ALBERT

Notes: Abstract Material imperfections usually play a substantial role in the early stages of fatigue cracking. This article presents some observations concerning fatigue crack initiating flaws and early crack growth in 7050-T7451 aluminium alloy specimens and in full-scale fatigue test articles with a production surface finish. Equivalent initial flaw size (EIFS) approaches used to evaluate the fatigue implications of metallurgical, manufacturing and service-induced features were refined by using quantitative fractography to acquire detailed information on the early crack growth behaviour of individual cracks; the crack growth observations were employed in a simple crack growth model developed for use in analysing service crack growth. The use of observed crack growth behaviour reduces the variability which is inherent in EIFS approaches which rely on modelling the whole of fatigue life, and which can dominate EIFS methods. The observations of realistic initial flaws also highlighted some of the significant factors in the fatigue life-determining early fatigue growth phase, such as surface treatment processes. Although inclusions are often regarded as the single most common type of initiating flaw, processes which include etching can lead to etch pitting of grain boundaries with significant fatigue life implications.

Notes: Abstract Thermal shock loading, such as that which occurs when a hot material is sprayed with cold water, produces a very high stress level near the exposed surface that eventually may lead to the development of cracks. Further growth of the cracks under repeated thermal shock is a very complex phenomenon due to the transient nature of the highly non-linear thermal stresses and the strong influence of the environment. There are cases in industry where cracks created by thermal shocks have arrested and stopped, and others where the cracks have progressed. Understanding this difference in behaviour is very important to the operators of pressure plant. This paper describes an experimental examination of crack growth in pressure vessel steel specimens exposed to repeated thermal shock. A test-rig that achieves large-scale thermal shocks through the repeated water quenching of heated flat plate specimens is used. The effect of steady-state loads on the growth is also analysed. Environmental effects due to the aqueous nature of the testing environment are found to be a major contributor to the crack growth kinetics.

Notes: Abstract A mechanism of the formation of multiscale self-similar crack structures in brittle materials is proposed based on the action of spatial random stress fluctuations (random stress fields) with vanishing mathematical expectation. The presence of self-equilibrating stress fluctuations is, in many cases, characteristic of heterogeneous brittle materials even in the absence of external loading. Some examples are given by residual stresses—stresses caused by phase transformations or internal microscopic heat sources. If the stress fluctuations are strong enough to cause cracking, the cracks will be originated in regions with and perpendicular to the highest local tension. As a legacy of this special location, additional local tractions opening the crack in its centre are developed even in self-equilibrating stress fields. This mechanism is modelled by disklike cracks opened by a pair of concentrated forces applied at the centre. Two cases are considered: (i) the crack growth in the moving equilibrium conditions caused by the self-equilibrating stress fluctuations of increasing amplitude; and (ii) the subcritical crack growth under the stress fluctuations of either sustained (creep) or oscillating (fatigue) amplitudes. As the cracks grow, the interaction between them leads to a separation of crack sizes. The effects of the interaction are modelled by the differential self-consistent method that is shown to become asymptotically accurate as the ratio between the sizes of the interacting cracks increases. The interaction results in the crack distribution tending to a self-similar one with the distribution function proportional to the inverse fourth power of the crack radius.

Notes: Abstract This paper presents the results of several DSTO research programmes which investigated the effectiveness of the fatigue life enhancement method used on RAAF F/A-18 aircraft – glass bead peening. The research identified ways in which process improvement could enhance this effectiveness, and developed a procedure for mid-life reworking of critical airframe parts to effectively restore the original fatigue life. The procedure included removing a very thin layer of material (and with it, any undesirable manufacturing features and accumulated fatigue cracking) from the surface. Further life recovery can be achieved, if required, by applying an optimized peening procedure. This process has been developed to allow restoration of fatigue life to critical airframe components which are thought to be accumulating fatigue crack damage faster than desired.

Notes: Abstract In order to develop an analytical method for quantifying the plastic-blunting behaviour of a short crack embedded in a notch plastic zone, the perturbation solution of He and Hutchinson is extended to include the effect of strain gradient. An edge-cracked plate subjected to a linearly varying remote strain is considered in this work to simulate the plastic deformation associated with a small crack at a notch root. The strain hardening of the material is assumed to obey a power-law. Comparison with finite-element (FE) computations demonstrates that this perturbation solution provides accurate values for the crack-tip opening displacement (CTOD) under gross-yielding conditions for a range of hardening parameters.

Notes: Abstract Experiments have been carried out to investigate whether reducing the solution heat-treatment time of Al-7Si-0.6Mg castings from the currently recommended values adversely affects their fatigue properties. Fatigue endurance tests have been carried out in zero-tension (R=0) and measurements made of the casting defects that initiated the fatigue cracks. The work has been limited to stresses that produce a fatigue life of ~105 cycles and to two solution–treatment times (8 and 4 h). Two statistical techniques have been applied to the fatigue life data and no effect of solution heat-treatment time was detected at a confidence level of better than 95%. Similarly, no effect of cyclic test frequency could be detected for tests carried out at 1 and 60 Hz. The conclusions are confirmed by an analysis of the relation between fatigue life and the size of the casting defects that initiated fatigue failure. The scatter in fatigue lives is related to the scatter in the sizes of casting defects in the specimens. It is clear that there is a potential for considerable savings in heat-treatment costs for castings of the size and shape chosen for the study.

Notes: 1010-cycle fatigue tests were conducted at 100 Hz for three years and at 20 kHz for one week on 1800 MPa-class JIS-SUP7 spring steel. Uniaxial tests up to 108 cycles were also conducted at 120 and 600 Hz. The 120 Hz tests had larger control volumes. The fatigue limit at 1010 cycles was lower than at 108 cycles, and any frequency effect was shown to be negligible. A size effect was found; the tests with larger control volumes showed results of lower fatigue strength.

Notes: A fatigue crack closure model is developed that includes the effects of, and interactions between, the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out-of-plane cracking and multi-axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two-dimensional sawtooths, whose geometry induces mixed-mode crack-tip stresses. Continuum mechanics and crack-tip dislocation concepts are combined to relate crack face displacements to crack-tip loads. Geometric criteria are used to determine closure loads from crack-face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs. The CROP model is verified with experimental data in part II of this paper.

Notes: In this paper, the effects of T-stress on steady, dynamic crack growth in an elastic–plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J2 flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T-stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T-stress for both ductile and cleavage mode of crack growth.

Notes: A multiaxial fatigue criterion for random loading is proposed. Firstly, the orientation of the critical plane, where fatigue life estimation is carried out, is determined from the weighted mean position of the principal stress directions. Then, the scalar value of the normal stress vector N(t) perpendicular to the critical plane is taken as the cycle counting variable since the direction of such a vector is fixed with respect to time (conversely to the time-varying direction of the shear stress vector C(t)), and a nonlinear combination of normal and shear stress components acting on the critical plane is used to define an equivalent stress amplitude. Finally, a damage accumulation model is employed to process such an equivalent stress amplitude and to determine fatigue endurance. This criterion is herein applied to some relevant random fatigue tests (proportional bending and torsion).

Notes: Finite element analyses were carried out on cracked 20 mm square plates and bars ranging in thickness from 2.5 mm to a length of 60 mm. The crack extended from the middle of one side of the square to its centre, and was modelled as a narrow, parallel-sided notch with a semicircular tip. An antiplane loading was applied to the side containing the crack. An infinitely long bar under the antiplane loading used is in pure Mode III. It was found that the central portions of 40, 56 mm and 60 mm long bars were in pure Mode III, and also that KIII was approximately constant. These central portions were therefore representative of an infinitely long bar. Towards the ends of a bar KIII decreased. At the ends of a bar corner point effects meant that Mode II stress intensity factors and displacements were induced in the corner region. The size of the corner region was independent of bar length. In the 2.5, 5 and 10 mm thick plates out of plane bending means that the antiplane loading became a mixed Mode II and Mode III loading. At a centre line KII is zero by symmetry. Behaviour in the corner region was a function of plate thickness. For both plates and bars, as has been predicted theoretically, the ratio KII/KIII tends to a constant value as a surface is approached. For a thickness of 20 mm, that is a 20-mm cube, behaviour represents a transition between plate and bar behaviour.

Notes: Delamination is one of the most frequent failure modes in laminated composites. Its importance is crucial, because a delamination can occur in the interior of a panel without any noticeable damage on the surface, drastically reducing its strength and stiffness. A study has to be made on critical dimensions of delaminations and their shape, through the calculation of the strain energy release rate (SERR), G. This study was performed numerically, for a given geometry, with varying loads and shapes of delamination, in pure and mixed-mode propagation. All numerical values were obtained with three-dimensional finite element (FE) analyses from a commercial package. The use of three-dimensional analyses in simple geometries helps establish the basis for the more complex ones, and the correspondence with the usual analytical or numerical bi-dimensional plane-strain analysis. The conclusions were (a) G is not constant along the crack tip, even for mode I propagation and straight crack tip; (b) the mean value of G obtained from a three-dimensional analysis equals the value obtained in bi-dimensional plane-strain analysis; (c) in mixed-mode propagation, the method exhibits a good correlation with experimental results and (d) the shape and mode partitioning of the SERR depend not only on the loading, but also on the shape of the crack front.

