ALBERT

Notes: This paper presents the results of fatigue crack growth and fatigue fracture toughness studies of a high-pressure vessel steel with particular emphasis on the influence of heat treatment, low temperatures, plastic prestraining, the stress ratio and specimen dimensions.It has been shown that steels in an embrittled state, caused primarily by thermal treatment and low-temperatures, exhibit unstable fatigue crack growth which is characterized by alternate crack jumps (cleavage zones) and zones of fatigue crack growth. The fatigue fracture toughness, which corresponds to the first crack jump, and final fracture can be appreciably lower (i.e. up to 50%) than the static fracture toughness under plane strain conditions at the corresponding temperature.An analysis has been performed of unstable and stable fatigue crack growth and a model of unstable crack propagation is proposed which accounts for the observed experimental behaviour.

Notes: Abstract— Elastic-plastic finite element analysis is used to study fatigue crack closure at three different crack length to width ratios for three plane stress specimen geometries: center-cracked plate, single-edge-cracked plate (tension), and single-edge-cracked plate (bend). The maximum stress to flow stress ratio, Smax/σO, which successfully describes closure results in many center-cracked plate configurations, does not correlate the effect of different geometries on the normalized opening stress, Sopen/Smax. Crack opening stresses for different geometries and crack lengths are successfully correlated by a normalized stress intensity parameter, Kmax/K0, where K0=σ0φa. The quality of the correlation is very high at small Kmax/K0, and gradually deteriorates as Kmax/K0 increases beyond the small-scale yielding regime.

Notes: Abstract— Fatigue crack propagation threshold values have been determined with two experimental methods, it., the constant R method and the constant Kmax method. Three materials, namely A17075-T7351 and Ti6A14V STA in the LT- and TL-orientations, and a Ti-turbine disk material (IMI 685) in the CR-orientation, were investigated.The paper is divided into 3 parts. In the first part the test conditions, the experimental results and the conclusions drawn from the experimental results are presented, namely that the three different functional dependencies of ΔKth on R cannot be reconciled with present continuum mechanics concepts. In the second part, some facts used in conjunction with the da/dN–ΔKeff methodology are applied to the non-propagation condition ΔKth. Parameters such as KOp, the threshold ΔKT, and a parameter “KLL” are investigated by numerical modelling of their individual influence on the ΔKth versus R curves. This modelling work shows that the individual ΔKth versus R curves are primarily dependent on the Kop behavior of the respective material. Further, it is shown that the threshold ΔKT is a constant value, independent of any particular cyclic loading condition. In the third part of the paper, the ΔKeff concept is applied to the experimental results obtained in the first part. Using either experimentally or semi-empirically determined Kop functions and the measured ΔKT values, the ΔKth versus R curves of the three materials investigated were accurately reconstructed. It follows that the ΔKth versus R curves of the individual materials are the natural consequence of the driving force for fatigue crack propagation, namely ΔKeff

Notes: Abstract— Anderson and Dodds have recently introduced a test specimen size requirement in the transition regime which they suggest must be satisfied for the cleavage fracture resistance to be size independent. This paper assesses the implications of imposing the size requirement in fracture toughness testing standards. It is shown that imposing the size requirement can lead to a size dependence in fracture toughness data. This observation raises the general question of whether even existing size requirements for the lower shelf and upper shelf regimes are capable of giving size independent data.

Notes: Abstract— A new method of analysis is proposed for an infinite solid containing an embedded plane crack of arbitrary shape. The analysis is fundamentally based on the body force method, but proper expressions of the body force densities are introduced and the stress conditions of the crack surface are replaced by the resultant force conditions in order to improve the accuracy and validity of the method. Numerical results for typical crack problems, based on coarse mesh patterns, are shown to be in remarkable agreement with known solutions. The method is also applied to the bending of circular and rectangular cracks generated from compressive surface contacts for which reliable solutions have not yet been proposed by any other methods. The results are found to be very different from conventional free-surface solutions.

Notes: Abstract— The cyclic stress-strain response of two heats of austenitic stainless steel 3 16L was experimentally studied under a wide range of cyclic plastic strain amplitudes. Three domains on the cyclic stress- strain curve were found. In the middle domain the plateau behaviour corresponds to fatigue softening. The domain at low plastic strain amplitudes is characterized by stabilized behaviour and the domain of the highest plastic strain amplitudes by continuous hardening. Individual domains were correlated with observed dislocation structures. The existence of the plateau can be related to the localization of the cyclic strain into persistent slip bands. A Manson-Coffin plot of the material over a wide cyclic amplitude range is curved and can be approximated by a double logarithmic dependence.

Notes: Abstract— Near crack tip stress and displacement fields are obtained for anisotropic bimaterial interface cracks. A contact zone model is used in order to get rid of the unphysical oscillatory interpenetration between the edges of the crack. Semi-infinite and the finite crack problems have been studied. Using the near crack tip results of this model crack branching angles can be predicted. These results are illustrated by numerical results for various materials.

Notes: Abstract— In order to investigate the fatigue strength and fracture mechanism of ceramic-sprayed steel, rotary bending fatigue tests were conducted at room temperature in air and 3% NaCl solution using specimens of a medium carbon steel (S45C) with sprayed coating layers of Ni-5% A1 (under-coating) and chromia (top-coating). The results obtained are discussed based on observations of fatigue cracks and experimental data on specimens subjected to individual treatments during the ceramic spraying process. It was found that at a very early stage of fatigue life, cracks were initiated at the interface between under- and top-coating layers, and grew rapidly into the ceramic-sprayed layer. However, these cracks did not propagate continuously into the substrate, and the final failure was led by the growth of a crack newly initiated at the surface of the substrate steel. Thus, the fatigue strength of the ceramic-sprayed steel in air could be evaluated due to the property of the substrate. The corrosion fatigue strength of ceramic- sprayed steel was improved when compared to that of the substrate steel. However, the coating layer contained many pores, through which NaCl solution was supplied from the specimen surface to the substrate. Corrosion pits were formed at the interface between the under-coating and the substrate. Subsequently, cracks initiated from the pits and grew into the substrate. Tests were also conducted on specimens whose pores were closed by a shielding treatment. In this case, NaCl solution was supplied to the substrate by cracks initiated in the top-coating layer. The shielding treatment was effective at low stress levels where fatigue life was more than 107 cycles, while it had little effect on improving corrosion fatigue strength at higher stress levels because of the many cracks initiated in the top-coating layer.

Notes: Abstract— The development of an elastic-plastic fracture mechanics model for predicting fatigue crack growth rates in notched specimens is presented in this paper. The model is based on experimental short and long crack growth results from un-notched specimens and the distribution of strain ahead of the notch root. This approach may be applied to the assessment of the lifetime of many high technology engineering components.

Notes: Abstract— By conducting creep tests and creep-fatigue tests at temperatures of 800°C, 900°C, and 1000°C, on centrifugal cast HK40 alloy (which is used for example for the steam reformer tubes of fuel cell plants) and varying the strain rate during the loading and unloading process, the influence of strain history on the life of the material has been clarified. Furthermore, the data obtained from these tests were subjected to analyses by means of life evaluation methods utilizing the life fraction rule, strain range partitioning method, and damage rate approach, and comparative studies were conducted on each life evaluation method. As a result, problematic points concerning the application of the life fraction rule, strain range partitioning method, and damage rate approach have been clarified and data which would be useful in establishing design guidelines for structures to be used under conditions such as involves the interaction of creep and fatigue have been obtained.

