The effect of the presence of a passivation layer on a metal rough surface during contact loading is investigated by means of dislocation dynamics simulations. The metal body is modeled as an FCC single crystal with a self-affine rough surface that is either bare, or covered by a thin coating, impenetrable to dislocations. This analysis permits to isolate the effect of surface roughening driven by dislocation motion: when the surface is bare the dislocations can glide out, leaving crystallographic steps at the surface that modify the local roughness; when the surface is passivated, dislocations are stopped by the interface.

@en

Viscoelasticity and roughness are among the possible causes of the adhesive hysteresis displayed by soft contacts. Viscoelasticity causes an increased effective work of adhesion due to stiffening of the contact, while roughness is responsible for elastic instabilities. Herein, we explore the interplay between viscoelasticity and roughness by simulating in two dimensions the retraction of a rigid cylinder, with wavy surface profile, from a viscoelastic half-space. The wave amplitude and length are varied to induce instabilities in the load–to–area response, while the retraction velocity is increased to promote viscoelasticity. Results show that, in the regime where viscoelasticity is confined to the edges of the wavy contact, the contributions of viscoelasticity and waviness to adhesive hysteresis are nearly independent and additive. At low retraction rates, the instabilities in the load-area curve typical of rough elastic contacts are suppressed by viscoelasticity: the contact stiffens to promote a stable decrease of the contact area with load. This occurs with a minimal change in work of adhesion. However, when the instantaneous limit is met at high retraction rates, mechanical instabilities appear.

@en

A seamless 2D dual-scale computational scheme is developed to study contact problems. The model consists of an atomistic domain close to the contact, coupled with an elastic continuum domain away from the contact. The atomistic formulation provides a description of the contact interaction through interatomic potentials and permits to capture atomic wear and defect formation in the contact region. The fields in the continuum domain are calculated by an efficient FFT-based Green's function method. The novel scheme is validated against full atomistic simulations and applied to study the effect of adhesion on the scratching of a rough copper surface by a rigid smooth spherical tip.

@en

Discrete dislocation plasticity is a modeling technique that treats plasticity as the collective motion of dislocations. The dislocations are described through their elastic Volterra fields, outside of a cylindrical core region, with a few Burgers vectors of diameter. The contribution of the core fields to the dislocation dynamics is neglected, because it is assumed that their range is too short to be of influence. The aim of this work is to assess the validity of this assumption. In recent ab-initio studies it has been demonstrated that the dislocation core fields are significant up to a distance of ten Burgers vector from the dislocation line. This is a longer range influence than expected and can give rise to changes in the evolving dislocation structure and in the overall response of a plastically deforming body. It is indeed experimentally observed that dislocations pile up against strong interfaces, and that the spacing between dislocations at the front of these pile-ups can be less than ten Burgers vectors. In this work, 2-D discrete dislocation plasticity simulations are performed to investigate the effect of core fields on edge dislocation interactions. The results of the simulations, which include core fields for the first time, show indeed that dislocations that are very closely spaced experience additional glide or climb due to core fields. The effect is however negligible when compared to glide and climb due to Volterra fields or due to the external load.

@en

It is well established that, at small loads, a linear relation exists between contact area and reduced pressure for elastic bodies with non-adhesive rough surfaces. In the case of adhesive contacts, however, there is not yet a general consensus on whether or not linearity still holds. In this work evidence is provided, through numerical simulations, that the relation is non-linear. The simulations here presented can accurately describe contact between self-affine adhesive rough surfaces, since they rely on Green's function molecular dynamics to describe elastic deformation and on coupled phenomenological traction-separation laws for the interfacial interactions. The analysis is performed for two-dimensional compressible and incompressible bodies under plane strain conditions. Interfaces with various roughness parameters and work of adhesion are considered.

@en

Although indentation of elastic bodies by self-affine rough indenters has been studied extensively, little attention has so far been devoted to plasticity. This is mostly because modeling plasticity as well as contact with a self-affine rough surface is computationally quite challenging. Here, we succeed in achieving this goal by using Green's function dislocation dynamics, which allows to describe the self-affine rough surface using wavelengths spanning from 5 nm to 100μm. The aim of this work is to gain understanding in how plastic deformation affects the contact area, contact pressure and hardness, gap profile and subsurface stresses, while the roughness of the indenter is changed. Plastic deformation is found to be more pronounced for indenters with larger root-mean-square height and/or Hurst exponent, and to be size dependent. The latter means that it is not possible to scale observables, as typically done in elastic contact problems. Also, at a given indentation depth (interference) the contact area is smaller than for the corresponding elastic contact problem, but gap closure is more pronounced. Contact hardness is found to be much larger than what reported by classical plasticity studies. Primarily, this is caused by limited dislocation availability, for which the stiffness of the deforming crystal is in between that of a linear elastic and an elastic-perfectly plastic material. When calculating hardness and nominal contact pressure, including very small wavelength in the description of the surface is not necessary, because below a given wavelength the subsurface stresses become invariant to a further decrease in true contact area. This is true for both elastic and plastic materials. Considering small wavelengths is instead required to capture accurately roughening and contact stress distribution.@en