Notes: The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔKIIth. The relationship ΔKIIth 〉 ΔKIth caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory-roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory-roofs were formed by crack branching into mode I. Crack branching started from small semi-elliptical cracks nucleated by shear at the tip of the original circumferential crack.

Notes: Fatigue crack propagation tests of through cracks in 3 mm thick aluminium alloy 6013-T6 plates, under combined membrane and bending stresses were carried out. Five different values for the ratio of bending to membrane stresses, SB, were examined: 0, 0.55, 1.25, 1.8 and 2.23. Firstly, the results were elaborated by taking into account only the membrane stress and the front dimension of the crack for the evaluation of the stress intensity factor range. The results relevant to the lower SB values, evaluated in this mode, show good agreement with the results obtained when only the membrane stress was applied, while the results obtained at the higher SB values exhibit a remarkable increase in the crack propagation rate. The results were successively evaluated on the basis of tabular stress intensity factor solutions available in the literature; the agreement between the predicted and the experimental data occurs when mean values of stress intensity factor, rather than local values, were used at the back face of the plate, i.e., the face where the bending produces a compressive stress, to counteract the high gradient of stress intensity factor present in this area.

Notes: Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce a crack closure effect. Moreover, it modifies the crack geometry by bridging the crack faces and so reduces the stress intensity range at the crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A crack growth induced debonded region in the adhesive-plate interface was observed using an optical technique. Moreover, the size of the debonded region significantly influences the efficiency of the crack repair. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique (MVCCT). A parametric analysis is performed to investigate the influence of some design parameters such as the composite patch Young's modulus, the adhesive thickness and the pretension level on the adhesive-plate interface debond.

Notes: Research results concerning the simulation of the crushing behaviour of composite systems with energy absorption characteristics are presented in the present work. The study is focused on the ‘tensor skin’ concept, an energy absorbing composite system that was originally developed to improve the crashworthiness of helicopters under water impact and which is promising for utilization in the construction of the lower part of composite fuselage aircraft. The ‘tensor skin’ concept comprises a folded or corrugated composite construction, which upon loading unfolds by forming ‘plastic hinges’, leading to an increase in the load bearing capability of the structure. The numerical modelling issues and the critical aspects of the simulation are discussed. Verification of the numerical simulation procedure is performed by experimental work. The experimental results utilized to assess and validate the numerical procedure were derived within the European Research Project ‘Design for Crash Survivability – CRASURV’ (BRITE – Aeronautics Area). The results of the simulations are generally in good agreement with experimental data.

Notes: This paper proposes a procedure for estimating the total fatigue life in fretting fatigue. It separately analyses the fatigue crack initiation and propagation lives. The correlation between crack initiation and propagation is made considering a non-arbitrary crack initiation length provided by the model. The number of cycles to initiate a crack is obtained from the stress distribution beneath the contact zone and a multiaxial fatigue crack initiation criterion. The propagation of the crack is considered using different fatigue crack propagation laws, including some modifications in order to take the short crack growth into account. The results obtained by this method are compared with the fatigue lives obtained in various fretting fatigue tests under spherical contact with 7075-T6 aluminium alloy.

Notes: An asymptotic elastic solution provides a good way of encapsulating the behaviour of the process zone at the edge of a complete contact. In this paper we examine the effect of a finite edge radius on the validity of such an approach, and provide clear recommendations on the tolerable edge radius if the asymptotic approach is to remain viable.

Notes: Rotary bending fatigue tests have been performed in 3%NaCl aqueous solution using specimens of a low alloy steel (Cr–Mo steel) with different nitride case depths. The effect of case depth on corrosion fatigue strength, the fracture process and mechanisms were studied. The corrosion fatigue strengths of the nitrided materials increased compared with the untreated material and increased with increasing thickness of the compound layer, but tended to saturate above a certain thickness. All the materials showed lower fatigue strength in 3%NaCl aqueous solution than in laboratory air and the reduction of fatigue strength decreased with increasing thickness of the compound layer, but remained nearly constant above a certain thickness. Corrosion pits were seen underneath the compound layer, from which cracks initiated. The corrosion fatigue strengths of the specimens whose compound layer was completely removed by electropolishing were almost the same as that of the untreated material, indicating a very significant role of the compound layer in improving corrosion fatigue strength. Because of the porous nature of the compound layer, particularly in the surface-adjacent part, the solution penetrated the compound layer and reached the base steel, thus the corrosion fatigue strength of the nitrided materials was controlled by the penetration of corrosive media.