Notes: Abstract— By adopting a suggestion made by Thomason, a new failure criterion for the Gurson-Tvergaard model has been recently introduced by the authors. In this study, a method based on the Gurson-Tvergaard constitutive model and the new failure criterion is applied to the analysis of ductile fracture. The main features of the method are that the material failure is a natural process of the development of Thomason's dual dilational constitutive responses, and the void volume fraction corresponding to the failure by void coalescence is not necessarily a material constant and is not needed to be fitted beforehand. Furthermore, void nucleation parameter(s) can be numerically fitted from experimental tension results. This method has been implemented into the ABAQUS finite element program via a user material subroutine and is applied to the prediction of tension problems conducted by the authors. In the analyses, two strain-controlled void nucleation models have been studied and compared. The void nucleation parameters corresponding to the two models have been calibrated. The crack initiation of both smooth and notched axisymmetric tensile specimens are well predicted by the method. Finally, several critical issues in the analysis of ductile fracture are discussed.

Notes: Abstract— A computer program that creates time histories for use in fatigue tests in servo-hydraulic machines is presented. The time histories can be tailored from certain user specifications, namely the irregularity factor and the level-crossing spectrum. The program is based on the theory of stochastic time series, and the formulae needed for the program are derived in the paper. Problems of optimality are treated both with respect to fulfilment of the specifications and with respect to machine performance. Examples from two fatigue-testing projects, where the program has been applied, are presented.

Notes: Abstract— The interaction between fatigue damage (i.e., fatigue crack propagation) and internal grain boundary damage (i.e., cavity formation at grain boundaries) has been studied for the Alloy 800H at 750°C for constant plastic strain ranges but different experimental conditions. Most experiments were performed at constant ranges of alternating tensile/compression stresses. Symmetrical as well as asymmetrical tests (with larger compression stresses) were performed. In comparison to the former tests, asymmetrical tests led to shorter cyclic lifetimes mainly due to cavity formation which was not observed for symmetrical tests. It could be shown that a fast compressive and a slow tensile half cycle (at large compressive and low tensile stresses) are ideal conditions for the nucleation and growth of cavities. Based on quantitative measurements of the cavity density from interrupted fatigue tests, a physical model is presented which can predict the number of cycles to failure. This cycle number is determined only by fatigue crack growth which is controlled by (a) athermal plastic deformation, (b) creep deformation and (c) rate enhancement by cavitation.

Notes: Abstract— The fatigue behaviour of a Ni-Cr-base powder flame-spray coating on a 0.4% C steel is investigated. Fatigue tests were carried out using mild hour-glass profile specimens. Cracks were detected and measured using plastic replicas and an image analysis system. Coated specimens showed a slightly lower fatigue endurance than plain specimens under torsion loading, while the opposite was observed for push-pull loading. Microcracks in coated specimens invariably form at pores.Contrary to the usual case of stage I shear growth for a plain 0.4% C steel in tension or torsion loading, the coated specimens show initial crack growth from pores along directions perpendicular to the maximum tensile stress. The crucial behaviour of short cracks, and their growth rates, relative to the thickness of the coating, are discussed in some detail.

Notes: Abstract— The effect of stress state on the time and strain to failure has been considered in terms of currently accepted models of cavity growth. It is shown that the increasing contributions of compressive stress cause changes in cavity growth mechanisms which lead to increases in ductility. A tensile component of stress is necessary to provide the driving force for cavity growth by diffusion of vacancies and hence only strains in the presence of a tensile stress can lead to creep-dominated failure in creep-fatigue.Equivalent stress functions for isochronous stress rupture have been derived in terms of the cavity growth models and their corresponding relationships for calculating damage in terms of strain fractions developed. It is shown that it is difficult to discriminate between the various models on the basis of available experimental data. However, the analysis allows data to be assessed within the framework of physically based mechanisms and suggests methods which lead to conservative lower bound estimates of endurance.It is concluded that the shape of the isochronous creep rupture locus depends on the controlling process of cavity growth and that a detailed analysis of uniaxial creep ductility is necessary to obtain a complete description of the multiaxial behaviour. In many instances such an analysis will prove more valuable than simply performing creep tests over a limited range of stress states. Increasing contribution of principal stress to the failure process leads to a greater value for the equivalent stress in the presence of a compressive component compared with the von Mises equivalent value. However, the equivalent stress is reduced in the tensile quadrant of bi-axial stress. Hence the degree of conservatism arising from using the von Mises equivalent stress will vary with stress and may become slightly non-conservative. The relationship between equivalent stress functions for application in a time fraction assessment of creep and the calculation of creep damage by a strain fraction method has been demonstrated. Finally, guidance is given on how a limited data base of uniaxial rupture properties can be used to obtain a conservative estimate of behaviour under multiaxial loading.

Notes: Abstract— Different aspects of fatigue design problems are indicated and uncertainties are listed. Scatter as observed in many laboratory studies is analyzed. It is argued that scatter of crack initiation and crack growth are different issues. Various sources of scatter are discussed and illustrative examples are presented. Comments are given on statistical distribution functions, scatter under Variable-Amplitude loading, and scatter in service. The discussion touches upon the experience and meaning of scatter of laboratory test series related to practical problems.

Notes: Abstract— The notched strengths of four woven laminates (two orthotropic, one quasi-isotropic and one square symmetrical) under monotonic uniaxial loading, predicted with the point and average stress criteria, the two parameter criterion, the progressive degradation model, and the initial and improved point and minimal strength models, have been respectively compared with the experimental data. The damage mechanisms for the laminates were tentatively studied. The results show that, for minimal experimental information, the notched strengths predicted by the improved minimal strength models are the most precise and the progressive degradation model can numerically illustrate the damage mechanisms in detail. The damage mechanisms of the woven laminates were found to be very different from those of non-woven laminates.

Notes: Abstract— The dislocation substructures of ferrite in plain carbon, ferrite plus martensite, dual-phase steels in different stages of fatigue crack propagation were examined by transmission electron microscopy. The experimental results show that the dislocations are in random arrays in the ferrite before cyclic loading. At stages of low ΔK (near threshold) values, parallel clusters of dislocations and prolonged dislocation lines can be observed. At stages of intermediate ΔK values, the dislocations are rearranged into networks and loops while at stages of high ΔK (prior to failure) values, they are changed into dislocation cells or patches. It was also found that the volume fraction and carbon content of martensite have significant effects on the dislocation substructures of ferrite after cyclic deformation.

Notes: Abstract— Thermo-mechanical fatigue stress-strain data on ferritic/austenitic steels and superalloys from a variety of sources are analysed with regard to hysteresis loop stress asymmetry. This arises from a decoupling of the thermal and mechanical strain signals in the test technique so that many tension-compression load combinations are possible. Data from simplified isothermal and bithermal tests are also examined. Taking a typical example of an “out-of-phase” thermo-mechanical loop on a 1/2 CrMoV steel cycled between 200 and 550°C, isothermal stress-strain data were generated at 50°C intervals on material from the same cast and, used in conjunction with the elastic characteristics of the apparatus, an attempt was made to re-create this loop. The methods employed were (i) a graphical construction between appropriate isothermal yield contours (ii) a tangent modulus calculation (iii) a secant modulus calculation. Method (i) appeared to give the closest agreement in the present case.

Notes: Abstract— The plastic deformation of thin-walled cylinders has been experimentally examined for the loading conditions of ±1% axial strain with hoop stresses of approximately 0, 1/4, 1/2 and 3/4 of the initial uniaxial yield stress.Two materials similar to those used in the pipework of PWR nuclear plant in the U.K. have been tested, namely 304S11 stainless steel and En6 low-carbon steel. The results of the tests were to be compared with the allowable stresses and deformations specified in the ASME Boiler and Pressure Vessel Code, Section III. The code specifies that a prescribed combination of primary stresses must not exceed 1.5Sm, where Sm is a stress value defined for each material.The results indicate that the limit of 1.5Sm is excessively low for both materials and that in particular, the stainless steel could tolerate 5Sm. Although the En6 steel is more prone to ratchetting than the stainless steel, the results suggest that it too could tolerate a higher primary stress than the code allows. Both materials are shown to satisfy the proposed ASME ratchet strain limit of 5% hoop strain after 10 cycles of ±1% axial strain range, for any value of internal pressure.

