Strain hardening in 2D discrete dislocation dynamics simulations: A new '2.5D' algorithm

The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called '2.5D' constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new '2.5D' DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations. (C) 2016 Elsevier Ltd. All rights reserved.

Multiscale Modelling of Irradiation Induced Effects on the Plasticity of Fe and Fe-Cr

Seyed Masood Hafez Haghighat

Degradation of mechanical properties due to nanometric irradiation induced defects is one of the challenging issues in designing ferritic materials for future nuclear fusion reactors. Various types of defects, namely dislocation loops, voids, He bubbles and Cr precipitates may be produced in ferritic materials due to high doses of irradiation with the 14 MeV neutrons stemming from the deuterium-tritium fusion reaction. Multiscale modelling methods, namely molecular dynamics (MD) and dislocation dynamics (DD) methods, are used here to study the impact of radiation-induced defects on the mechanical properties of model ferritic material. MD simulation is used to study the state of a nanometric helium bubble in α-Fe as a function of temperature, 10 to 700 K, and He content, 1 to 5 He atoms per vacancy. It appears that up to moderate temperatures the Fe lattice can confine He to solid state, in good agreement with known solid-liquid transition diagram of pure He. However, while for a given temperature and He density range where an fcc structure is expected, He in the bubble forms an amorphous phase. He bubble forms a polyhedron whose morphology depends on either the surface energy or elastic-plastic properties of Fe at either low or high pressure, respectively. At high He contents the bubble surface breaks down at the mechanical stability limit of the Fe crystal, leading to a pressure decrease in the bubble. The basic mechanisms of the interaction in α-Fe between a moving dislocation and a nanometric defect, as a function of temperature, interatomic potentials, interaction geometry and size are investigated using MD simulation. The stress-strain responses are obtained under imposed strain rate and using different interatomic potentials for Fe-Fe and Fe-He interactions. It appears that voids and He bubbles are strong obstacles to dislocation, which induce hardening and loss of ductility. A nanometric void is a stronger obstacle than a He bubble at low He contents, whereas at high He contents, the He bubble becomes a stronger obstacle. It also appears that different potentials give different strengths and rates of decrease of obstacle strength with increasing temperature. Temperature eases the dislocation release, due to the increased mobility of the screw segments appearing on the dislocation line upon bowing from the void or He bubble. Concerning the obstacle size at low content He bubble, where it is penetrable defect, size increase from 1 to 5 nm make them harder in agreement with the elasticity of continuum. At high He contents a size dependent loop punching is observed, which at larger bubble sizes leads to a multistep dislocation-defect interaction. Atomistic simulations reveal that the He bubble induces an inhomogeneous stress field in its surroundings, which strongly influences the dislocation passage depending on the geometry of the interaction. Fe-Cr alloys are also studied using MD simulations as model alloys for the ferritic base steels. Studying the flow stress of a moving edge dislocation in Fe(Cr) shows that the flow stress is not sensitive to temperature and strain rate, while it increases with Cr concentration. The flow stress of a screw dislocation is temperature dependant and its value is much higher than that of edge dislocation. Interaction in a pure Fe matrix of an edge dislocation with a nanometric Cr precipitate having various Cr content inside (Cr/Fe ratio) indicates that with the Cr/Fe ratio the obstacle strength increases, with a strong sensitivity to the short-range order. Temperature induces a monotonous decrease of the strength for all studied Cr/Fe ratios. DD calculation coupled to finite element method (FEM) is used to simulate the interaction of an edge dislocation with a void. DD calculations present a good match to the MD simulation results for the impact of image forces on the dislocation due to the free internal surface of the void. Using DD simulation, hardening due to the presence of nanometric defects, as immobile dislocation segments and spherical defect, are considered. The results of MD simulations for the strength of different defects are introduced in DD simulation. It appears that the presence of both immobile dislocation segments and nanometric defects may lead to the hardening of α-Fe. However, the defect density has more significant importance on the DD simulation, obtained here, than the strength of a single defect. TEM in-situ straining is used to validate simulations, in particular on the dislocation interaction mechanisms. Experiments were performed in ultra high purity Fe specimens. It appears that the microstructure of the material consists mainly in elongated screw dislocations. The in-situ straining tests led to the observation of the formation of screw dislocation dipoles in consistency with the MD simulation results. The interaction between a dislocation and an obstacle, as nanometric defect or immobile dislocations, leading to their shear or to Orowan loop formation were successfully observed. This work shows that using of different simulation methods can assist in the understanding of nano- and meso-scale phenomena occurring due to the presence of irradiation induced defects upon deformation of α-Fe. The information obtained from various microstructure mechanisms at lower scale simulations can be passed to higher scale simulation methods in order to realize the simulated phenomena. Experimental observations may validate what is observed in simulations provided the simulation scale is reachable in experimental observations.