Notes: Murakami and Endo have used the 〈inlineGraphic alt="inline image" href="urn:x-wiley:8756758X:FFE0636:FFE_0636_m102" location="equation/FFE_0636_m102.gif"/〉 parameter to successfully predict the endurance limits and the threshold levels for components, which contain small defects or cracks. The present paper uses a modified linear–elastic fracture mechanics (LEFM) approach to examine the mechanistic basis for these correlations. The modifications include consideration of the endurance limit rather than the threshold level as a factor controlling fatigue crack growth in the very short crack growth range, consideration of elastic–plastic behaviour, and consideration of the role of crack closure in the wake of a newly formed crack. Predictions based upon the modified LEFM behaviour are found to be consistent with the earlier predictions of Murakami and Endo.

Notes: In this work stress concentration factors (SCFs), Kt for a round bar with a fillet are considered on the basis of exact solutions, now available for special cases, and accurate numerical results. Then, a convenient Kt formula useful for any dimensions of the fillet is proposed. The conclusions can be summarised as follows: (i) For the limiting cases of deep (d) and shallow (s) fillet, the body force method is used to calculate the Kt values. Then, the formula are obtained as Ktd and Kts. (ii) On the one hand, upon comparison of Kt and Ktd, it is found that Kt is nearly equal to Ktd if the fillet is deep or blunt. (iii) On the other hand, if the fillet is sharp or shallow, Kt is mainly controlled by Kts and the fillet depth. (iv) The fillet shape is classified into several groups according to the fillet radius and fillet depth. Then the least squares method is applied for calculation of Kt/Ktd and Kt/Kts. (v) Finally, a convenient formula is proposed that is useful for any dimensions of fillet in a round bar. The formula give SCFs with less than 1% error in most cases for any dimensions of fillet under tension and bending.

Notes: This paper compares engineering estimation schemes of C* and creep crack opening displacement (COD) for cylinders with circumferential and axial through-thickness cracks at elevated temperatures with detailed 3D elastic-creep finite element results. Engineering estimation schemes include the GE/EPRI method; the reference stress (RS) method where the reference stress is defined based on the plastic limit load; and the enhanced reference stress (ERS) method where the reference stress is defined based on the optimised reference load, recently proposed by the authors. Systematic investigations are made not only on the effect of creep-deformation behaviour on C* and creep COD, but also on effects of the crack location, the cylinder geometry, the crack length and the loading mode. Comparison of the finite element (FE) results with engineering estimations provides that for idealised power law creep, estimated C* and COD rate results from the GE/EPRI method agree best with FE results, suggesting that published plastic influence functions for plastic J and COD for through-thickness cracked cylinders are reliable. For general creep-deformation laws where either primary or tertiary creep is important and thus the GE/EPRI method is hard to apply, on the other hand, the ERS method provides more accurate and robust estimations for C* and COD rate than the reference stress method. As these two methods differ only in the definition of the reference stress, the ERS method maintains benefits of the reference stress method in terms of simplicity, but improves accuracy of the estimated J, C* and COD results.

Notes: A diagram valid for the analysis of the fatigue limit of cracks and notches centred in an infinite plate was recently proposed by the authors of the present work with the aim to make explicit the bridging at the fatigue limit between defect sensitivity (correlated to the length parameter a0, according to El Haddad–Topper–Smith's definition) and notch sensitivity (correlated to a*, where a* is a particular notch depth corresponding to the intersection between the ΔKth and Δσ0/Kt curves). The expression 〈inlineGraphic alt="inline image" href="urn:x-wiley:8756758X:FFE0633:FFE_0633_m101" location="equation/FFE_0633_m101.gif"/〉 being valid, defect sensitivity and notch sensitivity were seen as two sides of the same medal. Such a diagram is now extended to finite size components by simply introducing the shape factor α commonly used in fracture mechanics. The obtained critical defect size is termed aD, which is a material and geometry dependent parameter, in order to distinguish it from a0, which is a material parameter. As a consequence the critical notch depth aN is introduced, such that . 〈inlineGraphic alt="inline image" href="urn:x-wiley:8756758X:FFE0633:FFE_0633_m102" location="equation/FFE_0633_m102.gif"/〉 This results in the proposal of a ‘universal’ diagram able to summarize experimental data related to different materials, geometry and loading conditions. The diagram, the validity of which is checked by means of several results available in the literature, is applied both to the interpretation of the scale effect and to the surface finishing effect.

Notes: This paper presents a global approach to the design of structures that experience thermomechanical fatigue loading, which has been applied successfully in the case of cast--iron exhaust manifolds. After a presentation of the design context in the automotive industry, the important hypotheses and choices of this approach, based on a thermal 3D computation, an elastoviscoplastic constitutive law and the dissipated energy per cycle as a damage indicator associated with a failure criterion, are first pointed out. Two particular aspects are described in more detail: the viscoplastic constitutive models, which permit a finite element analysis of complex structures and the fatigue criterion based on the dissipated energy per cycle. The FEM results associated with this damage indicator permit the construction of a design curve independent of temperature; an agreement is observed between the predicted durability and the results of isothermal as well as non isothermal tests on specimens and thermomechanical fatigue tests on real components on an engine bench. These results show that thermomechanical fatigue design of complex structures can be performed in an industrial context.

Notes: The propagation of a fatigue crack from an initial defect of the same order as the scale of the microstructure through to failure has been modelled using a representation of fatigue damage according to the Navarro–de los Rios (N–R) model. The fatigue processes are presented in the form of a fatigue damage map (FDM). It is shown how the map can be used to create a traditional S–N curve and to provide information suitable for estimating fatigue lifetimes under damage tolerant conditions.

Notes: Several criteria for the prediction of incipient crack path direction of non-proportional mixed-mode fatigue cracks, immediately after a change of load from steady mode I conditions are investigated. The analysis is based on two-dimensional plane strain FE-simulations in which the actual elasto-plastic stress distribution is used for the MTS, MTSR and MEPSR criteria. The purpose of the analysis is to compare the numerical results with experimental results as well as with previous predictions based on solely elastic stress analyses, taken from the literature. It is shown that the influence from elasto-plastic deformation on crack branching direction is of utmost importance. It is found that the incipient crack growth of metals falls into two categories: high strength metals follow the MTSp criterion whereas more ductile metals follow the MTSRp criterion. The subscript p indicates that the elasto-plastic evaluation of the respective criterion should be used.

Notes: An experimental method is presented, in which a sphere is repeatedly pressed against a surface with an inclined contact load. The method is a development of the normally loaded standing contact fatigue test. Experiments are performed for three inclination angles below the angle of friction and the results are compared to those of the normally loaded standing contact fatigue test. The influence of tangential load on endurance limit load, number of cycles to crack initiation, contact mark appearance and crack behaviour in the surface as well as in cut views are evaluated. The surface crack behaviour outside the contact mark is analysed based on the cyclic contact stresses in the test specimen. The trajectories of the largest principal stresses are followed in both the surface view and in the cut view on the symmetry plane. These stress trajectories are compared to the experimental crack results. The connection between the inclined standing contact fatigue cracks and surface distress micro-cracks is also discussed.

Notes: Predictions from an analytical model that considers contributions and interactions between plasticity, roughness, and oxide induced crack closure are presented and compared with experimental data. The analytical model is shown to correctly predict the combined influences of crack roughness, oxide debris, and plasticity in the near-threshold regime. Furthermore, analytical results indicate closure mechanisms interact in a non-linear manner such that the total amount of closure is not the sum of closure contributions for each mechanism.

Notes: An understanding into the macro kinetic and kinematic behaviour of fretted surfaces is provided. Making use of a modified version of a previously developed in-house two-dimensional elastic–plastic finite element analysis numerically simulates flat contact pad fretting fatigue tests. Basic macro mechanics concepts are adopted to idealise two bodies with rough contact surfaces and loaded at two different sites with arbitrary axial loading profiles. A time scale factor is devised to recognise the earliest candidate out of the events possibly accommodated at each loading increment.The present analysis utilises a relevant experimental set up developed in the Structural Integrity Research Institute of the University of Sheffield as an application. Computational results accurate to within 1.2% and corresponding to one contact pad span and six constant normal loads acting individually with four amplitudes of two sinusoidal axial load cycles are presented. The present computations include (1) the development of the global and local normal and tangential reactions and relative sliding displacement acting along the fretting surfaces and (2) contact pad deformation, generated stress fields and plasticity development within the neighbouring region of the fretted area.

