Three-parameter approach for elastic–plastic fracture of the semi-elliptical surface crack under tension

Systematic three-dimensional elastic–plastic finite element analyses are carried out for a semi-elliptical surface crack in plates under tension. Various aspect ratios (a/c) of three-dimensional fields are analyzed near the semi-elliptical surface crack front. It is shown that the developed J–Q annulus can effectively describe the influence of the in-plane stress parameters as the radial distances (r/(J/σ₀)) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/σ₀) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σ_e, the hydrostatic stress σ_m and the stress triaxiality R_σ, the three-parameter J–Q_T–T_z approach is proposed based on the numerical analysis as well as a critical discussion on the previous studies. By introducing the out-of-plane stress constraint factor T_z and the Q_T term, which is determined by matching the finite element analysis results, the J–Q_T–T_z solution can predict the corresponding three-dimensional stress state parameters and the equivalent strain effectively in the whole plastic zone. Furthermore, it is exciting to find that the values of J-integral are independent of n under small-scale yielding condition when the stress-free boundary conditions at the side and back surfaces of the plate have negligible effect on the stress state along the crack front, and the normalized J tends to a same value when φ equals about 31.5° for different a/c and n. Finally, the empirical formula of T_z and the stress components are provided to predict the stress state parameters effectively.     

Finite element analysis of the rake angle effects in orthogonal metal cutting

The plane-strain finite element method is developed and applied to model the orthogonal metal cutting of annealed low carbon steel with continuous chip formation. Four sets of simulation results for cutting with −2°, 0°, 5°, and 15° rake angle are summarized and compared to analyze the effects of rake angle in the cutting processes. The initial and deformed finite element meshes, as the cutting reaches steady-state condition, are first presented. Simulation results of the cutting forces and residual stresses, along with the X-ray diffraction measurements of the residual stresses generated using a worn cutting tool with 5° rake angle, are used to identify the influences of the rake angle and tool sharpness. Elements are selected to represent three sections along the shear and contact zones and under the cut surface. The normal and shear stresses, distributions of parameters along these three sections, and contours of temperature, plastic strain, and effective stress are then presented. Limitations of the finite element method for metal cutting simulation are discussed.     

Fretting fatigue of single crystal nickel at 600 °C

An experimental setup has been developed to conduct fretting fatigue tests at 610 °C and fretting fatigue lives are characterized for the contacting pair of IN100 and single crystal nickel subjected to a range of loading conditions. A well characterized set of experiments have been conducted to obtain the friction coefficient in the slip zone. A robust quasi-analytical approach, based on solution to singular integral equations, has been used to analyze the contact stresses. Different multi-axial fatigue parameters have been investigated for their ability to predict the initiation life of the specimens. An estimation of crack propagation life was made using conventional fracture mechanics approaches, after making certain assumptions to simplify the problem. Total life was predicted using nucleation life from different parameters and propagation life from conventional fracture mechanics approach. These predicted lives were compared with experimentally observed failure lives. The quality of the comparison provides confidence in the notion that conventional life prediction tools can be used to assess fretting fatigue at elevated temperatures.     

Lattice distortions in GaN on sapphire using the CBED–HOLZ technique

The convergent beam electron diffraction (CBED) methodology was developed to investigate the lattice distortions in wurtzite gallium nitride (GaN) from a single zone-axis pattern. The methodology enabled quantitative measurements of lattice distortions (α, β, γ and c) in transmission electron microscope (TEM) specimens of a GaN film grown on (0, 0, 0, 1) sapphire by metal-organic vapour-phase epitaxy. The CBED patterns were obtained at different distances from the GaN/sapphire interface. The results show that GaN is triclinic above the interface with an increased lattice parameter c. At 0.85 μm from the interface, α=90°, β=8905° and γ=11966°. The GaN lattice relaxes steadily back to hexagonal further away from the sapphire substrate. The GaN distortions are mainly confined to the initial stages of growth involving the growth and the coalescence of 3D GaN islands.     

Effects of Mn content and texture on fatigue properties of as-cast and extruded AZ61 magnesium alloys

Fatigue behavior of as-cast and extruded AZ61 magnesium alloys in ambient air (20 °C–55%RH) was investigated. It was found that size and distribution of cast defect influenced tensile and fatigue performance of the as-cast alloy. Fatigue limit of the as-cast alloy was significantly low compared to the extruded alloy. The casting defects served as stress concentration sites for fatigue crack nucleation. Fatigue tests were also carried out on a high Mn content alloy. All of the specimens failed from an inclusion near the specimen surface. Fatigue limit of Mg alloy with high Mn content was lower compared to that of the low Mn content alloy. Further, investigation on the effect of texture on fatigue and fatigue crack growth behavior of the extruded AZ61 magnesium alloy plate was carried out. The results showed that fatigue strength in the longitudinal direction to the extruded direction was higher compared to those in the transverse and 45° directions. Significant effect of specimen orientation on fatigue crack growth behavior for both short and long cracks was found near the threshold region. However, regardless of specimen orientation, the da/dN–ΔK_eff curves for all three kinds of specimens were in a narrow band. It is suggested that the difference in the fatigue life among the specimen orientations will be mainly due to the difference in the crack closure behavior. A transition of fracture mechanism was found for a long crack. Slip fracture mechanism was dominant above the transition point, whereas below the transition point, slip fracture mechanism was associated with cleavage fracture.     

Analysis of internal cracks in railway wheels under experimentally determined pressure distributions

In recent years much effort has been devoted to the definition of design approaches of railway systems based on the analysis of the system itself and on accurate knowledge of its effective working conditions. In this paper, the attention is focused on railway wheels. This latter component is subjected to different types of damage: sub-surface crack propagation is considered. The prediction of the evolution of this process depends on the knowledge of the stress intensity factors concerning modes I, II and III, which are dependant both on the total load acting on the wheel and on how the load is transmitted through the wheel/rail interface. However, until now the solutions commonly used consider a theoretical (Hertzian) pressure distribution, even if, due to wear or to the dynamic phenomena, the actual contact patch can be strongly different for most of the lifespan of the wheel. An approach is developed with the aim to solve the case of an internally cracked wheel subjected to an arbitrary contact patch and pressure distribution. It is based on Boussinesq's formulae and utilises a three-dimensional finite element model of the part of the wheel close to the crack to calculate the stress intensity factors along a curvilinear crack front. Pressure distributions experimentally determined by means of a technique based on the reflection of high-frequency ultrasonic waves from the wheel–rail interface were applied to internal cracks in wheels: the results were critically compared with the those obtained by considering Hertzian pressure distributions, the aim being the assessment of the influence of the contact conditions in respect of damage cause by internal crack propagation.     

Thermomechanical analysis of elastoplastic medium in sliding contact with fractal surface

The effects of mechanical and thermal surface loadings on deformation of elastic–plastic semi-infinite medium were analyzed simultaneously by using the finite element method. Rigid rough surface of a magnetic head and smooth surface of an elastic–plastic hard disk were chosen to perform a comprehensive thermo-elastic–plastic contact analysis at the head–disk interface (HDI). A two-dimensional finite element model of a rigid rough surface characterized by fractal geometry sliding over an elastic–plastic medium was then developed. The evolution of deformation in the semi-infinite medium due to thermomechanical surface loading is interpreted in terms of temperature, von Mises equivalent stress, and equivalent plastic strain. In addition to this, the effects of friction coefficient, sliding, and interference distance on deformation behavior were also analyzed. It is shown that frictional heating increases not only the contact area but also the contact pressure and stresses.     

Limit loads for cylindrical shells subjected to local longitudinal bending moments

Tests have been carried out on mild steel cylindrical shells, each with a radial square bar attachment welded at its mid length. Loads were applied to each attachment so that the shell was subjected to a longitudinal bending moment. On four specimens, elastic strains were measured so that stress distributions in the shell could be compared with theoretical distributions. Fourteen specimens were loaded so that gross deformation took place. Deformations and strains were measured and on two specimens, crack patterns on an oxide layer were observed. With increasing load, the plastic deformation of specimens developed gradually and not in the sudden manner associated with theoretical rigid-plastic collapse. Experimental plastic limit moments are compared with theoretical values calculated by an upper bound analysis. The range of radius/thickness values investigated was 18·3–53·5, and the half width/radius ratios were between 0·120 and 0·356.     

Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation

Many studies have shown that finite element modeling (FEM) can be used to fit experimental load–displacement data from nanoindentation tests. Most of the experimental data are obtained with sharp indenters. Compared to the spherical case, sharp tips do not directly allow the behavior of tested materials to be deduced because these produce a nominally-constant plastic strain impression. The aim of this work is to construct with FEM an equivalent stress–strain response of a material from a nanoindentation test, done with a pyramidal indenter. The procedure is based on two equations which link the parameters extracted from the experimental load–displacement curve with material parameters, such as Young's modulus E, yield stress Y₀ and tangent modulus E_T. We have already tested successfully the relations on well-known pure metallic surfaces. However, the load–displacement curve obtained using conical or pyramidal indenters cannot uniquely determine the stress–strain relationship of the indented material. The non-uniqueness of the solution is due to the existence of a characteristic point (ε_c, σ_c); for a given elastic modulus, all bilinear stress–strain curves that exhibit the same true stress σ_c at the specific true strain ε_C lead to the same loading and unloading indentation curve. We show that the true strain ε_c is constant for all tested materials (Fe, Zn, Cu, Ni), with an average value of 4.7% for a conical indenter with a half-included angle θ=70.3°. The ratio σ_c/ε_c is directly related to the elastic modulus of the indented material and the tip geometry.     

