Erosion of α-Fe by spherical glass particles

Polycrystalline α-Fe has been eroded at 30° and 90° with glass spheres of average diameters 70 μm and 200 μm in the velocity range 61–122 m s⁻¹. Detailed studies of the influence of the impact variables on the erosion rate as well as scanning electron microscopy studies of the eroded surfaces have been performed. It was observed that “breaking” waves developed on erosion at 30° and hills and valleys at 90°. Several different material loss processes that operate at various positions within waves, hills and valleys have been identified. It was clear that most material loss processes involved extensive localized shear and required the surface to become “conditioned” by a specific number of impacts before material loss began.     

Measurement of springback

Springback, the elastically-driven change of shape of a part after forming, has been measured under carefully-controlled laboratory conditions corresponding to those found in press-forming operations. Constitutive equations emphasizing low-strain behavior were generated for three automotive body alloys: drawing-quality silicon-killed steel; high-strength low-alloy steel; and 6022-T4 aluminum. Strip draw-bend tests were then conducted using a range of die radii (3<R/t<17), friction coefficients (0<μ<0.20), and controlled tensile forces (0.5<F_b/F_y<1.5). Springback angles and curvatures were measured for bend and bend–unbend areas of the specimen, the latter corresponding to the “sidewall curl” region, which dominates the geometric change and the dependence on process variables. Friction coefficient and R/t (die-radius-to-sheet-thickness) greater than 5 have modest but measurable effects over the ranges tested. As expected, strip tension dominates the springback sensitivity, with higher forces reducing springback. For 6022-T4, springback is dramatically reduced as the tensile stress approaches the yield stress, corresponding to the appearance of a persistent anticlastic curvature. The presence of this curvature, orthogonal to the principal curvature, violates the simple two-dimensional models of springback reported in the literature. The measured springback angles and curvatures are reported both in graphical summary and tabular form for use in assessing analytical models of springback.     

Mechanical analysis of the scratching of metals and polymers with conical indenters at moderate and large strains

Scratch test provides a convenient mean to study the surface mechanical properties and the tribological performances of materials. The representative strain of the material in this test increases with the attack angle β of the indenter and so for a conical indenter increases as its apical angle 2θ decreases. But the mechanical analysis of this test by analytic models is very intricate. First we perform a preliminary discussion of the various aspects of the problem by considering the plane strain scratching of materials by wedges. After we present the conditions of the numerical simulations of the scratch test with conical indenters with a three-dimensional (3D) finite element code. These simulations provide the scratch geometry (contact surface, elastic recovery), the plastic strain map and the volume average plastic strain, the scratch hardness and the force ratio, the apparent friction coefficient μ₀=F_t/W. So we compare the behaviour of polymeric and metallic materials in scratch test at low and large strain and relate their difference in scratching resistance to their rheological properties. Polymers develop more higher elastic strains than metals a phenomenon which is characterised at low strain by the yield stress to Young's modulus ratio ε_e=σ_y/E. For θ=70.3° where pure ploughing occurs we study the scratching of elastic perfectly plastic solids with various values of ε_e under zero friction. Some comparisons with the behaviour in indentation are performed and we study the influence of friction in the scratching of workhardened steel with the same cone. At high strain the main rheological difference is the workhardening behaviour: it is described by a power law for metals and an exponential law for polymers. For θ decreasing from 70.3 to 20° we compare the behaviour of a cold worked steel to the behavour of polycarbonate, a thermoplastic polymer: a transition from ploughing to ploughing–cutting occurs only for steel.     

