The effect of repeated loading on the yield surface

Summary In a previous paper [1] we introduced the concept of a loading surface which is distinct from and encloses the yield surface. The region between the two surfaces may be called the microstrain region. In this paper experiments with pure aluminium are presented in which the influence of repeated loading on the microstrain region is explored. It is seen that the microstrain region decreases in size with each cycle but that it does not necessarily become zero even after several cycles. It is also shown that the yield surface does not enclose the origin even at small values of plastic strain. At the end of the paper it is shown that considerable care should be exercised in the determination of the yield surface since in some cases its position and shape can be influenced to a considerable extent by the unavoidable penetration inside the plastic region while probing for it.

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Zusammenfassung In einer vorangegangenen Arbeit [1] haben wir das Konzept einer Belastungsfläche eingeführt, die verschieden ist von der Fließfläche, diese aber umschließt. Der Bereich zwischen den beiden Flächen soll Mikroverzerrungsbereich genannt werden. In dieser Arbeit werden Versuche mit reinem Aluminium angegeben, in welchen der Einfluß wiederholter Belastung auf den Mikroverzerrungsbereich untersucht wird. Es ist ersichtlich, daß der Mikroverzerrungsbereich mit jedem Belastungszyklus kleiner wird, aber er schrumpft auch nach oftmals wiederholten Belastungszyklen nicht notwendigerweise auf Null zusammen. Es wird ferner gezeigt, daß die Fließfläche den Ursprung nicht beinhaltet, auch nicht für kleine Werte der plastischen Verzerrung. Am Ende der Arbeit wird gezeigt, daß eine gewisse Sorgfalt bei der Bestimmung der Fließfläche nicht außer acht gelassen werden darf, da in einigen Fällen ihre Lage und Gestalt bis zu einem gewissen Grade durch das unvermeidliche Eindringen in die plastische Region während des Experiments beeinflußt wird.

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With 19 Figures

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This work was sponsored by the National Science Foundation of the United States Government.     

The effect of substrate surface roughness on the wettability of Sn-Bi solders

The effect of substrate surface roughness on the wettability of Sn-Bi solders is investigated by the eutectic Sn-Bi alloy on Cu/Al₂O₃ substrates at 190 °C. To engineer the surface with different roughnesses, the Cu-side of the substrates is polished with sandpaper with abrasive number 100, 240, 400, 600, 800, 1200, and 1 m alumina powder, respectively. Both dynamic and static contact angles of the solder drops are studied by the real-time image in a dynamic contact angle analyzer system (FTA200). During dynamic wetting, the wetting velocity of the solder drop decreases for the rougher surface. However, the time to reach the static contact angle seems to be identical with different substrate surface roughness. The wetting tip of the solder cap exhibits a waveform on the rough surface, indicating that the liquid drop tends to flow along the valley. As the solder drops reach a static state, the static contact angle increases with the substrate surface roughness. This demonstrates that the wettability of solders degrades as the substrates become rough.     

The effect of fibre surface roughness on the mechanical behaviour of ceramic matrix composites

The interface between the matrix and the fibre plays an important role in controlling the strength and toughness of ceramic matrix composites. It has been found experimentally that depending on manufacturing process, the interface may show substantial surface roughness, which has been modelled analytically with certain degree of success. The analytical models, however, do not take into account the interface geometry. Instead, only the magnitude of the surface undulation is included. In this paper, a direct simulation of fibre–matrix interface roughness by the finite element method is performed on an axisymmetric unit cell with a fully debonded interface. The simulation is employed to account for the three dimensional stress state, surface roughness and interface friction, which are normally simplified or idealised in theoretical studies. The model gives the highly non-uniform interface shear and pressure, which have direct implications on the interface damage and composite behaviour. Under the approximation made in the model, the positive transverse strains does not show up in the simulation despite the fact that two different surface roughness are used.     

Investigation of granular surface roughness effect on electrostatic charge generation

Electrostatic charge generation is a multivariable and complex issue whose working mechanism has never been fully understood. The objective of this paper is to investigate the effect of granule surface roughness on electrostatic charge generation. Two kinds of granule material, Polyvinyl chloride (PVC) and polypropylene (PP) were used with the granule size of 4 mm diameter, 2 mm height and the shape was cylinder or semi-cylinder. The working surfaces were grounded and roughness ranged from 0.140 to 8.600 μm. It was found that uneven surfaces tended to give rise to voids between two solids, where air stored in the voids was able to accelerate discharging. With the same roughness, PVC tended to generate more electrostatic charge than PP by one order of magnitude. For both materials, electrostatic charge generation first increased with surface roughness and then decreased. The maximum electrostatic charge generated was found to occur when the effects of interaction, contact area and voids discharging were at equilibrium. With the combined effect of humidity, surface roughness and contact area, highest electrostatics generation occurred near the mid-roughness tested in this work. Humidity had more effect on electrostatic charge generation as the granule working surface had lower roughness.     

Modelling the combined effect of surface roughness and topography on bacterial attachment

Bacterial attachment is a complex process affected by flow conditions,imparted stresses,and the sur-face properties and structure of both the supporting material and the cell.Experiments on the initial attachment of cells of the bacterium Streptococcus gordonii (S.gordonii),an important early coloniser of dental plaque,to samples of stainless steel (SS) have been reported in this work.The primary aim motivating this study was to establish what affect,if any,the surface roughness and topology of sam-ples of SS would have on the initial attachment of cells of the bacterium S.gordonii.This material and bacterium were chosen by virtue of their relevance to dental implants and dental implant infections.Prior to bacterial attachment,surfaces become conditioned by the interfacing environment (salivary pellicle from the oral cavity for instance).For this reason,cell attachment to samples of SS pre-coated with saliva was also studied.By implementing the Extended Derjaguin Landau Verwey and Overbeek(XDLVO) theory coupled with convection-diffusion-reaction equations and the surface roughness infor-mation,a computational model was developed to help better understand the physics of cell adhesion.Surface roughness was modelled by reconstructing the surface topography using statistical parame-ters derived from atomic force microscopy (AFM) measurements.Using this computational model,the effects of roughness and surface patterns on bacterial attachment were examined quantitatively in both static and flowing fluid environments.The results have shown that rougher surfaces (within the sub-microscale) generally increase bacterial attachment in static fluid conditions which quantitatively agrees with experimental measurements.Under flow conditions,computational fluid dynamics (CFD) simula-tions predicted reduced convection-diffusion inside the channel which would act to decrease bacterial attachment.When combined with surface roughness effects,the computational model also predicted that the surface topographies discussed within this work produced a slight decrease in overall bacterial attachment.This would suggest that the attachment-preventing effects of surface patterns dominate over the adhesion-favourable sub-microscale surface roughness;hence,producing a net reduction in adhered cells.This qualitatively agreed with experimental observations reported here and quantitatively matched experimental observations for low flow rates within measurement error.     

Nanometer surface roughness effect on the magnetic properties of CoFeHfO thin films

This article reports the effects of nanometer surface roughness on the magnetic properties of CoFeHfO thin films, as deposited on Si (100) substrates. The surface roughness was controlled via the working pressure during the sputtering time. When the working pressure increases from 0.5 to 3 mT, the surface roughness (R) of CoFeHfO thin films, formed by islands with the average high R, increases from 0.25 nm to 4.66 nm, respectively. At surface roughness (R) = 4.66 nm, coercivity (H(c)) reaches the highest value of 0.42 Oe and magnetic anisotropy (H(k)) drops to the lowest value of 33 Oe. This suggests that the quality of the soft magnetic properties of thin film decrease due to the increase in surface roughness. However, at very low working pressure, thin films become a homogeneous structure which also exhibits poor soft magnetic properties. The optimum value, with H(c) of 0.10 Oe and H(k) of 50 Oe, were obtained at 1.5 mT of working pressure. The model of the roughness effect on the magnetic properties is introduced and discussed.     

The effect of varying chill surface roughness on interfacial heat transfer during casting solidification

Experiments to investigate interfacial heat transfer mechanisms during casting solidification were carried out by varying the surface roughness of a Cu chill used to bring about unidirectional solidification of an Al-4.5 wt.% Cu alloy. Little variation in interfacial heat transfer coefficient with varying chill surface roughness was found, confirming previously published results. Examination of the as-cast surface of the casting showed the presence of predendritic contact areas, and also that the casting surface roughness did not form as a replica of the chill surface, as has often been proposed. Rather, the casting surface roughness was consistently greater than that of the chill, but varied little in the experiments. A sum surface roughness parameter was devised to characterise the casting–chill interface that included the roughness of both surfaces. The value of this parameter was strongly influenced by the greater roughness of the casting surface, rather than the chill surface roughness, and therefore also varied little in the experiments. This lack of variation in the casting surface roughness and hence the sum surface roughness parameter showed how interfacial heat transfer should be more strongly influenced by the greater roughness of the casting surface than of the chill surface, and explains why the interfacial heat transfer coefficient was not strongly influenced by the chill surface roughness in these types of experiments. At the time the work was carried out the authors were in the Manchester Materials Science Centre, University of Manchester and UMIST, Manchester M1 7HS, UK.     

The sensitivity of surface crack initiation to surface roughness in low-cycle fatigue at high temperature

Low-cycle fatigue tests have been carried out on AISI 304L stainless steel and Cr---Mo---V steel specimens with two different modes of surface roughness at 823 K. In the case of Cr---Mo---V steel, grain boundary cavities were not formed during the test. Transgranular cracks were formed and then propagated. The number of cycles required for the crack initiation was observed to be a very large fraction of the toral fatigue life. In the case of AISI 304L stainless steel, grain boundary cavities formed and intergranular crack initiation and propagation was also observed to occur. The number of cycles required for crack initiation was negligible in comparison with the total low-cycle fatigue life.     

The effect of thermal loading on the yield surface of aluminium. An experimental investigation

Summary Paper presents the results of an experimental investigation dealing with the effects on the motion and deformation of the room temperature yield curve and on the plastic strain resulting from a substantial penetration of the yield surface by: (1) loading paths with constant stress combined with variable temperature and (2) isothermal loading paths. The results are interpreted with the help of the concept of the equilibrium stress-strain curves which is expanded to include both increasing and decreasing stress as well as changing temperature.With 17 FiguresThis research was supported by the National Science Foundation.     

Application of level set method in simulation of surface roughness in nanotechnologies

One of the limiting factors in applications of plasma etching in nanotechnologies in general will be the control of plasma induced roughness or perhaps control of surface roughness by plasma etching. In this paper we consider roughening of nanocomposite materials during plasma etching for two etching modes (isotropic and anisotropic) by using a level set method. It was found that the presence of two phases with different etch rates (the ratio of the two etch rates is s and the abundance of one phase is p) affects the evolution of the surface roughness and that the etch rate is higher during the isotropic process as compared to the anisotropic process for all values of s and p. At the same time, in case of isotropic process, the higher s leads to a higher overall etch rate. The obtained results apart from their theoretical relevance, have practical implications for surface treatment of nanocomposite materials.     

The effect of heat transfer additive and surface roughness of micro-scale hatched tubes on absorption performance

The objectives of this paper are to investigate the effect of heat transfer additive and surface roughness of micro-scale hatched tubes on the absorption performance and to provide a guideline for the absorber design. Two different micro-scale hatched tubes and a bare tube are tested to quantify the effect of the surface roughness on the absorption performance. The roughness of the micro-scale hatched tubes ranges 0.39–6.97 μm. The working fluid is H₂O/LiBr solution with inlet concentration of 55, 58 and 61 wt.% of LiBr. Normal Octanol is used as the heat transfer additive with the concentration of 400 ppm. The absorber heat exchanger consists of 24 horizontal tubes in a column, liquid distributor at the liquid inlet and the liquid reservoir at the bottom of the absorber. The effect of heat transfer additive on the heat transfer rate is found to be more significant in the bare tube than that in the micro-scale hatched tubes. It is found that the absorption performance for the micro-hatched tube with heat transfer additive becomes up to 4.5 times higher than that for the bare tube without heat transfer additive. It is concluded that the heat transfer enhancement by the heat transfer additive is more significant than that by the micro-scale surface treatment.     

The influence of surface roughness on the starved lubrication of ball bearings

Abstract

A theoretical analysis is made for starved lubrication of a rigid point contact under the influence of surface roughness. The results show that both the directional property and the standard deviation of the combined surface roughness can affect the load carrying capacity of the lubricant film as well as the friction on the solid surfaces. The combined effects of speed ratio of the contiguous surfaces and the roughness on starved lubrication are also obtained. The results show that the effects of surface roughness may improve the starvation a little, but that they are not remarkable. A regression equation is found for determining the critically starved lubricant inlet level. Such an inlet level can indicate the minimum limit of lubricant supplied quantity, and, beyond this limit, the load carrying capacity of the lubricant film will decrease sharply. In addition, experiments have been carried out to observe the starved lubrication of a ball rolling on a flat glass disc. It is shown that higher surface speeds may make the starved condition much worse.     

