Alexander Hartmaier

Influence of crystal anisotropy on elastic deformation and onset of plasticity in nanoindentation: A simulational study

Using molecular-dynamics simulation we simulate nanoindentation into the three principal surfaces—the (100), (110), and (111) surface—of Cu and Al. In the elastic regime, the simulation data agree fairly well with the linear elastic theory of indentation into an elastically anisotropic substrate. With increasing indentation depth, the effect of pressure hardening becomes visible. When the critical stress for dislocation nucleation is reached, even the elastically isotropic Al shows a strong dependence of the force-displacement curves on the surface orientation. After the load drop, when plasticity has set in, the influence of the surface orientation is lost, and the contact pressure (hardness) becomes independent of the surface orientation.

Ab initio calculation of traction separation laws for a grain boundary in molybdenum with segregated C impurites

We have determined the influence of carbon on mechanical properties such as grain boundary energy, work of separation (WoS) and fracture strength of the ?5(3?1?0)[0?0?1] symmetrical tilt grain boundary (STGB) in molybdenum with ab initio methods. From our ab initio results, we derived traction?separation laws that can be used in continuum simulations of fracture employing cohesive zones. Our results show that with an increasing number of C atoms at the grain boundary, the energy of the grain boundary is lowered, indicating a strong driving force for segregation. Uni-axial tensile tests of the grain boundary reveal that there is only a small effect of segregated C atoms on the cohesive energy or WoS of the grain boundary, while the strength of the ?5(3?1?0)[0?0?1] STGB increases by almost 30% for a complete monolayer of C. This increase in strength is accompanied by an increase in grain boundary stiffness and a decrease of the interface excess volume. The characteristic parameters are combined in the concentration-dependent traction?separation laws. A study of the scaling behaviour of the different investigated systems shows that the energy?displacement curves can be well described by the universal binding energy relationship even for different C concentrations. These findings open the way for significant simplification of the calculation of ab initio traction separation laws for grain boundaries with and without impurities.

Image stresses in a free-standing thin film

Three-dimensional discrete dislocation dynamics (DDD) has been used successfully to investigate different aspects of plasticity. An investigation of thin-film plasticity with the help of these DDD schemes requires detailed modelling of the interfaces and surfaces of the film. One possible method is to compensate for the normal stresses that a dislocation population exerts on a surface by appropriate point loads. This traction compensation method is extended to a free-standing film, where the interaction of the two opposing free surfaces must be taken into account. The influence of the free surfaces on the operation of a Frank-Read source is investigated.

Ab initio tensile tests of Al bulk crystals and grain boundaries: Universality of mechanical behavior

We have performed ab initio tensile tests of bulk Al along different tensile axes, as well as perpendicular to different grain boundaries to determine mechanical properties such as interface energy, work of separation, and theoretical strength. We show that all the different investigated geometries exhibit energy-displacement curves that can be brought into coincidence in the spirit of the well known universal binding energy relationship curve. This simplifies significantly the calculation of ab initio tensile strengths for the whole parameter space of grain boundaries.

Determining Burgers vectors and geometrically necessary dislocation densities from atomistic data

We describe a novel analysis method to quantify the Burgers vectors of dislocations in atomistic ensembles and to calculate densities of geometrically necessary and statistically stored dislocations. This is accomplished by combining geometrical methods to determine dislocation cores and the slip vector analysis, which yields the relative slip of the atoms in dislocation cores and indicates the Burgers vectors of the dislocations. To demonstrate its prospects, the method is applied to investigate the density of geometrically necessary dislocations under a spherical nanoindentation. It is seen that this local information about dislocation densities provides useful information to bridge the gap between atomistic methods and continuum descriptions of plasticity, in particular for non-local plasticity.

Transition of effective hydraulic properties from low to high Reynolds number flow in porous media

We numerically analyze fluid flow through porous media up to a limiting Reynolds number of O(103). Due to inertial effects, such processes exhibit a gradual transition from laminar to turbulent flow for increasing magnitudes of Re. On the macroscopic scale, inertial transition implies nonlinearities in the relationship between the effective macroscopic pressure gradient and the filter velocity, typically accounted for in terms of the quadratic Forchheimer equation. However, various inertia-based extensions to the linear Darcy equation have been discussed in the literature; most prominently cubic polynomials in velocity. The numerical results presented in this contribution indicate that inertial transition, as observed in the apparent permeability, hydraulic tortuosity, and interfacial drag, is inherently of sigmoidal shape. Based on this observation, we derive a novel filtration law which is consistent with Darcys law at small Re, reproduces Forchheimers law at large Re, and exhibits higher-order leading terms in the weak inertia regime.