Notes: Abstract— The susceptibility of an X65 line pipe steel to hydrogen-induced stress corrosion cracking (SCC) is investigated. SCC tests on the steel are carried out in three environments of different aggressivity based on a NACE TM-01-77 solution with dissolved gaseous H2S. The threshold stress intensity factor is calculated for each environment using the multiple specimen technique. The steel is tested in the as-received condition and after homogenisation. Permeation tests are carried out on specimens of the same steel in the same environment. The relationship between threshold stress intensity factor and hydrogen concentration is obtained. The results from these studies are used to generate the parameters in the micro-mechanic model of Akhurst and Baker. The validity and physical significance of the model is assessed.

Notes: Abstract— Measurements of the effect of stress ratio on the constant amplitude fatigue crack growth rates in four quenched and tempered steels in the Paris regime are reported. This data and published data for other alloys (including lower strength steels and non-ferrous alloys) are evaluated, and a correlation function suitable for practical fatigue life calculations is derived. In addition to stress intensity factor range and stress ratio, other significant parameters are the yield stress of the material and its thickness. For the four steels on which new measurements were made, the degree of dependence of the crack growth rate on stress ratio may be related to sensitivity to environmental conditions.

Notes: Abstract— A model based upon linear elastic bridging and fiber crack tip shielding is proposed for predicting fatigue crack growth in a SCS-6/Ti-6–4 composite. The model is characterized by the fiber/matrix debond length rather than the fiber/matrix interfacial frictional shear strength used in most current fatigue models. Finite elements combined with fracture mechanics are applied for computing the local stress intensity. The local stress intensity in the matrix is then utilized to predict crack growth in the composite via comparison to monolithic fatigue crack propagation data for a similar Ti-6–4 matrix material.

Notes: Abstract— The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements.Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for center crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.

Notes: Abstract— Experiments have been performed on specimens subjected to strain cycles similar to those experienced by sub-surface elements of material in rolling/sliding contact. It has been observed that if the strain cycle is closed then failure takes place by low cycle fatigue and the Coffin-Manson relationship may be used to predict the number of cycles to failure. If however, the strain cycle is open, so that the material accumulates unidirectional plastic strain (the situation known as “ratchetting”) a different type of failure, which is termed ratchetting failure may occur. It occurs when the total accumulated plastic strain reaches a critical value which is comparable with the strain to failure in a monotonic tension test. The number of cycles to failure under these circumstances may be estimated by dividing this critical strain by the ratchetting strain per cycle. It is suggested that low cycle fatigue and ratchetting are independent and competitive mechanisms so that failure occurs by whichever of them corresponds to a shorter life. The results of both uniaxial and biaxial tests reported in the literature have been re-evaluated and these, together with new data on biaxial tests on copper, found to be consistent with this hypothesis.

Notes: Abstract— A hypothesis on the statistical relation between the local microscopic directions of fatigue crack growth and the macroscopic crack front shape is postulated. The method of fractographic reconstitution of the fatigue crack front shape from local microscopic directions of crack growth is proposed and tested in two different applications.

Notes: Abstract— Large scale, structurally representative, double tension crack arrest tests have been undertaken at temperatures between −99°C and −87°C. Applied stresses and the length of the embrittled crack starter sections were varied to give different applied stress intensity factors in the tests. The results indicate that crack arrest in structures is not governed solely by a so-called crack arrest temperature but that static linear elastic fracture mechanics can be used to describe it. The measured crack arrest toughness temperature curve of the 1.5%Ni TMCP steel investigated lies at the lower bound of published data.

Notes: Abstract— The criteria for determining whether ferritic material exhibits fully ductile behaviour are generally based on the fracture toughness vs temperature relationship determined from standard laboratory test pieces (e.g. Charpy V Impact tests or fracture toughness specimens). This relationship defines a ductile-brittle transition region. When fully ductile, microvoid coalescence behaviour is experienced, and fracture toughness is described as being on the “upper shelf”. At “off the shelf” temperatures brittle, cleavage fracture is experienced. On the lower shelf the material is entirely brittle, exhibiting 100% crystallinity on the fracture face. As the temperature increases, initiation of tearing by microvoid coalescence occurs and some stable tearing can occur prior to the cleavage event. Material toughness increases with temperature until the upper shelf condition is achieved.The characteristics of fracture toughness tests in terms of the toughness level exhibited and the extent of ductile tearing experienced have been used as a guide to whether the structural application (e.g. a pressure vessel) will behave in a brittle or a ductile manner. This paper reports on a feasibility study where various worked examples have been performed to examine the concept of using a “cut off” on the failure assessment diagram, determined from the conditions required to cause plastic collapse of a pressure vessel, as a criterion for defining effective “ductile” operation. Fracture assessment procedures (R6 revisions 2 and 3 and PD6493 levels 2 and 3) have been utilised to determine the influence on pressure vessel performance of the behaviour of fracture toughness test specimens.The procedure of plotting a structural collapse “cut off” on a failure assessment diagram enables the assessment of whether a particular flaw geometry would result in gross deformation of the structure at failure. The use of this procedure provides an unambiguous demarcation between “fracture dominated” and “collapse controlled” conditions. This procedure facilitates judgements on the level of toughness necessary to ensure ductile operation and whether a “tearing plus toughness” requirement is necessary.It is recommended that consideration be given to including structural collapse into fracture assessment procedures carried out using R6 revision 3 or PD 6493:1991 procedures in order to determine the conditions when enhanced toughness no longer influences structural performance (i.e. when effective “upper shelf” conditions are attained).

Notes: Abstract— The use of a previously presented general criterion of failure for high cycle multiaxial fatigue, τa/tA,B+σn.max/2σT= 1, is extended to cases where the shear and normal stress on the critical plane are non-proportional and also to give life predictions in the range of 104 to 106 cycles. The criterion takes account of whether case A cracks, growing along the surface, or case B cracks, growing in from the surface, occur.

Notes: Abstract— The successful implementation of a fracture mechanics approach to the in-service structural integrity assessment of welded and machined components requires an accurate and reliable NDT method for detecting and sizing surface breaking cracks. This paper discusses and compares the crack depth sizing abilities of two theoretically-based NDT techniques: alternating current potential difference (ACPD) and alternating current field measurement (ACFM). Surface fatigue cracks of high and low aspect ratio are used in the investigation. It is demonstrated that ACPD is capable of accurately sizing long shallow cracks and that ACFM provides accurate crack depth predictions for small deep cracks.

Notes: Abstract— Conventional mechanical tests and fracture mechanics experiments were carried out at – 196°C on a low alloy steel (A508 class 3) which was investigated under two different conditions: (i) a reference condition in which the failure mode was cleavage and (ii) an embrittled condition in which the fracture mode was either partly or predominantly intergranular fracture. These experiments, performed with a new specimen geometry, a ring specimen instrumented to measure also the crack velocity, were used to determine the fracture toughness at crack initiation (KIc) and at crack arrest (KIa). It is confirmed that the reduction in KIc measured in the embrittled material is associated with the appearance of intergranular fracture. It is also shown that KIa, determined by a static analysis decreases rapidly with crack velocity when the fracture mode is predominantly cleavage. On the other hand, KIa, corresponding to intergranular fracture seems to be much less dependent on crack speed. This difference in the sensitivity of both modes of brittle fracture to crack velocity is briefly discussed.

