Multi-scale simulation of radiation damage accumulation and subsequent hardening in neutron-irradiatedα-Fe

Abstract

A hierarchical methodology is introduced to predict the effects of radiation damage and irradiation conditions on the yield stress and internal stress heterogeneity developments in polycrystalline α-Fe. Simulations of defect accumulation under displacement cascade damage conditions are performed using spatially resolved stochastic cluster dynamics. The resulting void and dislocation loop concentrations and average sizes are then input into a crystal plasticity formulation that accounts for the change in critical resolved shear stress due to the presence of radiation induced defects. The simulated polycrystalline tensile tests show a good match to experimental hardening data over a wide range of irradiation doses. With this capability, stress heterogeneity development and the effect of dose rate on hardening is investigated. The model predicts increased hardening at higher dose rates for low total doses. By contrast, at doses above 10−2 dpa when cascade overlap becomes significant, the model does not predict significantly different hardening for different dose rates. The development of such a model enables simulation of radiation damage accumulation and associated hardening without relying on experimental data as an input under a wide range of irradiation conditions such as dose, dose rate, and temperature.

An accurate scheme to solve cluster dynamics equations using a Fokker–Planck approach

“…For higher dimensions, stochastic methods are probably more appropriate due to the increase in the number of equations to solve [12,13,14].…”

“…This can become prohibitively large in terms of computational time and memory use, even when the sparsity of the matrix is taken into account [11]. Alternatively, stochastic methods can be used [12,13,14]: they do not require the storage of the Jacobian matrix but the time step is often much smaller than with deterministic methods.…”

On the transfer of cascades from primary damage codes to rate equation cluster dynamics and its relation to experiments

“…The simulation of nucleation and growth of interstitial and vacancy clusters under irradiation can be performed with various methods, such as kinetic Monte Carlo (KMC) [1][2][3][4], phase field [5] and rate equation cluster dynamics (RECD) [6][7][8][9][10][11]. Among these methods, RECD is in general the most efficient owing to its mean field formalism.…”

“…The combination of efficient time solvers [12] and numerical approximations such as grouping methods [6] or the Fokker-Planck equation [13] make this method unrivalled to reach doses as high as 100 dpa (displacements per atom) in a few minutes of wall-clock time [14,10,15]. For systems with clusters containing three types of elements or more, deterministic solving becomes numerically difficult and stochastic approaches can be used [16,17,11].…”

Rate theory modeling of dislocation loops in RAFM steel under helium ion irradiation and comparison with experiments

“…Therefore modeling plays an important role in theoretical analysis due to its convenience and effectiveness for solving these problems. The rate theory is one of the fruitful modeling methods capable of treating the long term kinetic evolution of microstructures in metals under irradiation [5][6][7]. To build up the rate theory model, it is essential to understand the detailed evolution of defects.…”