A universal slip-line model with non-unique solutions for machining with curled chip formation and a restricted contact tool

A universal slip-line model and the corresponding hodograph for two-dimensional machining which can account for chip curl and chip back-flow when machining with a restricted contact tool are presented in this paper. Six major slip-line models previously developed for machining are briefly reviewed. It is shown that all the six models are special cases of the universal slip-line model presented in this paper. Dewhurst and Collins's matrix technique for numerically solving slip-line problems is employed in the mathematical modeling of the universal slip-line field. A key equation is given to determine the shape of the initial slip-line. A non-unique solution for machining processes when using restricted contact tools is obtained. The influence of four major input parameters, i.e. (a) hydrostatic pressure (P_A) at a point on the intersection line of the shear plane and the work surface to be machined; (b) ratio of the frictional shear stress on the tool rake face to the material shear yield stress (τ/k); (c) ratio of the undeformed chip thickness to the length of the tool land (t₁/h); and (d) tool primary rake angle (γ₁), upon five major output parameters, i.e. (a) four slip-line field angles (θ, η₁, η₂, ψ); (b) non-dimensionalized cutting forces (F_c/kt₁w and F_t/kt₁w); (c) chip thickness (t₂); (d) chip up-curl radius (R_u); and (e) chip back-flow angle (η_b), is theoretically established. The issue of the “built-up-edge” produced under certain conditions in machining processes is also studied. It is hoped that the research work of this paper will help in the understanding of the nature and the basic characteristics of machining processes.     

Fretting cracking behaviour on pre-stressed aluminium alloy specimens

A new testing rig has been developed which enables fretting tests on pre-stressed specimens to be carried out. Three aluminium alloys, Al-Li 2091, Al-Cu 2024 and Al-Zn 7075, were used in the tests. The imposed amplitude D ranged from ± 10 to ± 75 μm and normal load F_n from 500 to 1000 N. The static external stress σ_S was set as σ_D/10, σ_D/2 and σ_D (σ_D is the fatigue limit). The tests were carried out with a frequency of 1 or 5 Hz up to 10⁶ cycles. In this paper, analysis of fretting behaviour has been carried out using the fretting map concept. The effect of the axial load (pre-stress) on fretting cracking is emphasized.     

Strengthening caused by power law creep deformation of dispersed particles in an elastic matrix

The interaction energy is approximated between an edge dislocation and a particle deformable by power law creep in an elastic matrix. The stress required to overcome the interaction energy barrier is found to be greater than the Orowan stress, and the dislocation bulges to escape the particle. If the ratio of the shear modulus of the matrix to the viscosity of the particle (μt^m/σ₀) is large, the stress required to climb over the particle is larger than the Orowan stress and the dilocation bulges before it climbs. It is concluded that even if the particle is soft enough to exhibit creep, the strengthening of alloys can be achieved by an Orowan mechanism. The critical resolved shear stress (CRSS) of Cu-B₂O₃, obtained experimentally by Onaka et al. [11], agrees closely with that obtained in our analysis. This supports our analysis that the strength of Cu-B₂O₃ alloy at high temperature may be accounted for by the Orowan mechanism and the attraction between a dislocation and viscous particles. The energy and the force to overcome the energy barrier increases significantly with decrease of m, the strain rate exponent associated with the power law creep particle. It is found through analysis that for m < 1.0 and for certain values of μt^m/σ₀ > 1, the particle repulses the dislocation, while for m = 1.0 and for all values of μt^m/σ₀ > 1, the particle attracts the dislocation, which is the expected interaction between an elastic particle and a dislocation in an elastic matrix.     

