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

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.

Finite element modeling and experimental study of brittle fracture in tempered martensitic steels for thermonuclear fusion applications

Pablo Federico Mueller

In this work we have studied brittle fracture in high-chromium reduced activation tempered martensitic steels foreseen as structural materials for thermonuclear fusion reactors. Developing the adequate materials that can withstand the severe irradiation conditions of the burning plasma in a future fusion reactor is one of the major challenges to be solved in order to make profit from the great advantages of thermonuclear fusion as an energy source. High-chromium tempered martensitic steels such as F82H and the most advanced version Eurofer97 are among the main candidate materials for structural applications in future fusion power plants due to low irradiation-induced swelling, good mechanical and thermal properties, and reasonably fast radioactive decay. The most concerning drawback of these kind of steels is irradiation embrittlement, which is manifested by a ductile-to-brittle transition temperature shift to higher temperatures after irradiation whose amplitude depends on the irradiation conditions (temperature, neutron flux, neutron fluence, etc). The aim of this work was to study and model brittle fracture in the ductile-brittle transition region of this kind of steels in the as-received unirradiated conditions. It is necessary to be able to transfer laboratory specimen fracture data to real components and structures in order to assess the performance of these steels in the different operating and transient conditions they could find during the operation life of a fusion reactor. In order to do so, the specimen geometry effects and specimen size effects on measured fracture toughness need to be properly understood, taken into account and predicted with an appropriate model. In particular, specimen size effect on measured toughness is a major concern for the nuclear materials research community owing to the limited irradiation volume in current and planed materials irradiation facilities. The main results of this PhD work are summarized below. The microstructure of Eurofer97 and F82H has been characterized and compared by means of optical microscopy, scanning electron microscopy, transmission electron microscopy and energy-dispersive X-ray spectroscopy in order to identify microstructural features that could play a role in the measured fracture toughness. Both steels have similar but slightly different chemical composition and final heat-treatments but the prior austenitic grain size measured in F82H is approximately 8 times larger than in Eurofer97. It was shown that the alloying element Tantalum, added to stabilize the austenite grain size, played a different role in both steels. After a careful analysis of the particles present in both steels, it was found that Tantalum in Eurofer97 formed carbides of an average size around 100 nanometers. In contrast in F82H it did not form small carbides but formed big oxide inclusions with a size up to 30 µm. These large particles do not effectively pin the grain boundaries. The different behavior of Tantalum in these steels is believed to be mainly a consequence of the larger content of Oxygen present and the smaller amount of Aluminum in F82H compared to Eurofer97. The Master-Curve ASTM-E1921 standard is a method initially developed to determine the ductile-to-brittle transition reference temperature, T0, in fission reactor ferritic steels from a small number of experiments. In this work the applicability of the Master-Curve method to reduced activation tempered martensitic steels such as Eurofer97 and F82H was studied in detail. Fracture tests with pre-cracked sub-sized compact tension specimens (three different sizes, 0.18T, 0.35T and 0.87T of Eurofer97) were carried out in the temperature range [-196 °C, -40 °C]. The toughness-temperature behavior and scatter were shown to deviate from the ASTM-E1921 standard predictions near the lower shelf. Using the method of maximum likelihood, the athermal component of the Master-Curve was calculated to better fit our fracture toughness data from the lower to the middle transition region. We showed that these Master-Curve adjustments are necessary to make the T0 values obtained near the lower shelf with 0.35T size C(T) specimens consistent with those obtained in the middle transition region with 0.87T C(T) specimens. The ASTM-E1921 specimen size limitations, setting the maximum toughness measurable with a given specimen size, were found to be too lenient for this kind of steels. This problem was especially evident in fracture toughness data of Eurofer97 and F82H obtained in the upper transition temperature range with two different specimen sizes. Thus a more stringent specimen size requirement was proposed to avoid inconsistent transition temperature determinations. A promising local fracture model with the potential of predicting cleavage fracture toughness was studied. Finite element simulations were undertaken for compact specimens, notched specimens and tensile specimens of Eurofer97 steel tested from 20 °C down to -197 °C. Three and two dimensional as well as axisymmetric simulations were run in order to calculate the stress and strain fields at the onset of brittle fracture. For each tested temperature, the calculated load-displacement curves were found to reproduce very well those of the experiments. A local approach fracture criterion was studied. This criterion states that when the maximum principal stress is larger than a critical stress within a critical volume ahead of the crack tip, notch or neck, cleavage is triggered leading to macroscopic fracture of the specimen. It was shown that this model is able to predict the minimum fracture load of the notched specimens with the same values of critical stress and critical volume that were calibrated to predict the lower bound of fracture in compact specimens. This local approach model was also successfully used to predict the strong size effect observed experimentally in pre-cracked compact tension specimens in the upper transition region. The critical fracture stress determined in the standard tensile specimens was found higher than that of the fracture specimens. It was suggested that this difference stems from a significant difference in the stress state between the different specimens (triaxiality). Finally, the comparison between the overall fracture behavior in the transition between F82H and Eurofer97 steels indicated that these two materials are quite similar. A difference in the reference temperature T0 of about 20 °C was found, with a nominal value of -100 °C and -80 °C for F82H and Eurofer97 respectively. However, some excessive scatter in the toughness data was found in F82H with more data points than expected lying below the 1% tolerance bound; this was not observed in Eurofer97. From an engineering point of view, the entire fracture databases of these two steels are encompassed practically by the same lower tolerance bound.