Mechanisms of anisotropic friction in nanotwinned Cu revealed by atomistic simulations

The nature of nanocrystalline materials determines that their deformation at the grain level relies on the orientation of individual grains. In this work, we investigate the anisotropic response of nanotwinned Cu to frictional contacts during nanoscratching by means of molecular dynamics simulations. Nanotwinned Cu samples containing embedded twin boundaries parallel, inclined and perpendicular to scratching surfaces are adopted to address the effects of crystallographic orientation and inclination angle of aligned twin boundaries cutting the scratching surface. The transition in deformation mechanisms, the evolution of friction coefficients and the friction-induced microstructural changes are analyzed in detail and are related to the loading conditions and the twinned microstructures of the materials. Furthermore, the effect of twin spacing on the frictional behavior of Cu samples is studied. Our simulation results show that the crystallographic orientation strongly influences the frictional response in different ways for samples with different twin spacing, because the dominant deformation mode varies upon scratching regions of different orientations. A critical inclination angle of 26.6. gives the lowest yield strength and the highest friction coefficient, at which the plasticity is dominated by twin boundary migration and detwinning. It is demonstrated that the anisotropic frictional response of nanotwinned Cu originates from the heterogeneous localized deformation, which is strongly influenced by crystallographic orientation, twin boundary orientation and loading condition.

A discrete dislocation plasticity model of creep in polycrystalline thin films

A mesoscopic discrete dislocation dynamics is presented which is used to study constrained diffusional creep in polycrystalline thin films. Recent experimental work has shown that ultrathin polycrystalline films on substrates reveal a transition in the deformation behavior. Continuum modeling and atomistic simulation were used successfully to explain this transition as a shift from plastic deformation by dislocation slip on inclined slip planes for larger film thicknesses to diffusional creep for the smallest film thicknesses. During the creep process material from the surface migrates into the grain boundaries. Due to the constraint of the substrate, this diffusional creep builds up large internal stresses that are responsible for dislocation glide on slip planes parallel to the film surface on which there is no resolved shear stress in the overall equibiaxial stress field. This process is investigated quantitatively with a discrete dislocation model describing diffusional creep as climb of dislocations and taking into account the slip on parallel slip planes relaxing the internal stresses. The results are shown to be consistent with experiment under certain assumptions, and thus help to identify the critical deformation processes during creep of ultrathin films.

The brittle-to-ductile transition and dislocation activity at crack tips

Dislocation activity in the vicinity of a crack tip and the brittle-to-ductile transition (BDT) are analysed using discrete dislocation dynamics simulations. The comparison of these simulations with fracture experiments on tungsten single crystals helps to identify the decisive mechanisms for the BDT of this material. Dislocation nucleation and the availability of active sources are shown to be limiting plasticity at low temperatures and partly in the semi-brittle regime. At elevated temperatures, fracture toughness, crack tip plasticity and the BDT itself can all be viewed as thermally activated processes, which can all be scaled by the same activation energy. It is concluded that they must be controlled by dislocation mobility.

Scaling relations for crack-tip plasticity

Abstract The fracture toughness of semibrittle materials such as bcc transition metals or semiconductor crystals strongly depends on loading rate and temperature. If crack-tip plasticity is considered to be thermally activated, a strong correlation between these quantities is expected. An Arrhenius-like scaling relation between the loading rate and the brittle-to-ductile transition temperature has already been reported. In the present work, two-dimensional discrete dislocation dynamics simulations of crack-tip plasticity are employed to show that the different combinations of loading rates and temperatures which yield the same fracture toughness are indeed correlated by a scaling relation. This scaling relation is closely related to the law used to describe dislocation motion. A strong correlation between loading rate and temperature is found in the entire temperature regime in which crack-tip plasticity is controlled by dislocation mobility. This shows the importance of dislocation mobility for fracture toughness below the brittle-to-ductile transition and for the transition itself. The findings of our simulations are consistent with experimental data gathered on tungsten single crystals and suggest that non-screw dislocations are dominating crack-tip plasticity in the semibrittle regime of this material.