Distinct stick-slip modes in adhesive polymer interfaces

Stick-slip, manifest as intermittent tangential motion between two solids, is a well-known friction instability that occurs in a number of natural and engineering systems. In the context of adhesive polymer interfaces, this phenomenon has often been solely associated with Schallamach waves, which are termed slow waves due to their low propagation speeds. We study the dynamics of a model polymer interface using coupled force measurements and high speed \emph{in situ} imaging, to explore the occurrence of stick-slip linked to other slow wave phenomena. Two new waves---slip pulse and separation pulse---both distinct from Schallamach waves, are described. The slip pulse is a sharp stress front that propagates in the same direction as the Schallamach wave, while the separation pulse involves local interface detachment and travels in the opposite direction. Transitions between these stick-slip modes are easily effected by changing the sliding velocity or normal load. The properties of these three waves, and their relation to stick-slip is elucidated. We also demonstrate the important role of adhesion in effecting wave propagation.Comment: 22 pages, 9 figure

Double and multiple contacts of similar elastic materials

Ongoing fretting fatigue research has focussed on developing robust contact mechanics solutions for complicated load histories involving normal, shear, moment and bulk loads. For certain indenter profiles and applied loads, the contact patch separates into two disconnected regions. Existing Singular Integral Equation (SIE) techniques do not address these situations. A fast numerical tool is developed to solve such problems for similar elastic materials for a wide range of profiles and load paths including applied moments and remote bulk-stress effects. This tool is then used to investigate two problems in double contacts. The first, to determine the shear configuration space for a biquadratic punch for the generalized Cattaneo-Mindlin problem. The second, to obtain quantitative estimates of the interaction between neighboring cylindrical contacts for both the applied normal load and partial slip problems up to the limits of validity of the halfspace assumption. In double contact problems without symmetry, obtaining a unique solution requires the satisfaction of a condition relating the contact ends, rigid-body rotation and profile function. This condition has the interpretation that a rigid-rod connecting the inner contact ends of an equivalent frictionless double contact of a rigid indenter and halfspace may only undergo rigid body motions. It is also found that the ends of stick-zones, local slips and remote-applied strains in double contact problems are related by an equation expressing tangential surface-displacement continuity. This equation is essential to solve partial-slip problems without contact equivalents. Even when neighboring cylindrical contacts may be treated as non-interacting for the purpose of determining the pressure tractions, this is not generally true if a shear load is applied. The mutual influence of neighboring contacts in partial slip problems is largest at small shear load fractions. For both the pressure and partial slip problems, the interactions are stronger with increasing strength of loading and contact proximity. A new contact algorithm is developed and the SIE method extended to tackle contact problems with an arbitrary number of contact patches with no approximations made about contact interactions. In the case of multiple contact problems determining the correct contact configuration is significantly more complicated than in double contacts, necessitating a new approach. Both the normal contact and partial slip problems are solved. The tool is then used to study contacts of regular rough cylinders, a flat with rounded punch with superimposed sinusoidal roughness and is also applied to analyze the contact of an experimental rough surface with a halfspace. The partial slip results for multiple-contacts are generally consistent with Cattaneo-Mindlin continuum scale results, in that the outermost contacts tend to be in full sliding. Lastly, the influence of plasticity on frictionless multiple contact problems is studied using FEM for two common steel and aluminum alloys. The key findings are that the plasticity decreases the peak pressure and increases both real and apparent contact areas, thus ‘blunting’ the sharp pressures caused by the contact asperities in pure elasticity. Further, it is found that contact plasticity effects and load for onset of first yield are strongly dependent on roughness amplitude, with higher plasticity effects and lower yield-onset load at higher roughness amplitudes

Deformation field in deep flat punch indentation and the persistence of dead-metal zones

