K L Johnson

Bio: K L Johnson is an academic researcher from University of Cambridge. The author has contributed to research in topics: Contact mechanics & Surface forces apparatus. The author has an hindex of 15, co-authored 16 publications receiving 8023 citations.

Surface energy and the contact of elastic solids

Abstract: This paper discusses the influence of surface energy on the contact between elastic solids. Equations are derived for its effect upon the contact size and the force of adhesion between two lightly loaded spherical solid surfaces. The theory is supported by experiments carried out on the contact of rubber and gelatine spheres.

Shear behaviour of elastohydrodynamic oil films

Abstract: A simple constitutive equation is proposed for the isothermal shear of lubricant films in rolling/sliding contacts. The model may be described as nonlinear Maxwell, since it comprises nonlinear viscous flow superimposed on linear elastic strain. The nonlinear viscous function can take any convenient form. It has been found that an Eyring 'sinh law' fits the measurements on five different fluids, although the higher viscosity fluids at high pressure are well described by the elastic/perfectly plastic equations of Prandtl-Reuss. The proposed equation covers the complete range of isothermal behaviour: linear and nonlinear viscous, linear viscoelastic, nonlinear viscoelastic and elastic/plastic under any strain history. Experiments in support of the equations are described. The nonlinear Maxwell constitutive equation is expressed in terms of three independent fluid parameters: the shear modulus $G$, the zero-rate viscosity $\eta $ and a reference stress $\tau _{0}$. The variations of these parameters with pressure and temperature, deduced from the experiments, are found to be in broad agreement with the Eyring theory of fluid flow.

Surface interaction between elastically loaded bodies under tangential forces

Abstract: This paper describes an experimental investigation of the micro-displacement between two bodies in contact under the action of a tangential force less than that of limiting friction. Experiments have been performed for the unlubricated contact of a hard steel ball with a hard steel flat, under a range of normal loads, using balls of varying diameter. Measure­ments of micro-displacement have been made under the action of both steady and oscillating tangential forces. In the latter case vibrational energy is dissipated at the interface and fretting of the surfaces occurs. The mechanism of these processes has been studied and is discussed. The quantitative results of the experiments provide considerable support for Mindlin’s theoretical elastic analysis. For small tangential forces the displacements are almost entirely elastic and the compliance of the two bodies is given exactly by the elastic theory. As the tangential force approaches the value to cause slipping, the displacement exhibits a non­-elastic component arising from the relief of an infinite shear stress which ideally elastic behaviour predicts at the boundary of the circle of contact. Observation of the surfaces after subjection to a sustained oscillating force showed that intimate metal-to-metal contact occurs only at the crests of the surface asperities as sug­gested by Bowden & Tabor. Fretting takes place over an annular area round the boundary of the contact circle and spreads radially inwards with increasing tangential force. Measure­ments of the energy loss suggest that for small amplitudes of oscillating force the theoretic­ally infinite stress is accommodated by predominantly elastic distortion of the surface asperities. Under larger forces, however, the asperities are deformed plastically through large strains, which leads to eventual fatigue and fretting of the surfaces over the annular region of high stress. The amount of energy so dissipated agrees quantitatively with that calculated by Mindlin, showing that the degree of plastic strain occurring at the interface is governed by the stress distribution in the elastic hinterland.

An alternative to the Maugis model of adhesion between elastic spheres

Abstract: The problem of how contact between elastic spheres is modified by the surface forces which act between them is becoming of great interest with the possibility of studying such contacts experimentally in the atomic force microscope and in the surface force apparatus. Experiments are frequently interpreted with the help of the JKR adhesion theory, in which the action of the surface forces is represented by the change in surface energy involved in uniting or separating the two surfaces. This has two drawbacks: it is strictly valid only when the Tabor parameter is large, though in fact it appears that the condition is sufficient, and it gives no help with the attractive forces before contact takes place, which may cause `jumping on'. However, it has one enormous virtue: the results are described by simple algebraic equations, which all can manipulate as required. In contrast, full numerical analyses, such as the pioneering solution by Muller, Derjaguin and Toporov and a more recent solution by Greenwood, give only the results the authors choose to pass on. These establish when the JKR solution is valid and indicate the ways in which it is incomplete; but stop there. For this reason, an analytical solution by Maugis using a simplified force-separation law, that the adhesive stress has a fixed value whenever the separation is less than a critical distance, has proved most valuable. However, it too has a drawback, though a minor one: the shape of the gap involves elliptical integrals, which is inconvenient when the extension to visco-elastic spheres is considered. Here we present an alternative to the Maugis theory, based on the combination of two Hertzian pressure distributions. The results are very close to those of the Maugis model, but the gap shape now involves only elementary functions.

Plastic ratchetting as a mechanism of metallic wear

Abstract: Many researchers have observed metallic wear debris in the form of very thin platelets. In particular Akagaki & Kato (1987) revealed how such debris can be formed by progressive plastic extrusion from the edges of the irregularities on the softer of two sliding surfaces. This behaviour has been reproduced in experiments reported here, in which a single soft asperity is modelled by a blunt copper wedge in sliding contact with a flat hard steel surface under conditions of boundary lubrication. This progressive extrusion with continuous sliding is attributed to ‘plastic ratchetting’ and two ways in which the process can be driven have been identified: (i) pummelling of the soft surface by the asperities of the hard surface and (ii) cyclic stressing of the soft surface by the stress concentrations which occur at the edges of a hard slider. The kinematical shakedown theorem from the theory of plasticity is used to determine the asperity contact pressure necessary to drive these ratchetting processes. A significant feature of this mechanism is that it can occur under frictionless conditions.

Thin Film Materials: Stress, Defect Formation and Surface Evolution

Abstract: 1. Introduction and overview 2. Film stress and substrate curvature 3. Stress in anisotropic and patterned films 4. Delamination and fracture 5. Film buckling, bulging and peeling 6. Dislocation formation in epitaxial systems 7. Dislocation interactions and strain relaxation 8. Equilibrium and stability of surfaces 9. The role of stress in mass transport.

Mussel-Inspired Adhesives and Coatings

Abstract: Mussels attach to solid surfaces in the sea. Their adhesion must be rapid, strong, and tough, or else they will be dislodged and dashed to pieces by the next incoming wave. Given the dearth of synthetic adhesives for wet polar surfaces, much effort has been directed to characterizing and mimicking essential features of the adhesive chemistry practiced by mussels. Studies of these organisms have uncovered important adaptive strategies that help to circumvent the high dielectric and solvation properties of water that typically frustrate adhesion. In a chemical vein, the adhesive proteins of mussels are heavily decorated with Dopa, a catecholic functionality. Various synthetic polymers have been functionalized with catechols to provide diverse adhesive, sealant, coating, and anchoring properties, particularly for critical biomedical applications.