Viscoplastic Layer Research Articles

Turbulent impingement jet cleaning of thick viscoplastic layers

An experimental study is conducted on the use of a normally impinging turbulent water jet (with the Reynolds number of Re≈11800), for cleaning thick layers of a Newtonian fluid and two viscoplastic fluids (i.e., transparent Carbopol solutions). The layer thickness is larger than the jet radius. Non-intrusive techniques are used to track the geometrical features of the cleaning process in real time. The effects of layer thickness and fluid yield stress on removal behavior, including cleaning radius, cavity radius, and angle, are investigated. A yield stress promotes the initial formation of a blister rather than a cavity, and the rate of removal decreases with increasing layer thickness and yield stress. A relation is presented for the growth of the cavity radius, which fits our experimental observations well. A comparative analysis of submerged and impinging jets reveals, for the first time, the role of air entrainment in the process, with bubble characteristics such as trajectory, size distribution (diameter), and velocity being determined by the yield stress.

Scraping of a thin layer of viscoplastic fluid

We analyze the scraping of a thin layer of viscoplastic fluid residing on a horizontal surface by a translating rigid scraper. This motion generates a mound of fluid upstream of the scraper and a residual layer behind it, both of which are modelled using a shallow layer theory for a Bingham or Herschel-Bulkley fluid. The flows ahead of and behind the scraper are coupled by the motion in the gap under the scraper, which is driven both by the translation of the scraper and by the induced pressure gradient due to the difference in flow thickness upstream and downstream. When the gap between the scraper and the underlying surface is sufficiently small, we find that a steady state emerges after a relatively long transient and that en route to this state, the unsteady dynamics exhibit a variety of regimes that are self-similar to leading order. We construct these solutions explicitly and derive key scalings for the temporal development of the flowing viscoplastic layer, as well as identifying the timescales at which there are transitions between the regimes. These predictions are confirmed by comparison with results from the numerical integration of the full system. Finally, we report results from preliminary laboratory experiments, which are compared with predictions from the shallow-layer theory, obtaining reasonable agreement once a slip boundary condition is included in the model, as motivated by experimental observations. Published by the American Physical Society 2024

A viscoelastic-viscoplastic damage model with a cohesive zone in between

The present research sheds light on a first viscoelastic-viscoplastic damage model with a cohesive zone in between, implemented in finite element method. The viscoelastic layer, and viscoplastic layer were developed individually, which were then combined. The damage evolution was then observed, taking into account the rate-dependent behaviors. Three damage evolutions were possible, which are ‘viscoelastic-viscoplastic coupled damage, viscoelastic rate-dependent damage, and viscoplastic rate-dependent damage’. It was found during damage that the failure of one layer may be understood through the micromechanics of another layer, and that the work of separation was dependent on interfacial strength. The cohesive zone was thus observed as separated zone, and deformed zone. The separated zone signified viscoelastic activity, while the deformed zone signified viscoplastic activity. It was shown that the developed model may evolve as a function of measured properties. The model is capable of performing extensive dimensionless parametric studies. This finds application in biomedical science, structural engineering, materials design, among others.

Mechanical and wear behavior of al-steel solid state cladding produced by friction stir surfacing

Friction surfacing (FS) is a solid-state cladding method that produces a coating with minimum dilution and good metallurgical bonding. Deposition of aluminium over mild steel with using fusion based joining process is not feasible sue to the formation of iron aluminide and Fe and Al are metallurgically immiscible to each other. Hence, deposition of aluminium on steel with solid-state condition is feasible and most viable option. During the process, a rotating consumable rod is rubbed against the substrate plate under an applied axial load. The friction between rod and substrate generates a visco-plastic layer at the end of rod tip. The high temperature and pressure at interfaces aids in the cladding of the rod material on the substrate. Aluminium alloy 6351 T6 rod of 22 mm diameter was used as consumable material for surfacing on a 6mm thick SA516 Gr70 steel substrate plate. Optimized process parameters were used for the final experimental trials. Multilayer samples generated at constant Friction Surfacing variables were subjected to Pin-on-disc wear test at 40N load. Mechanical interlocking was also observed at the interface of the layers. The process was also observed to produce extremely fine grain microstructures of the deposited material due to the hot forging action involved resulting in superior wear properties.

