Plastic Boundary Layer Research Articles

Lie group analysis of bingham plastic flow over a straining surface in the presence of magnetohydrodynamic effects and slip conditions

This paper investigates the two-dimensional flow of a Bingham plastic over a straining surface subjected to an externally applied magnetic field and surface slips. The study aims to understand the behavior of such flows and their response to external factors, which has applications in various industrial processes involving complex fluid dynamics. Through Lie group analysis, a new set of similarity transformations are derived to reduce the number of variables in the governing partial differential equations, facilitating a more tractable analysis. These transformations enable the conversion of the partial differential equations into a self-similar system of ordinary differential equations. A high-order, three-stage Lobatto IIIa formula along with appropriate boundary conditions is applied to solve this system. The solutions obtained for various physical parameters lead to several key deductions. It is found that under constant physical parameter values, the velocity layer thickness of the plastic flow is lower compared to the thermal layer thickness, indicating the dominance of the plastic flow behavior. Additionally, an increase in the magnetic field results in a reduction in the thickness of the plastic boundary layer, highlighting the significant influence of magnetic fields on the flow characteristics. These findings provide valuable insights into the control and optimization of processes involving Bingham plastic flows, particularly in the presence of magnetic fields and surface slips.

Effects of interface friction states on plastic deformation in metal surface and bulk

Interface friction at the tool/die-material interface plays a pivotal role in metal plastic processes, significantly impacting material deformation behavior near the contact surface. This study focuses on understanding friction-induced deformation, particularly the plastic boundary layer and surface expansion behavior, at the tool/die-material interface by employing direct in-situ observations, coupled with high-speed imaging and particle image velocimetry techniques. It proves that interface friction determines the wall-slip behaviors and subsequently results in the non-uniform surface expansion distribution. Moreover, our results indicate that the application of lubricant alters the wall-slip velocity and localized surface expansion by 60% and 76%, respectively, at the contact interface. Based on these observations, a quantitative method for assessing the effectiveness of lubrication is proposed.

A Plastic Boundary Layer in Wedge Indentation of Aluminum

We study plastic flow in the vicinity of an indenter-material interface in wedge indentation of aluminum using high speed in situ imaging and particle image velocimetry (PIV) analysis. Displacement and strain fields in the indentation zone are obtained at high-resolution for different indenter angles and two lubrication conditions. These fields can be used to demarcate essential features of the material flow phenomena. The deformed layers close to the indenter wall fit a classical boundary layer profile in the framework of a Bingham-solid. Equivalent Bingham viscosities and boundary layer scaling relations are obtained. The viscosity values appear to reflect the nature of the friction interaction at the indenter-material interface and can potentially be used as a discriminating parameter for evaluating contributions to deformation and dissipation arising from interface friction.

Evidence for Bingham plastic boundary layers in shear banding of metals

We study material flow in the vicinity of single shear bands in high strain-rate (104–105 per second) deformation of metals. Shear band plastic flow, in three different materials, is shown to resemble unsteady planar Couette flow (Stokes first problem) of a Bingham fluid. Equivalent shear band viscosities and yield stresses are obtained, with the former similar to liquid metal viscosities and the latter being ∼0.5 times the band nucleation stress. Reynolds and Bingham numbers, computed based on the shear band displacement measurements, are suggestive of boundary layer formation, consistent with the severe localization of deformation within shear bands.

Modeling of banded structure in friction stir weld in strain rate–hardening materials of Zener–Hollomon type

This article presents a shear localization model for simulating the shear band formation process uniquely associated with friction stir welding. By introducing a thermal and plastic deformation boundary layer definition, the shear band formation process can be modeled as shear localization phenomena using one-dimensional coupled elastic visco-plastic model. Material constitutive behavior is assumed to follow Zener–Hollomon constitutive equation. With this model, shear band width, formation time and propagation speed can be theoretically estimated as a measure of friction stir weldability. As such, the shear band propagation speed serves as a theoretical estimate of the maximum possible welding speed under given base material and welding conditions, such as stir pin rotational speed and torque level. The model is shown to provide reasonable estimates of shear localization parameters when compared with recent experimental data on titanium alloy Ti-6Al-4V. With this model, some fundamental questions such as why titanium alloys are more difficult to weld than aluminum alloys or steels can be more quantitatively addressed. And consequently, potential means for mitigating some of the difficulties in friction stir welding of some of the alloys can be theoretically examined to provide guidance for cost-effective development of welding process parameters for new applications.

