bluuebunny/crossref_metadata_2025 huggingface dataset:
THE GROWTH OF SHORT CRACKS UNDER CYCLIC COMPRESSION
Authors: Pippan R.
Published: April 2007

The fatigue crack growth behaviour, the length of the arrested cracks and the shape of the crack front were investigated for cyclic compression. Specimens with deep sharp notches were used. The experiments were performed for different load amplitudes and load ratios under conditions of small scale yielding. The material used was ARMCO‐iron. The growth rate and length of the arrested cracks were estimated and compared with the experimental results. The crack growth rate of very short cracks is determined by the stress intensity and is independent of the stress ratio. The length of the arrested cracks depends on the stress ratio and is bounded by the size of the cyclic and the monotonic plastic zones.
AN ANALYSIS OF CRACK TIP SHIELDING IN ALUMINUM ALLOY 2124: A COMPARISON OF LARGE, SMALL, THROUGH‐THICKNESS AND SURFACE FATIGUE CRACKS
Authors: Ritchie R. O. , Yu W. , Blom A. F. , Holm D. K.
Published: April 2007

Abstract— The development of crack closure during the plane strain extension of large and small fatigue cracks has been investigated in a 2124 aluminum alloy using both experimental and numerical procedures. Specifically, the growth rate and crack closure behavior of long (∼17–38 mm) cracks, through‐thickness physically‐short (50–400 μm) cracks, and naturally‐occurring microstructurally‐small (2–400 μm) surface cracks have been examined experimentally from threshold levels to instability (over the range 10–12–10–6m/cycle). Results are compared with those predicted numerically using an elastic‐plastic finite element analysis of fatigue crack advance and closure under both plane stress and plane strain conditions. It is shown that both the short through‐thickness and small surface cracks propagate below the long crack threshold at rates considerably in excess of long cracks, consistent with the reduced levels of closure developed in their limited wake. Numerical analysis, however, is found consistently to underpredict the magnitude of crack closure for both large and small cracks, particularly at near‐threshold levels; an observation attributed to the fact that the numerical procedures can only model contributions from cyclic plasticity, whereas in reality significant additional closure arises from the wedging action of fracture surface asperities and corrosion debris. Although such shielding mechanisms are considered to provide a prominent mechanism for differences in the growth rate behavior of large and small cracks, other factors such as the nature of the stress and strain singularity and the extent of local plasticity are shown to play an important role.
THE EFFECT OF FREQUENCY IN ENVIRONMENTAL FATIGUE TESTS
Authors: Gabetta G.
Published: April 2007

Abstract— The complex dependence of environmental fatigue crack growth rate on loading variables, has been studied for a pressure vessel steel in a pure water environment. Attention has been focused on the frequency effect, which has been interpreted by using a superposition model. With this approach, the maximum expected crack growth rate can be quantitatively estimated as a function of frequency; critical ΔK values for the onset of stress corrosion fatigue can be calculated as a function of crack tip strain rate, which depends on applied load, load rise time and crack length.

The approach has been verified by a comparison with experimental data from two laboratories. The agreement of data with the prediction is quite good.
DAMAGE PRODUCTION DURING HIGH TEMPERATURE‐LOW CYCLE FATIGUE OF A TITANIUM ALLOY (IMI 829)
Authors: Plumbridge W. J.
Published: April 2007

Abstract— The microstructural damage produced at 600°C by low cycle fatigue, with and without dwell periods at peak strain, has been investigated. Most surface fatigue cracks are produced by compressive‐only and balanced dwell cycles and these waveforms are associated with the minimum endurance. High tensile mean stresses and deleterious environmental effects, respectively, are responsible. Internal, principally intergranular, damage results only after unbalanced tensile dwell cycling, although failure remains fatigue dominated. In comparison to pure fatigue, this waveform has little effect on lifetime. However, it is argued that small changes in the test parameters could render such damage influential and induce a transition in the dominant failure mode.
MIXED MODE SMALL CRACK GROWTH
Authors: Socie D. F. , Hua C. T. , Worthem D. W.
Published: April 2007