Buoyant miscible viscoplastic displacements in vertical pipes: Flow regimes and their characterizations

We experimentally study miscible displacement flows of a light Newtonian fluid by a heavy viscoplastic fluid, in a vertical pipe with a large aspect ratio (δ−1≫1). We use camera imaging, laser-induced fluorescence, and ultrasound Doppler velocimetry techniques, to capture and process data. Four dimensionless parameters, namely, the Reynolds (Re), Bingham (B), viscosity ratio (M), and densimetric Froude (Fr) numbers (or their combinations), mainly govern the flow dynamics. We identify and characterize three distinct flow regimes, including plug, separation, and mixing regimes, while we describe each regime's dynamics in detail, particularly in terms of the velocity and concentration fields as well as the displacement front velocity. In addition, we analyze the plug regime concerning the residual wall layers, the separation regime in terms of the separation dynamics, spatiotemporal separation zone, and viscoplastic layer thinning, and the mixing regime regarding the mixing index and macroscopic diffusion. Finally, we develop a simplified model to help delineate the flow regime classification, in the plane of Re/Fr2 and M.

Investigation of “elephant skin” on UHPC surface via a new test method: Influencing factors, formation mechanism and control measures

Shortly after the mixing of ultra-high performance concrete (UHPC), a viscoplastic layer forms on the surface, which is often colloquially called elephant skin. This layer can hinder the venting, through which air bubbles accumulate below the concrete surface, causing poor surface quality and aesthetics after finishing or resulting in an inferior composite in the case of multi-layer structural components. This paper aims to improve the surface performance of UHPC by reducing the effect of elephant skin. In the present work, the influence of various factors on the “elephant skin” formation on UHPC surface is firstly investigated using a newly developed test method that measures the development of the surface resistance of “elephant skin” on UHPC with time, based on the Vicat apparatus for testing the setting time of cement. Then, the formation mechanism of “elephant skin” on the surface of UHPC is discussed. Finally, some measures to minimize the effect of “elephant skin” on the UHPC surface are proposed. The results reveal that next to controlling the ambient relative humidity (RH) and temperature, an optimization of the concrete mix composition and manufacturing process, such as an increase of superplasticizer (SP) dosage, paste content and water-to-binder (W/B) ratio can help to slow down the “elephant skin” formation on UHPC surface, minimizing its negative effect while without significantly compromising the concrete compressive strength.

Two-layer gravity currents of generalized Newtonian fluids

We examine gravity-driven two-layer flow of generalized Newtonian fluids. The two layers have different densities and constitutive laws, and the flow is assumed to be shallow and inertia-less. A depth-integrated model for flow over one-dimensional topography is derived with the volume fluxes written in terms of functions that depend only on the fluids’ rheology. The model enables two-layer flows of any combination of generalized Newtonian fluids to be computed without explicit knowledge of the velocity profile. For viscoplastic layers, the formulation provides a convenient way to determine the layer evolution without having to analyse the multiple yield surfaces that may occur. Motivated by the lubricated flow of ice sheets, we analyse the case in which the lower layer is relatively thin. The model reduces to a one-layer flow with an effective slip law that encapsulates the thickness and generalized Newtonian rheology of the lower layer. For flow over two-dimensional topography, a depth-integrated two-layer model cannot generally be derived because the direction of the shear stress varies across the lower layer. Progress is possible in the special cases that the lower layer is Newtonian or is relatively thin.

Cleaning-in-place: Case studies of coupled flows and complex fluids

Many modern food, pharmaceutical and fast moving consumer goods manufacturing facilities clean their process equipment by automated circulation of cleaning solutions through the units. The soiling layers are often non-Newtonian, soft solids while the fluid mechanics are inherently dynamic and involve coupling between the cleaning solution and the soil. This talk will present results from recent studies of the removal of viscoplastic layers from smooth rigid surfaces by coherent, turbulent, impinging water jets, where there is a rich range of fluid phenomena on display. We pose the engineering question: what level of detailed modelling do we require to obtain acceptable predictive capability, and along the way introduce some of the challenges that colleagues might want to look into.

