A fractographic study of fatigue failure in two high strength steels

Results are given of a detailed fractographic study of a commercial 1 1/2 Ni-Cr-Mo steel (S95 Specification) and a high purity laboratory-made steel of similar alloy content tested in uniaxial alternating and pulsating loading. The specimens were hardened by oil quenching and tempering to strength levels of 1544 and 1930 MN/m² (100 and 125 tonf/sq. in.). tested at room temperature and the fractures examined by scanning-electron and optical microscopes and by the electron microscope employing a two stage replication technique.All fractures consisted essentially of a fatigue region and a region of tensile failure; the former appeared, in all instances, to be nucleated at non-metallic inclusions. The fatigue regions were composed of smooth featureless areas (probably resulting from micro-cleavage in the tempered martensite), areas of intergranular separation along prior austenite grain boundaries (although very seldom observed in the high purity alloy) and areas exhibiting characteristic striation. The nature of the regions of tensile failure was markedly dependent on steel purity; the primary mode of fracture in the commercial steel was along prior austenite grain boundaries while in the high purity alloy final separation occurred predominantly by ductile shearing. Estimates of fatigue crack growth rates derived from striation spacing data are given.The authors are indebted to Mr. B. E. Hopkins for his advice and encouragement throughout the programme. They would like to thank Mrs. Daphne Thomas for her painstaking work with the scanning electron microscope. The assistance of Mr. K. B. Armstrong, Mr. N. B. Owen and Mr. J. M. Jennings with the fatigue testing phase of the investigation is gratefully appreciated.The work described above has been carried out as part of the General Research Programme of the National Physical Laboratory.     

Three-dimensional effects in the modelling of ICPTs

In this paper, we numerically investigate the 3-D effects of different flow operating conditions and of complete or simplified treatments of the electromagnetic field on the characteristics of Ar and Ar/N₂ discharges in inductively coupled plasma torches working at atmospheric pressure. Simulations are performed by means of the commercial code FLUENT suitably customized to solve the electromagnetic field equations in the frame of an extended grid model. Steady state continuity, momentum and energy equations are solved for optically thin plasmas under the assumption of LTE and laminar flow. Results of parameterization on the net amount of power dissipated in the discharge, frequency of the RF generator, flow rate distribution of inlet gases and swirl velocity are presented, showing the impact of these parameters on the fluid dynamic and electromagnetic behaviour of the plasma.Received: 22 May 2003, Published online: 5 August 2003PACS: 52.75.Hn Plasma torches - 52.65.-y Plasma simulation - 52.80.Pi High-frequency and RF discharges     

强磁场对铝合金中溶质组元分布状态的影响效果

合金中溶质组元的组织形态和分布对于改善合金的组织和性能具有重要意义.本文研究了铝合金在强磁场作用下的凝固行为,考察了Al-Cu，Al-Mg合金中溶质组元的相形态、分布状况随高强度均恒磁场和梯度磁场的强度和方向变化的规律.研究发现，由于Cu元素和Mg元素的物性不同导致其在基体中受到的电磁力不同，在均恒磁场作用下，铝合金中Cu元素和Mg元素在α-Al基体晶粒内和晶界上的分布变化规律相反；在梯度磁场作用下，Cu元素和Mg元素在铝基体中含量和分布状态也有显著的差异.本研究为利用强磁场有效控制不同物性的溶质元素在合金基体中组织状态和分布提供了实验依据. 关键词： 强磁场 铝合金 溶质元素分布 凝固组织 凝固过程     

Numerical modelling of free interaction of shock waves in corner flows

The inviscid supersonic flows in corners between intersecting compression wedges were studied numerically. Under usual conditions, the flows in such corner configurations are conically self-similar. Besides, shock waves formed by wedges are plane and they interact with one another in these flows and the downstream development of the shock interaction structure at that occurs in a region which is bounded in cross-sectional directions by the walls and contracts towards the corner rib, and in this sense the above interaction of shocks may be subjected to influence of the rib. The corner flows of another type with an interaction of shocks not subjected to the “rib effect”, in other words free, were considered. This was ensured by that the corner configurations were designed with a gradually expanding gap along the rib in a way that the reflected shocks arising as a result of interaction passed through the gap without falling onto the walls. This eliminated the influence of a local flow near the corner rib on the interaction of plane shock waves formed by the wedges. The inviscid flows symmetric with respect to the bisector plane of the corner dihedral angle were considered. The computations showed that, in the gapped corner configurations with the free interaction of shocks, if these interactions were irregular, the cross-flow patterns were practically the same as in the original corner configurations without a gap. The conditions for the flows over corner configurations were also considered under which the interaction of shocks corresponded to the Neumann criterion of mechanical equilibrium. These conditions are equivalent to those, which take place in two-dimensional steady flows, when a hysteresis phenomenon is possible, which manifests itself in changing the moment of transition from a regime of regular reflection of shocks to an irregular one and conversely at a direct and inverse courses of varying the flow parameters—the Mach number and the inclination angle of the wedges. The conducted computations showed that a hysteresis is possible for considered corner flows in gapped configurations, but it must be followed by a detachment of shocks from the corner apex and a breakdown of the conical flow structure.     

