Ab initio Modelling of the Early Stages of Precipitation in Al-6000 Alloys

Age hardening induced by the formation of (semi)-coherent precipitate phases is crucial for the processing and final properties of the widely used Al-6000 alloys. Early stages of precipitation are particularly important from the fundamental and technological side, but are still far from being fully understood. Here, an analysis of the energetics of nanometric precipitates of the meta-stable $\beta''$ phases is performed, identifying the bulk, elastic strain and interface energies that contribute to the stability of a nucleating cluster. Results show that needle-shape precipitates are unstable to growth even at the smallest size $\beta''$ formula unit, i.e. there is no energy barrier to growth. The small differences between different compositions points toward the need for the study of possible precipitate/matrix interface reconstruction. A classical semi-quantitative nucleation theory approach including elastic strain energy captures the trends in precipitate energy versus size and composition. This validates the use of mesoscale models to assess stability and interactions of precipitates. Studies of smaller 3d clusters also show stability relative to the solid solution state, indicating that the early stages of precipitation may be diffusion-limited. Overall, these results demonstrate the important interplay among composition-dependent bulk, interface, and elastic strain energies in determining nanoscale precipitate stability and growth

Modelling Plasticity in Nanoscale Contact

The problem of mechanical contact is a truly multiscale one. Atomistic effects that violate continuum theory dominate the deformations of contacting asperities, while the interactions between distant asperities occur through long-range elasticity. This thesis concentrates on the numerical modelling of nanoscale frictional contact between crystalline metals by using both single-scale atomistic methods and improving concurrent multiscale methods. A novel approach to quantify frictional work and the energy associated with plastic activity in \md simulations is presented. In combination with a statistical criterion to determine the significance of simulation box size, microstructure and sliding rate effects on the frictional quantities such as the friction coefficient and stored plastic energies, the method is used in a large parametric molecular dynamics study of single-asperity nanoscratch on monocrystalline and polycrystalline aluminium substrates. Some fundamental differences in the friction mechanisms between monocrystalline and polycrystalline substrates are presented. The study shows the limitations of single-scale modelling and highlights the importance of developing appropriate multiscale methods for nanoscale plasticity. One such method is the Coupled Atomistics and Discrete Dislocations (CADD), which previously only existed for two-dimensional problems. A three-dimensional version of the CADD method is presented theoretically as well as a detailed practical road map for its efficient implementation. The foundations of three-dimensional CADD are presented using practical test cases. CADD avoids ghost forces at the coupling interfaces through displacement-coupling. I reveal that such displacement-coupling methods generally exhibit an inherent dynamic instability which makes them particularly ill suited for finite temperature calculations, despite their wide use. The instability is analysed in detail. Multiple remedies to manage it are discussed and a fundamental solution to the underlying problem is presented in the form of a new coupling method

Efficient topology optimization using compatibility projection in micromechanical homogenization

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas Fourier-based solvers have recently shown large efficiency gains for homogenization problems. In this paper, we derive the discrete adjoint method for Fourier-based solvers that employ compatibility projection. We demonstrate the method on the optimization of composite materials and auxetic metamaterials, where void regions are modelled with zero stiffness.Comment: 17 pages, 5 figure

The emergence of small-scale self-affine surface roughness from deformation

Most natural and man-made surfaces appear to be rough on many length scales. There is presently no unifying theory of the origin of roughness or the self-affine nature of surface topography. One likely contributor to the formation of roughness is deformation, which underlies many processes that shape surfaces such as machining, fracture, and wear. Using molecular dynamics, we simulate the biaxial compression of single-crystal Au, the high-entropy alloy Ni36.67Co30Fe16.67Ti16.67, and amorphous Cu50Zr50 and show that even surfaces of homogeneous materials develop a self-affine structure. By characterizing subsurface deformation, we connect the self-affinity of the surface to the spatial correlation of deformation events occurring within the bulk and present scaling relations for the evolution of roughness with strain. These results open routes toward interpreting and engineering roughness profiles

Plastic activity in nanoscratch molecular dynamics simulations of pure aluminum

Atomistic models for friction suffer from the severe length- and time-scale restrictions of molecular dynamics. Even when they yield good qualitative results, it is difficult to draw meaningful quantitative conclusions from them. In this presentation, a novel approach to quantify the scratching work and the energy associated with plastic activity is used. The approach is combined with a statistical criterion to determine the significance of simulation box size, microstructure and sliding rate effects on the friction coefficient. These two methods are applied to a large parametric molecular dynamics study of single-asperity aluminum nano-scratch on mono-crystalline and poly-crystalline substrates. The results show that the simulation size effects are a considerable obstacle to understanding the atomistic origins of friction -- using present-day computing hardware -- as they have a strong influence on the core mechanisms of sliding friction, therefore motivating the development of 3D multi-scale methods for a hybrid nano- and micro-scale description of plasticity