Abstract— The fatigue crack growth behavior of small part‐through cracks in 1045 steel and Inconel 718 subjected to biaxial loading has been investigated. Experiments were performed on thin‐wall tubular specimens loaded in tension, torsion and combined tension torsion. Crack sizes analyzed ranged from 20 μm to 1 mm and growth rates ranged from 10‐7 to 10‐4 mm/cycle for 1045 steel and from 10‐5 to 10‐2 mm/cycle for Inconel. Nucleation and the early growth of cracks occurs on planes of maximum shear strain amplitude for both of these materials even in tensile loading. An equivalent strain based intensity factor was employed to correlate the crack growth rate under mixed mode loading conditions In loading conditions other than torsion, a transition from mode II to mode I was observed for 1045 steel. Principal strains were used to analyze mode I cracks. Cracks in Inconel 718 grow in mode II for the majority of the fatigue life. The maximum shear strain amplitude and the tensile strain normal to the maximum shear strain amplitude plane were used to calculate the strain based intensity factor for mixed mode loading.
DRAFT EGF RECOMMENDATIONS FOR DETERMINING THE FRACTURE RESISTANCE OF DUCTILE MATERIALS: EGF PROCEDURE EGF P1–87D
Authors: Schwalbe K.‐H. , Neale B. K. , Ingham T.
Published: April 2007

Abstract— The EGF Working Party on Fracture Mechanics Testing Standards has written a draft ECF Procedure for determining the crack growth fracture resistance of ductile materials. either in terms of the J‐integral or the crack tip opening displacement. Methods are also given for deriving J and δ fracture parameters related to initiation of crack growth. The multiple specimen method is taken as the reference method. Several single specimen techniques are described in Appendices. The EGF Procedure is currently being validated by an experimental round robin.
THE EFFECTS OF STRESS RATIO, COMPRESSIVE PEAK STRESS AND MAXIMUM STRESS LEVEL ON FATIGUE BEHAVIOUR OF 2024‐T3 ALUMINIUM ALLOY
Authors: Ibrahim Faisal Khalil
Published: April 2007

Abstract— Fatigue crack growth behaviour of 2024‐T3 aluminium alloy is investigated as a function of stress ratio, compressive peak stress and maximum stress level. It is found that as the stress ratio and the magnitude of the compressive peak stress are increased, the threshold stress intensity range decreased linearly. Intermediate and near threshold growth rate data are analysed with different formulae for effective stress intensity range. The data covered different values of stress ratio, compressive peak stress and maximum stress level. A formula for the crack opening stress level is introduced as a function of stress ratio, compressive peak stress and maximum stress level. The formula permitted a good correlation between crack growth data for both positive stress ratio and negative compressive peak stress values. Using the new formula, intermediate and near threshold crack growth data for the 2024‐T3 aluminium alloy yielded a unique crack growth rate vs effective stress intensity range curve for all stress ratio and compressive peak stress values investigated. This suggests that for the 2024‐T3 aluminium alloy the crack growth rate vs effective stress intensity range curve does not depend on stress ratio, compressive peak stress, or maximum stress level. The significance of the new equation and the crack growth rate versus effective stress intensity range curve is that they allow a designer to find crack growth rate vs stress intensity range data for the 2024‐T3 aluminium alloy in both intermediate and near threshold regions for the particular stress ratio, compressive peak stress and maximum stress level conditions of the component under investigation.
INFLUENCE OF SECONDARY VOID DAMAGE IN THE MATRIX MATERIAL AROUND VOIDS
Authors: Li G. C. , Guennouni T. , Franclois D.
Published: April 2007

Abstract— The mechanism of ductile damage caused by secondary void damage in the matrix around primary voids is studied by large strain, finite element analysis. A cylinder embedding an initially spherical void, a plane stress cell with a circular void and plane strain cell with a cylindrical or a flat void are analysed under different loading conditions. Secondary voids of smaller scale size nucleate in the strain hardening matrix, according to the requirements of some stress/strain criteria. Their growth and coalescence, handled by the empty element technique, demonstrate distinct mechanisms of damage as circumstances change. The macroscopic stress‐strain curves are decomposed and illustrated in the form of the deviatoric and the volumetric parts. Concerning the stress response and the void growth prediction, comparisons are made between the present numerical results and those of previous authors. It is shown that loading condition, void growth history and void shape effect incorporated with the interaction between two generations of voids should be accounted for besides the void volume fraction.
NOTCH SIZE EFFECT IN FATIGUE
Authors: Lukás P. , Kunz L. , Weiss B. , Stickler R.
Published: April 2007

