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.     

Radial fretting behaviours of dental ceramics

Radial fretting tests on a Si₃N₄ ceramics ball opposite to the two dental ceramics flats (Vita VMK95 and Cerec Vita Mark II) have been carried out. The test apparatus was developed from a tension-compression hydraulic machine. Maximum normal load (F_max) was varied from 100 to 800 N with a speed of 6 mm/min, and the number of cycles from 1 to 10⁵. The fretting scars were examined by optical microscope and laser confocal scanning microscope (LCSM). The results of kinetics behaviours showed that all loading and unloading curves of load (F)–displacement (D) curves were almost superposed in the whole fretting process for two dental ceramics under a lower normal load (), and all F–D curves opened, correspondingly some micro-cracks initiated and developed in contact area, when the normal load increased to a higher level (). Under lower normal load, the fretting scars displayed the worn zones in shape of annulus. The cracks in shape of homocentric circularity can be observed for Vita VMK95 at and for Cerec Vita Mark II at . Therefore, there is better radial fretting damage resistance for Cerec Vita Mark II. In the microslip zone, the microscopic analysis showed that the particles detached by the mechanism of delamination. It the meantime, the competing mechanisms of fatigue cracks and wear also were discussed in this paper.     

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.     

A full factorial investigation of the erosion durability of automotive clearcoats

A full factorial experimental investigation has been carried out into factors affecting the resistance of a commercial acrylic/melamine automotive clearcoat to erosion by silica sand particles. The factor variables and their ranges were: particle size 125–425 μm; temperature 30°C–65°C; impact angle 30°–90°; particle velocity 35 m s⁻¹–55 m s⁻¹; and the baking process applied to the coating. An empirical linear regression model for the erosion response of the coating with R²_adj=97.5% was generated from the data. The regression coefficients of this model quantify the relative strengths of the effects of each of the factors. Several interactions between the factor variables were identified. In particular, the glass transition of the coating, which occurs at 40°C, has a significant effect on its response to erosion. The study has allowed the combinations of conditions that would be of most concern for automotive paint users to be identified.     

Dual-motion fretting behavior of mandibular cortical bone against pure titanium

Dual-motion fretting tests of flat cortical bone specimens from fresh human mandible against pure titanium (TA2) ball were carried out on a modified test rig with tilt angle of 45°. The imposed maximal loads varied from 100 to 200 N. Dynamic characteristics of dual-motion fretting tests were analyzed in combination with micro-examinations via optical microscopy (OM), laser confocal scanning microscopy (LCSM) and scanning electron microscopy (SEM) together with energy dispersive X-ray spectrum (EDX). Two types of F-D curves (the trapezoid and elliptic mode) were recorded during the tests. The examination showed that the wear scars of the dual-motion fretting were asymmetric, and the tangential component of dual-motion fretting was in the mixed fretting regime. Under the lower imposed load, only some detachment of particles and scratches without cracking were observed even after 5×10⁴ cycles. The main wear mechanisms of the dual-motion fretting damage were the abrasive and adhesive wear. Under higher imposed loads, the cracks initiated and propagated mainly at the high stress side of contact edges. The wear mechanisms of the dual-motion fretting of cortical bone under higher imposed loads were the combination of the adhesive wear, abrasive wear, cracking and lubrication of the human bone tissue debris. And the lubrication of the debris played an important role during the dual-motion fretting processes.     

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.     

Low-Friction MoS x Coatings Resistant to Wear in Ambient Air of Low and High Relative Humidity

The investigation of the tribological performance of MoS₂-based coatings in air of high humidity is critical for the future use of such low-friction and high-wear-resistant coatings in ambient air. Sulfur-deficient MoS _x coatings with a basal plane (x = 1.3) and a random (x = 1.8) crystallographic orientation were produced by planar magnetron sputtering. The coefficient of friction and the wear loss of MoS_x coatings in comparison with TiN and amorphous TiB₂ coatings were investigated in bi-directional sliding fretting tests performed in ambient air of different relative humidity. The wear rate expressed as a volumetric loss per unit of dissipated energy was determined. From these results, the best friction and wear performance was achieved with basal-plane-oriented MoS _x coatings tested at a relative humidity in the range of 10-50%. A coefficent of friction of 0.06-0.08 and a wear rate of 4 × 10³ m³J^-1, at a normal load of 1 N and a fretting frequency of 10 Hz, were recorded for that type of MoS _x coatings.     