Buckling of thin cylindrical shells: an attempt to resolve a paradox

The classical theory of buckling of axially loaded thin cylindrical shells predicts that the buckling stress is directly proportional to the thickness t, other things being equal. But empirical data show clearly that the buckling stress is actually proportional to t^1.5, other things being equal. As is well known, there is wide scatter in the buckling-stress data, going from one half to twice the mean value for a given ratio R/t. Current theories of shell buckling explain the low buckling stress—in comparison with the classical—and the experimental scatter in terms of “imperfection-sensitive”, non-linear behaviour. But those theories always take the classical analysis of an ideal, perfect shell as their point of reference.Our present principal aim is to explain the observed t^1.5 law. So far as we know, no previous attack has been made on this particular aspect of thin-shell buckling. Our work is thus breaking new ground, and we shall deliberately avoid taking the classical analysis as our starting point.We first point out that experiments on self-weight buckling of open-topped cylindrical shells agree well with the mean experimental data mentioned above; and then we associate those results with a well-defined post-buckling “plateau” in load/deflection space, that is revealed by finite-element studies. This plateau is linked with the appearance of a characteristic “dimple” of a mainly inextensional character in the deformed shell wall. A somewhat similar post-buckling dimple is also found by quite separate finite-element studies when a thin cylindrical shell is loaded axially at an edge by a localised force; and it turns out that such a dimple grows under a more-or-less constant force that is proportional to t^2.5, other things being equal.This 2.5-power law can be explained by analogy with the inversion of a thin spherical shell by an inward-directed force. Thus, the deformation of such a shell is generally inextensional except for a narrow “knuckle” or boundary layer in which the combined local elastic energy of bending and stretching is proportional to t^2.5, other things being equal. Similarly, the modes of deformation in the post-buckling dimples in a cylindrical shell are practically independent of thickness, except in the highly deformed boundary-layer regions which separate the inextensionally distorted portions of the shell. These ideas lead in turn to an explanation of the t^1.5 law for the post-buckling stress of open-topped cylindrical shells loaded by their own weight.We attribute the absence of experimental scatter in the self-weight buckling of open-topped cylindrical shells to the statical determinacy of the situation, which allows a post-buckling dimple to grow at a well-defined “plateau load”. Conversely, the large experimental scatter in tests on cylinders with closed ends may be attributed to the lack of statical determinacy there.Our paper contains several arguments that are not mathematically water-tight, in contrast to many reports in the field of mechanics of structures. We plead that the problem which we have tackled is so difficult that the only way forward is one of “over-simplification”. We hope that our work will be judged not with respect to its absence of mathematical precision, but by the light which it sheds upon the problem under investigation.     

New cylinder liner surfaces for low oil consumption

Anticipated emission legislation and reduced fuel consumption are the main driving forces when developing new engines. Optimization of the active surfaces in the piston system is one possible way to meet the above demands. In this study the effects of surface topography and texture direction of the ring/liner contact on oil film thickness and friction were simulated and experimentally tested. “Low wear” results from the experimental wear tests with “glide honed” smooth liner surfaces supported the “low friction” simulation results. In addition a new wear volume sensitive surface roughness parameter, R_ktot, based on the Abbot–Firestone bearing area curve was introduced.     

The influence of water vapour in air on the friction behaviour of pure metals during fretting

An investigation was conducted to determine the effect of water vapour content in air on the frictional behaviour during fretting of pure metals: iron, aluminium, copper, silver, chromium, titanium and nickel. The fretting experiments were carried out under various humidity levels, ranging from dry air to 50% relative humidity at 23°C. During the experiment the frictional force between fretting surfaces was measured. Pure metals, except iron, were found to have a maximum value of the coefficient of friction during the steady-fretting stage (μ_s) at a specific humidity (RH_max). Iron showed a rapid decrease in μ_s with increasing humidity at RH_max. Each pure metal also exhibited maximum fretting wear at RH_max. The value of μ_s at RH_max for each metal was strongly related to the heat of formation of the lower metal oxide, indicating that the adhesive contact area was larger at RH_max for the fretting of metals with less chemical activity. At high humidity levels water vapour generally reduced the coefficient of friction, μ_s.     

Friction, wear and material transfer of sintered polyimides sliding against various steel and diamond-like carbon coated surfaces

Polyimide cylinders are slid under 50 N normal load and 0.3 m/s sliding velocity against carbon steel (R_a=0.2 and 0.05 μm), high-alloy steel (R_a=0.05 μm), diamond-like carbon (DLC, R_a=0.05 μm) and diamond-like nanocomposite (DLN, R_a=0.05 μm). Only for a limited range of test parameters, the friction of polyimide/DLN is lower than for polyimide/steel, while polyimide shows higher wear rates after sliding against DLN compared to steel counterfaces. The DLN coating shows slight wear scratches, although less severe than on DLC-coatings that are worn through thermal degradation. Therefore, also friction against DLC-coatings is high and unstable. Calculated bulk temperatures for steel and DLN under mild sliding conditions remain below the polyimide transition temperature of 180 °C so that other surface characteristics explain low friction on DLN counterfaces, as surface energy, structural compatibility and transfer behaviour. Friction is initially determined through adhesion and it is demonstrated that higher surface energy provides higher friction. After certain sliding time, different polyimide transfer on each counterface governs the tribological performance. Polyimide and amorphous DLC structures are characterised by C–C bonds, showing high structural compatibility and easy adherence of wear debris on the coating. However, it consists of plate-like transfer particles that act as abrasives and deteriorate the polyimide wear resistance. In sliding experiments with high-alloy steel, wear debris is washed out of the contact zone without formation of a transfer film. Transfer consists of island-like particles for smooth carbon steel and it forms a more homogeneous transfer film on rough carbon steel. The latter thick and protective film is favourable for low wear rates; however, it causes higher friction than smooth counterfaces.     