Abstract— The notch size effect (i.e. the decrease of the notched fatigue limit with increasing notch size for the same stress concentration factor) was quantitatively derived by describing the threshold conditions for the propagation of a short semi‐elliptical crack nucleated at the notch root. A close relation between the Kitagawa—Takahashi diagram for the short crack threshold stress and the dependence of the notched fatigue limit on the notch size was shown. The derived relation for the notch size effect was experimentally verified for several specimen/notch geometries in the cases of pressure vessel steel and copper.
FATIGUE CRACK GROWTH AND CLOSURE THROUGH A TENSILE RESIDUAL STRESS FIELD UNDER COMPRESSIVE APPLIED LOADING
Authors: Kang K. J. , Song J. H. , Earmme Y. Y.
Published: April 2007

Abstract— —Fatigue crack growth and closure through a tensile residual stress field under an applied compressive loading is investigated by carrying out various applied stress ratio tests ranging from R= 0 to R= It is found that even under applied compressive loading, fatigue crack growth rates are well correlated with the effective stress intensity factor range and the behaviour of crack closure through a tensile residual stress field is uniquely controlled by an effective stress ratio which takes account of residual stresses. Consequently, the method of predicting fatigue growth rates, using da/dN vs ΔK data from residual stress‐free specimens, can be successfully applied to crack growth through a tensile residual stress field. However, previously used simple assumptions may lead to non‐conservative estimates of crack growth rates.
FRETTING FATIGUE AT ELEVATED TEMPERATURES IN TWO STEAM TURBINE STEELS
Authors: Mutoh Y. , Satoh T. , Tanaka K. , Tsunoda E.
Published: April 2007

Abstract— —Fatigue tests and fretting fatigue tests of two steam turbine steels at room temperature and 773 K were carried out. The reduction of fatigue life and strength in the fretting test were significant at 773 K as well as at room temperature. The values of the friction coefficient at 773 K was almost equal to those at room temperature. The geometry of the fretting fatigue crack was flat in the early stage of fatigue life where a significant effect of fretting was observed. With increasing crack length and with a reducing effect of fretting, the fatigue crack shape changed to a semi‐circular form. The fretting fatigue lives predicted on the basis of elastic‐plastic fracture mechanics analysis, with the frictional force between the fretting pad and the specimen taken into consideration, agreed well with experimental results at both temperatures.
DETERMINATION OF STRESS CORROSION CRACK INITIATION STRESS AND CRACK VELOCITIES USING SLOWLY STRAINED TAPERED SPECIMENS
Authors: Yu J. , Xue L. J. , Zhao Z. J. , Chi G. X. , Parkins R. N.
Published: April 2007

Abstract— Previous work has shown that a single tapered cylindrical specimen subjected to slow strain rate testing can provide data for the crack initiation stress of 70/30 brass in 1N NaNO2 solution. In order to test the wider applicability of that technique, crack initiation stresses of a further five systems were measured. These were 70/30 brass in an ammoniacal solution, copper in sodium nitrite and mild steel in carbonate–bicarbonate, hydroxide or nitrate solutions. The results are compared with those obtained from tests on plain cylindrical specimens subjected to interrupted slow strain rate tests or to constant load tests, and the agreement is reasonable. The method also is capable of providing data on the stress dependence of crack velocities.
FATIGUE OF THICK‐SECTION COLD‐EXPANDED HOLES WITH AND WITHOUT CRACKS
Authors: Pell R. A. , Beaver P. W. , Mann J. Y. , Sparrow J. G.
Published: April 2007

Abstract— Fatigue tests under spectrum loading were conducted to evaluate hole cold‐expansion in thick‐section open‐hole aluminium alloy specimens, some of which contained residual fatigue cracks before cold expansion. Cold expansion resulted in an increase in life by a factor of about 7. