPFL2008