Narayan K. Sundaram

Surface folding in metals: a mechanism for delamination wear in sliding

Using high-resolution, in situ imaging of a hard, wedge-shaped model asperity sliding against a metal surface, we demonstrate a new mechanism for particle formation and delamination wear. Damage to the residual surface is caused by the occurrence of folds on the free surface of the prow-shaped region ahead of the wedge. This damage manifests itself as shallow crack-like features and surface tears, which are inclined at very acute angles to the surface. The transformation of folds into cracks, tears and particles is directly captured. Notably, a single sliding pass is sufficient to damage the surface, and subsequent passes result in the generation of platelet-like wear particles. Tracking the folding process at every stage from surface bumps to folds to cracks/tears/particles ensures that there is no ambiguity in capturing the mechanism of wear. Because fold formation and consequent delamination are quite general, our findings have broad applicability beyond wear itself, including implications for design of surface generation and conditioning processes.

Geometric flow control of shear bands by suppression of viscous sliding.

Shear banding is a plastic flow instability with highly undesirable consequences for metals processing. While band characteristics have been well studied, general methods to control shear bands are presently lacking. Here, we use high-speed imaging and micro-marker analysis of flow in cutting to reveal the common fundamental mechanism underlying shear banding in metals. The flow unfolds in two distinct phases: an initiation phase followed by a viscous sliding phase in which most of the straining occurs. We show that the second sliding phase is well described by a simple model of two identical fluids being sheared across their interface. The equivalent shear band viscosity computed by fitting the model to experimental displacement profiles is very close in value to typical liquid metal viscosities. The observation of similar displacement profiles across different metals shows that specific microstructure details do not affect the second phase. This also suggests that the principal role of the initiation phase is to generate a weak interface that is susceptible to localized deformation. Importantly, by constraining the sliding phase, we demonstrate a material-agnostic method—passive geometric flow control—that effects complete band suppression in systems which otherwise fail via shear banding.

Numerical Analysis of Double Contacts of Similar Elastic Materials

A fast numerical method based on the Cauchy singular integral equations is presented to determine the contact pressure and extents for the contact of two-dimensional similar isotropic bodies when the contact area consists of two separate regions. The partial-slip problem is then solved to determine shear tractions using an equivalence principle. The extents of the contact are not all independent but related to a compatibility equation constraining the displacements of an elastic body in contact with an equivalent rigid body. A similar equation is found for the extents of the stick zones in partial-slip problems. The effects of load history are incorporated into the shear solution. The method is applicable to a wide range of profiles and it provides significant gains in computational efficiency over the finite element method (FEM) for both the pressure and partial-slip problems. The numerical results obtained are compared with that from the FEM for a biquadratic indenter with a single concavity and showed good agreement. Lastly, the transition behavior from double to single contacts in biquadratic profiles is investigated.

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.

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.

A micropolar peridynamic theory in linear elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems

Distinct stick-slip modes in adhesive polymer interfaces

Abstract 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 slow propagation speeds. We study the dynamics of a model polymer interface using coupled force measurements and high speed 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.

Shape and eccentricity effects in adhesive contacts of rodlike particles.

The effects of shape and eccentricity on adhesion and detachment behavior of long, rodlike particles in contact with a half-space are analyzed using contact mechanics. The particles are considered to have cross sections that are squarish, oblate, or prolate rather than circular. Such cross sections are represented very generally by using superellipses. The contact mechanics model allows deduction of closed-form expressions for the contact pressure, load-contact size relation, detachment load, and detachment contact size. It is found that even relatively small deviations in shape from a cylinder have a significant influence on the detachment load. Eccentricity also affects the adhesive behavior, but to a lesser extent, with oblate shapes requiring larger separation loads than prolate shapes. The load-contact size solution reduces to that for a right-circular, cylindrical rod when the appropriate limit is taken. The detachment behavior of right-circular cylinders is also found to be mimicked by an entire family of rod shapes with different cross sections.

Mechanics of Modulation Assisted Machining

The controlled application of low-frequency modulation to machining — Modulation Assisted Machining (MAM) — effects discrete chip formation and disrupts the severe contact condition at the tool-chip interface. The role of modulation in reducing the specific energy of machining with ductile alloys is demonstrated using direct force measurements. The observed changes in energy dissipation are analyzed and explained, based on the mechanics of chip formation.Copyright

Multiple Contacts of Similar Elastic Materials

The contact problem for an elastic body indenting a similar half-space resulting in multiple contacts is important for various applications. In this paper an exact fast numerical method based on singular integral equations is developed to solve the normal contact (including applied moments), partial slip, and shear-reversal problems for such contacts. The contact patches are considered to be fully interacting, with no simplifying assumptions. A contact algorithm to automatically generate trial values based on an analysis of the profile and to subsequently guide the solver toward convergence is detailed. Some applications are discussed, including regular rough cylinders and a regularly rough flat punch with rounded edges. The examples involve between 3 and 29 contacts. The partial slip problems include demonstration of cases with multiple stick zones in some contact patches and complete sliding in others.