Free vibration analyses of simply supported beams carrying multiple point masses and spring-mass systems with mass of each helical spring considered

In the conventional finite element method (FEM), the dynamic characteristics of a longitudinally vibrating rod with mass density ρ_r, Young's modulus E_r, cross-sectional area A_r and total length ℓ_r are considered to be the same as those of a helical spring with stiffness constant k_r=A_rE_r/ℓ_r and total mass m_r=ρ_rA_rℓ_r. For a lumped-mass model, the mass matrix of a rod element is a 2×2 diagonal one with each of its non-zero coefficients to be equal to one half of the total rod mass (i.e., 0.5m_r). Furthermore, the dynamic characteristics of a rod on the basis of last “lumped-mass” model have been found to be very close to those on the basis of “consistent-mass” model. Thus, one can easily take into account of the inertial effect of a helical spring using a massless one with “one half of its total mass”, respectively, concentrated at its two ends (in Method 2) instead of modeling it by an elastic rod with uniform mass per unit length (in Method 1). When one more spring-mass system is attached to the beam, the total number of unknown constants increases “one” in Method 2 and “two” in Method 1, thus, Method 2 will reduce more effort than Method 1 for studying the dynamic behaviors of a beam carrying a number of spring-mass systems with mass of each helical spring considered. In this paper, the formulations of Methods 1 and 2 are presented first and then the numerical examples are illustrated to confirm the reliability of the presented theory and the developed computer programs. Finally, the effect concerning mass of each helical spring of the spring-mass systems is studied.     

Twin shear stress yield criterion

A twin shear stress yield criterion is described. This criterion was proposed by the author in 1961[1]. It assumes that yielding begins when the sum of the two larger principal shear stresses reaches a magnitude C. Thus the initial yield function is f = τ₁₃ + τ₁₂ = σ₁ − 1/2(σ₂ + σ₃) = c[(τ₁₃ + τ₁₂) ± c][τ₂₃ + τ₂₁) ± c][τ₃₁ + τ₃₂) ± c] = 0.     

Three-dimensional kinematical analyses for surface grinding of large scale substrate

Sponsored by New Energy and Industrial Technology Development Organization (NEDO) and the Ministry of Education, Science and Culture (MESC) of Japan, this project has developed an advanced machining system for 300 mm silicon wafer, using fixed abrasive instead of conventional free slurry, to provide a totally integrated solution for achieving the surface roughness R_a<1 nm (R_y<5–6 nm) and the global flatness <0.2 μm/ 300 mm. Use of state-of-the-art technologies for ultra precision machine tools has made it possible to precisely control the motion and repeatability of each cutting edge. The behavior of each grain and its effect on surface generation become analytical in 2D manner [J JSPE 68(1) (2002) 125]. Taking one step further, this paper has developed a 3D model for infeed grinding which is often used in silicon grinding systems, and mathematically described the cutting path and effects on the surface roughness and flatness.     

Reference stresses and temperatures for cylinders and spheres under internal pressure with a steady heat flow in the radial direction

The paper examines the creep behavior of thick cylinders and spheres subjected to internal pressure and a negative temperature gradient in the radial direction. It is found that at stationary state the rate of radial displacement of the vessel wall is simply proportional to the material creep behavior associated with a single stress and temperature. Such “reference stresses” and “reference temperatures” are defined for spheres and cylinders of varying wall thicknesses. These reference stresses and reference temperatures are valid for any creep problem where the material behavior may be characterized by a function of the form exp (γT)σ^m. The extension of these results to variable pressure and temperature loading cases is discussed.     