Notes: The equivalent initial flaw size (EIFS) concept was developed nearly 30 years ago in an attempt to account for the initial quality, both manufacturing and material properties, of a structural detail prone to fatigue cracking. Widespread use of this concept has been limited due to the large amount of test data required to develop a reliable EIFS distribution. In this effort, an EIFS distribution was determined for four types of flat, production like transport aircraft fuselage skin joints loaded by remote tension. Two crack growth prediction codes, AFGROW and FASTRAN, were used to not only develop the EIFS but also to compare the crack growth algorithms in each code. The EIFS calculations are prone to compounding errors in the crack growth analysis due to the changing stress intensity factor solutions and stress fields as the crack gets longer. Thus, only including EIFS calculations for mechanically small cracks, crack lengths less than 1.27 mm, results in a mean EIFS of 18.0 μm with a standard deviation of 3.78 μm.

Notes: Optimal rework shapes for the most critical stiffener runout fatigue locations in the F-111 wing pivot fitting have been determined using a recently developed finite-element-based gradient-less shape optimization procedure. The resulting precise free-form shapes render the local notch stress distributions near uniform and typically provide a 30–40% reduction in peak elastic stresses as compared to the current rework shapes that exist for aircraft in service with the Royal Australian Air Force. The present numerical results are also consistent with recent preliminary experimental results, and a significant program of further validation testing is envisaged. Hence it is expected that the stress reductions predicted in the present work will be sufficient to provide a basis for extending inspection intervals by at least a factor of two; from 500 to 1000 h. Implementation of such an extension to the F-111 fleet in service with the Royal Australian Air Force would provide a very significant maintenance cost saving. The anticipated reduction in local crack growth rates would also allow achievement of the planned withdrawal date for the aircraft.

Notes: Abstract  This paper presents computational and theoretical investigations of the plasticity-induced crack-closure of a plane-strain crack under large-scale yielding conditions. Solutions of the crack-tip opening displacements for a stationary crack and a growing fatigue crack have been obtained using the finite element method. The self-similar crack-closure model has been extended to the plane strain case by introducing two plastic constraint factors: one for tension yielding and the other for compression yielding. These two plastic constraint factors are identified by matching the model predictions with the computational results. It is shown that the first constraint factor decreases rapidly with the applied stress while the second constraint factor is approximately equal to unity. The findings of this study allow the cohesive-zone based crack-closure model to be extended to plane-strain cracks, especially under large-scale yielding conditions.

Notes: Estimation of fatigue strength under biaxial and multiaxial loading is usually based on the assumption that fatigue limit is the limit stress for crack nucleation. However, in presence of defects and inhomogeneities the fatigue limit is determined by the threshold condition of small cracks. Nevertheless, multiaxial criteria, especially the Dang Van's criterion, could be successfully applied to defective materials. The scope of this paper is to discuss the differences in the two approaches (multiaxial criteria versus mechanics of the small cracks) for fatigue design of components containing defects subjected to biaxial and multiaxial in-phase loading. In particular it will be discussed, on the basis of the fatigue properties of large springs, the need of a correct description of the fatigue mechanism in order to determine the lower bound of fatigue strength in presence of defects.

Notes: This paper presents the experimental evaluation of the fatigue behaviour of welded components under non-proportional variable amplitude biaxial loads. The study was undertaken on welded mountain bike handlebar stems, which were different in terms of geometry and technology and tested with load histories that were reconstructed and accelerated from recorded field data. Loads measured in the field were decomposed into bending and torsional components; a synchronous Peak-Valley counting, a spectrum inflation technique, a spline interpolation and a final amplification were applied to the measured signals in order to obtain test drive signals with the correct content of biaxial non-proportional loadings. After evaluation of the bending and torsion load-life curves of components under constant amplitude fatigue, the resulting data from biaxial variable amplitude fatigue tests were analysed in order to evaluate the damage contribution as a result of the two load components and an equivalent simplified two-stage constant amplitude fatigue test was proposed to the working group ISO/SC1/TC149/WG4.

Notes: Multiaxial stress states occur in many welded constructions like chemical plants, railway carriages and frames of trucks. Those stresses can have constant and changing principal stress directions, depending on the loading mode. Latest research results on welded steel joints show a loss of fatigue life for changing principal stress directions simulated by out-of-phase bending and torsion compared to constant directions given by in-phase loading. However, aluminium welds reveal no influence of changing principal directions on fatigue life compared to multiaxial loading with constant principal stress directions. This behaviour is not predictable by any conventional hypothesis. A hypothesis on the basis of local normal and shear stresses in the critical plane has been developed and applied to aluminium weldings.

