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A seamless multi-scale model for contact, friction, and solid lubrication

Periodic Reporting for period 2 - FricLess (A seamless multi-scale model for contact, friction, and solid lubrication)

Reporting period: 2017-06-01 to 2018-11-30

Friction and wear are liable for enormous losses in terms of energy and resources in modern society. Costs related to unwanted friction in industrialised countries are estimated to be about 3% of the gross domestic product. Also, with the advent of miniaturisation, micro-machines are built with moving parts that have large surface-to-bulk ratio, and are therefore more susceptible the effect of frictional forces. Although promising the first micro-motor never worked because of excessive friction. It is therefore important, both from a technological and a financial viewpoint, to find solutions to reduce friction.

Lubrication is a commonly adopted solution to reduce friction. Graphite is a broadly used solid lubricant for large scale applications, while the lubricating properties of a few-layers graphene hold great promise especially for smaller scale applications. At present, our knowledge of the friction and lubrication of rough surfaces is not satisfactory and essentially phenomenological. This is because friction is only deceivingly a simple mechanisms, which instead requires understanding of physical phenomena simultaneously acting at different length scales. The change in contact size, which controls the friction stress, depends on nano-scale phenomena such as atomic de-adhesion, sliding, dislocation nucleation in metals, but also on micro- and macro-scale phenomena as (size-dependent) plastic deformation.

The objective of this work is to reach an unprecedented understanding of metal friction and lubrication by accounting, for the first time, for all relevant phenomena occurring from the atomic to the macro-scale, and their interplay.

To this end, a seamless concurrent multi-scale model will be developed. The power of this new model lies in its capability of describing three-dimensional bodies with realistic roughness in sliding lubricated contact, with the accuracy of an atomistic simulation. This research builds towards a complete picture of metal friction and lubrication. The materials chosen for the proposed research are copper and multi-layer graphene. However, the model that will be developed is general and can be used to study different materials, lubricants and environmental conditions.
The first step of this project involved the development of a modeling technique that we called Green's Function Dislocation Dynamics (GFDD), see [1]. The technique is suited for modeling contact between plastically deformable metal single crystals with dimensions at the micro-scale having a self-affine surface roughness. Plasticity in the crystal is modeled through the nucleation and glide of dislocations on the crystallographic slip planes. The surface of the crystal can be represented as a self-affine rough surface. Thanks to the new model, the roughness of the surface can be described with sufficient accuracy and include all typical wavelength observed in real metal surfaces, i.e. from 100 nm up to 100 μm. Results of the simulations show that the local contact pressure is much less homogeneous than reported in previous studies that considered classical plasticity and is made of very large stress peaks. Moreover, the plastic response is size-dependent. This means that although elastically the response can be scaled with the dimensions of the bodies in contact, plastically smaller systems have to support larger contact pressure. Details can be found in [2].

The GFDD model just discussed is obtained from the combination of two modelling techniques: dislocation dynamics, to model the motion and interaction between dislocations, and Green’s function molecular dynamics (GFMD), which takes care of solving the elastic boundary value problem. The latter is a fast converging boundary element method which was suited for studying contact of semi-infinite incompressible bodies. To make GFMD suitable for being merged into GFDD, it was necessary to extend it to include finite heights, and bodies of generic Poisson’s ratio, given that metals are compressible. This was done for two-dimensional bodies in [3].

In order to compare the two-dimensional results for randomly rough surfaces obtained through the GFDD model, that at this stage of the project is still two-dimensional with two-dimensional elastic results, simulations were performed to find the proportionality constant between area and load [4] using the GFMD model in [3].


[1] S.P. Venugopalan, M.H. Mueser and L. Nicola `Green’s function molecular dynamics meets discrete dislocation plasticity’ Model Simul Mater Sc Eng 25 065018 (2017)
[2] S.P. Venugopalan and L. Nicola `Indentation of a plastically deforming metal crystal with a self-affine rigid surface: A dislocation dynamics' Acta Mater https://doi.org/10.1016/j.actamat.2018.10.020
[3] S.P. Venugopalan, L. Nicola, M.H. Mueser, Green’s function molecular dynamics: including finite heights, shear, and body fields, Model Simul Mater Sc Eng 25 034001 (2017)
[4] J-S. van Dokkum, M.K. Salehani, N. Irani, L. Nicola `On the proportionality between area and load in line contacts’ Tribol Let 66 115 (2018).
Compared to the state of the art the progress has been twofold: new modelling techniques have been developed and thanks to those techniques new insight has been obtained related to the contact response of solids.
As previously mentioned, the Green’s function molecular dynamics model was extended to be suitable for the study of boundary value problems for compressible bodies with finite height, both in two- and in three-dimensions.
The model was then merged to discrete dislocation plasticity in order to study the plastic deformation of metal crystals indented by a rigid rough body. Simulations showed that when accounting for the discreteness of dislocations the mean contact pressure is significantly larger than when plasticity is described through classical plasticity and much less homogeneous. Additionally the response is size dependent, therefore it does not scale with the dimensions of the bodies, or the roughness of the surface.
The model at this point of the project is two-dimensional. Work is in progress to extend it to three dimensions as well as to merge it with a molecular dynamics domain.
Also, work is in progress to study the frictional behaviour of the rough bodies in contact, while so far we have focused only to their contact behavior.
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