Persson's theory allows for a fast and effective estimate of contact area and contact stress distributions when a flat and a self-affine rough surface are pressed into contact. For elastic bodies, the results of the theory have been shown to be in very good agreement with rather costly simulations. The theory has also been extended to plastic bodies. In this work, the results of Persson's theory for plastic bodies are compared with those of discrete dislocation plasticity. The area–load curves obtained by theory and simulations are found to be in good agreement when the rough surface has a very small root-mean-square (rms) height. For larger rms heights, which are more realistic for metal surfaces, the agreement is no longer good unless in the theory, instead of a size-independent material strength, one uses a rms height- and resolution-dependent yield strength. A modification of this type, i.e., the use of a yield strength dependent on size, does however not lead to agreement between the probability distributions of the contact stress, which is much broader in the simulations than in the theory. The most likely reason for this discrepancy is that the theory, apart from neglecting plasticity size dependence, only applies to elastic-perfectly plastic bodies and therefore, neglects strain hardening.

@en

During plastic deformation, metal surfaces roughen and this has a deleterious impact on their tribological performance. It is therefore desirable to be able to predict and control the amount of roughening caused by subsurface plasticity. As a first step, we focus on modelling plastic deformation during contact shearing of an FCC metallic single crystal, employing a finite strain Discrete Dislocation Plasticity (DDP) formulation. This formulation allows us to capture the finite lattice rotations induced in the material by shearing and the corresponding local rotation of the crystallographic slip planes. The simulations predict a pronounced material pile-up in front of the contact and a sink-in at its rear, which are strongly crystal-orientation dependent. By comparing finite and small strain DDP, we can assess the effect of slip plane rotation on surface roughening and on metal plasticity in general. Results of the simulations are also compared with crystal plasticity, which is also capable of predicting a pile-up and sink-in, but not the crystal-orientation dependency of roughening.@en

The contact mechanical response of various polymers is controlled by the viscoelastic behavior of their bulk and the adhesive properties of their interface. Due to the interplay between viscoelasticity and adhesion it is difficult to predict the contact response, even more when surfaces are rough. Numerical modeling could be of assistance in this task, but has so far mostly dealt with either adhesion or viscoelasticity and focused on simple geometries. Ideally, one would need a model that can concurrently describe viscoelasticity, surface roughness, and interfacial interactions. The numerical technique named Green's function molecular dynamics (GFMD) has the potential to serve this purpose. To date, it has been used to model contact between adhesive elastic bodies with self-affine surfaces. Here, as a first step, we extend the GFMD technique to include the transient contact response of frictionless viscoelastic bodies. To this end, we derive the constitutive equation for a viscoelastic semi-infinite body in reciprocal space, then integrate it using the semi-analytical method, and find the quasi-static solution through damped dynamics of the individual modes. The new model is then applied to study indentation as well as rolling of a rigid cylinder on a frictionless isotropic half-plane that follows the Zener model when loaded in shear. Extension of the method to a generalized viscoelastic model is straightforward, but the computational effort increases with the number of time-scales required to describe the material. The steady-state response of the rolling cylinder was provided analytically by Hunter in the sixties. Here, we use his analytical solution to validate the steady-state response of our model and provide additionally the transient response for bodies with various shear moduli.@en

Pseudoelasticity in NiTi shape memory alloy single crystals depends on the loading direction. Here, we present a comprehensive study in which molecular dynamics simulations of austenitic bulk single crystals under strain-controlled tensile and compressive loading along the 〈110〉,〈111〉 and 〈100〉 directions are performed, and the mechanical response of the crystals are contrasted. All simulations are performed using the MEAM interatomic potential proposed by Ko et al. (2015). The transformation strains and the Young's modulus of the initial austenitic and the final martensitic phases are compared with values obtained from the lattice deformation model and experimental results from the literature. Results show that depending on orientation the transformation occurs either through the formation of martensitic Lüders bands or through the transient formation of a multivariant martensite which, upon reorientation, becomes a dominant final single variant. Simulations are also performed to assess the orientation-dependent behavior of nano-wires subjected to bending, since the flexibility of the wires is orientation dependent.

@en

This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and microscales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.

@en

The relative contact area of rough surface contacts is known to increase linearly with reduced pressure, with proportionality factor κ. In its common definition, the reduced pressure contains the root-mean-square gradient (RMSG) of the surface. Although easy to measure, the RMSG of the entire surface does not coincide, at small loads, with the RMSG over the actual contact area g¯ _r, which gives a better description of the contact between rough surfaces. It was recently shown that, for Hertzian contacts, linearity between area and load is indeed obtained only if the RMSG is determined over the actual contact area. Similar to surface contacts, in line contacts, numerical data are often studied using theories that predict linearity by design. In this work, we revisit line contact problems and examine whether or not the assumption of linearity for line contacts holds true. We demonstrate, using Green’s function molecular dynamics simulations, that κ for line contacts is not a constant: It depends on both the reduced pressure and the Hurst exponent. However, linearity holds when the RMSG is measured over the actual contact area. In that case, we could compare κ for line and surface contacts and found that their ratio is approximately 0.9. Finally, by analytically deriving the proportionality factor using g¯ _r in the original model of Greenwood and Williamson, a value is obtained that is surprisingly in good agreement with our numerical results for rough surface contacts.

@en

Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent.@en

The Green's function molecular dynamics (GFMD) method for the simulation of incompressible solids under normal loading is extended in several ways: shear is added to the GFMD continuum formulation and Poisson numbers as well as the heights of the deformed body can now be chosen at will. In addition, we give the full stress tensor inside the deformed body. We validate our generalizations by comparing our analytical and GFMD results to calculations based on the finite-element method (FEM) and full molecular dynamics simulations. For the investigated systems we observe a significant speed-up of GFMD compared to FEM. While calculation and proof of concept were conducted in two-dimensions only, the methodology can be extended to the three-dimensional case in a straightforward fashion.

@en

A comparison of the EAM-Finnis-Sinclair and the MEAM potential, two of the recently developed potentials to model NiTi, is carried out. The potentials are compared by studying the pseudo-elastic behavior in bulk NiTi for one specific crystallographic orientation. To this end we perform, for the first time, simulations where the transformation occurs not only under compressive but also under tensile loading along 〈100〉_B2 using both potentials. Results indicate that in both cases the MEAM potential captures the pseudo-elastic behavior more accurately. By using a lattice deformation model, it is demonstrated that the inaccurate transformation strains predicted by the EAM-Finnis-Sinclair potential are a direct consequence of its inability to predict experimental values of the lattice constants. Similarly, it is shown that the more precise values of the Young's modulus of the initial austenitic and the final martensitic phase estimated by the MEAM potential are the result of its ability to predict elastic constants more accurately than the EAM-Finnis-Sinclair potential. As a result, it is concluded that the MEAM potential is better suited to study the overall pseudo-elastic behavior in NiTi.

@en

Metals deform plastically at the asperity level when brought in contact with a counter body even when the nominal contact pressure is small. Modeling the plasticity of solids with rough surfaces is challenging due to the multi-scale nature of surface roughness and the length-scale dependence of plasticity. While discrete-dislocation plasticity (DDP) simulations capture size-dependent plasticity by keeping track of the motion of individual dislocations, only simple two-dimensional surface geometries have so far been studied with DDP. The main computational bottleneck in contact problems modeled by DDP is the calculation of the dislocation image fields. We address this issue by combining two-dimensional DDP with Green's function molecular dynamics. The resulting method allows for an efficient boundary-value-method based treatment of elasticity in the presence of dislocations. We demonstrate that our method captures plasticity quantitatively from single to many dislocations and that it scales more favorably with system size than conventional methods. We also derive the relevant Green's functions for elastic slabs of finite width allowing arbitrary boundary conditions on top and bottom surface to be simulated.@en

It is customary to simplify the analysis of contact between two elastically deformable bodies by treating an equivalent problem where only one body is deformable and the other is rigid. This is possible provided that the gap geometry and the effective elastic modulus of the bodies in the simplified problem are the same as in the original problem. However, the question arises on whether – and to which extent – the simplification is still valid even when (size-dependent) plasticity occurs. Studies using discrete dislocation plasticity have also, so far, addressed simple contact problems where only one body can deform plastically. Here, we extend the analysis to two bodies in contact that can both deform by dislocation plasticity and investigate under which conditions the response agrees with that of an equivalent simplified problem. The bodies in contact are metal single crystals with sinusoidal and flat surface. It is found that the response of two plastically deformable bodies in contact can be simplified to an equivalent problem where one body is rigid and the other can deform plastically. Also, a plasticity size effect is observed, but the effect fades when the platen becomes more plastically deformable.@en