Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson‟s ratio f 0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 m with a von Mises model, and from 0.09 to 0.02 m with Drucker-Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

Effect of Coulomb blockade, gold resistance, and thermal expansion on the electrical resistance of ultrathin gold films

Controlling the electrical resistance of granular thin films is of great importance for many applications, yet a full understanding of electron transport in such films remains a major challenge. We have studied experimentally and by model calculations the temperature dependence of the electrical resistance of ultrathin gold films at temperatures between 2 K and 300 K. Using sputter deposition, the film morphology was varied from a discontinuous film of weakly coupled meandering islands to a continuous film of strongly coupled coalesced islands. In the weak-coupling regime, we compare the regular island array model, the cotunneling model, and the conduction percolation model with our experimental data. We show that the tunnel barriers and the Coulomb blockade energies are important at low temperatures and that the thermal expansion of the substrate and the island resistance affect the resistance at high temperatures. At low temperatures our experimental data show evidence for a transition from electron cotunneling to sequential tunneling but the data can also be interpreted in terms of conduction percolation. The resistivity and temperature coefficient of resistance of the meandering gold islands are found to resemble those of gold nanowires. We derive a simple expression for the temperature at which the resistance changes from non-metal-like behavior into metal-like behavior. In the case of strong island coupling, the total resistance is solely determined by the Ohmic island resistance.

An Investigation of Friction During Friction Stir Welding of Metallic Materials

The technique of friction stir welding (FSW) puts effective use frictional heat for the purpose of joining metallic materials. In this research article, we present and discuss an experimental method to determine the coefficient of friction during FSW. The experiments were conducted to study the interaction between the FSW tool (a die steel) and the base metal (a high strength aluminum alloy) at various contact pressures (13MPa, 26MPa, and 39MPa) and rotation speeds (200rpm, 600rpm, 1000rpm, and 1400rpm). The experimental results, the microstructure, and the process temperature reveal the experimental setup to be capable of simulating the conditions during FSW. The coefficient of friction was found to vary from 0.15 to 1.4, and the temperature increased to as high as 450C. The coefficient of friction was found to increase with temperature. There exists a critical temperature at which point a steep increase in the coefficient of friction was observed. The critical temperature decreases from 250C at a contact pressure of 26MPa to 200C at contact pressure of 34MPa. Below the critical temperature at a specific contact pressure the maximum coefficient of friction is 0.6, and above the critical temperature it reaches a value as high as 1.4. The steep increase in the coefficient of friction is found to be due to the seizure phenomenon and the contact condition during FSW between the tool and the workpiece (base metal) is found to be sticking.

Influence of friction during forming processes-a study using a numerical simulation technique

Friction has an important influence in metal forming operations, as it contributes to the success or otherwise of the process. In the present investigation, the effect of friction on metal forming was studied by simulating compression tests on cylindrical Al-Mg alloy using the finite element method (FEM) technique. Three kinds of compression tests were considered wherein a constant coefficient of friction was employed at the upper die-work-piece interface. However, the coefficient of friction between the lower die-work-piece interfaces was varied in the tests. The simulation results showed that a difference in metal flow occurs near the interfaces owing to the differences in the coefficient of friction. It was concluded that the variations in the coefficient of friction between the dies and the work-piece directly affect the stress distribution and shape of the work-piece, having implications on the microstructure of the material being processed.

Effect Of Directionality Of Grinding Marks On Friction And Formation Of Transfer Layer

Surface texture influences friction and transfer layer formation during sliding. In the present investigation, basic studies were conducted using inclined pin-on-plate sliding tester to understand the effect of directionality of surface grinding marks of hard material on friction and transfer layer formation during sliding against soft materials. 080 M40 steel plates were ground to attain different surface roughness with unidirectional grinding marks. Then pins made of soft materials such as pure Al, pure Mg and Al-Mg alloy were slid against the prepared steel plates. Grinding angle (i.e., the angle between direction of sliding and grinding marks) was varied between 0 degrees and 90 degrees in the tests. Experiments were conducted under both dry and lubricated conditions on each plate in ambient environment. It was observed that the transfer layer formation and the coefficient of friction, which has two components adhesion and plowing - depend primarily on the directionality of grinding marks of the harder mating surface, and independent of surface roughness of the harder mating surface. For the case of pure Mg, stick-slip phenomenon was observed under dry condition for all grinding angles and it was absent upto 20 degrees grinding angles under lubricated condition. However, for the case of Al, it was observed only under lubricated conditions for angles exceeding 20 degrees. As regards the alloy, namely, Al-Mg alloy, it, was absent in both conditions. For the case of pure Mg and Al, it was observed that the amplitude of stick-slip motion primarily depends on plowing component of friction. The grinding angle effect on coefficient of friction was attributed to the variation of plowing component of friction with grinding angle.