The indentation of metal by a flat punch is a model system for forming processes and intimately linked with hardness testing. Here, we perform first-in-class, high-fidelity finite element (FE) simulations in an arbitrary Lagrangian-Eulerian (ALE) framework to study the deformation field in deep punch indentation of annealed copper. The use of ALE allows indentation depth to punch width ratios as high as 1.6, while the use of Lagrangian tracer particles reveals pathlines of material transport. Field quantities such as the plastic strain, strain rate and velocity are obtained at high resolution. A low-strain, dead-metal zone (DMZ) that is stationary with respect to the indenter forms immediately below the punch. Crucially, it is found that DMZs are unavoidable in deep punch indentation, forming at the outset and irrespective of the coefficient of friction. However, the area of this zone shrinks as the indentation progresses at a rate that is inversely related to the friction. The simulations thus explain why Prandtl's view of punch indentation, which incorporates DMZs, is physically more accurate than Hill's view. The computations successfully reproduce the strain field inhomogeneity seen in recent in situ imaging experiments. While DMZ formation is impervious to the hardening model used, Zerilli-Armstrong hardening provides more accurate indentation force estimates than Johnson-Cook hardening. Lastly, the residual impression and factors affecting its shape are studied. The sides of impressed metal are never vertical, but at an inclination to it. Methods to modify such features, of potential interest in metal forming, are discussed briefly

Interaction of a Sliding Wedge with a Metallic Substrate Containing a Single Inhomogeneity

Surface folding is a recently discovered unsteady plastic flow mode in metal sliding, caused by microstructure-related spatial heterogeneity. In this work, we simulate a wedge sliding against a metallic specimen with a single, near-surface inhomogeneity or pseudograin, representative of unit asperity-grain interactions. The inhomogeneity is either plastically softer or harder than the surrounding substrate and is perfectly bonded to it. Remarkably, this simple model is able to reproduce numerous experimentally observed aspects of unsteady sliding, including the development of bumps and depressions on the prow, surface self-contact (fold) formation and the development of crack-like damage features on the residual surface. It is found that a hard inhomogeneity causes surface depressions, while a soft inhomogeneity causes surface bumps. Both features develop into folds, and subsequently, crack-like damage features. The model also reproduces the effects of sliding incidence angle, friction and size of inhomogeneity on the sliding response. The propensity to bump and fold formation decreases on increasing the depth at which the inhomogeneity is embedded. Analysis reveals that plastic buckling is a plausible mechanism for the development of perturbations on the surface of the prow. The present model differs from the classical triboplastic models of Oxley and Torrance mainly by way of the added inhomogeneity and is a minimal model to produce folding and associated damage in a single sliding pass. Implications for wear and deformation processing are discussed

Partial slip contact of a rigid pin and a linear viscoelastic plate

This paper analyzes partial slip contact problems in the theory of linear viscoelasticity under a wide variety of loading conditions, including cyclic (fretting) loads, using a semi-analytical method. Such problems arise in applications like metal-polymer contacts in orthopedic implants. By using viscoelastic analogues of Green's functions, the governing equations for viscoelastic partial-slip contact are formulated as a pair of coupled Singular Integral Equations (SIEs) for a conforming (pin-plate) geometry. The formulation is entirely in the time-domain, avoiding Laplace transforms. Both Coulomb and hysteretic effects are considered, and arbitrary load histories, including bidirectional pin loads and remote plate stresses, are allowed. Moreover, the contact patch is allowed to advance and recede with no restrictions. Viscoelasticity necessitates the application of the stick-zone boundary condition in convolved form, and also introduces additional convolved gap terms in the governing equations, which are not present in the elastic case. Transient as well as steady-state contact tractions are studied under monotonic ramp-hold, unload-reload, cyclic bidirectional (fretting) and remote plate loading for a three-element solid. The contact size, stick zone size, indenter approach, Coulomb energy dissipation and surface hoop stresses are tracked during fretting. Viscoelastic fretting contacts differ from their elastic counterparts in notable ways. While they shakedown just like their elastic counterparts, the number of cycles to attain shakedown states is strongly dependent on the ratio of the load cycle time to the relaxation time. Steady-state cyclic bulk hysteretic energy dissipation typically dominates the cyclic Coulomb dissipation, with a more pronounced difference at slower load cycling. However, despite this, it is essential to include Coulomb friction to obtain accurate contact stresses. Moreover, while viscoelastic steady-state tractions agree very well with the elastic tractions using the steady-state shear modulus in load-hold analyses, viscoelastic fretting tractions in shakedown differ considerably from their elastic counterparts. Additionally, an approximate elastic analysis misidentifies the edge of contact by as many as 7 degrees in fretting, showing the importance of viscoelastic contact analysis. The SIE method is not restricted to simple viscoelastic networks and is tested on a 12-element solid with very long time scales. In such cases, the material is effectively always in a transient state, with no steady edge-of-contact. This has implications for fretting crack nucleation. (C) 2016 Elsevier Ltd. All rights reserved

