Multiscale Modeling of Radiation Hardening in RPV and Austenitic Stainless Steels : from the Atomic to the Continuum Scale

Given the nanometric size of radiation defects, Radiation Induced Hardening (RIH) is a textbook case of multiscale physical phenomena. On the one hand, pure atomic features that cannot be described by elasticity contribute strongly to the dislocation interaction. Individual interactions – depending on temperature, dislocation velocity, defect nature and size – can be characterized only when these feature are fully identified and quantified. On the other hand, RIH is usually observed at the macroscopic scale, where its technological impact is the deepest. Physically based modeling of RIH must thus integrate materials properties from the atomic level. Since explicit and direct integration is not possible, investigations at intermediate scales associated with appropriate transition methods are thus necessary. Pertinent links are known to be the intragranular and the crystalline aggregate scales. The first one provides constitutive equations controlling plastic flow, including RIH, and the second one delivers the homogenized mechanical behavior.

Given the nanometric size of radiation defects, Radiation Induced Hardening (RIH) is a textbook case of multiscale physical phenomena.On the one hand, pure atomic features that cannot be described by elasticity contribute strongly to the dislocation interaction.Individual interactionsdepending on temperature, dislocation velocity, defect nature and sizecan be characterized only when these feature are fully identified and quantified.On the other hand, RIH is usually observed at the macroscopic scale, where its technological impact is the deepest.Physically based modeling of RIH must thus integrate materials properties from the atomic level.Since explicit and direct integration is not possible, investigations at intermediate scales associated with appropriate transition methods are thus necessary.Pertinent links are known to be the intragranular and the crystalline aggregate scales.The first one provides constitutive equations controlling plastic flow, including RIH, and the second one delivers the homogenized mechanical behavior.
In this paper, we present recent progress in multiscale modeling of RIH in Reactor Pressure Vessel (RPV) steels and internal steels.We first show that the yield stress prior to irradiation has a nonnegligible effect on the RIH, which is found to superpose quadratically with the forest and precipitate hardening.Then, we show how Dislocation Dynamics (DD) simulations can integrate atomistic results and elaborate constitutive equations of plastic behavior.In the following, we present two typical application of our modeling approach.
In internal steels, RIH at doses of some dpa is known to increase tremendously the yield stress.However, the density and the size of the observed radiation defectsformed mostly of dislocation loopsare found (thanks to DD simulations) to provide weak hardening, even when they are considered of extreme strength.The origin of RIH looked difficult to explain.Recently, Atom Probe Tomography (APT) characterization of radiated internal steels have invariably revealed a large density of nanometric solute clusters, which were identified as segregation on small dislocation loops [1].
On the other hand, atomistic simulations have shown that dislocation interactions with dislocation loops leads very often to absorption, as long as the loop is small enough.These experimental observations coupled to atomistic findings inspired a recent investigation [2] in which dislocation interaction with a large number of small dislocation loops were simulated using the DD technique.Since the outcome of individual interactions is invariably absorption, only collinear dislocation loops (i.e.sharing the same Burgers vector as the mobile dislocation) were considered.Interaction with a pure edge dislocation is found to initiate a collective motion of loops in front of the moving dislocation.In contrast, interaction with a pure screw dislocation leads to a large number of collinear interactions strongly pinning the dislocation by forming many helical turns.The stress increment associated with the presence of these loops is depicted on Fig 1a .Hardening is seen to scale with µb√, where µ, b, D and C are respectively the shear modulus, the Burgers vector, the loop size and density.It is clearly seen that the slop of the straight line is close to 0.5, representing the average interaction coefficient.This value falls within the values reported in experiment.Consequently, results suggest that RIH in internal steels can be attributed to the so called "black dots", which are frequently observed in experiments, rather than the faulted (or unfaulted) large dislocation loops that can be easily resolved in Transmission electron microscopy.
The second example, deals with the possible hardening induced by solute clusters, frequently observed in RPV steels.Since solute clusters are directly revealed by APT in all RPV steels and irradiation conditions, they are suspected to be at the origin of RIH in RPV steels.The main difficulty is that it is not possible to use atomistic simulations to compute their resistance, since they are of unknown structure formed of several elements.It is thus necessary to compute the induced hardening as a function of the shear resistance that can be attributed to them.To do so, DD simulations were used to compute hardening induced by a distribution of precipitates of different size, density and shear resistance [3].
Modeling radiation hardening at the grain scale • 20 000 precipitates

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nd Int.Workshop Irradiation of Nuclear Materials: Flux and Dose Effects November 4-6, 2015, CEA -INSTN Cadarache, France 2 Centre of Excellence for Nuclear Materials

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Atomistic simulations of edge dislocation • Interactions with simple defects (Cr, Cr prcp, loops, voids, SFT, etc.) • Dislocation Dynamics simulations of precipitation hardening • DD simulations of hardening induced by small loops • Construction of crystalline laws for RPV and internal steels Future challenges: • Prediction and modeling of radiation microstructure • Investigating solute segregation effects (decoration, mobility, strength) • Dislocation interaction with grain boundaries • Accounting for softening in crystalline laws in macroscopic modeling • Allowing for mesh-independent strain heterogeneity