A study of the wear behavior of polymer–matrix composites containing discontinuous nanocrystalline alloy reinforcements

The tribological behavior of bakelite resin–matrix composites reinforced with nanocrystalline Al 6061 T6 particles produced by machining (grain size 70–500 nm) has been studied using block-on-ring and pin-on-disk tests. The polymer–matrix composite reinforced with nanostructured Al 6061 particles aged for 10 h [Al 6061 (3) 10 h] shows a wear reduction of around 60% with respect to the conventional microstructured reinforcement. Also it shows the lowest wear rates when compared with the nanostructured reinforcements aged for 5 h or 1 h, respectively. Friction coefficients and wear rates increased with increasing sliding speed and normal load. Under 10 N and 0.10 m s⁻¹, Al 6061 (3) 10 h showed an initial friction and contact temperature increase and a very severe wear with material transfer to the steel ball surface. Increasing the steel–composite contact temperature to 100 °C (1 N; 0.05 m s⁻¹) produced a one order of magnitude decrease both in friction and wear. Wear mechanisms for the polymer matrix and the aluminum reinforcement are discussed on the basis of SEM and EDS observations.     

A study on the initial crack curving angle of isotropic/orthotropic bimaterial

In this paper, when the initial propagation angle of a branched crack is calculated from the maximum tangential stress criterion (MTSC) and the minimum strain energy density criterion (MSEDC), it is essential that you use stress components in which higher order terms are considered and stress components at the position in a distance 0.005 mm from the crack tip ( =γ . When an interfacial crack propagates along the interface at a constant velocity, the initial propagation angles of the branched crack are similar to the mode mixities (phase angle) and the theoretical values obtained from MTSC and MSEDC. The initial propagation angle of the branched crack depends considerably on the stress intensity factor K{IN2}.     

Fatigue behaviour of a commercial zinc-aluminium eutectoid alloy

Constant-amplitude, flexural-fatigue tests have been carried out over the frequency range 8–100 Hz and the temperature range 293–373°K on a commercial zinc-aluminium alloy of basically eutectoid composition. This alloy is highly superplastic at 530°K, when the strain-rate sensitivity of the flow stress index, m, 0·5. At 293°K some residual superplasticity exists and this manifests itself as a frequency effect in the fatigue behaviour. This effect is almost certainly the result of room-temperature, strainrate sensitivity; it is shown by the fact that when the superplastic microstructure is destroyed, the frequency effect disappears. Finally, it is shown that the model proposed by Morrow successfully predicts the fatigue life of this alloy.     

Dry wear and friction behaviour of plasma nitrided Ti–6AL–4 V alloy after explosive shock treatment

The unlubricated wear behaviour of explosive shock treated and, subsequently plasma nitrided Ti–6Al–4 V alloy was studied using a ball-on-disc wear tester. Plasma nitriding was carried out at three different temperatures (700, 800 and 900 °C) for 3, 6, 9 and 12 h. Plasma nitriding after explosive shock treatment enabled a reduction in the wear rate of two orders of magnitude. Detailed investigations of this improved wear performance dependent on the nitriding temperature and time were carried out. The friction and wear data showed a clear breakthrough transition from the nitrided layer to the core of the Ti–6Al–4 V alloy matrix. The lowest wear volume was obtained for the sample, nitrided at 900 °C for 12 h, especially at loads of 2.5, 5 and 7.5 N. Obviously, the hard nitride layers were intimately associated with low wear rate, providing a smooth low friction surface. The coefficient of friction reduced from 0.46 to 0.2 due to a thick and hard compound layer resulting from a high nitrogen diffusion rate caused by explosive shock treatment that expected to increase point defects in the alloy. Detailed examination of the wear tracks showed that plasma nitriding changes the mechanism of wear from one of adhesion for untreated Ti–6Al–4 V to both delamination and mild abrasive.     

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.     

Fretting fatigue behaviour of Ti–6Al–4V alloy under plane bending stress and contact stress

Fretting fatigue tests for Ti–6Al–4 V alloy were conducted by use of the plate fatigue specimen with bolt-tightened shoe on both sides of the plate. It was clarified that the repeated bending stress at the contact area where fretting fatigue failure starts linearly decreased as stress over the contact area increased. Fretting fatigue crack starts from the pit where stress concentrate. The pit initiates when fretting debris were removed from the surface striation formed due to the contact slip movement. The fretting fatigue crack initiation mode was transgranular, while the fretting fatigue crack propagation mode was striation.     

Dry sliding wear of Cu–15Ni–8Sn alloy

Using a pin-on-disc apparatus, the wear behavior of Cu–15Ni–8Sn alloy aged for different periods of time at 400 °C was investigated under dry condition. The results showed the wear rate was inversely proportional to the hardness of the alloy, but the maximum wear resistance was not consistent with maximum hardness. The alloy contained about 10% (volume) cells precipitated along grain boundaries had the lowest wear rate. The friction coefficient was constant for different hardness. SEM micrographs of the debris and pin revealed that the removal process of surface material involved subsurface deformation, crack nucleation, crack propagation and delamination of the material.     

Progression of fretting fatigue damage in Ti–6Al–4V

An investigation was conducted to explore the nature of fretting fatigue damage in the stages prior to crack formation. In the unique experimental apparatus employed in this study, where total slip never occurs, several locations on each test specimen exist where cracks can develop due to local contact conditions. Under the test conditions used, not all of the sites had cracks upon test completion. This study evaluated the condition of non-cracked sites on several fretted specimens in an effort to identify differences between these and sites where small cracks were observed.A single test condition of 620 MPa average applied static clamping stress and 250 MPa applied axial fatigue stress for R=0.5 was selected, which corresponds to a fretting fatigue life of 10⁷ cycles based on prior work. For specimens tested to 10⁶ cycles, or 10% of life, several destructive and non-destructive characterization methods were chosen: scanning electron microscopy (SEM), residual stress measurement and transmission electron microscopy (TEM). Each site at which crack nucleation could be expected was inspected in the SEM and was then characterized using surface X-ray diffraction to quantify the residual stresses field near that location. Then TEM foils were cut from one area on a specimen with tiny cracks and dislocation densities were observed. A novel technique was used which permitted TEM samples to be obtained from regions in close proximity on the original specimen.Comparisons were made between as-received (AR) and stress-relief annealed (SRA) specimens, on which the stress-relief was applied prior to fretting fatigue testing. SEM inspection was useful for qualitative analysis of wear debris and identification of cracks as small as 20 μm, but was unable to provide quantitative data on the level of fretting fatigue damage beyond crack size. Although differences were noted in the residual stresses for the SRA versus the AR specimens, no residual stress peaks were noted in the edge of contact regions where cracks would eventually develop. TEM observations in the vicinity of the crack nucleation region showed that the dislocation structure decayed rapidly into the specimen thickness. The cause of the dislocations was attributed to plastic deformation caused by the clamping stresses.     

Characterization of fretting fatigue crack initiation processes in CR Ti–6Al–4V

A study was conducted to quantify fretting fatigue damage and to evaluate the residual fatigue strength of specimens subjected to a range of fretting fatigue test conditions. Flat Ti–6Al–4V specimens were tested against flat Ti–6Al–4V fretting pads with blending radii at the edges of contact. Fretting fatigue damage for two combinations of static average clamping stress and applied axial stress was investigated for two percentages of total life. Accumulated damage was characterized using full field surface roughness evaluation and scanning electron microscopy (SEM). The effect of fretting fatigue on uniaxial fatigue strength was quantified by interrupting fretting fatigue tests, and conducting uniaxial residual fatigue strength tests at R=0.5 at 300 Hz. Results from the residual fatigue strength tests were correlated with characterization results.While surface roughness measurements, evaluated in terms of asperity height and asperity spacing, reflected changes in the specimen surfaces as a result of fretting fatigue cycling, those changes did not correspond to decreases in residual fatigue strength. Neither means of evaluating surface roughness was able to identify cracks observed during SEM characterization. Residual fatigue strength decreased only in the presence of fretting fatigue cracks with surface lengths of 150 μm or greater, regardless of contact condition or number of applied fretting fatigue cycles. No cracks were observed on specimens tested at the lower stress condition. Threshold stress intensity factors were calculated for cracks identified during SEM characterization. The resulting values were consistent with the threshold identified for naturally initiated cracks that were stress relieved to remove load history effects.     

Fretting fatigue strength estimation considering the fretting wear process

In fretting fatigue process the wear of contact surfaces near contact edges occur in accordance with the reciprocal micro-slippages on these contact surfaces. These fretting wear change the contact pressure near the contact edges. To estimate the fretting fatigue strength and life it is indispensable to analyze the accurate contact pressure distributions near the contact edges in each fretting fatigue process.So, in this paper we present the estimation methods of fretting wear process and fretting fatigue life using this wear process. Firstly the fretting-wear process was estimated using contact pressure and relative slippage as follows:

W=K×P×S,