On the measurement of friction coefficient utilizing the ring compression test

The main objective of this research was to investigate whether generalized friction calibration curves, as recommended in the literature for use with ring compression tests, are applicable to all types of materials and test conditions. Specifically, the effects of material properties, strain-rate sensitivity, and “barreling” on the behavior of friction calibration curves were investigated. To this end, a series of ring compression tests were conducted in order to determine the magnitude of the friction coefficient, μ, as well as the corresponding calibration curves for two types of modeling materials, white and black Plasticine. The experiments were first conducted using the Physical Modeling Technique (PMT) and then simulated via an elastic–plastic finite element code (ABAQUS). In contrast to the results available in the literature, where the same friction calibration curves are recommended for all types of materials and test conditions, the results of this investigation showed that friction calibration curves are indeed affected by the material properties and test conditions and every material possesses its own distinctive friction calibration curve.     

Evaluation of the friction of WC/DLC solid lubricating films in vacuum

The accuracy of nanopositioning is to a large extent limited by the friction-caused errors, particularly in vacuum environments. An investigation of the friction behaviour of sp²-bonds dominating diamond like carbon (DLC) coatings and WC_1−x/DLC, WC(N)/DLC multilayer coatings, which are considered to be used in nanopositioning in vacuum, have been performed by a vacuum microtribometer. By using an atomically smooth Si sphere as a counterface, the reciprocating sliding friction was measured at a normal load <5 mN, and running speed at a 1–100 μm/s in ambient air and in ultra high vacuum (UHV) at 10⁻⁷ Pa, and correlated with microstructures and properties of the coatings. When tested in UHV, the coefficient of friction (COF) for pure DLC coatings (thickness: 700 nm) changes significantly between 0.2 and 0.4. Once the thickness of DLC layers is limited to 5 nm by formation of multilayer coatings, the COF in UHV decreases by nearly one order to 0.02–0.05. We suggest that the deformation of DLC films and the transfer films determines COF. Thick DLC coatings can induce more plastic deformation and consumes more energy in sliding resulting in a high COF. Thickening of the transfer film in running leads to a continuous decrease of COF since the deformation of the transfer films turns easier. The low COF of multilayer coatings is mainly due to their confinement of the thickness of DLC films. A consistent velocity-strengthening frictional behaviour of both WC_1−x/DLC and WC(N)/DLC coatings in UHV indicates that the transfer films acting as a thin layer of granular material. Further study of the friction behaviour with the presence of such granular materials might be interesting for the further development of tribological coatings for vacuum applications.     

Ceramic-ceramic composite materials with improved friction and wear properties

Dry friction and wear tests were performed with self-mated couples of SiC containing 50% TiC, Si₃N₄---BN, SiC---TiB₂ and Si₃N₄ with 32% TiN at room temperature and 400°C or 800°C.Under room temperature conditions, the friction coefficient of the couple SiC---TiC/SiC---TiC is only half of that of the couple SiC/SiC and the wear is one order of magnitude smaller. At 400°C, it exceeds the friction coefficient of SiC/SiC except at the highest sliding velocity of 3 m s⁻¹. At lower sliding velocities the wear coefficient of SiC---TiC/SiC---TiC is lower than that of SiC/SiC.The couple Si₃N₄---TiN/Si₃N₄---TiN exhibits high friction coefficients under all test conditions. At room temperature the wear volume of the self-mated couples of Si₃N₄ and Si₃N₄---TiN after a sliding distance of 1000 m is similar, but Si₃N₄---TiN shows a running-in behaviour. At 800°C the wear coefficient of Si₃N₄---TiN/Si₃N₄---TiN is approximately two orders of magnitude smaller than that of Si₃N₄/Si₃N₄, and equal to those at room temperature. At 22°C the addition of BN reduces the friction of Si₃N₄. The wear coefficient is independent of sliding velocity and the self-mated couples showing running-in. Friction and wear increase with increasing temperature. The wear coefficient of SiC---TiB₂ above 0.5 m s⁻¹ at 400°C is advantageously near 10⁻⁶ mm³ (Nm)⁻¹. With the other test conditions the wear behaviour is similar to SSiC.     