EPFL2010

Submonolayer growth of cobalt on metallic and insulating surfaces studied by scanning tunneling microscopy and kinetic Monte-Carlo simulations

Philipp Buluschek

Submonolayer epitaxial growth is obtained by the deposition of less than a complete layer of atoms on a single crystal surface. It is of fundamental interest for industrial applications (e.g. in the semiconductor industry) as well as from the point of view of basic research. For example, it is known that nanometer-sized atomic structures (nanostructures) exhibit remarkable physical and chemical properties which can differ greatly from those of bulk matter. In order to investigate these properties, it is often necessary to create large quantities of well defined and possibly spatially ordered nanostructures. One way to achieve this result is self-organized growth where one deposits atoms on a clean crystalline surface and lets the growth process evolve freely. Here, nanostructures result from the atomic diffusion and aggregation processes taking place at the surface. Understanding the exact nature of these processes is of ongoing interest in the field of nanostructure growth. In this thesis we report about submonolayer growth experiments of the ferromagnetic transition metal cobalt. Cobalt was chosen because it exhibits remarkable magnetic properties. These experiments were performed in an ultra-high vacuum chamber and molecular beam epitaxy was used to grow the nanostructures. Observations of the surface were made using a variable-temperature scanning tunneling microscope (STM). In order to get a better understanding of the atomic processes happening at the surface, we developed two adapted computational simulation methods. Kinetic Monte-Carlo (KMC) simulations were used to get an atomistic picture of the surface while mean field rate equations were integrated numerically to yield cluster densities. We study the growth of cobalt on three different surfaces. By depositing Co on a clean Pt(111) crystal surface, we observe that the platinum surface reconstructs by forming star-shaped partial dislocations for sample temperatures above 180 K (-93°C). We also observe that island densities deviate from predictions of all known models towards higher values for these same temperatures. By simulation we are able to show that insertion of Co into the topmost platinum layer creates a repulsive network of dislocations. We show that these dislocations act as diffusion inhibiting barriers and thus influence the island density by constraining the free movement of atoms at the surface. We also show that the Co dimer and trimer diffuse on Pt(111) before dissociating and are able to extract corresponding activation barriers. We also study the deposition of Co on a Ru(0001) surface which shows a more conventional temperature dependence. By comparing simulation and experiment we extract all relevant diffusion activation barriers and show that at high temperatures the Co dimer and trimer dissociate. Finally, we investigate the growth of Co on the hexagonal boron nitride superlattice which forms on a Rh(111) surface. On this surface Co clusters form three-dimensional hemispherical dots. We show how the substrate corrugation influences diffusion of Co atoms and that clusters up to the size of the pentamer can diffuse. By simulation, we also extract the relevant migrations and desorption barriers.

EPFL2008

Nanocrystalline metals: transient testing during in situ X-ray diffraction and molecular dynamics

Zhen Sun

Nanocrystalline (NC) metals have attracted widespread interest in materials science due to their high strength compared to coarse-grained counterparts. It is well know that during uniaxial deformation, the stress-strain behaviour exhibits an extraordinary work-hardening followed by an early observation of constant flow stress. Information on possible deformation mechanisms have been gathered by extensive research combining in situ deformation experiments, electron microscopy observations and computational modelling. Generally, these mechanisms are categorized into two types: dislocation slip and grain boundary (GB) accommodation processes, as for instance, GB sliding based mechanisms and GB migration eventually coupled to the shear stress. However, the interplay between these mechanisms resulting in the constant deformation resistance is not fully understood. Transient testing has proven to be a suitable tool to gather information on the rate limiting deformation mechanisms that are activated during the deformation path. In particular in stress reduction experiments, after an intermediate/large stress drop thermally activated dislocation slip is suppressed so that other underlying mechanisms are brought into foreground during subsequent transient creep. Those mechanisms may play a minor role in the determination of the flow stress but might still be essential to the development of a constant deformation resistance. Within this thesis, transient testing is combined with in situ X-ray diffraction at the Swiss Light Source. Therefore, the transient responses are captured in terms of evolution of macrostrain as well as diffraction peak broadening. Since dislocation slip and GB accommodation have an opposite footprint on the peak broadening, the presence of these two types of mechanisms can be distinguished. Three electrodeposited NC materials with different grain sizes are investigated: two NC Ni batches and one NC Ni50Fe50 batch. The results reveal that the constant flow stress reached during uniaxial deformation of electrodeposited NC metals reflects a quasi-stationary balance between dislocation-based mechanisms and GB-mediated accommodation. The latter plays an important role in producing plastic strain and recovering the defects and internal stress. Depending on the magnitude of the stress drop, a non-monotonic behaviour of the diffraction peak width is observed, suggesting an alternation of mechanisms. Also, by comparing transient responses among different NC materials, the relative contributions of dislocation slip and GB accommodation mechanisms are discussed in terms of grain size and alloying. Finally, different magnitudes of stress reduction are carried out by molecular dynamics (MD) simulations with the aim to verify in situ experimental results and explore the mechanisms responsible for GB accommodation. MD simulations confirm that dislocation slip is reduced after a moderate stress drop, however can continue to operate after adaption of the GB structures by a variety of GB accommodation mechanisms explaining the non-monotonic behaviour of the peak broadening during transient creep.

EPFL2016