Microbuckling of viscoplastic composites by the high-fidelity generalized method of cells micromechanics

The high-fidelity generalized method of cells (HFGMC) micromechanical analysis is employed for the prediction of microbuckling stresses of composite materials which are composed of elastic–viscoplastic constituents. The inelastic material behavior is represented by a unified viscoplasticity theory which can model non-proportional loading paths, namely it is capable of providing the effect of axial loading on the reduction of shear modulus which dominates the microbuckling. By applying an incremental procedure and in conjunction with the instantaneous stiffnesses of the viscoplastic material, an eigenvalue problem at each time step is established by the HFGMC micromechanical method, which is modified to include the buckling terms arising from the linearization of the nonlinear equations of equilibrium. These buckling terms are provided by HFGMC analysis which predicts the local stress field and the effective current tangent properties of the composite. The present approach is verified by comparison of its predictions with an exact solution that can be established in the special case of composites that consist of periodic viscoplastic layers. Applications are given for the prediction of the microbuckling stresses of bi-layered, continuously reinforced and aligned short-fiber viscoplastic composites. In addition, the microbuckling stresses of viscoplastic lattices and layered plates are presented.

In-situ measurement of the critical stress of viscoplastic soil layers

Predicting the removal of residual layers or soiling deposits from process equipment surfaces requires knowledge of the rheology of the layer material. Removing a sample for analysis in a rheometer is likely to disrupt its structure, thereby changing its rheological behaviour. The millimanipulation device presented by Magens et al . (2017, J. Food Eng , 197 , 48–59) was employed here as an in situ rheometer to estimate the critical (yield) stress of layers of viscoplastic food and fast-moving consumer goods (FMCG) products on steel plates using the protocol reported by Tsai et al . (2020, J. Food Eng , 285 , 48–59). Measures of the critical stress of 15 materials, including spreads, cosmetics and ointments, were obtained on a rotational rheometer using increasing shear stress ramp, shear stress step, and oscillatory shear stress amplitude sweep testing. Reasonably good agreement ( ± 30 % ) was obtained between these values (ranging from 70 to 2000 Pa) and those obtained with the millimanipulation device, indicating that the latter could be used to study soil layers in situ . Better agreement was obtained for materials with a high yield stress, where the shape of the accumulated berm was more easily identified. The use of the millimanipulation device to quantify spreadability is compared with the strain-energy-at-yield metric obtained from rotational rheometry. • The deformation of viscoplastic layers was studied using a scraping blade device. • Interrupted motion testing allows the yield stress to be estimated. • Layers of food and FMCG products with critical stresses 70-2000 Pa were tested. • Reasonable agreement obtained between in situ testing and rheometer.

Modelling the cleaning of viscoplastic layers by impinging coherent turbulent water jets

Impinging liquid jets are widely used to clean unwanted soil layers from the walls of structures and vessels. When the soil is a thin layer of an immiscible viscoplastic material, removal involves the growth of a cleared area (which is circular for a jet impinging normally) bounded by a berm of displaced material. Glover et al. [1] presented a semi-empirical model relating the rate of removal to the momentum flow rate in the liquid film. We present a first-order model for cleaning thin layers of these materials based on the rate of viscous dissipation in a shallow wedge of material at the cleaning front. This yields a result of the form of the model in [1], with expressions linking the kinetic parameters to measurable quantities including the rheology of the soil. The fully coupled problem is not solved: the wedge angle and residual layer thickness need to be specified and were obtained here by fitting to the data. The model is compared with experimental results obtained for three soft solids – two petroleum jellies and a soft paraffin – which exhibited Bingham plastic behaviour and creep, for jet Reynolds numbers between 10,000-37,000, and 0.1<h¯/δo<1.5, where h¯ is the average film depth and δo the layer thickness. The data show reasonable agreement with the model.

Onset of flow in a vibrated thin viscoplastic layer

The onset of flow in vibrated layer of viscoplastic fluid is investigated theoretically, using a lubrication approximation. The rheological behavior of the fluid is described by the Herschel–Bulkley model. The equation describing the evolution of the free surface is derived. Four different regimes are found depending on the ratio χ of the gravitational acceleration to the acceleration of vibration and the ratio of the yield stress to the shear-stress at the vibrated wall. Furthermore, a necessary condition for instability is derived. The different regimes are illustrated in the case of a 1D problem.