Notes: Abstract— Low cycle fatigue (LCF) testing of powder metallurgy (PM) superalloys has determined that LCF cracks initiate from defects such as pores and ceramic inclusions located either at the surface or internally. The ratio of surface-to-internal crack initiation sites depends upon experimental conditions. In the current work, a probabilistic model is presented that describes the competition between these two failure mechanisms from a single experimental parameter, μ. The model predicts the size distribution of defects which initiate LCF cracks, as well as the proportion of specimens which fail as a result of internally located defects. Model predictions were found to correlate well with experimental LCF data obtained from a N18 PM Ni-base superalloy. The model further enables evaluation of a “size effect”, as it predicts that internal crack initiation is favoured for larger components/specimens.

Notes: Abstract— A fatigue scatter band has been computed for laser welded austenitic stainless steel joints. These laser welded steels have a very small heat affected zone. The unified scatter band provided by standards for welded structural steels does not adequately describe the trend of the experimental data of laser welded steels and this makes their design parameters scarcely realistic. The scatter band proposed in this paper has been computed by re-sorting experimental data relative to joints with high stress concentration factors and has subsequently been assessed with data relevant to butt welded joints.

Notes: Abstract— Energy dissipation rate, D, and crack tip opening angle (CTOA) have been related for large amounts of ductile crack growth in a fully plastic two-dimensional model of real elastic plastic material. Several J-type rising R-curves have been constructed and related, some based on the cumulative energy dissipated and some as a characterising term that relates closely to the far-field J contour value. These two meanings co-exist but the relationship is geometry dependent. For deep notch bend (DNB) cases the non-dimensional group Lα/r* (where L is normalised load, α is CTOA and r* defines the position of the instantaneous centre of rotation) governs the value of dJ. Certain DNB cases where R-curves vary with size are resolved by this group rather than by CTOA itself whereas for centre-cracked tension there is a higher value of CTOA than for DNB.

Notes: Abstract— Failure of ceramic materials occurs when the stress intensity factor of the most serious crack in a component reaches a critical value KI,C, the fracture toughness of the material. In case of ideal brittle materials the fracture toughness is independent of the crack extension and, consequently, identical with the stress intensity factor KI,Onecessary for the onset of stable crack growth. It is a well-known fact that failure of several ceramics is influenced by an increasing crack-growth resistance curve. The effect of increasing crack resistance has consequences on many properties of ceramic materials. In this report the authors discuss some aspects of R-curve behaviour as represented by stress intensity factors or energies.

Notes: Abstract— The transferability of fracture results between homogeneous and cladded specimens was studied in single edge-notched bend specimens. The test material was of A533-B steel with a clad layer deposited by a commercial strip welding process. The fracture resistance properties were developed independently for cladding and base material using homogeneous specimens of each material. The experimental data from tests on cladded specimens were analysed with the finite element method. The 3D J-values were compared with values evaluated using the measured crack extension in the cladded specimen and the JR-data of the respective material provided from homogeneous specimens. A reasonably good agreement was obtained in this comparison for a limited amount of crack growth.

Notes: Abstract— Basic diagrams of the cyclic crack growth resistance of two of the most investigated titanium alloys, namely Ti-6A1–4V and Ti-6A1–6V-2Sn, are presented. Diagrams are plotted for, in-air, distilled water and 3.5% NaCl solution, which are necessary for lifetime calculations of structural elements made of these metals. The dependency of cyclic crack growth resistance on the yield strength is established. It is shown that cyclic crack growth resistance of titanium alloys in corrosive environments is determined not only by the stress-strain state but also by the electrochemical conditions at the corrosion fatigue crack tip, which for aqueous environments can be characterized integrally by the hydrogen index of the environment and the electrode potential of the metal. Therefore, cyclic corrosion crack growth resistance testing should be performed under constant electrochemical conditions at the corrosion fatigue crack tip or these conditions should be taken into account. A new method of plotting the basic cyclic corrosion crack growth resistance diagrams of titanium alloys is considered.

Notes: Abstract— A fretting fatigue crack growth model is proposed accounting for the effects of tribological parameters of the contacting materials and the biaxiality of contact together with bulk stresses, upon fretting fatigue crack growth rate and direction of growth in the fretting-zone subsurface layers. Based on this model a new technique is developed to determine fatigue life and predict the fatigue limit in an aluminium alloy, AMg6N, and a titanium alloy, VT9, under fretting conditions. For the above cases, fretting fatigue crack growth behaviour predicted by the proposed model is in good agreement with the experimental results.

Notes: Abstract— Mode I fatigue crack growth has been studied in notched specimens of 7017-T651 aluminium alloy subjected to fully compressive cyclic loads. The specimens were first subjected to a deliberate compressive preload which causes plastic deformation at the notch tip. On unloading, this region developed a residual tensile stress field and on subsequent compressive cyclic loading in laboratory air, a fatigue crack was nucleated at the notch and grew at a diminishing rate until it stopped. The final crack length increased with an increase in the value of the initial compressive preload and with an increase in the negative value of the applied cyclic mean load. To gain a better understanding of crack growth in residual stress fields, the magnitude and extent of residual stress induced from compressive preloads have been analysed. This was achieved when extending the notch by cutting while recording the change in the back face strain. From residual strain models it was found that the fatigue crack growth was confined to a region of tensile cyclic stress within the residual stress field. The effective stress intensity range was investigated at selected mean loads and amplitudes, for correlating purposes, using both the compliance technique and by invoking the crack growth rate behaviour of the alloy. Finally, a brief discussion of the fracture morphology of cracks subjected to cyclic compression is presented.

Notes: The cylindrical specimen is a common configuration adopted for biaxial fatigue testing. A rigorous yet practical analysis is presented here under the framework of incremental plasticity. The cyclic stress-strain curve is obtained from four different plasticity models, and correlated with twenty-six in-phase biaxial tests on En15R steel. Stabilized hysteresis loops can also be derived based on the cyclic stress-strain curve under a J2-kinematic hardening formulation with special consideration of the rounding transition at the instant of yielding. A correlation for the hysteretic strain hardening exponent N is required for materials that exhibit non-Masing behaviour; i.e. do not allow a full description of hysteresis loops from knowledge of the cyclic stress-strain curve. The solution is further generalized to out-of-phase loading, where the rotation of the active stress state around the yield surface is illustrated. This compares favourably with ten out-of-phase tests on En15R steel.

Notes: As is well known, the fatigue strength reduction factor due to a notch (Kf) in the modified Neuber's rule should not be considered a constant since it varies with different stress levels. In this paper, the definition and the variation of Kf are discussed on the basis of theoretical and experimental analyses, leading to the presentation of a variable Kf-Neuber's rule. Comparing the results of experimental stress analyses and the fatigue life tests of specimens, the variable Kf-Neuber's rule gives good predictions and is applied to the life prediction of an aircraft component.

Notes: Fatigue crack growth behaviour under intermittent overstressing was investigated in dry air with a low carbon steel under tension-compression and tension-tension loading with different mean stress levels. A very small number of cycles of overstress applied intermittently during a very large number of cycles of understress below threshold caused, in all cases, a significant acceleration in crack growth rate as compared to the case of steady cyclic stress. The acceleration for the case with tensile mean stresses was a little smaller than in the case without mean stress and it was related to a little higher crack closure level in the former case. Stress history in the precracking process had some effect on crack closure and, consequently, on the acceleration. A fairly good correlation was obtained between the acceleration and the effective stress intensity range. The acceleration under multi-level intermittent overstresses with different mean stresses could be predicted by linear summation from two-level intermittent overstress test data. No difference was recognized in the fracture surface morphology between the cases with different mean stress level including the cases of multi-level stresses, indicating that the micromechanism of crack growth acceleration would be the same in all cases.