EPFL2009

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

Investigations and numerical modeling of mechanical properties of tempered martensitic steel Eurofer97 at various loading rates, temperatures and after spallation irradiation

Serafin Knitel

The reduced activation tempered martensitic steel Eurofer97 is a reference steel for a structural applica-tions in fusion reactors. The first-wall and blanket materials will be subjected to high thermal and neutron fluxes and will experience very complex, time-dependent mechanical loading. Owing to impinging neutrons in materials, points defects and gasesous impurities (hydrogen and helium) are created and accummulated in the form of small defect clusters in the microstructure altering the mechanical properties. Notably, fracture toughness decreases as strength increases. Eurofer97, being a body centered cubic alloy, presents a ductile-to-brittle transition temperature T0 that shifts to higher temperatures after irradiation. The main objective was to study the loading rate and irradiation effects on plastic flow and fracture properties of Eurofer97. Tensile and fracture tests were performed at temperatures in the transition region, at low and high loading rates on unirradiated material. Tensile properties of irradiated material were assessed after irradiation in the Swiss neutron spallation source SINQ to a dose of about 11 dpa and helium content of 500 appm at about 250 Â°C. The information gathered from the mechanical tests was used either as input in finite element models of fracture specimens, or as benchmark data to calibrate and verify the predictions of the models. Fractographic observations were also conducted. The tensile tests on unirradiated Eurofer97 showed a strong temperature dependence and strain rate sensitivity of the stress at low temperature, consistent with a mechanism of nucleation and propagation of double kink on screw dislocation. At high loading rate, the strain rate hardening was partially compensated by thermal softening due to quasi-adiabatic heating. The tensile properties after irradiation showed strong irradiation hardening (increase of the yield stress) accompanied by a drastic decrease of uniform elongation. The constitutive behavior at large strains, representative of those at crack tip, was obtained with an inverse method, based on finite element (FE) models of tensile specimens, developed to derive the true stress-strain curves from the load-displacement ones. These curves were used as input for the FE models of fracture specimens. Comparative fractographic observations on unirradiated and irradiated specimens did not reveal any strong effect of irradiation or helium on fracture mechanism, which remains transgranular cleavage. This observation indicates that higher helium concentration than 500 appm is necessary to initiate intergranular cleavage by helium bubble precipitation on grain boundaries. Dynamic fracture tests were performed on unirradiated Eurofer97. A shift of about 10 Â°C of T0 by one order of magnitude in loading rate was determined, which was in good agreement with results obtained on different ferritic steels. Static fracture toughness tests were also performed on disk compact tension specimens that can be accommodated in irradiation tubes of SINQ. Different FE models of fracture specimens were developed to include strain-rate sensitivity of flow stress, heating resulting from the plastic work in the fracture process zone and loading rate. The structure of the stress field at the crack tip was studied and the temperature dependence of a lower bound to toughness data in the transition was reconstructed using a calibrated criterion of local approach to brittle fracture.

EPFL2018