Efficient implementation of atom-density representations

Physically motivated and mathematically robust atom-centered representations of molecular structures are key to the success of modern atomistic machine learning. They lie at the foundation of a wide range of methods to predict the properties of both materials and molecules and to explore and visualize their chemical structures and compositions. Recently, it has become clear that many of the most effective representations share a fundamental formal connection. They can all be expressed as a discretization of n-body correlation functions of the local atom density, suggesting the opportunity of standardizing and, more importantly, optimizing their evaluation. We present an implementation, named librascal, whose modular design lends itself both to developing refinements to the density-based formalism and to rapid prototyping for new developments of rotationally equivariant atomistic representations. As an example, we discuss smooth overlap of atomic position (SOAP) features, perhaps the most widely used member of this family of representations, to show how the expansion of the local density can be optimized for any choice of radial basis sets. We discuss the representation in the context of a kernel ridge regression model, commonly used with SOAP features, and analyze how the computational effort scales for each of the individual steps of the calculation. By applying data reduction techniques in feature space, we show how to reduce the total computational cost by a factor of up to 4 without affecting the model’s symmetry properties and without significantly impacting its accuracy

Investigation of the size of plastic zones in nano indentation and nano scratching

Friction and the associated wear are important but still poorly understood phenomena with strong impacts on our every day lives. Several mechanisms, such as plasticity, lattice vibration, and third-body interactions contribute to the dissipation of energy in friction phenomena. This physical complexity is further increased by the inherently multiscale nature of contact. Indeed, it is well known that roughness exists over multiple length scales, which imposes a multiscale numerical treatment. Our objective in this study is to analyse the development of plastic events at contacting asperities in fcc metals. Dislocation nucleation can happen at the contact surface or – in special cases – as bulk nucleation [1] underneath the surface. We capture these dislocations by molecular dynamics (MD) mod- elling of the contact zones. As dislocation activity extends far away from the contact, it is not feasible to tackle this problem via MD alone. Therefore, to reduce computational cost, we resort to coupling MD to a discrete dislocation dynamics (DD) domain [2], into which MD dislocations may enter. The coupling method used is the recently proposed coupled atomistics and discrete dislocations (CADD) method [3, 4, 5]. It has so far been implemented only in 2D and therefore effectively models asperities with an infinite third dimension (cylindrical asperities). In the first part of our presentation, we evaluate the systematic differences between 2D and 3D contact in pure MD calculations. We use this comparison to motivate 2D simulations. Finally, we present simulation results obtained at different scratching speeds for several normal forces and indenter sizes and shapes. We monitor the friction coefficient and scratching forces and relate them to the energy dissipated in the form of discrete plasticity events

Linking Discrete Dislocations and Molecular Dynamics in 3D: a Start

Many phenomena in crystalline metals such as friction, nano-indentation and ductile fracture are plasticity-driven and poorly understood. The physical complexity is further increased by the inherently multiscale nature of contact and fracture [1]. This study is aimed at a realistic numerical treatment of plasticity during nanoscale scratching of crystalline metal. The principal mechanism of plasticity is dislocation nucleation and motion. Nucleation is an atomic nanoscale phenomenon and is often localised at interfaces, crack tips, etc., while dislocation motion is a microscale phenomenon occurring within grains in a polycrystalline microstructure [2]. The molecular dynamics (MD) method is able to accurately predict dislocation nucleation, however the time and length scale limitations [3] of MD do not permit for the description of the motion of entire dislocation networks. The latter are computed much more efficiently [4] with the discrete dislocation dynamics (DD) method where the details of the atomistic core are eliminated from consideration. We present a method to extend to 3D the coupled atomistics and discrete dislocations (CADD) method [5, 6, 7]. To date, CADD has been restricted to plane strain problems with straight disloca- tions. In 3D CADD, the solid is split into two regions (e.g. Figure 1(a)): the MD region, where highly non-linear deformations (i.e. dislocation nucleation) and complex defect interactions are expected that require atomic resolution, and the DD region, where plastic behaviour due to dislocation motion can be computed at much lower cost. To couple these regions, the MD/DD interface (see Figure 1(b)) uses a layer in the MD region where approaching dislocations are detected and a layer in the DD region where fictitious pad atoms serve as boundary conditions for the MD region. An iterative solution permits for the tracking of dislocation lines that span the MD and DD regions, with minimal spurious forces due to the interface coupling. We apply the 3D coupling scheme to the simplest problem - motion of a straight edge dislocation under a uniform applied shear. The results will be used to show capabilities and limitations of the method, and will guide the extension to more complex problems

contact.engineering -- Create, analyze and publish digital surface twins from topography measurements across many scales

The optimization of surface finish to improve performance occurs largely through trial and error, despite significant advancements in the relevant science. There are three central challenges that account for this disconnect: (1) the challenge of integration of many different types of measurement for the same surface to capture the multi-scale nature of roughness; (2) the technical complexity of implementing spectral analysis methods, and of applying mechanical or numerical models to describe surface performance; (3) a lack of consistency between researchers and industries in how surfaces are measured, quantified, and communicated. Here we present a freely-available internet-based application which attempts to overcome all three challenges. First, the application enables the user to upload many different topography measurements taken from a single surface, including using different techniques, and then integrates all of them together to create a digital surface twin. Second, the application calculates many of the commonly used topography metrics, such as root-mean-square parameters, power spectral density (PSD), and autocorrelation function (ACF), as well as implementing analytical and numerical calculations, such as boundary element modeling (BEM) for elastic and plastic deformation. Third, the application serves as a repository for users to securely store surfaces, and if they choose, to share these with collaborators or even publish them (with a digital object identifier) for all to access. The primary goal of this application is to enable researchers and manufacturers to quickly and easily apply cutting-edge tools for the characterization and properties-modeling of real-world surfaces. An additional goal is to advance the use of open-science principles in surface engineering by providing a FAIR database where researchers can choose to publish surface measurements for all to use.Comment: 19 pages, 6 figure