Notes: In this paper the Rousselier ductile damage model is used to simulate the softening behaviour of notched bars and crack growth in a pre-cracked specimen of an A508 pressure vessel steel. The effect of the internal parameters needed to represent the damage on the calculated results is studied. The interactions between these parameters and their effects on the calibration process are discussed. The effect of the cell size on the values of the damage parameters obtained during calibration and on the response of the specimens is briefly reviewed.

Notes: Both high-cycle and low-cycle fatigue properties of hot-extruded powders of a Ni3Al-based alloy, IC218, have been evaluated. High cycle fatigue measurements were performed under stress controlled conditions at temperatures ranging from 25°C to 850°C. Tests were made in both laboratory air and vacuum environments. Low cycle fatigue tests were conducted under total strain control in a laboratory air environment at 650°C. In high cycle fatigue, high ratios of the fatigue limit (Δσ at 106 cycles) to monotonic yield strength (σys), of approximately Δσ/σys∼1, were obtained in the powder extruded IC218 alloy for temperatures ranging from 25°C to 650°C. In low cycle fatigue, a substantial decrease in fatigue life occurred at 650°C, compared to results obtained previously at 25°C. High cycle fatigue performance at low stress/strain amplitudes is better than expected when compared to precipitation strengthened superalloys. The improved performance is explained in terms of the cyclic hardening behavior of the alloy.

Notes: A theoretical study of the conditions for coalescence of two fatigue cracks in a multi-crack system is presented. As both cracks grow, the near-side plastic zone sizes of the interacting cracks increase more rapidly than the off-side zone sizes which results in higher overall crack propagation rates for an interacting crack growth system than the simple addition of individual crack growth rates. The use of a single crack growth model to predict failure in the presence of two or more cracks may therefore underestimate the interaction between cracks and lead to un-conservative predictions. Some of the theoretical predictions were confirmed by published results of experimental measurements of crack interaction distances in multi-crack systems.

Notes: Hydrogen induced cracking (HIC) initiation sites and their correlation with the critical stress intensity factors of hydrogen charged specimens were studied under combined I/II mode loading. Two series of tests, is. constant load (CL) tests and slow strain rate (SSR) tests, were carried out. Experimental results showed that in CL tests, irrespective of the ratio KIJKl, the HIC initiation sites always correspond to the point of maximum hydrostatic stress; which is located some distance ahead of the notch tip. However, for SSRT tests, when K11/K1〉 1, HIC started at the notch tip which corresponds to the point of maximum equivalent plastic strain. When K11/K1〈1 in SSR tests, HIC occurred initially some distance ahead of the notch tip.The relationship between the critical stress intensity factor for HIC and K11/K1 was shown to be different for the two types of test. Multiple effects of stress and strain on hydrogen redistribution and hence on HIC initiation sites, as well as critical stress intensity factors, are discussed.

Notes: Abstract— Two methods are employed, namely the Charpy impact test and a strain gauge technique, for the determination of the dynamic fracture toughnesses of CrNiMoV27 and CrNiMoV45 alloy steels under various impact loading rates and heat treatments. The results show that the dynamic fracture toughness KId is significantly affected by impact velocity and that tempering has a greater influence on KId than quenching. It is also shown that the alloy containing a greater amount of vanadium yields consistently a higher value of Kid.

Notes: Abstract— The paper deals with the analytical representation of the cyclic stressstrain curve, the hysteresis loop and the hysteresis energy for a single-phase α-brass. The one- and two-parameter elastic-plastic models that were used were so chosen as to produce compatible representation of both the stress-strain relationship and the hysteresis loop. The models were checked with experimental data. The specimens were tested in uniaxial tension-compression (Rε=−1) under total strain amplitude control. The experiments covered a broad spectrum of lives from the low-cycle region through to the high-cycle regime, i.e. up to lives of N= 1 × 106 cycles. The adopted measurement method enabled the cyclic deformation curve, hysteresis loop and hysteresis energy to be determined independently. It was shown that the modifed Ramberg-Osgood model is a good approximation to actual cyclic behaviour of α-brass.

Notes: Abstract— Fretting fatigue tests of an austenitic stainless steel used for a propeller tail shaft were carried out in seawater and in air. In seawater, fretting significantly reduced the fatigue strength, however, the fretting fatigue lives at higher levels of stress were longer than those in air. The tangential force coefficient (defined as the ratio of the frictional force amplitude and the contact load) in seawater was much lower than that in air and varied in the range from 0.3 to 0.5 during the fretting fatigue tests. The lower tangential force coefficient in seawater seems to be the main reason for the longer fretting fatigue life in seawater. The prediction of fretting fatigue life was made on the basis of elastic-plastic fracture mechanics, where the frictional force between the specimen and the contact pad was taken into consideration. The predicted fatigue lives agreed well with the experimental results in both air and seawater.

Notes: Abstract— Fatigue crack initiation and propagation in duplex stainless steels are strongly affected by microstructure in both inert and aggressive environments. Fatigue crack growth rates in wrought Zeron 100 duplex stainless steel in air were found to vary with orientation depending on the frequency of crack tip retardation at ferrite/austenite grain boundaries. Fatigue crack propagation rates in 3.5% NaCl solution and high purity water are increased by hydrogen assisted transgranular cyclic cleavage of the ferrite. The corrosion fatigue results are interpreted using a model for the cyclic cleavage mechanism.

Notes: Abstract— The morphologies of failures in synchronous belts were observed following four types of fatigue test. Two modes of initiation were observed. One was due to cord failure which was observed under various conditions. Detailed observations showed that the interfaces between stranded glass filaments were separated at the centre of the cords. The extended direction of the separations was mainly vertical to the back face of the synchronous belt. The second mode of crack initiation was observed under relatively high loadings of the mating flank of the belt tooth. The cracks were initiated at the tooth roots of the synchronous belts. Finally, the deformation behaviour of a synchronous belt was measured under static loading.

Notes: Abstract— The effect of mean stress on near threshold fatigue crack growth behaviour under mixed mode I+II loading has been studied in a structural steel BS4360 50D in laboratory air at room temperature. It was found that the branch crack threshold decreased significantly as R ratio (Pmin/Pmax) increased from 0.1 to 0.7. A simple model is proposed to predict the branch crack threshold behaviour for R-ratio sensitive materials. Further investigation is required to model the mode II dominant situations where the branch crack thresholds tend to converge on a high value.

Notes: Abstract— Although there has been considerable success in the development of design methods for assessment of fatigue and creep fatigue damage there is need for further improvement particularly for creep damage estimation. Strain based creep-fatigue rules have been developed for liquid metal fast breeder reactor technology (LMFBs) which give improved estimation of fatigue and creep damage compared with presently available procedures in commercially available high temperature design codes such as ASME CCN47 and RCC-MR. Presently however their scope is confined to full in-elastic analyses.This paper provides a summary of the approach used in the strain based rules in relation to base material and weldments of 316L(N) austenitic steel. The paper examines the application of the strain method to thermal shock tests on long cylinders in which the testing cycle includes periods of constant temperature and some of the test pieces contain circumferential welds. Comparisons are made with time fraction based estimates and those of full cyclic in-elastic analyses. Conclusions are drawn concerning the benefits of the method compared with presently available code procedures. The experience to date shows that the strain based rules give a more realistic interpretation of thermal shock experiments.