The Acheron Dorsum on Mars: A novel interpretation of its linear depressions and a model for its evolution

The Acheron Dorsum north of Olympus Mons on Mars is a unique 800 km-long arcuate ridge apparently unrelated to other adjacent morphologies. Acheron Dorsum is crossed by deep and wide fractures (“fossae”, here referred to also as Linear Depressions or “LDs”), commonly interpreted as grabens formed by local lithosphere stress in response to endogenous mantle upwelling. We suggest an alternate view that the linear depressions may result from gravitational self-adjustment of a loose deposit similar to the Deep-Seated Gravitational Slope Deformations (DSGSD or Sackung), a kind of slow mass movement well documented on Earth. Numerical simulations based on a finite difference numerical model devised for terrestrial DSGSDs reproduce the timing and position of LDs reasonably well provided that the viscosity of the viscoplastic layer is between ≈71015 and ≈1017 Pas. While rock masses typically exhibit much higher values, based on comparison with glacial examples, we find that these viscosities could be compatible to a rock–ice mixture.This leads to the hypothesis that the rock underneath Acheron Dorsum may be highly fragmented and that ice might have been involved in its deformation. Our hypothesis could shed light on the puzzling stress pattern on Acheron Dorsum, which follows approximately the ridge, without requiring the presence of hypothetical small-scale, endogenous currents.

On the solvability of incompressible Stokes with viscoplastic rheologies in geodynamics

AbstractPlasticity/failure is an essential ingredient in geodynamics models as earth materials cannot sustain unbounded stresses. However, many questions remain as to appropriate models of plasticity as well as effective solvers for these strongly nonlinear systems. Here we present some simplified model problems designed to elucidate many of the issues involved for the description and solution of viscoplastic problems as currently used in geodynamic modeling. We consider compression and extension of a viscoplastic layer overlying an isoviscous layer and introduce a single plastic yield criterion which includes the most commonly used viscoplasticity models: von Mises, depth‐dependent von Mises, and Drucker‐Prager. We show that for all rheologies considered, successive substitution schemes (aka Picard iteration) often stall at large values of the nonlinear residual, producing spurious solutions. However, combined Picard‐Newton schemes can be effective for rheologies that are independent of the dynamic pressure. Difficulties arise when solving incompressible Stokes problems for rheologies that depend on the dynamic pressure such as Drucker‐Prager viscoplasticity. Analysis suggests that incompressible Stokes can become ill‐posed when the dependence of the deviatoric stress tensor on dynamic pressure (i.e., ) becomes large. We demonstrate empirically that, in these cases, Newton solvers can fail by introducing spurious shear bands and discuss the consequence of interpreting the results of nonconverged computations. Even for problems where solvers converge, Drucker‐Prager viscoplasticity can produce dynamic pressures that deviate significantly from lithostatic and both the velocity and pressure fields should be evaluated to determine whether solutions are geologically reasonable.

Dynamics of the removal of viscoplastic fluids from inclined pipes

The dynamics of the removal of a viscoplastic fluid by a Newtonian fluid is investigated experimentally and theoretically in an inclined pipe based on our previous studies on near-horizontal and highly inclined configurations. The fluids are miscible. The displacing Newtonian fluid is heavier than the displaced viscoplastic one i.e. the configuration is density-unstable. In our earlier work it was found that two major flow regimes, namely center-type and slump-type, might occur depending on the density difference. These flows are explored in great details through measurements of the displacement speeds and hydraulic Reynolds numbers. The residual viscoplastic layer unevenness is characterized revealing that the flows are in the range of large roughness regimes. Through an integrated experimental-theoretical approach, estimates of the interfacial and wall shear stresses are given which is of great importance in designing the displacement and cleaning processes involving fluids with yield stress. Accompanied by Ultrasonic Doppler Velocimetry (UDV) data, the dynamics of the removal of the viscoplastic fluid from a pipe is elucidated suggesting three distinct phases in the displacement process namely a plug flow, inertial multi-dimensional flow at the displacing front and steady multi-layer developed flow. Finally, the viscoplastic displacement flow results are compared against the predictions of the closure model, previously proved successful for Newtonian and shear-thinning fluids displacement in pipe. It is found that in the case of viscoplastic fluids the closure model always over predicts the displacing front velocity due to the inertial stresses present at the front not captured in the model.