Simulation of Sinuous Flow in Metal Cutting

Sinuous flow is a recently discovered mode of unsteady plastic flow in the cutting of metal involving large plastic strains, extensive material folding, and consequences ranging from paradoxically large cutting forces to poor surface finish. Here we use full-scale simulations to show how sinuous flow, and the concomitant redundant plastic deformation in cutting, are caused by microstructure-related inhomogeneity. The computations are carried out in a Lagrangian continuum mechanics framework using a simple, but effective, pseudograin model to represent metal as a polycrystalline aggregate. Our simulations successfully capture all experimentally observed aspects of sinuous flow in metals, including highly undulating, non-laminar streaklines of flow in the chip, folds, and mushroom-like features, and severely deformed high aspect ratio grains. The simulations also shed light on the mechanism of sinuous flow, and the effect of deformation geometry, explaining why it is suppressed at high rake angles. We find that folding and sinuous flow can occur even at low friction, for grain sizes as small as 25-50 microns, and at very low-cutting speeds. Our study clearly points at the critical importance of incorporating microstructure in cutting simulations of pure metals

THE MICROSTRUCTURAL ORIGIN OF SINUOUS FLOW IN METAL CUTTING

In situ, high-speed imaging experiments have revealed the existence of sinuous flow, a recently discovered mode of chip formation in machining. The origin and consequences of sinuous flow are still being investigated, but it is now known that sinuous flow involves extensive redundant plastic deformation, poor surface finish and paradoxically high cutting forces. Here, we use full-scale simulations to show that microstructure related inhomogeneity is a major cause of sinuous flow. The simulations are conducted in a Lagrangian FE framework, and use a simple pseudograin model to represent the metal workpiece as a polycrystalline aggregate. The model successfully captures all essential features of sinuous flow in metals like OFHC copper and CP aluminum, and points to the importance of including material microstructure in cutting simulations

Slow wave propagation in soft adhesive interfaces

Stick-slip in sliding of soft adhesive surfaces has long been associated with the propagation of Schallamach waves, a type of slow surface wave. Recently it was demonstrated using in situ experiments that two other kinds of slow waves-separation pulses and slip pulses-also mediate stick-slip (Viswanathan et al., Soft Matter, 2016, 12, 5265-5275). While separation pulses, like Schallamach waves, involve local interface detachment, slip pulses are moving stress fronts with no detachment. Here, we present a theoretical analysis of the propagation of these three waves in a linear elastodynamics framework. Different boundary conditions apply depending on whether or not local interface detachment occurs. It is shown that the interface dynamics accompanying slow waves is governed by a system of integral equations. Closed-form analytical expressions are obtained for the interfacial pressure, shear stress, displacements and velocities. Separation pulses and Schallamach waves emerge naturally as wave solutions of the integral equations, with oppositely oriented directions of propagation. Wave propagation is found to be stable in the stress regime where linearized elasticity is a physically valid approximation. Interestingly, the analysis reveals that slow traveling wave solutions are not possible in a Coulomb friction framework for slip pulses. The theory provides a unified picture of stick-slip dynamics and slow wave propagation in adhesive contacts, consistent with experimental observations