Atomistic modeling of the strengthening mechanisms in FCC and HCP metals

Abstract

El endurecimiento por precipitatacion es uno de los mecanismos mas eficaces para mejorar el limite elastico de aleaciones metalicas. El movimiento de las dislocaciones es impedido por la presencia de una distribucion homogenea de precipitados intermetalicos de tamano nanometrico, lo que conlleva el aumento de la tension de cizalla en el plano de deslizamiento para rebasar este obstaculo. Los precipitados de gran tamano (> 50 nm) son rebasados formando un lazo de Orowan y diversas investigaciones han estudiado en detalle los mecanismos de interaccion entre la dislocation y el precipitado usando modelos continuos. Estos modelos se apoyan en la interaccion elastica entre la linea de la dislocacion y el precipitado. Los precipitados mas pequenos suelen ser cizallados por las dislocaciones y los mecanismos de endurecimiento asociados (quimicos, fallos de apilamiento, diferencias en las constantes elasticas, deformaciones de coherencia y orden) son mas dificiles de cuantificar. Ademas, las hipotesis del continuo no se pueden aplicar en el caso de precipitados muy pequenos, como las zonas de Guinier-Preston. El estudio de los mecanismos de interaccion entre precipitados de pequeno tamano ( 50 nm) are normally overcome by the formation of Orowan loops. In this case, the mechanisms of dislocation/precipitate interaction have been extensively analyzed in the past by means of continuummodels based on the elastic interactions of the dislocation line with the precipitate. Smaller precipitates are often sheared by the dislocations and the associated strengthening mechanisms (chemical, stacking fault, elastic mismatch, coherency strains, and order) are more difficult to quantify. Moreover, the continuum hypothesis breakdown in the case of very small precipitates, such as Guinier-Preston zones. Classical atomistic simulations, based on either molecular statics or dynamics and path sampling methods, are another type of strategies that can be used to analyze the interaction mechanisms between dislocations and precipitates in the case of small precipitates (< 20 nm). Nevertheless, their application is not straightforward and requires to overcome several challenges: selection of the appropriate interatomic potential, building atomistic models with realistic interfaces between the precipitate and the metallic matrix, development of robust methodologies to calculate the energy barrier in the case of very rough energy landscapes, extension of the atomistic results to the typical strain rates of most engineering applications, etc. This doctoral thesis was aimed at developing methodologies to tackle these problems, so classical atomistic simulations can be eventually used to design novel precipitate-strengthened metallic alloys. Three different problems were analyzed in this thesis. The first one was the interaction of dislocations with Guinier-Preston zones in an Al-Cu alloy by means of molecular mechanics simulations. A novel molecular statics - thermal annealing strategy was used to simulate the shearing of the Guinier-Preston zones the dislocations and the thermodynamic functions that control the dislocation/precipitate interaction were obtained from atomistic simulations in combination with transition state theory. This information was used to estimate the critical resolved shear stress as a function of temperature and strain rate, which was compared with experimental results in the literature. Dislocation cross-slip is another mechanism to overcome the precipitates and it is also important to simulate the formation of dislocation networks during deformation. The nudged elastic band method was employed to determine the activation energy barrier for dislocation cross-slip in the absence of thermal energy, while the cross slip rate was determined by molecular dynamics as a function of the Schmid stress on the cross-slip plane, and of the Escaig stresses on the cross-slip and glide planes in Al. Based on these results, an analytical expression of the activation free energy barrier for cross-slip in Al as a function of the Schmid and Escaig stresses was developed and validated. Finally, atomistic simulations were used to evaluate the interaction of basal dislocations with _-Mg17Al12 precipitates in Mg-Al alloys. A strategy was developed to insert a lozenge-shaped Mg17Al12 precipitate with Burgers orientation relationship within the Mg matrix in an atomistic model ensuring that the matrix/precipitate interfaces were close to minimum energy configurations. It was found that the dislocation bypassed the precipitate by the formation of an Orowan loop, that entered the precipitate. Within the precipitate, the dislocation was not able to progress further until more dislocations overcome the precipitate and push the initial loop to shear the precipitate along the (110) plane, parallel to the basal plane of Mg. This process was eventually repeated as more dislocations overcome the precipitate in agreement with experimental observations and indicate that precipitate shearing by basal dislocations in Mg-Al alloys is favored because the (0001) Mg basal plane is parallel to the (110) crystallographic plane of the precipitate. This process is likely to occur for other precipitates in Mg and is responsible for the limited precipitation hardening of Mg alloys.