Environment effects and surface roughness on fatigue crack growth at negative R-ratios

Fatigue crack growth has been widely studied, since it plays an important role on the damage tolerance analysis of mechanical components and structures. The environment, material properties and stress ratio significantly influence the fatigue crack growth behaviour of materials. Experimental tests were performed in M(T) specimens of a normalized DIN Ck45 steel at constant load ratios for R = 0.7, 0.5, 0, −1, −2, −3, in ambient air and vacuum conditions, using a new and patented chamber of vacuum. Special emphasis is given to the study of environment effects, stress ratios and related effects of crack roughness. Fracture surface roughness and crack closure effect were systematically measured for all tests in order to compare the influence of different environment and R-ratios. Results have shown that fatigue crack growth rates are higher in air than in vacuum and the fracture surface roughness is also higher in air than in vacuum for comparable stress ratios. The effect of the environment on fatigue crack growth rates seems to be more significant than any mechanical contributions such as plasticity, oxide and roughness which can induce the so-called crack closure.     

The influence of surface roughness on fluid flow through cracks

ABSTRACT Leak‐before‐break (l‐b‐b) safety cases depend on predictions of flow rate through postulated cracks. The calculated flow rates are dependent upon assumptions made about a number of features including fluid friction, and this in turn is influenced by surface roughness and flow regime. This paper considers the uncertainties associated with flow rate prediction in both the laminar and fully rough turbulent regimes as influenced by fluid friction. It shows how uncertainties can be bounded. In particular it discusses the maximum values for fluid friction that might arise in practice. The use of computational fluid dynamics in future analyses could significantly reduce the uncertainties associated with fluid friction in cracks.     

A three-dimensional non-epitaxial atomistic growth model for thin-film deposition: effect of surface mobility

The effect of the atomic mobility on a film surface has been studied by using a three-dimensional atomistic thin-film deposition model which simulates three-dimensional thin-film images, surface profiles and cross-sectional area pictures. In addition, quantitative results of surface RMS roughness, average film thickness, atomic coordination number and its distribution, and solid fraction of the deposited thin films, were obtained from the simulations. When the film surface mobility increased from 0.3 to 3.0, RMS roughness decreased from 6.5 to 1.1, solid fraction increased from 0.27 to 0.56 and average film thickness decreased from 40 to 28, due to the reduction of the voids within the film. The full-width half magnitude of the atomic coordination distribution became narrower indicating the increased degree of crystallization. With increase in surface mobility crossing the boundary to 1.5, the film evolved from a porous or loose columnar structure with voids, to a densely packed fibrous grain structure which can be categorized by the zone structure models.     

The effect of roughness of the inner surface of the pipeline on the error of measurements using immersed vortex flow meters

The additional systematic errors of measurements which arise when using immersed vortex flowmeters, due to the roughness of the inner surface of the pipeline, are considered. A procedure for estimating these errors and correcting the frequency division factor in the measurement channel of the instrument in order to eliminate these errors partially, is proposed. __________ Translated from Izmeritel’naya Tekhnika, No. 2, pp. 42–44, February, 2006.     

Mathematical modelling of the effect of surface roughness on magnetic field profiles in type II superconductors

One of the defining characteristics of a superconductor is the Meissner effect, in which an external magnetic field is expelled from the bulk of a sample when cooled below the critical temperature. Although there has been considerable theoretical work on the Ginzburg–Landau theory of superconductors, the effects of interest in this paper can be modelled with the simpler London equation. This equation predicts an exponential decay of the local magnetic field magnitude as a function of the distance into the superconductor from a flat surface in the London limit where $\kappa =\lambda /\xi $ , defined as the ratio between the penetration depth and coherence length, is much greater than 1. However, recent measurements of the field profile in high $\kappa $ superconductors show that the observed decay is non-exponential near the surface. In particular, the measured field profiles indicate that the decay rate in the field magnitude is smaller than expected from a simple London model on a short length scale $d$ near the surface. In this paper, we examine the effects of surface roughness on magnetic field penetration into a high $\kappa $ superconductor. We model the roughness as a sinusoidal perturbation from a flat interface and investigate the effect using both an asymptotic method, based upon a small-amplitude perturbation, and a numerical method, using a finite difference discretization with a coordinate mapping from an underlying rectangular domain. A novel discretization is used in the case of 3D calculations and a fast, preconditioned GMRES solver is developed. A careful comparison of asymptotic and numerical methods validates both approaches for small perturbations, but the numerical approach allows for the investigation of rougher surfaces. Our results show that surface roughness reduces the decay rate in the average magnetic field near the surface relative to a London model. However, the reduction is more gradual than the simple dead layer model currently being used to fit experimental data. In addition, we discover some interesting new phenomena in the 3D case.