Notes: Abstract— In order to study the relation between the scatter characteristics of small crack growth behaviour and fatigue life, rotatory bending fatigue tests of smooth specimens were carried out using 0.21% carbon steels of different ferrite grain sizes. Fifteen to eighteen specimens were fatigued at each stress amplitude, and the initiation and propagation behaviour of the cracks which led to the final fractures were examined for all the specimens. The physical basis of scatter in fatigue life was investigated, based on the successive observation of fatigue damage on the surface using the plastic replica technique, followed by an analysis of the data assuming a Weibull distribution. A statistical investigation of the physical basis of scatter in relation to the ferrite grain size was performed, i.e. the distributions for crack initiation life, crack propagation life, fatigue life and growth rate of small cracks. Finally, the fluctuation of crack growth rate was studied in relation to the application of a crack growth law for microstructurally small cracks.

Notes: Abstract— When incompletely mixed hot and cold fluid streams pass adjacent to the surface of a component or a structure, they can cause thermal fatigue damage. An analytical model, based on linear elastic fracture mechanics and the frequency response method, is presented for the assessment of thermal fatigue damage. Various shapes of surface temperature-time histories, represented by their power spectral densities, are examined. The model is compared with an alternative method based on the impulse response method and good agreement is found. This kind of thermal fatigue is of particular concern in various types of nuclear reactors and rapid shut-downs of hot plant. The model proposed is intended as an engineering design tool and has been developed as a computer code known as “TBL”.

Notes: Abstract— Plasticity-induced crack closure is associated with a wedge of material in the wake of a fatigue crack. A model is proposed to explain the development of this wedge under plane strain conditions. This model is based on the non-linearity of the crack path. If the plastic zone size is an order of magnitude or larger than the characteristic length of a crack deflection, then the plastic deformation changes the shape of both crack flanks in different ways. This causes a residual displacement on the crack flanks. Different examples for the development of such plasticity induced wedges are shown.

Notes: Abstract— An experimental investigation of the effects of small surface scratches on the fatigue behavior of Al-Li alloys has been carried out. Small scratches were generated onto the specimen surface which were then subjected to fatigue testing. These scratches were characterized by three different parameters, scratch angle, scratch tip radius of curvature, and scratch depth. These parameters have exhibited an important influence on the fatigue life of the scratched samples. In particular, it was found that the fatigue life decreased sharply as the scratch depth increased. In addition, the scratch surface and fracture surfaces were examined under a scanning electron microscope. The observations helped in the assessment and identification of the mechanisms responsible for failure.

Notes: Abstract— A finite element analysis and fatigue crack growth studies are made of dovetail joints in aeroengine compressor discs. Three aspects are examined: the first deals with the finite element stress analysis of the critical geometrical features and interface conditions of different dovetail configurations, thus enabling an assessment to be made of the critically loaded regions in the disc. The second deals with the prediction of the direction of potential fatigue cracks, which were allowed to initiate in the finite element model at the regions where fretting damage is most likely to occur, using an incremental crack tracking criterion. The third is concerned with the verification of the above modelling techniques with fatigue tests on a uniaxial back-to-back arrangement, which attempts to simulate the stress fields of a rotating disc.

Notes: Abstract— Fatigue strengths of Sic whisker or Sic particulate reinforced 6061-T6 aluminum matrix composite (SiCw/Al or SiCp/Al), fabricated by a high pressure infiltration method, were obtained in laboratory air, ion exchanged water and a 3 pct NaCl aqueous solution. A comparison was made with the properties of the matrix aluminum alloy 6061-T6. The SiCw/Al composite maintained a higher fatigue resistance than the SiCp/Al composite or the monolithic 6061 Al, even in a 3 pct NaCl solution. Good correlation was observed between a deterioration in the fatigue strength and the value of the corrosive potential and current, when changing the environment from laboratory air or ion-exchanged water to a 3 pct NaCl aqueous solution.

Notes: Abstract— A series of crack growth experiments has been preformed on the near alpha titanium alloy, Ti-1100, to determine the mechanism of the creep-fatigue interaction. Based on pure creep crack growth results, the increase in the creep-fatigue crack growth rate is not amenable to separate contributions of creep crack growth and fatigue crack growth.A mechanism has been proposed to account for the increase in creep-fatigue crack growth rate that is based on the planar slip of titanium alloys which results in the formation of dislocation pileups at the prior beta grain boundaries and leads to intergranular fracture. This mechanism has been validated through crack growth experiments preformed on a Ti-1100 that has been microstructurally modified through the precipitation of internal slip barriers. These show that the intergranular fracture and increase in crack growth rate are absent.

Notes: Abstract— Previous work has shown that the inclusion of the strain energy released by crack blunting leads to an energy minimum for fatigue crack growth that can be used to predict stage II fatigue crack growth. The present work assumes a polynomial relation between crack blunting and crack extension to derive an expression for the rate of fatigue crack growth that is dependent upon only the applied ΔK, E, σys, Kc, and the exponent p in the relation between crack blunting and crack extension. This expression is thought to be generally valid since it accurately predicts fatigue crack growth rates for a wide variety of titanium, nickel, aluminium and steel alloys. A unique characteristic of the model is its ability (for long crack, slow crack growth) to account for the different slope for different materials in the Paris Law region of the da/dN vs. δK curve. The model specifically shows that this slope, m, is dependent solely upon the exponent, p, in the relation between crack blunting and crack extension.

Notes: Abstract— This paper compares the fracture toughness values obtained from two different specimen geometries, i.e. pre-cracked compact tension and chevron-notched short rod. The former is in widespread use, however, the latter has significant advantages in that no pre-cracking is required resulting in more economical use of material and reduced machining. Four 6061-aluminium-matrix composites reinforced with discontinuous alumina particles were investigated. Good agreement in fracture toughness values from the two specimen geometries was obtained for all the materials and all the heat treatments examined. Detailed analyses of the fracture surfaces were used to identify the fracture mechanisms. The effects of specimen geometry, volume fraction of reinforcement and ageing treatment on fracture toughness are discussed.

Notes: Abstract— The improvement of a material's toughness has significant industrial applications. An example is the manufacture and maintenance of commercial gas containers made in the form of aluminium cylinders; a challenging design problem since they are susceptible to crack growth under a static load (internal pressure). In this investigation a new thermo-mechanical technique was used to improve the apparent fracture toughness. This could increase significantly the safety margin and life of the cylinders. The determination of fracture toughness was carried out using a newly developed small cylindrical specimen which has a considerable cost advantage over the standard compact tension specimen. Experiments on aluminium 6351-T6 cylindrical specimens confirmed the possibility of improving the toughness of this alloy.

Notes: Abstract— The effects of cyclic frequency, hold time, and stress-intensity-factor range (δK) on rates of fatigue crack growth in air at 500-700°C have been studied for Waspaloy—a nickel-based superalloy used for gas-turbine engine discs. The main effects observed were: (i) higher rates of crack growth for lower cyclic frequencies at high δK at 600 and 700°C. and (ii) lower rates of crack growth at low δK (and higher δK thresholds) for longer hold times at 700°C, compared with those at a baseline frequency of 2 Hz. Metallographic and fractographic observations suggested that the effects of cyclic frequency and hold time could be rationalised in terms of the competing effects of enhancement of cracking due to creep and inhibition of cracking caused by oxide-induced crack closure, fracture-surface-roughness induced crack closure, and crack-branching/deflection. Possible mechanisms for promoting intergranular and transgranular cracking at low cyclic frequencies or long hold times are discussed.

