Guillaume Anciaux

From infinitesimal to full contact between rough surfaces: Evolution of the contact area

We carry out a statistically meaningful study on self-affine rough surfaces in elastic frictionless non-adhesive contact. We study the evolution of the true contact area under increasing squeezing pressure from zero up to full contact, which enables us to compare the numerical results both with asperity based models at light pressures and with Persson’s contact model for the entire range of pressures. A good agreement of numerical results with Persson’s model is obtained for the shape of the area-pressure curve especially near full contact, however, we obtain qualitatively different results for its derivative at light pressures. We investigate the effects of the longest and shortest wavelengths in surface spectrum, which control the surface Gaussianity and spectrum breadth (Nayak’s parameter). We revisit the influence of Nayak’s parameter, which is frequently assumed to play an important role in mechanics of rough contact.

Contact between representative rough surfaces

A numerical analysis of mechanical frictionless contact between rough self-affine elastic manifolds was carried out. It is shown that the lower cutoff wave number in surface spectra is a key parameter controlling the representativity of the numerical model. Using this notion we demonstrate that for representative surfaces the evolution of the real contact area with load is universal and independent of the Hurst roughness exponent. By introducing a universal law containing three constants, we extend the study of this evolution beyond the limit of infinitesimal area fractions.

The Contact of Elastic Regular Wavy Surfaces Revisited

Abstract We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we discover previously overlooked transition regimes. These are seen in particular in the evolution with applied load of the contact area and perimeter, the mean pressure and the probability density of contact pressure. These transitions are correlated with the contact area shape, which is affected by long range elastic interactions. Our analysis has implications for general random rough surfaces, as similar local transitions occur continuously at detached areas or coalescing contact zones. We show that the probability density of null contact pressures is nonzero at full contact. This might suggest revisiting the conditions necessary for applying Persson’s model at partial contacts and guide the comparisons with numerical simulations. We also address the evaluation of the contact perimeter for discrete geometries and the applicability of Westergaard’s solution for three-dimensional geometries.

Toward a 3D coupled atomistic and discrete dislocation dynamics simulation: dislocation core structures and Peierls stresses with several character angles in FCC aluminum

BackgroundWe present a robust method to obtain the displacement field of a dislocation core, which is one of the building blocks for the development of a direct multiscale method coupling an atomistic domain to a discrete dislocation dynamics engine in 3D (e.g. CADD3D).MethodsThe core structure is achieved by modeling of a straight dislocation with an arbitrary mixed angle using atomistic simulation. In order to validate the obtained atomistic core structures, a variational Peierls-Nabarro method is extended to include arbitrary characters.ResultsBoth methods show comparable dislocation core structures for all studied angles. We provide also the Peierls stress for a wide range of character angles.ConclusionsThe obtained displacement fields for the dislocation cores were fully validated. These can consequently be employed to construct the described CADD3D coupling scheme.

Friction at the tool?chip interface during orthogonal nanometric machining

Understanding the unfolding of friction between the tool and the generated chip is of fundamental importance to nanometric machining processes. To this end, this paper investigates the influence of tool geometry, lattice orientation, machining velocity and machined thickness on the resistance encountered by a diamond tool during orthogonal cutting of a copper substrate. A salient result of our molecular dynamics simulations is that the degree of adhesion at the tool-chip interface is a key contributor to friction. Adhesion can be reinforced by varying the tool rake angle and by choosing specific lattice orientations that yield commensurate contact at the interface. On the other hand, we show that increasing the machining velocity reduces frictional forces due to thermal softening. Furthermore, increasing the machined thickness decreases the relative contribution of adhesive forces and thus lowers overall friction.

The autocorrelation function for island areas on self-affine surfaces

The spatial distribution of regions that lie above contours of constant height through a self-affine surface is studied as a function of the Hurst exponent H. If the surface represents a landscape, these regions correspond to islands. When the surface represents the height difference for contacting surfaces, the regions correspond to mechanical contacts in the common bearing area model. The autocorrelation function C(Δr) is defined as the probability that points separated by Δr are both within islands. The scaling of C has important implications for the stiffness and conductance of mechanical contacts. We find that its Fourier transform C(q) scales as a power of the wavevector magnitude q: [Formula: see text] with μ = 2 + H rather than the value μ = 2 + 2H reported previously. An analytic argument for μ = 2 + H is presented using the distribution of areas contained in disconnected islands.

On the accurate computation of the true contact-area in mechanical contact of random rough surfaces

We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments, and apart from the contact area itself requires only one additional quantity to be computed: the length of contact/non-contact interfaces. The new technique enables to evaluate accurately the true contact area using a very coarse mesh, for which the shortest wavelength in the surface spectrum reaches the grid size. The validity of the approach is demonstrated for surfaces with different fractal dimensions and different spectral content using a properly designed mesh convergence test. In addition, we use a topology preserving smoothing technique to adjust the morphology of contact clusters obtained with a coarse grid.

The role of the roughness spectral breadth in elastic contact of rough surfaces

We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pressure. This accuracy enables us to draw conclusions on the role of the surface’s spectrum breadth (Nayak parameter) in the contact area evolution. We show that for a given normalized pressure, the contact area decreases logarithmically with the Nayak parameter. By linking the Nayak parameter with the Hurst exponent (or fractal dimension), we show the effect of the latter on the true contact area. This effect, undetectable for surfaces with poor spectral content, is quite strong for surfaces with rich spectra. Numerical results are compared with analytical models and other available numerical results. A phenomenological equation for the contact area growth is suggested with coefficients depending on the Nayak parameter. Using this equation, the pressure-dependent friction coefficient is deduced based on the adhesive theory of friction. Some observations on Persson’s model of rough contact, whose prediction does not depend on Nayak parameter, are reported. Overall, the paper provides a unifying picture of rough elastic contact and clarifies discrepancies between preceding results.

Impact of internal crystalline boundaries on lattice thermal conductivity: Importance of boundary structure and spacing

The low thermal conductivity of nano-crystalline materials is commonly explained via diffusive scattering of phonons by internal boundaries. In this study, we have quantitatively studied phonon-crystalline boundaries scattering and its effect on the overall lattice thermal conductivity of crystalline bodies. Various types of crystalline boundaries such as stacking faults, twins, and grain boundaries have been considered in FCC crystalline structures. Accordingly, the specularity coefficient has been determined for different boundaries as the probability of the specular scattering across boundaries. Our results show that in the presence of internal boundaries, the lattice thermal conductivity can be characterized by two parameters: (1) boundary spacing and (2) boundary excess free volume. We show that the inverse of the lattice thermal conductivity depends linearly on a non-dimensional quantity which is the ratio of boundary excess free volume over boundary spacing. This shows that phonon scattering across crystalline boundaries is mainly a geometrically favorable process rather than an energetic one. Using the kinetic theory of phonon transport, we present a simple analytical model which can be used to evaluate the lattice thermal conductivity of nano-crystalline materials where the ratio can be considered as an average density of excess free volume. While this study is focused on FCC crystalline materials, where inter-atomic potentials and corresponding defect structures have been well studied in the past, the results would be quantitatively applicable for semiconductors in which heat transport is mainly due to phonon transport.

The existence of a critical length scale in regularised friction

We study a regularisation of Coulombs friction law on the propagation of local slip at an interface between a deformable and a rigid solid. This regularisation, which was proposed based on experimental observations, smooths the effect of a sudden jump in the contact pressure over a characteristic length scale. We apply it in numerical simulations in order to analyse its influence on the behaviour of local slip. We first show that mesh convergence in dynamic simulations is achieved without any numerical damping in the bulk and draw a convergence map with respect to the characteristic length of the friction regularisation. By varying this length scale on the example of a given slip event, we observe that there is a critical length below which the friction regularisation does not affect anymore the propagation of the interface rupture. A spectral analysis of the regularisation on a periodic variation of Coulombs friction is conducted to confirm the existence of this critical length. The results indicate that if the characteristic length of the friction regularisation is smaller than the critical length, a slip event behaves as if it was governed by Coulombs law. We therefore propose that there is a domain of influence of the friction regularisation depending on its characteristic length and on the frequency content of the local slip event. A byproduct of the analysis is related to the existence of a physical length scale characterising a given frictional interface. We establish that the experimental determination of this interface property may be achieved by experimentally monitoring slip pulses whose frequency content is rich enough.