An FFT based approach to account for elastic interactions in OkMC: Application to dislocation loops in iron

Object kinetic Montecarlo (OkMC) is a fundamental tool for modeling defect evolution in volumes and times far beyond atomistic models. The elastic interaction between defects is classically considered using a dipolar approximation but this approach is limited to simple cases and can be inaccurate for large and close interacting defects. In this work a novel framework is proposed to include "exact" elastic interactions between defects in OkMC valid for any type of defect and anisotropic media. In this method, the elastic interaction energy of a defect is computed by volume integration of its elastic strain multiplied by the stress created by all the other defects, being both fields obtained numerically using a FFT solver. The resulting interaction energies reproduce analytical elastic solutions and show the limited accuracy of dipole approaches for close and large defects. The OkMC framework proposed is used to simulate the evolution in space and time of self-interstitial atoms and dislocation loops in iron. It is found that including the anisotropy has a quantitative effect in the evolution of all the type of defects studied. Regarding dislocation loops, it is observed that using the "exact" interaction energy result in higher interactions than using the dipole approximation for close loops.Comment: Accepted in Journal of Nuclear Material

Determination of precipitate strengthening in Al-Cu alloys through micropillar compression: Experiments and multiscale simulations

Al-Cu alloys are efficiently strengthened by different types of precipitates: Guinier-Preston zones, θ\u27\u27 (Al3Cu) and θ\u27 (Al2Cu). The contribution of each type of precipitate to the strengthening of the alloy was determined by means of a high-throughput strategy based on micropillar compression. To this end, an Al-4 wt.% Cu alloy was manufactured by casting, following by several homogenization heat treatments at high temperature. The alloy was aged at 23ºC and 180ºC for different times to produce different precipitate structures [1]. Micropillars were machined using a focus ion beam in grains oriented for single and multiple slip and compressed at ambient temperature. The critical resolved shear stress was determined as a function of the applied strain for micropillars with different sizes oriented for single slip to assess the size effect. It was found that the properties of the bulk crystals could be obtained by testing square micropillars with cross-section \u3e 5 x 5 µm2. In addition, the precipitate type and spatial distribution as well as the mechanisms of dislocation/precipitate interaction were studied in the transmission electron microscope from lamella extracted from the deformed micropillars. It was found that Guinier-Preston zones and small θ\u27\u27 precipitates (\u3c 50 nm) were sheared by dislocations while dislocations formed Orowan loops around large θ\u27 precipitates. Afterwards, the effect of latent hardening for the different types of precipitates was studied by compression of micropillars oriented for double slip (coplanar and non-coplanar) as well as for multiple slip. In parallel, the critical resolved shear stress in the overaged Al-Cu alloys containing large θ\u27 precipitates was simulated by means of dislocation dynamics simulations using the discrete-continuous method in combination with a fast Fourier transform solver to compute the mechanical fields [2]. Simulations took into account the effect of precipitate shape, orientation and volume fraction as well the elastic mismatch between the matrix and the precipitate, the stress-free transformation strain around the precipitate and the dislocation character as well as dislocation cross-slip. In addition, the results of the micropillar compression tests were used to calibrate the latent hardening parameters of a crystal plasticity model, so they can be used to predict the mechanical behavior of polycrystals by means of computational homogenization. Overall, the results of this investigation show how micropillar compression can be used as a high-throughput technique to obtain the bulk properties of precipitation-strengthened alloys as well as to validate the results of simulation strategies at lower length scales (dislocation dynamics) and to provide input information for simulations at larger length scales (computational homogenization of polycrystals). [1] A. Rodríguez-Veiga, B. Bellón, I. Papadimitriou, G. Esteban-Manzanares, I. Sabirov, J. LLorca. A multidisciplinary approach to study precipitation kinetics and hardening in an Al-4wt.%Cu alloy. Journal of Alloys and Compounds, 757, 504-519, 2018. [2] R. Santos-Güemes, G. Esteban-Manzanares, I. Papadimitriou, J. Segurado, L. Capolungo, J. LLorca. Discrete dislocation dynamics simulations of dislocation- θ’ precipitate interaction in Al-Cu alloys. Journal of the Mechanics and Physics of Solids, 118, 228-244, 2018

Analysis of precipitation hardening in metallic alloys by means of dislocation dynamics

El endurecimiento por precipitación es uno de los mecanismos de refuerzo más eficaces para aumentar el límite elástico de las aleaciones metálicas. La presencia de una distribución de precipitados intermetálicos en el material dificulta la propagación de las dislocaciones en sus planos de deslizamiento, aumentando la tensión cortante necesaria para producir deformación plástica. Los mecanismos de interacción entre las dislocaciones y los precipitados dependen de diferentes factores, entre los que se incluyen el tamaño, la geometría y la distribución espacial de los precipitados, la coherencia de su intercara, así como las distorsiones elásticas debido a la coherencia, la diferencia de módulo elástico entre la matriz y los precipitados, etc. y las dislocaciones pueden rebasar los precipitados mediante la formación de un bucle a su alrededor o cizallándolos. En las últimas décadas se han desarrollado diferentes propuestas para modelar este mecanismo de refuerzo, tanto de forma analítica como mediante métodos numéricos. Estos modelos han sido capaces, en general, de reproducir cualitativamente las tendencias que se observan experimentalmente. Sin embargo, todavía no se ha conseguido un modelo fiable que proporcione predicciones cuantitativas de la tensión crítica de cizalladura producida por el endurecimiento por precipitación en aleaciones metálicas debido a la complejidad de los mecanismos, que incluyen un gran número de fenómenos físicos. El objetivo de esta tesis doctoral es el desarrollo de una metodología capaz de proporcionar predicciones cuantitativas de la tensión crítica de cizalladura en aleaciones endurecidas por precipitación. Este es un paso necesario para optimizar de forma virtual este tipo de aleaciones o incluso diseñar otras in silico antes de fabricarlas en el laboratorio. Para ello, las interacciones entre dislocaciones y precipitados se han analizado mediante una aproximación multiescala basada en simulaciones de dinámica de dislocaciones. Los principales factores que controlan estas interacciones (heterogeneidad elástica, movilidad de las dislocaciones, frecuencia de deslizamiento cruzado, tamaño y forma de los precipitados, tensión necesaria para cizallar los precipitados, endurecimiento por solución sólida, deformaciones de coherencia, etc.) se han incluido en las simulaciones de manera rigurosa y su magnitud se obtuvo a partir de simulaciones atomísticas o de resultados experimentales independientes. La estrategia de simulación se aplicó para predecir la tensión crítica de cizalladura de dos aleaciones Al-Cu que contienen precipitados _0 o _00. Las predicciones de la tensión crítica de cizalladura coincidieron con resultados experimentales de compresión de micropilares en monocristales orientados para deslizamiento simple, validando la estrategia de simulación empleada. Además, se descubrió que las deformaciones de coherencia asociadas con la nucleación y crecimiento de los precipitados y el endurecimiento por solución sólida eran los mecanismos de endurecimiento principales en las aleaciones Al-Cu que contienen precipitados _0 impenetrables. En el caso de aleaciones Al-Cu que contienen precipitados cizallables _00, el endurecimiento estaba dominado por las contribuciones de solución sólida y del mecanismo de Orowan, mientras que las deformaciones de coherencia tenían un papel secundario. El efecto de la heterogeneidad elástica fue despreciable en ambas aleaciones. Por último, la herramienta de simulación basada en dinámica de dislocaciones se empleó para calibrar los parámetros de un modelo de tensión de línea generalizado, que es capaz de proporcionar estimaciones rápidas de la tensión crítica de cizalladura de una distribución aleatoria de precipitados esféricos teniendo en cuenta el efecto de su diámetro y fracción volumétrica, la diferencia de módulo elástico entre matriz y precipitados y la tensión necesaria para cizallar los precipitados. ----------ABSTRACT---------- Precipitation hardening is one of the most efficient strengthening mechanisms to increase the yield strength of metallic alloys. The presence of a dispersion of intermetallic precipitates within the material hinders the movement of dislocations, increasing the critical resolved shear stress to produce plastic deformation. The mechanisms of dislocation/ precipitate interaction depend on several factors such as the size, shape and spatial distribution of the precipitates, the coherency of their interface as well as the coherency strains, the elastic mismatch between matrix and precipitates, etc. Dislocations can overcome precipitates by either looping or shearing. Different approaches have been developed in the last decades to model these mechanisms, including analytical and numerical strategies. These efforts have led to different models that, in general, are able to reproduce qualitatively the experimental trends observed in precipitation hardened alloys. Nevertheless, accurate quantitative predictions of the critical resolved shear stress due to precipitation hardening in metallic alloys have not been obtained due to the complexity of the precipitation strengthening mechanisms, where many different physical phenomena are involved. The objective of this doctoral thesis is to develop a methodology capable of providing quantitative predictions of the critical resolved shear stress in precipitation hardened alloys. This is a necessary step towards the virtual optimization of such alloys or even the virtual design of new ones before they are actually manufactured. To this end, the dislocation/precipitate interactions have been analyzed through a multiscale approach based on dislocation dynamics simulations. The main factors that control the dislocation/precipitate interactions (elastic heterogeneity, dislocation mobility, crossslip rate, size and shape of precipitates, friction stress of the precipitate, solution hardening, coherency strains, etc.) were rigorously included in the simulations and their magnitude was obtained from either lower scale simulation techniques or independent experimental observations. The simulation strategy was applied to predict the critical resolved shear stress of two Al-Cu alloys containing either _0 or _00 precipitates. The predictions of the critical resolved shear stress were in good agreement with experimental results of micropillar compression tests in single crystals oriented for single slip, validating the simulation strategy. Moreover, it was found that the stress-free transformation strains and solution hardening were the main hardening mechanisms in Al-Cu alloys containing impenetrable _0 precipitates. In the case of Al-Cu alloys containing shearable _00 precipitates, the strength was dominated by the contributions of solution hardening and the Orowan mechanism while the coherency strains played a minor role. The effect of the elastic mismatch was negligible in both alloys. Finally, the dislocation dynamics simulation tool was used to calibrate the parameters of a generalized line tension model, which is capable of providing fast estimations of the critical resolved shear stress of random distributions of spherical precipitates taking into account the effect of the precipitate diameter and volume fraction, the elastic mismatch between matrix and precipitates, and the friction stress necessary to shear the precipitates