Notes: Abstract— Through-thickness reinforcement is effective in suppressing delamination in composite laminates. It provides bridging in the crack wake during delamination crack growth. The closure traction behind the crack tip due to this bridging increases the delamination toughness significantly. The effect of bridging may be analysed using the stress intensity approach or the Griffith energetic approach. In this paper, delamination crack growth resistance KR,(Δa) of a double-cantilever-beam specimen, with through-thickness reinforcement, under Mode I delamination is determined using these two approaches. Additionally, the J-integral analysis is also employed. A comparison between the theoretical results predicted by these three methods is provided using the example of stitched CFRP.

Notes: Abstract— Fatigue crack growth in a commercial grade ABS over the temperature range - 50°C to 80°C has been studied. An Arrhenius type relationship between fatigue crack growth rate and absolute temperature was found to describe the experimental data. At ΔK= 1 MPa√m, the activation energy for crack growth in the temperature range −50°C to 19°C is 3.47 kJ/mole and in the temperature range 30°C to 80°C it is 19.63 kJ/mole. The two different activation energies were found to be associated with the roughness of the fracture surfaces. The roughness of the fracture surfaces is discussed in relation to modes of fatigue crack growth. In the low temperature range (− 50°C to 19°C) the fracture surfaces were found to be rather coarse, whereas in the high temperature range (30°C to 80°C) they were found to be somewhat smooth. These different roughnesses were deduced to be due to different modes of crack branching influenced by crazing. A “stress intensity factor”-biased Arrhenius equation for fatigue crack growth successfully predicts growth rates at various temperatures.

Notes: Abstract— When an initially-parallel-sided tab of material, cut into an isotropic finite-width sheet, is torn by pulling the outer tabs in one direction, and the center in the opposite, the cracks may follow a parallel path, diverge outwards, or converge inwards depending on the widths of the inner and outer “legs”. At the same time, the untorn portion of the material may rotate relative to the pulling axis. The phenomenon is observed in globally elastic tearing, elastoplastic tearing, and in rigid-plastic tearing. A fracture mechanics model using minimum energy explains the tear paths and rotations. Experiments on NS4 aluminium alloy confirm the analysis. The relationship of leg widths and bend radii with standard trousers tear testing of ductile materials is explained.

Notes: Abstract— Since heat-treated high strength steels are often used as materials for machines and structures that operate under severe service conditions, it is important to evaluate their fatigue life. Hence the growth law of a small fatigue crack must be known in order to estimate the fatigue life of machines and structures since the life of such members is controlled mainly by the behaviour of a small crack. The growth rate of a small crack can not be predicted usually by linear elastic fracture mechanics, but can be determined uniquely by the term σnal, where σa is stress amplitude, l is crack length and n is a material constant. In this paper, the small-crack growth law of heat-treated carbon steels and low alloy steels was studied. An effective and convenient method based on a small-crack growth law, dl/dN=C3(σa/σa)nl is proposed, where σu is the ultimate tensile strength, for predicting the small crack propagation life of heat- treated steels with different tensile strength levels, together with a method for determining the fatigue life of plain members.

Notes: Abstract— Five kinds of silicon nitride samples with different microstructure were prepared in order to examine the effect of sintering condition on grain size and mechanical properties. The degradation in strength of ceramics caused by grinding is investigated in detail. It is shown that the critical process zone size is closely related to the grinding process. Futhermore, the crack size caused by grinding is estimated by the process zone size failure criterion and the Newman-Raju formula. It can be concluded that the process zone size failure criterion is useful when evaluating the sensitivity of ceramics to grinding.

Notes: Abstract— A study has been made of fatigue crack formation and growth at the root of different notch profiles in a structural steel subjected to fully reversed tension-compression loading. The scale of stage I microstructural crack growth at notches decreased with increasing notch root strain and was comparable to the size of stage I cracks in shallow hourglass profile specimens at the same strain. Stage II crack growth rates were faster within the notch plastic field than in the elastic stress field of the bulk material.

Notes: Abstract— Several surface cold work procedures are developed to induce compressive residual stresses adjacent to a notch in a flat element. It would appear that they should all lead to fatigue life enhancement. For sharp notched specimens excellent fatigue life enhancement is observed. For moderately notched specimens only one of the procedures produces this enhancement. In order to shed light on the shortcomings of two of the procedures, the residual stress field is determined by means of finite element analyses in two and three dimensions. It is observed that the two-dimensional analyses predict a residual stress field which should lead to fatigue life enhancement. It is the three-dimensional analyses which help to explain why two of the cold work procedures fail.

Notes: Abstract— Fatigue crack growth in an α+β titanium alloy (TA6V) with three microstructural conditions is studied in high vacuum at 300°C. The faster growth rates are observed in the material with a low content of primary α phase and a fine equiaxed microstructure. Near the threshold regime, a slow crystallographic Stage I-like propagation is observed in the three microstructural types where slip occurs along a single-plane system which develops within the α grains. These crystallographic facets are identified using an electron backscattering pattern (EBSP) technique and were found to lie on basal planes.

Notes: Abstract— Fatigue tests were carried out on welded T-joints of JIS A5083P-O Al-Mg alloy under constant amplitude and superimposed random load waves. Each random wave was generated by superimposing a secondary zero-mean random process on a constant amplitude pulsating trapezoidal wave, which simply simulated the GAG (ground-air-ground) stress cycles, or on a constant d.c. (direct current) component. It is proved that the 1-dimensional rainflow method is insufficient as the mean stress effects are not considered. From a procedure using a 2-dimensional rainflow method and the original and a modified Goodman diagram, it was concluded that the mean stress effects on secondary waves are larger in the case of GAG than d.c. Considering this, a life estimation procedure is proposed that gives consistent and acceptable estimation results.

Notes: Abstract— An efficient and accurate method for computing the fatigue-life distribution of metal structures is presented. The problem is governed by the basic equations of the Coffin-Manson-Neuber local-strain fatigue theory for notched components. The coefficients of fatigue strength and fatigue ductility, the fatigue notch factor as well as the nominal-stress amplitude may be random variables with an arbitrary joint distribution. In order to arrive at a direct solution for the fatigue-life distribution, hence an assessment of the reliability of a component, a collocation method has been developed which gives the total-strain amplitude as an explicit function of the stress amplitude and the fatigue notch factor. This explicit equation has very close conformity to the corresponding, true, implicit equation. The fatigue-life distribution is finally expressed in a multiple-integral closed form. A simple algorithm termed the “complete-probability fast integration” (CPFI) is developed which gives the exact solution, to any desired accuracy, for the entire ranges of fatigue-life and reliability. CPFI is superior when compared to the results and procedures of the approximate methods currently employed.

Notes: Abstract— Micro-crack behaviour under axial and torsional loading at 550°C was observed by replica techniques. Cracking behaviour and micro-damage observations were correlated using several parameters that are based on equivalent strain parameters. From the observations, micro-cracking of the oxide films at the crack tip in the strain localized regions seems to be a dominant micromechanism of fatigue crack growth. The maximum principal strain has been identified as an important parameter in multiaxial fatigue at high temperature. A good correlation was obtained between the principal strain range and the crack growth rate. Finally, a life prediction method was proposed based on maximum crack length.

Notes: Abstract— Fracture mechanics analyses are carried out on a cracked machine element of complex geometry to predict its fatigue behaviour. Usually, in order to obtain reliable values of stress intensity factors, it is necessary to realize three-dimensional meshes or to utilize the energy approach. An alternative, simplified and approximate approach is proposed here. It is based on the construction of simple two-dimensional models to obtain accurate values of the geometry factors of the component at the deepest point of the crack. Experimental tests show that the relation between the depth and the length of the crack on the free surface is linear. Hence it is possible to reduce the problem to two dimensions with a consequent saving of calculation time. A comparison with experimental data indicates that a satisfactory prediction is obtained by the proposed method.

Notes: Abstract— An ultrasonic surface acoustic wave technique for studying the growth behaviour of small fatigue cracks is described. The technique allows crack depth and opening stress to be monitored continuously during the course of a fatigue test. Results are given for a 1740 MPa yield strength, silicon-modified, AISI 4340 steel tested under zero-to-tension cyclic loading. Good agreement is shown between acoustically determined crack depth and that measured by post-fracture optical microscopy. The monitoring of changing crack depth-to-surface length ratios during tests is also demonstrated. Acoustically determined crack opening stresses were found to be about 10% higher than values determined by measurements of crack tip opening displacements by scanning electron microscopy. Effects on crack growth of two different specimen surface preparations, electropolishing and diamond paste polishing, are also reported. Growth rates in electropolished specimens were as much as an order of magnitude higher than in diamond paste polished specimens which had a shallow but significant layer of compressive residual stress.

Notes: Abstract— Several experimental techniques used in fracture toughness tests are based on the “Plastic hinge” model that permits different fracture mechanics parameters to be determined. This model is only valid under the following conditions: small displacements, small stable crack growth, and small distances between knife edges and the apparent centre of rotation. A generalized model for a two-dimensional situation is presented which permits a better representation of the phenomena that occur in a test involving crack growth and large displacements. The use of a two-dimensional factor, that corrects the measured displacements by converting them into ones that would be measured under a one-dimensional hypothesis, is proposed. In this way the same methodology used for CTOD determination, may again be used.

Notes: Abstract— A mathematical model of crack propagation due to the formation of a fractal cluster of voids and microcracks is presented. The initiation of a microcrack from a pile-up of dislocations in the vicinity of a crack tip is modelled. A method to determine the fractal dimension of a crack, based on the crack growth analysis, is developed. A crack length versus crack velocity relation, based on the physical mechanisms of crack growth and the fractal nature of a crack, is deduced. A formula for the time to fracture is obtained.

Notes: Abstract— Knowledge of the behaviour of interacting and irregularly oriented multiple cracks is very limited. The recharacterisation rules for such cracks are usually empirical. In order to provide more reasonable rules for an engineering assessment of fatigue growth of irregularly oriented multiple cracks, this paper first studies the mechanics of fatigue growth of two-dimensional non-coplanar cracks. Uniaxial and biaxial fatigue testing on specimens with various multiple cracks are then carried out. Possible errors in the assessment of the cracks using the current rules are discussed. An improved procedure for the fatigue life assessment is developed.

Notes: Abstract— Mode I and mode II stress intensity factors for two half-spaces connected by a circular patch were used to develop a mixed-mode stress intensity factor (termed the stress index Ki) which can correlate the fatigue life of all spot weld geometries, base metals, and specimen dimensions. Empirical corrections were applied to Broek's equivalent stress intensity factor (Klq) to account for the weldment geometry (sheet thickness, nugget diameter, specimen width) and the effect of mean stress. The final expression, (Ki), is a measure of the notch-root stress field in the location where crack initiation and early crack growth occur. The stress index (ki) should be a useful tool for spot-weld fatigue design.

Notes: Abstract— The distribution of hydrogen in the vicinity of a crack tip was studied using SIMS (Secondary Ion Mass Spectrometry) under different ratios of I/II mixed mode loads. Modified WOL specimens with kinked slits were employed in the course of the experimental work. Spectrographic measurements show that under I/II mixed mode loading, both in the HIC and in the rmaxp directions, there are two hydrogen accumulation peaks ahead of the crack tip, corresponding to the location of the maximum hydrostatic stress and maximum equivalent plastic strain, respectively. Based on results obtained over a range of loading conditions from mode I to a high KII/ KI, ratio, it is shown that the mode II component has a clear influence on both peaks. The conditions for hydrogen redistribution are discussed in terms of crack tip stress-strain fields.

Notes: Abstract— The conventional use of continuum ductile damage mechanics in finite element analyses identifies the “cell” in which damage occurs with the finite elements in which the distribution of stress and strain is modelled. Since the cell size is a fixed, metallurgically-defined, property of the material being analysed, this methodology forces a minimum size for the finite element mesh. Mesh refinement is thereby disallowed. This paper presents one way of avoiding the problem by developing a mesh-independent cell model which, with a fixed cell size, allows the finite element mesh to be refined to any degree within the cells. Procedures which average some state variables within the cells are introduced to prevent the localisation of damage after a certain critical stage is reached. The method has been tested in numerical simulations of (a) the deformation of a notched tensile bar, (b) a 35 mm compact tension specimen and (c) the first of the AEA spinning cylinder tests. There is a reasonable agreement between the results of the computer simulations and those of the experiments.

Notes: Abstract— Based on the assumption that normalized Kitagawa-Takahashi diagrams for different materials are the same, a unified model for microstructurally small fatigue crack and physically small fatigue crack growth rates was developed to describe their behaviour under different fatigue stress ranges. The stress-sensitive blocking effect of microstructural barriers to small fatigue crack growth is satisfactorily simulated by the model. Incorporated with the materials fatigue limit and microstructural barrier spacing, this model can be easily used in the prediction of small fatigue crack lifetime. Small fatigue crack growth rates of previous experimental studies in 7075-T6 Aluminium alloy and HT60 steel under different stress ranges are in an envelope between two boundary prediction curves corresponding to the largest and smallest stress ranges applied in the experiments. Problems concerning model accuracy and model application are also discussed in the present paper.

Notes: Abstract— Isothermal and thermal-mechanical strain fatigue tests were conducted in air on representative service alloys; a 1 CrMoV steel, and two batches of 316 stainless steel. Data was obtained for thermal-mechanical in-phase and out-of-phase cycles, and also for isothermal tests at the maximum, minimum, and mid-temperature of the thermal-mechanical cycle. Dwell periods were also incorporated in the cycle to assess their effects.A comparative evaluation has been made on the basis of the materials' cyclic stress response. In general, the results have shown that the thermal-mechanical strain cycling tests cause a large increase in stress range over those tested under isothermal conditions at maximum temperature. In addition, mean stress and strain offsets were developed in continuous cycle thermal-mechanical tests, whereas negligible offsets occurred in isothermal tests.It appears that the response of the materials could not always simply be explained by reference to the temperature change itself.

Notes: Abstract— There is a critical stress rate Kc for each of the three ZrO2 ceramics tested. Fracture is controlled by the materials polycrystal fracture toughness, Kcp, if the stress rate is less than Kc. Otherwise, fracture is controlled by the single crystal fracture toughness, Kcs. The crack growth parameters determined by dynamic fatigue experiments can only represent macrocrack growth behaviour although the fracture of specimens in experiments originates from small surface flaws.

Notes: An analysis is made of shear lip measurements as observed on fatigue crack surfaces of an aluminium alloy sheet material. It is shown that, for biaxial cyclic loads at stress ratios 1 and various R-ratios, shear lips were controlled by an equivalent intensity factor Ke=K1F(λ,R).For crack growth in air the shear lip width ts was approximately proportional to K2e at ts 〈 t*s= 2.5 × 10−4 m and K4E, at ts 〉 t*s where t*s is the critical value of the shear lip dimension. The initiation of shear lips and the orientation of crack growth for different parameters of the loading cycle are briefly considered in the discussion.

Notes: Improvements in acoustic emission (AE) test techniques have lead to developments whereby reliable acoustic emission measurements as a fatigue damage indicator were made at room temperature on Incoloy 901 smooth specimens, over a stress-ratio range of −1.0≤R≤0.2. Fatigue damage accumulation was evaluated in terms of an AE damage definition and a damage function was developed. Thus, various damage phases in the cumulative damage process were identified by their AE signature, and then formulated and analyzed in terms of cumulative AE ringdown counts.