Experimental and numerical studies of initial cracking in CFRP cross-ply laminates

This work is concerned with the conditions for formation of the first (initial) cracks in composite laminates with cutouts or ply drop-offs subjected to in-plane loading. We study here the crack formation on the free edge of CFRP cross-ply laminates experimentally and by numerical stress and failure analysis. The free-edge surface strains are measured by the digital image correlation (DIC) technique. The numerical analysis consists of a two-scale approach, where the macro-level analysis is performed with a three-dimensional finite-element method (3D FEM) and the micro-level analysis uses a periodic unit-cell (PUC) in the transverse plies. The constitutive assumption made for the macro-level analysis is an orthotropic linear thermo-elastic solid for the unidirectional plies with a thin isotropic viscoplastic layer between the longitudinal and transverse plies. In the PUC, the fibers are assumed linear elastic, while the matrix is modeled as an elastic–viscoplastic solid. Crack formation is assumed to occur in the matrix by the dilatation induced brittle failure mechanism for which the dilatation energy density criterion is used.

Steel-aluminum layered composite with a nanostructured intermediate layer

The results of an investigation into the influence of the degree of deformation on the structure of components of the layered steel-aluminum composite are presented. It is shown that the noticeable structural variations start from reduction ratio ɛ > 75%, or e > 1.54 in logarithmic units. The plastic deformation mechanism of a brittle intermetallic layer is described. It is shown that the viscoplastic intermediate layer of the steel-aluminum layered composite can be obtained by rolling when bringing the deformation ratio to 90%. As for the submicron structure, it can be obtained at ɛ > 95%, or e > 3.

Shear flows in a plane viscoplastic layer with the plasticity criterion weakly depending on pressure

A possible formulation of a spatial boundary value problem of viscoplastic flow is presented for the general case in which the criterion of plasticity depends on all invariants of the stress tensor. In the plane strain condition, this criterion involves pressure and stress intensity. If the behavior of the yield surface as a constitutive function of the medium weakly depends on the pressure, then one can seek solutions of the problems in the form of perturbations near the solutions obtained in using the classical von Mises-Hencky criterion. Linearized problems in perturbations simulating steady motion of a heavy viscoplastic layer on an inclined plane and a steady flow under the action of a pressure drop in a flat layer are investigated. In the first problem, the presence of weak dependence of the plasticity criterion on the pressure in the model keeps the one-dimensional nature of the problem, while, in the other problem, this makes the task essentially two-dimensional.

Quasi-static compression and spreading of an asymptotically thin nonlinear viscoplastic layer

The problem of quasi-static compression and spreading (squeezing) of a thin viscoplastic layer between approaching absolutely rigid parallel-arranged plates is solved using asymptotic integration methods rapidly developed in recent years in the mechanics of deformable thin bodies. A solution symmetric about the coordinate axes is sought in the same region of the layer as in the classical Prandtl problem. The layer material is characterized by a yield point and a hardening function relating the intensities of the stress and strain rate tensors. The conditions of no-flow and reaching certain values by tangential stresses are imposed on the plate surfaces. The coefficients at the terms of the asymptotic expansions corresponding to the minus first and zero powers of the small geometrical parameter are obtained. An approximate analytical solution in the case of power hardening and large Saint-Venant numbers is given. The physical meaning of the roughness coefficient characterizing the cohesion between the plates and viscoplastic material is discussed.

Viscoplastic lubrication theory with application to bearings and the washboard instability of a planing plate

We consider lubrication theory for a two-dimensional viscoplastic fluid confined between rigid moving boundaries. A general formulation is presented which allows the flow field and pressure to be calculated given an arbitrary rheological model; the Herschel–Bulkley law is used for illustration. The theory is first applied to a (full) viscoplastic journal bearing with arbitrary motions allowed for the inner cylinder (either prescribed, or arising from an imposed load and torque). Conditions are derived determining when motion is arrested by the yield stress. We next apply the theory to a slider bearing filled with Bingham fluid, computing the lift force on the bearing and the fluid flux through it. The results are then extended to model an inclined plate that is towed at constant horizontal speed over a shallow viscoplastic layer but is able to move vertically. Steady planing solutions are stable at low towing speeds, but give way to unstable vertical oscillations of the plate at higher speed; the yield stress has a relatively weak effect on this instability. The pattern imprinted on the fluid layer by the oscillations provides an analogue of the washboard phenomenon on gravel roads.