The high strain rate compression of 7039 aluminium

Aluminium alloy 7039 was compressed at strain rates between 2 × 10³ and 2·5 × 10⁴s⁻¹ using a modified Hopkinson bar. At strain rates between 2 × 10³ and 1·2 × 10⁴s⁻¹ there was a linear relationship between the flow stress and strain-rate with a slope corresponding to a macroscopic viscosity of 2·9 kPa s. At strain rates between 1·2 and 2·5 × 10⁴s⁻¹ there was a levelling out of the flow stress, but the data was too scattered to give a definite trend. Due to the opposing effects of linear work-hardening and adiabatic heating, at strains above 0·15 the specimens work-softened at a rate inversely proportional to the square root of the strain rate. At the higher strains, specimens cracked along the dominant adiabatic shear band formed during the compression.     

An experimental investigation on composite fretting mode

An apparatus for composite fretting tests on a steel ball opposite to the inclined steel flat with different inclined angles (60° and 45°) have been carried out. During the tests, the maximum imposed loads were varied from 200 N to 400 N and 800 N at a constant loading speed of 12 mm/min. Dynamic analysis in combination with microscopic examinations through optical microscopy, profilometery, and SEM have been performed. Composite fretting behaviour has been analyzed and compared with the conventional fretting.     

Closed-form solution for wedge cutting force through thin metal sheets

A simple kinematic model is developed which describes the main features of the process of the cutting of a plate by a rigid wedge. It is assumed in this model that the plate material curls up into two inclined cylinders as the wedge advances into the plate. This results in membrane stretching up to fracture of the material near the wedge tip, while the “flaps” in the wake of the cut undergo cylindrical bending. Self-consistent, single-term formulas for the indentation force and the energy absorption are arrived at by relating the “far-field” and “near-tip” deformation events through a single geometric parameter, the instantaneous rolling radius. Further analysis of this solution reveals a weak dependence on the wedge angle and a strong dependence on friction coefficient. The final equation for the approximate cutting force over a range of wedge semiangles 10° ≤ θ ≤ 30° and friction coefficients 0.1 ≤ μ ≤ 0.4 is: F = 3.28σ₀(δ_t)^0.2l^0.4t^1.6μ^0.4, which is identical in form and characteristics to the empirical results recently reported by Lu and Calladine [Int. J. Mech. Sci.32, 295–313 (1990)].This analysis is believed to resolve a controversy recently developed in the literature over the interpretation of plate cutting experiments.     

A new method for determining the mechanical stability of lubricating greases

Mechanical stability is of central importance when dealing with the long-term service-length of grease-lubricated roller bearings. Poor stability will lead to consistency degradation of the grease, because of mechanical forces between the rolling parts of the bearing. The result can be leakage of grease through seals, or at worst a total failure of the bearing. The present investigation was initiated because present-day methods for prediction of mechanical stability show weak correlation with real service-length. The aim of the project was to develop a useful alternative. In order to fulfil this, both field tests and laboratory tests were carried out. In the field tests, nine different commercial greases were examined in the wheel bearings of five ore waggons, used for transporting ore by railroad from the Kiruna Mine in northern Sweden to Narvik in northern Norway for shipping to foreign markets. The test ore waggons travelled a distance of about 300,000 km during a period of 3 years. Small samples of greases were taken, on eight different occasions, for consistency testing. After the end of the test period, the damage on the bearings was also studied. In the laboratory tests, new undestroyed greases of the same brand as in the field tests were examined using conventional methods, such as the V2F, the Roll Stability Test and the Grease Worker. Comparisons between the field tests and these laboratory tests indicate poor correlation. In addition to these conventional methods, the relevance of the shear strength of the greases to the prediction of the mechanical stability was also tested. The shear stress τ_L depends on the applied pressure p, thus τ_L=τ₀+γ·p where τ₀ is the shear stress at atmospheric pressure. γ is a property of the lubricant in the same way as viscosity or density. It was found that γ correlates well with the mechanical stability in service. Increased γ values lead to a decrease in the mechanical stability. One reasonable explanation is that high γ values correspond to high shear stresses in the grease, and thus severe conditions for the thickener.     