Dynamic characterisation and longitudinal strength of swaged joints

Swaging is a cold working process involving plastic deformation of the work piece to change its shape. A swaged joint is a connection between two components whereby a swaging tool induces plastic deformation of the components at their junction to effectively bind them together. This is commonly used when welding or other standard joining techniques are not viable. Swaged joints can be found for example, in nuclear fuel assemblies to connect the edges of thin rectangular plates to a supporting structure or frame. The aim of this work is to find a model to describe the vibrational behaviour of a swaged joint and to estimate its strength in resisting a longitudinally applied load. The finite element method and various experimental rigs were used in order to find relationships between the natural frequencies of the plate, the joint stiffness and the force required to shift the plate against the restraining action of the swage connection. It is found that a swaged joint is dynamically equivalent to a simple support with the rotation elastically restrained and a small stiffness is enough to resist an important load.     

Three-dimensional modelling of micromachined-ultrasonic-transducer arrays operating in water

We report on the 3-D modelling of periodic arrays of capacitive micromachined ultrasonic transducers (cMUTs) operating in fluid. Specific developments have been performed to model biperiodic transducer arrays and to take into account radiation into any stratified media at the front-side as well as the back-side of the device. The model is based on a periodic finite-element-analysis/boundary-element-method (FEA/BEM). It is applied to micromachined ultrasonic transducers (MUTs), based on silicon-nitride-circular-membrane arrays on a silicon substrate, and operating in water. The spectrum characteristics of MUTs excited in phase are investigated, showing that very-large-band emission is achievable as previously demonstrated by many authors. However, other contributions are also found, depending on the excitation conditions, that do not radiate in the fluid. These contributions are identified as guided modes that could generate significant cross-talk effects. The origin and the nature of these modes is analyzed to gain insight in the actual operation of MUTs.     

Interaction of re-radiated Rayleigh waves with fatigue cracks

The usefulness of ultrasonic re-radiated Rayleigh waves for the detection of small surface-connected fatigue cracks in titanium alloy has been demonstrated. The variation in the frequency spectrum of re-radiated Rayleigh waves in the presence of a fatigue crack has been observed, and the sensitivity of this acoustic propagation mode in a scanning operation has been studied.     

Three-dimensional modelling of inductively coupled plasma torches

A three-dimensional model has been developed for simulating the behaviour of inductively coupled plasma torches (ICPTs), using customized CFD commercial code FLUENT ^?. The helicoidal coil is taken into account in its actual 3-D shape, showing the effects of its non-axisymmetry on the plasma discharge. Steady state, continuity, momentum and energy equations are solved for argon optically thin plasmas under the assumptions of LTE and laminar flow. The electromagnetic field is obtained by solving the 3-D vector potential equation on a grid extending outside the torch region. In order to evaluate the importance of various 3-D effects on calculated plasma temperature and flow fields, comparisons of our new results with the ones obtainable from conventional 2-D models and from an improved 2-D model that includes 3-D coil effects are presented. The presence of wall temperature hot spots due to plasma discharge displacement from the torch axis is evidenced, while the use of the new 3-D code for optimization of induction coil geometry and plasma gas inlet features is foreseen. Received 5 September 2002 Published online 13 December 2002 RID="a" ID="a"e-mail: colombo@ciram.ing.unibo.it     

Mathematical modelling of ultrasonic wave scattering by sub-surface cracks

Scattering of ultrasonic signals by a sub-surface crack in a specimen which is immersed in a water bath has been analysed on the basis of a mathematical model, which accounts for: (1) signal transmission across the water-solid interface; (2) partial illumination of the crack; (3) the relaiton between the crack-opening displacement and the received transducer signal; and (4) an accurate mathematical computation of the crack-opening displacement in the frequency domain. The modelling from the specified initial electrical pulse to the measured scattered signal is completed by converting the frequency-domain results to the time domain. Results are presented for both the pulse-echo and the pitch-catch configuration, and for a number of crack orientations and crack depths.     

Measurement of the growth of sub-microscopic fatigue cracks by ellipsometry

Aluminum (1100) samples have been monitored with ellipsometry during fatigue cycling. Large changes in the ellipsometric parameters Δ and ψ are believed to be primarily associated with the formation of a sub-microscopic network of cracks. The ellipsometric results are interpreted in terms of the Fenstermaker-McCrackin model for surface roughening modified to simulate the crack system.     

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of “edge functions” that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1−c/a), and the notch angle is defined as (360°−α). For a very small notch angle (1° or less), the notch may be regarded as a “sharp radial crack.” Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°−α), depths (1−c/a), and thickness ratios (a/h for plates and h/a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r(θ), several of which are described for future investigations and close extensions of this work.     

Study on probability of detection for fatigue cracks in sonic infrared imaging

Detection reliability of sonic infrared imaging is one of the increasingly important aspects for out of lab applications. And for the detection reliability evaluation, probability of detection (POD) for different defects under given test conditions has been successfully used as an accepted quantitative measurement. In this study, we test a set of C45 ferritic steel plates with artificial fatigue cracks. Experimental results show that the crack heating response increases with the increasing crack length, and the relationship between the logarithmic form of heat response signal and the crack length appears to be linear. Based on the above statistic characteristics, the linear regression analysis and the Wald method are adopted to estimate the POD function and its confidence interval. The study aims to provide a quantitative evaluation method for detection reliability in sonic infrared imaging.     

Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of micro-crack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field.     

Pervasive randomness in physics: an introduction to its modelling and spectral characterisation

An introduction to the modelling and spectral characterisation of random phenomena is detailed at a level consistent with a first exposure to the subject at an undergraduate level. A signal framework for defining a random process is provided and this underpins an introduction to common random processes including the Poisson point process, the random walk, the random telegraph signal, shot noise, information signalling random processes, jittered pulse trains, birth–death random processes and Markov chains. An introduction to the spectral characterisation of signals and random processes, via either an energy spectral density or a power spectral density, is detailed. The important case of defining a white noise random process concludes the paper.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

On-line detection of fatigue cracks using an automatic mode tracking technique

Experimental fatigue tests usually require large testing times. In addition to the resulting increased time-to-market, the large fatigue test time also implies that any structural health monitoring technique that is used should be automatic. When using the modal parameters as damage indicators, an important amount of user interaction is still needed to separate physical poles from computational ones. In this paper, an experimental framework will be developed to automatically track the health of the structure on-line with the performance of fatigue tests. The modal parameters are tracked using a combination of the maximum likelihood estimator and an auto-regressive model. Since confidence levels on the modal parameter are available it is possible to detect if damage is present. In addition, the quasi-static stiffness with computed confidence levels is also used as a damage indicator. The proposed techniques are demonstrated on a steel beam with a propagating fatigue crack.     

Sound strength and reverberation time in small concert halls

Sound strength and reverberation time measurements have been carried out in six small concert halls in Cambridge, UK. The sound strength G is a measure of the physical sound level in a concert hall and is closely related to the subjective sensation of loudness. It compares integrated impulse responses at a point in the measured room with that measured at ten metres distance in the free field.The aim of the measurements is to investigate the acoustic characteristics of the halls concerning sound strength and reverberation time. Furthermore the effect of the variable acoustics in the halls on these parameters is discussed in this paper. Especially for bigger ensembles it is often desirable to reduce the sound level in a small concert hall. The measurement results show that for a fixed hall volume, this can primarily be achieved by decreasing the reverberation time in the hall. However, with regard to the sound quality of a hall and the recommended reverberation times for chamber music, reverberation time cannot be reduced by an arbitrary extent. Therefore reverberation time and strength have to be balanced very carefully in order to obtain sufficient reverberation whilst at the same time avoiding excessive loudness. Finally the measured strength levels are compared to values derived from traditional and revised theory [Barron M, Lee L-J. Energy relations in concert auditoriums. J Acoust Soc Am 1988;84(2):618-28] on strength calculations in order to assess the accuracy of the theory for small chamber music halls. Possible reasons for the low measured strength levels observed are discussed with reference to related design features and objective acoustic parameters.