Studies On Friction And Formation Of Transfer Layer In Hcp Metals

Surface texture plays an important role in the frictional behavior and transfer layer formation of contacting surfaces. In the present investigation, basic experiments were conducted using an inclined pin-on-plate sliding apparatus to better understand the role of surface texture on the coefficient of friction and the formation of a transfer layer. In the experiments, soft HCP materials such as pure Mg and pure Zn were used for the pins and a hardened 080 M40 steel was used for the plate. Two surface parameters of the steel plates—roughness and texture—were varied in tests that were conducted at a sliding speed of 2 mm/s in ambient conditions under both dry and lubricated conditions. The morphologies of the worn surfaces of the pins and the formation of the transfer layer on the counter surfaces were observed using a scanning electron microscope. In the experiments, the occurrence of stick-slip motion, the formation of a transfer layer, and the value of friction were recorded. With respect to the friction, both adhesion and plowing components were analyzed. Based on the experimental results, the effect of surface texture on the friction was attributed to differences in the amount of plowing. Both the plowing component of friction and the amplitude of stick-slip motion were determined to increase surface textures that promote plane strain conditions and decrease the textures that favor plane stress conditions.

Correlating The Features Of Topography To Friction By Sliding Experiments

Friction can influence the quality of the finished product to a large extent in certain manufacturing processes. Sheet metal forming is a particular case, where the friction between the hard-die and the relatively soft work-piece can be extremely important. Under such conditions, topography of the harder surface can influence the resistance to traction at the interface. This paper discusses about the correlation between certain features of the surface; topography and coefficient of friction based on experiments involving sliding of a few soft metal pins against a harder material. A brief description of the experimental procedure and the analysis are presented. A hybrid parameter which encapsulates both the amplitude features as well as the relative packing of peaks is shown to correlate well with the coefficient of friction.

Fasteners in Composite Plates - Effects of Interfacial Friction

The effects of tangential friction at pin—hole interfaces are appropriately modelled for the analysis of fasteners in large composite (orthotropic) plate loaded along its edges. The pin—hole contact could be of interference, clearance or neat fit. When the plate load is monotonically increased, interference fits give rise to receding contact, whereas clearance fits result in advancing contact. In either case, the changing contact situations lead to non-linear moving boundary value problems. The neat fit comes out as a special case in which the contact and separation regions are invariant with the applied load level and so the problem remains linear. The description of boundary conditions in the presence of tangential friction, will depend on whether the problem is one of advancing or receding contact, advancing contact presenting a special problem. A model is developed for the limiting case of a rigid pin and an ideally rough interface (infinitely large friction coefficient). The non-linearity resulting from the continuously varying proportions of contact and separation at the interface, is handled by an “Inverse Formulation” which was successfully applied earlier by the authors for smooth (zero friction) interfacial conditions. The additional difficulty introduced by advancing contact is handled by adopting a “Marching Solution”. The modelling and the procedure are illustrated in respect of symmetric plate load cases. Numerical results are presented bringing out the effects of interfacial friction and plate orthotropy on load-contact relations and plate stresses.

Effect of inter-edge Coulomb interactions on transport through a point contact in nu=5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, we show that the stable fixed point corresponds to a point contact that is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G(H) = 1/2e(2)/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G(H) = 5/2e(2)/h) and the fully disconnected case (G(H) = 0).

Influence of inclination angle of plate on friction, stick-slip and transfer layer-A study of magnesium pin sliding against steel plate

In this study, sliding experiments were conducted using pure magnesium pins against steel plates using an inclined pin-on-plate sliding tester. The inclination angle of the plate was varied in the tests and for each inclination angle, the pins were slid both perpendicular and parallel to the unidirectional grinding marks direction under both dry and lubricated conditions. SEM was used to study morphology of the transfer layer formed on the plates. Surface roughness of plates was measured using an optical profilometer. Results showed that the friction, amplitude of stick-slip motion and transfer layer formation significantly depend on both inclination angle and grinding marks direction of the plates. These variations could be attributed to the changes in the level of plowing friction taking place at the asperity level during sliding.

Studies on friction and formation of transfer layer when Al-4Mg alloy pins slid at various numbers of cycles on steel plates of different surface texture

In the present investigation, various kinds of textures, namely, unidirectional, 8-ground, and random were attained on the die surfaces. Roughness of the textures was varied using different grits of emery papers or polishing powders. Then pins made of Al-4Mg alloys were slid against steel plates at various numbers of cycles, namely 1, 2, 6, 10 and 20 under both dry and lubricated conditions using an inclined pin-on-plate sliding tester. The morphologies of the worn surfaces of the pins and the formation of transfer layer on the counter surfaces were observed using a scanning electron microscope. Surface roughness parameters of the plate were measured using an optical profilometer. It was observed that the coefficient of friction and formation of transfer layer during the first few cycles depend on the die surface textures under both dry and lubricated conditions. It was also observed that under lubricated condition, the coefficient of friction decreases with number of cycles for all kinds of textures. However, under dry condition, it ecreases for unidirectional and 8-ground surfaces while for random surfaces it increases with number of cycles