Onset of matrix cracking in angle-ply ceramic matrix composites

The problem of initial damage in angle-ply [−θ_m/0_n/θ_m] and [−θ/θ] ceramic matrix composites subjected to axial tension is considered in this paper. The damage is in the form of matrix cracks that may appear in either inclined (−θ and θ lamination angle) or longitudinal layers. As follows from the analysis, if the lamination angle of the inclined layers is small, the initial failure occurs in the 0-layers of [−θ_m/0_n/θ_m] composites or in [−θ/θ] composites in the form of bridging cracks. However, if the inclined layers form a larger angle with the load direction, they fail due to tunneling cracks. It is shown that the boundary between two different modes of failure in a representative SiC/CAS composite corresponds to a lamination angle equal to 35° in the case of [−θ_m/0_n/θ_m] composites. In the case of [−θ/θ] laminates, the boundary value of the lamination angle is equal to 45°, i.e. bridging cracks form if θ<45° and tunneling cracks appear if θ>45°.     

The friction behavior of Ni-, SiO2- and mica sodium silicate-based solid lubrication composites

The friction behavior of Ni⁻-, SiO⁻₂- and mica sodium silicate-based lubricant composites, which included BN, WS₂ and graphite as lubricants, were examined. A ring-on-disk apparatus, in which a solid lubricant composite disk was held against a rotating stainless ring, was used as the test configuration. The tests were run with a load from 62 to 250 N in temperatures from 20 to 800°C in the laboratory environment. The wear surface was characterized by scanning electron microscope and X-ray photo spectroscopy. The major findings were that both mica sodium silicate- and SiO⁻₂-based composites failed at above 500°C due to severe wear and surface damage; in contrast, Ni⁻-based composite showed a stable friction coefficient and low wear from 20 to 800°C.     

Rotor dynamic instability analysis on hybrid air journal bearings

Hybrid air journal bearings with multi-array of 1, 2, 3, 4, or 5-row orifice feedings are analyzed for the problem of rotor dynamic instability. The bearing stiffness and damping coefficients are calculated numerically to determine threshold rotor mass under various operating conditions. The hybrid porous air journal bearings are also analyzed for comparison to investigate the similarities in dynamic characteristics between the multi-array of orifice feeding bearings and the porous bearings. The results show that the porous bearing is more stable than the orifice feeding bearing at lower rotation speeds (Λ<0.1) or at higher rotation speeds (Λ>1) with lower feeding parameters (λ_P<10⁻⁸). The 5-row orifice feeding bearing is more stable than the porous bearing at moderate speeds (0.3<Λ<0.6) with lower feeding parameters (λ₀<10⁻⁴).     

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.     