Asymptotic analysis of extrusion of porous metals

Plane strain extrusion of fully dense and porous metals is analysed using asymptotic techniques. The extrusion die is assumed to taper gradually down the extrusion axis. The asymptotic expansions are based on a small parameter ε which is defined as the ratio of the total reduction of the original cross-section to the length of the reduction region. Coulomb's law is used to model the frictional forces that develop along the metal-die interface and the coefficient of friction is assumed to be of order ε. Analytical solutions for the first two terms in the expansions are obtained. In the case of the fully dense metals, it is shown that the leading order [O(1)] solution involves “slab flow.” It is also shown that the next term in the expansion of the solution is O(ε²), and this provides a theoretical justification for the use of the so-called “slab methods” of analysis for dies of moderate slope. An asymptotic analysis of the extrusion of porous metals with dilute concentration of voids is also carried out. Gurson's plasticity model is used to describe the constitutive behavior of the material. The leading order solution is the same as that of the fully dense material and the effects of porosity enter as an O(ε) correction. In order to verify the asymptotic solutions developed, detailed finite element calculations are carried out for both the fully dense and the porous material. The asymptotic solutions agree well with the results of the finite element calculations.     

An elastic–plastic stress analysis steel-reinforced thermoplastic composite cantilever beam

In the present study an analytical elastic–plastic stress analysis is carried out for a low-density homogeneous polyethylene thermoplastic cantilever beam reinforced by steel fibers. The beam is loaded by a constant single force at its free end. The expansion of the region and the residual stress component of σ_x are determined for 0°, 30°, 45°, 60° and 90° orientation angles. Yielding begins for 0° and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. However, it starts first at the upper surface for 30° and 45° orientation angles. The elastic–plastic analysis is carried out for both the plastic region which spreads only at the upper surface and the plastic region which spreads at the upper and lower surfaces together. The residual stress components of σ_x and τ_xy are also determined. The intensity of the residual stress component is maximum at the upper and lower surfaces of the beam, but the residual stress component of τ_xy is maximum on or around the x-axis. The beam can be strengthened by using the residual stresses. The distance between the plastically collapsed point and the free end is calculated for the same load in the beam for 0°, 30°, 45°, 60° and 90° orientation angles.     

Study of tribofilms formed during dry sliding of Ta2AlC/Ag or Cr2AlC/Ag composites against Ni-based superalloys and Al2O3

Herein we show that dry sliding, in air, in the 25–550 °C temperature range, of the novel Ta₂AlC/20 vol.% Ag and Cr₂AlC/20 vol.% Ag composites against Ni-based superalloys (SAs) and alumina led to the formation of steady-state tribofilms whose thicknesses and compositions varied depending on sliding conditions. At elevated temperatures, under both isothermal and thermocyclic conditions, relatively thick (>0.5 μm) well-compacted “glaze” lubricious tribofilms were developed as a result of joint action of tribo-chemical and tribo-mechanical factors involving repeated tribo-oxidation, mixing, fracturing, sintering, etc. They were mainly composed of oxidized constituents from both counterparts (if slid vs. SA) or solely from MAX-Ag ones (vs. Al₂O₃) and possessed a fine multi-layered microstructure, i.e. a more oxidized thin outermost layer and a less oxidized carbide-containing thicker inner layer. During thermocycling the tribofilms adapted to 25–550 °C temperature variations and preserved their primary macro- and microstructure, hardness, good adhesion to the matrix and lubricating characteristics. Consequently, the tribological properties of MAX-Ag/SA tribocouples did not deteriorate, but slightly improved with sliding distance. A possible mechanism of tribofilm generation and their transformations at various temperatures is discussed. The effect of SA and alumina counterparts on the formation and degradation of the tribofilms are also discussed.