The energetics and interactions of random dislocation walls

Regular dislocation walls, where dislocations are spaced equally along the wall direction, are a popular idealization for modelling the arrangement and interactions of excess dislocations in plastic deformation. The assumption of regular walls is motivated by the fact that such walls represent minimum energy arrangements for dislocations of the same sign, and it allows to use the analytically known short-ranged stress fields of such walls for analyzing the structure of plastic boundary layers. In order to critically evaluate the physical robustness of models based on regular walls, we investigate their random counterparts and demonstrate that the energetics and interactions of such non-periodic dislocation arrangements differ completely from the periodic wall arrangements. Implications of our results for the modelling of plastic boundary layers and dislocation-grain boundary interactions are discussed.

Discrete dislocation dynamics simulation and continuum modeling of plastic boundary layers in tricrystal micropillars

Since the mid 80s various gradient plasticity models have been developed for obtaining the plastic response of materials at the micron- and submicron- scales. In particular, gradient terms have been proven to be crucial for understanding size effects in constrained plastic flow, which are related to the emergence of plasticity boundary layers near passive (plastically not deformable) boundaries. In spite of the success of gradient theories in modeling boundary layer formation, there remain unresolved issues concerning the physical interpretation of the internal length scale involved in the theoretical formulation. Physically, boundary layer formation is related to the piling up of dislocations against the boundaries. This phenomenon is investigated by performing discrete dislocation dynamics (DDD) simulations on a tri-crystal with plastically non-deforming grain boundaries. Strain distributions are derived from the DDD simulations and matched with the results of gradient plasticity calculations, in order to identify the internal length scale governing the boundary layer width.

Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium

The self-similar elastoplastic field induced by dynamic expansion of a pressurized spherical cavity is investigated for pressure sensitive solids. Material behavior is described by the hypoelastic model of the Drucker–Prager material with a non-associated flow rule, with arbitrary strain-hardening. We examine in detail the external elastic field, which is expected to develop at a distance from the cavity prior to plastic yielding. A new observation that emerges from that elastic solution is the possible existence of a compressive elastic zone where yielding is prevented since the effective stress remains negative. Simple analytical solutions are given for the fully incompressible elastic/perfectly plastic material with a non-associated flow rule. In particular, we study the influence of plastic pressure sensitivity on the dynamic cavitation pressure. A few useful relations are derived for the cavitation pressure which reveal the coupled effect of plastic pressure sensitivity and material inertia. A separate numerical analysis is given for the fully incompressible strain-hardening solid with a non-associated flow rule. Several numerical illustrations are presented for the solid with an associated flow rule along with a plastic boundary layer analysis for the thin singular zone near the cavity wall.

Material characterization in the chip-tool deformation zone: An application of boundary-layer theory

In high speed metal cutting the shear strain in the secondary shear zone is confined to a plastic boundary layer which is similar to that fluid mechanics. The material behavior in this zone can be described in terms of rheology as a Bingham plastic flow. In the present paper Oldroyd's solution for the plastic boundary layer near a semi-infinite thin knife is applied to the secondary shear zone. Results for boundary-layer thickness, shear strain rate and shear flow strength are obtained and compared with experimental data. The comparisons are encouraging.

Creeping motion of a sphere through a Bingham plastic

A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite-element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionless value of the critical yield stressYgbelow which the material acts as a solid. The computed flow fields differ appreciably from Stokes’ solution. The sphere will fall only whenYgis below 0.143 For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary-layer scalings give the correct forms of the dependence of the drag coefficient and mass-transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value ofYgthere is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations For the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit.

Plastic boundary layers induced by variable wall friction

Plastic boundary layers induced by variable wall friction

Helical flow of plastic materials

An exact closed form solution is given for steady helical flow of plastic materials. Material behaviour is governed by the von-Mises flow rule in conjunction with a rigid/linear-hardening stress-strain characteristic. A restricted version of the general solution is used, as an example, for simulating the helical motion of a rough rigid tool through a circular cylindrical tunnel which is embedded in an infinite plastic medium. It is shown that wall friction induces a plastic boundary layer into the medium. The influence of wall pressure, wall friction and material properties on the behaviour within the boundary layer is discussed. It is also pointed out that no such helical flow pattern is possible for a rigid/perfectly-plastic material.

Couette flow of rigid/hardening solids

Steady Couette-type flow of rigid/linear-hardening solids is investigated. Material behaviour is governed by the von-Mises flow rule. The general flow problem is reduced to a semi-coupled system of two partial differential equations. A few possible boundary conditions are suggested. An exact solution for the plane strain problem is derived. That solution is used, in conjunction with average stress boundary data, for simulating a simple Couette-type flow problem through a curved tube with a rectangular cross section. It is shown that wall friction induces plastic boundary layers into the material. The essential features of these boundary layers are discussed.

An analogy between rectilinear flow of plastic solids and Saint-Venant torsion

This paper presents a new analogy between steady rectilinear flow of plastic materials and Saint-Venant torsion of elastic bars. Material behaviour is modelled as rigid/linear-hardening in conjunction with the von Mises flow rule. Focusing attention on steady flow through pipes with simply connected cross sections and perfectly rough walls, we arrive at a Dirichlet-type problem. The mathematical formulation of this problem is analogous to that of Saint-Venant torsion of elastic bars. This analogy provides a number of exact solutions for steady rectilinear flow of plastic materials, through pipes with various cross sections. A few simple examples are discussed with emphasis on the growth of plastic boundary layers induced by wall friction. The influence of stress singularities near corners, at the boundary, is also investigated.

Application of Plastic Boundary Layer Theory to Metal Machining

In the metal machining operation, material is deformed at high rates in thin plastic zones. This paper explores the possibility that the features of such shear zones can be described by a theory for plastic boundary layers. The analysis draws on Oldroyd’s solution for the two-dimensional plastic flow of a Bingham solid over a flat knife. The way in which such a solution can be adapted to both the secondary and primary deformation zones in machining is described. A theoretical equation is derived that uses material properties to predict the tool-face pressure gradient along the contact length. An analysis for brass gives very good agreement between this approach and the experimental data for the tool-face pressure gradient obtained by Rowe and Wilcox.

Investigations into the reaction of metallic bodies in tribological systems

Surface zones of metallic bodies are formed by reaction layers which often prevent a direct metal-to-metal contact. In most engineering materials, friction forces cause intensified reaction layer formation as a consequence of plastic boundary layer deformation. New surface analysis techniques are described with which the composition of the reaction layer and the presence of individual oxides can be determined. Initial results confirm the reaction layer structure stated in the relevant literature.

Plastic boundary layers

Plastic boundary layers that develop in steady rectilinear flow of rigid/linear-hardening materials, near rough walls, are investigated. The general rectilinear flow problem is reduced to two semi-coupled partial differential equations. A few exact solutions for steady flow through simple cross sections are derived and used for a detailed study of plastic boundary layers. Material behaviour is governed by the usual von-Mises flow rule. The results reveal the influence of wall friction, wall pressure and material hardening on the boundary layers.

A Theoretical Analysis of Temperature Distributions in the High Speed Forging of Hot Steel

The power and forces required to fill a corner cavity in closed-die forging depend on the amount of transient thermal conduction from the heated billet into the cold die. The amount of this conduction is calculated numerically for a steel billet and a steel die, by neglecting the flow of heat in the direction parallel to the movement of metal. The theory takes account of variations in the flow stress consequent on temperature change within the bulk of the plastic material and in the plastic boundary layer near the interface.

The Filling of the Flash Gap in Closed-Die Forging

The pressures required to drive overflow material into a flash gap of annular shape and ever-decreasing thickness are calculated in the presence of thermal conduction into the die. The behavior of the plastic boundary layer near the die surface is also examined in relation to the transient flow of heat into the die. The energy expended in material acceleration is considered in the analysis and is shown to have a dominant influence on power requirement in some instances.