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This paper presents a nanoscale-inspired continuum model to capture the coupling of adhesion and friction in contact-mechanics problems. The method relies on Green's function molecular dynamics to calculate the elastic body fields and on a phenomenological mixed-mode coupled cohesive-zone model to describe the interplay between normal and tangential tractions, i.e. adhesion and friction. While the presented formulation is applicable to linearly elastic solids with generic surface roughness, the focus of our analysis is on the indentation of an array of circular rigid punches into a flat, deformable solid. Our results show that the coupling between adhesion and friction leads to an increase in the contact size and a decrease in the pull-off load.

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.

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.

© 2016 Elsevier LtdFracture of engineering alloys in the presence of hydrogen commonly occurs by decohesion along grain boundaries via a mechanism known as hydrogen induced decohesion (HID). This mechanism is investigated here by analysing the mode-I fracture of a single crystal with plastic flow in the crystal described by discrete dislocation plasticity (DDP) and material separation (decohesion) modelled using a cohesive zone formulation. The motion of dislocations is assumed to be unaffected by hydrogen diffusion. While the cohesive strength is assumed to be reduced proportional to the local hydrogen concentration. Two limiting cases are analysed: (i) the fast diffusion limit where the hydrogen within the material is assumed to be at chemical equilibrium throughout the loading so that there is a high hydrogen concentration in the regions of high hydrostatic stress around dislocations and near the crack tip and (ii) the slow diffusion limit where we assume that there is no appreciable hydrogen diffusion over the duration of loading and thus the hydrogen concentration remains spatially uniform as in a stress-free material. The lower cohesive strength at high hydrogen concentrations results in reduced dislocation activity around the crack tip and a reduction in the material toughness. In fact, at the highest hydrogen concentrations analysed here, crack growth primarily occurs in an elastic manner. However, surprisingly the calculations predicted that the toughness in the fast diffusion case was no more than 12% lower compared to the slow diffusion case suggesting that the stress concentrations due to the dislocation structures and the crack tip fields have only a minor effect on the toughness reduction in the presence of hydrogen. The DDP calculations are finally used to investigate the sensitivity of the material toughness to the grain boundary cohesive strength. The calculations show that the toughness of materials with a small cohesive opening at the peak cohesive traction are more sensitive to hydrogen loading. We speculate that this result might be used as a guide in grain boundary engineering to design alloys that are less sensitive to hydrogen embrittlement by the HID mechanism.

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.

Experiments show that when an adhesive contact is subjected to a tangential load the contact area reduces, symmetrically or asymmetrically, depending on whether the contact is under tension or compression. What happens after the onset of sliding is more difficult to be assessed because conducting experiments is rather complicated, especially under tensile loading. Here, we provide through numerical simulations, a complete picture of how the contact area and tractions of an adhesive circular smooth punch evolve under mixed-mode loading, before and after sliding. First, the Green’s function molecular dynamics method is extended to include the description of the interfacial interactions between contacting bodies by means of traction–separation constitutive laws that enforce coupling between tension (or compression) and shear. Next, simulations are performed to model sliding of a circular smooth punch against a flat rigid substrate, under tension and compression. In line with the experimental observations, the reduction in the contact area during shear loading is found to be symmetric under tension and asymmetric under compression. In addition, under tensile loading, full detachment is observed at the onset of sliding with a non-zero value of the tangential force. After the onset of sliding and the occurrence of slip instability, the contact area abruptly increases (reattachment), under both tension and compression. For interfaces with high friction, the reattachment occurs only partially. However, a full reattachment is attainable when friction is low.

The relative contact area of rough surface contacts is known to increase linearly with reduced pressure, with proportionality factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{g}}_{\text {r}}$$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document}κ for line and surface contacts and found that their ratio is approximately 0.9. Finally, by analytically deriving the proportionality factor using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{g}}_{\text {r}}$$\end{document}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.

© 2017, The Author(s). Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.