Linear free vibration analysis of cross-ply laminated cylindrical helical springs

A linear free vibration analysis of symmetric cross-ply laminated cylindrical helical springs is performed based on the first-order shear deformation theory. Considering the rotary inertia, the shear and axial deformation effects, governing equations of symmetric laminated helical springs made of a linear, homogeneous, and orthotropic material are presented in a straightforward manner based on the classical beam theory. The free vibration equations consisting of 12 scalar ordinary differential equations are solved by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy. The soundness of the present results are verified with the reported values which were obtained theoretically and experimentally. After presenting the non-dimensional graphical forms of the free vibrational characteristics of (0°/90°/90°/0°) laminated helical spring made of graphite-epoxy material (AS4/3501-6) with fixed–fixed ends, a non-dimensional parametric study is worked out to examine the effects of the number of active turns, the shear modulus in the 1–2 plane (G₁₂), the ratio of the cylinder diameter to the thickness (D/d), and Young's moduli ratio in 1 and 2 directions (E₁/E₂) on the first six natural frequencies of a uniaxial composite helical spring with clamped-free, clamped-simple, and clamped–clamped ends.     

Study of seizure of coated and treated titanium alloy under fretting conditions

Titanium alloys are well known to present poor sliding behaviour and high wear values. Various coatings (soft thick coatings and thin hard coatings) and treatments have been tested to prevent such an occurrence under fretting conditions at high frequency of displacement (100 Hz). An original test apparatus, using an open-loop system, has been performed to directly display the phenomenon of seizure. No seizure was recorded at low load (6 N), while, at higher load (10 N), all samples undergo a more or less early seizure. The total sliding distance D₀ proved to be a pertinent parameter to study the seizure resistance. Furthermore, the results highlight that D₀ is linked to the total energy dissipated in the contact, E_dt, and reveal two distinct behaviours at low load, which suggest two distinct dissipating mechanisms of energy. The first trend can be connected with the plastic deformation and the trapping process of debris within the contact zone occurring on soft coatings. The second trend can be related to the higher debris ejection observed on hard samples. So, soft thick coating satisfies most of the chosen criteria except those of wear. In contrast, thin and hard coatings are not sufficient to totally protect the substrate but they are already able to efficiently reduce wear.     

Plate-like wear particle formation in a lubricated ball-on-plate friction pair

The mechanism of formation of plate-like wear particles in a ball-on-plate lubricated friction pair has been examined for wear constants of K < 10⁻¹⁰ (mm³ mm⁻¹ N⁻¹). The plate Vicker's hardness was 2.80–3.00 kN/mm², the sliding speed 1.74 m s⁻¹ and the load 50 N. The following mechanism is suggested: scratching of the surface and formation of ridges at the scratch border, lateral deformation of ridges and formation of thin sheets, and cracking and separation of plate-like particles from these sheets.     

Large deformation compression–torsion behaviour of a titanium alloy and its modelling

A range of sequential and compound compression-torsion tests has been carried out on titanium alloy IMI834 at 1000°C and nominal true strain rate 5 × 10⁻³ s⁻¹, typical of forging conditions. The tests were used to investigate initial and subsequent yield and flow behaviour, the nature of the material hardening and the effect of flow softening on subsequent deformation. In addition, a material model with isotropic or directional hardening has been used to predict the material behaviour.The results show that the material behaviour at large strains is reasonably isotropic, although a directional hardening model provides slightly better quantitative agreement with the experimental results. Large pre-strains (0.4), either axial or torsional, are found not to change significantly subsequent material behaviour. A stress state dependence of flow softening is observed to exist.The material model presented is shown to give good quantitative agreement of predicted and experimental results.     

Fretting behaviour of galvanised steel

The present work describes research conducted on the fretting behaviour of S 355 MC galvanised steel sheet. In order to study the influence of the normal load and the displacement effect, some of the specimens were galvanised by hot dipping and the rest were only polished before being tested. Fretting tests were carried out on a specially developed fretting rig prototype under ‘crossed-cylinders’ contact geometry. Tests were done during 0.72×10⁶ cycles in laboratory air conditions. The tangential force and the displacement were measured in order to establish the fretting cycles for each fretting condition. The fretted surfaces were analysed by means of optical and scanning electron microscopes to identify the main wear mechanisms. Three different fretting regimes were identified: the stick regime; the slip regime; and the mixed stick–slip regime, which depended mainly on the influence of the normal load and the stroke.