Notes: The purpose of this paper is to present a unified analysis to both high and low cycle fatigue based on shakedown theories and dissipated energy. The discussion starts with a presentation of the fatigue phenomena at different scales (microscopic, mesoscopic and macroscopic) and of the main shakedown theorems. A review of the Dang Van high cycle fatigue criterion shows that this criterion is essentially based on the hypothesis of elastic shakedown and can therefore be expressed as a bounded cumulated dissipated energy. In the low cycle fatigue regime, recent results by Skelton and Charkaluk et al. show that we can speak of a plastic shakedown at both mesoscopic and macroscopic scale and of a cumulated energy bounded by the failure energy. The ideas are also justified by infrared thermography tests permitting a direct determination of the fatigue limit.

Notes: Effects of microstructural modifications, that are a consequence of adding minor grain boundary strengthening elements (C, Hf), on the fatigue response of an experimental single crystal superalloy have been studied. Investigations show that in the modified alloys, as a consequence of the casting process, the population of pores is reduced, but the average pore size increases and larger pores occur close to the fatigue sample surface. Such porosity changes in the modified alloys are an important contributor to their low cycle fatigue (LCF) properties. At the high stress range of LCF tests undertaken, the growth of cracks initiates from pores and their location in the modified alloys are responsible for decreased fatigue lives. At lower stress ranges, crack initiation consumes a considerable proportion of fatigue life. Since crack initiation involves strain localisation at or near the specimen surface where there is interaction with the environment, the population of pores near the specimen surface and the increased length of the tests plays a significant role in governing fatigue lives. The modified alloys benefit from their lower density of pores in the vicinity of the free surface, and tend to have comparable fatigue lives to that of the base alloy at the lower stress level.

Notes: Fretting fatigue crack nucleation in Ti−6Al−4V when fretted against itself is investigated to determine the influence of contact pressure, stress amplitude, stress ratio, and contact geometry on the degradation process. For the test parameters considered in this investigation, a partial slip condition generally prevails. The resulting fatigue modifying factors are 0.53 or less. Cycles to crack nucleation, frictional force evolution, crack orientations and their relationship to the microstructure are reported. The crack nucleation process volume is of the same order as the microstructural length scales with several non-dominant cracks penetrating 50 μm or less. The effective coefficient of friction increases during early part of fretting. Observations suggest that cyclic plastic deformation is extensive in the surface layers and that cyclic ratchetting of plastic strain may play a key role in nucleation of the fretting cracks. A Kitagawa–Takahashi diagram is used to relate the depth of fretting damage to the modifying factor on fatigue life.

Notes: Abstract Current designs which involve the use of composite materials in primary aircraft structures are often conservative. This, in turn, significantly lowers the weight advantage that composites have over established metallic airframe materials. Strain restrictions are often applied because the failure mechanism(s) in (fibre) composite joints and stiffener runouts where the stress state is often complex, are not fully understood. Nevertheless, from the airworthiness perspective it is essential that both the static strength and the fatigue behaviour of the components subjected to complex multiaxial stress conditions are both understood and predicted. This topic is extremely complex, and numerous criteria ranging from the purely empirical to the theoretical have been proposed. In both cases, it is necessary to know the localised stress–strain history.One common design methodology is to keep the stresses so low that fatigue will not be an issue. However, this can lead to an overly conservative design. On the other hand, while a detailed (nonlinear) finite element analysis can be performed it is often both resource-intensive and time-consuming. The present paper shows that Glinka's hypothesis can be used in order to calculate the localised stresses and strains for a bonded joint subjected to cyclic loading.This is a new result and has not previously been noted. It has the potential to extend the Hart-Smith design methodology to the adhesively bonded joints in order to encompass durability considerations. This formulation also raises the possibility of enabling the degree of conservatism inherent in traditional joint design to be relaxed provided that failure occurs in the adhesive.This paper also addresses the problem of variable adhesive thickness. We show that while variable adhesive thickness can change the stress and the energy fields, the peak in the strain energy density is relatively insensitive to the stress–strain relationship for the adhesive and that Glinka's hypothesis still appears to be true. This means that, for the present class of problems, even if there is variability in the thickness of the adhesive bond the energy field and, hence, the strength of the joint can be estimated from a purely linear elastic analysis of the joint, provided that failure occurs in the adhesive.

Notes: Abstract Extensive studies involving multilevel loading have been performed to study the interaction effects of High–Low and Low–High loading sequences on various metals.1–10 High–Low sequences generally yield ‘damage’ sums less than unity while ‘damage’ sums for Low–High sequences are typically 〉 1. It can be appreciated that the mechanisms governing fatigue behaviour under elastically dominant conditions differ from those observed under predominantly plastic conditions. This paper presents results on the interaction between plastically dominant fatigue (PDF) and elastically dominant fatigue (EDF) in 316L stainless steel and 6061-T6 aluminium alloy. In addition, overstraining effects coupled with PDF and EDF interaction in 316L stainless steel are also reported.

Notes: A plane-strain upper bound limit load solution for weld strength overmatched middle cracked tension specimens (M(T) specimens), is found. It is assumed that the weld material is isotropic, but the base material is orthotropic and its axes of orthotropy are straight and parallel to the axes of symmetry of the specimen. A quadratic orthotropic yield criterion is adopted. The solution is based on a simple discontinuous kinematically admissible velocity field and is an extension of the corresponding solution for the specimen made of isotropic materials. These two solutions are compared to demonstrate the influence of anisotropy on the magnitude of the limit load.

Notes: Residual stresses generated by the mismatch of thermal expansion coefficients of ceramics and metals affect the strength of ceramic–metal joints. An interlayer metal can be inserted between the ceramic and metal in order to relax this stress. An analysis was carried out of the residual stresses produced during joint-cooling and in 4-point bending tests. The effects of interlayer thickness on ceramic–metal joint strength were then studied by considering a superimposed stress distribution of the residual stress and the bending stress. Finally, joint strength was estimated from fracture mechanics and strength probability analysis by considering the residual stress distribution, defect size and position of pre-existing defects in the ceramic parts. As a result of this study, we suggest an optimum material selection and interlayer thickness for ceramic–metal joint structures. This approach is generally suitable for the design of electrical and mechanical structures.

Notes: It has not been clear whether the conventional effective volume proposed for dense brittle materials can be applied satisfactorily to the strength evaluation of porous ceramics. In the present study, a modified effective volume was proposed by incorporating the porosity effect in the statistical evaluation of strength properties of porous ceramics. The modified effective volume was derived as the conventional effective volume multiplied by a function of porosity p. In this work, a power function of (1 + p)a was adopted as the simplest porosity function. To clarify the applicability of the modified effective volume, bending tests were conducted using smooth and notched specimens of 3 wt% MgO partially stabilised zirconia with six different porosities. The porosity dependence appeared in the relation between the conventional effective volume and the mean strength of various zirconia ceramics with different porosities. The exponent a of the porosity function was determined from experimental data obtained by using identically shaped specimens with distinct porosities, and the modified effective volume was calculated for several types of specimens used in the experiments. It was revealed that the mean strength was almost uniquely correlated with the modified effective volume independent of porosity. The experimental correlation verified the applicability of the modified effective volume to strength evaluation of porous ceramics.

Notes: Failure of the ceramic gun-barrel lining during single-shot and burst firing events has been studied by combining a finite-element method based thermo-mechanical analysis with a structural reliability analysis. An initial distribution of residual stresses in the lined barrel, as introduced during shrink-fitting of the steel jacket over the ceramic lining, is taken into account. Forced-convection boundary conditions at the inner surface of the barrel are determined by carrying out an internal-ballistic analysis, followed by compressible boundary-layer modeling of the heat transfer coefficient. The results obtained reveal that due to thermal expansion of the steel jacket during single-shot and burst ballistic events, tensile axial stresses develop in the ceramic lining near the barrel ends. These stresses are sufficiently high, particularly in the case of burst firing, that they can induce formation of circumferential cracks and, in turn, failure of the lining. Using the Weibull structural reliability analysis, the failure probability for the lining has been computed as 0.0025 and 0.0121 for the single-round and the 10-round firing modes, respectively. Optimization of the main design, materials and processing parameters in order to minimize the failure probability for the lining is also discussed.

Notes: According to experimental evidence, the early stages of fatigue crack propagation under fretting conditions are strongly influenced by the stress gradient generated in the material near the contact zone. This suggests that the crack growth process can be analysed using methodologies similar to those employed to predict the fatigue behaviour of notched elements. This paper assesses the applicability of a number of models originally developed for notched components to fretting fatigue problems. The ability of such models to predict fatigue failure is discussed and compared with experimental results for Al 7075-T6 specimens that were subjected to fretting fatigue under spherical contact.

Notes: The paper presents a new model for three-dimensional progressive failure analysis of adhesive joints. The method uses interface elements and includes a damage model to simulate progressive debonding. The interface finite elements are placed between the adherents and the adhesive. The damage model is based on the indirect use of fracture mechanics and allows the simulation of the initiation and growth of damage at the interfaces without considering the presence of initial flaws. The application of the model to single lap joints is presented. Experimental tests were performed in aluminium/epoxy adhesive joints. Linear elastic and elastoplastic analyses were performed and the predicted failure load for the elastoplastic case agrees with experimental results.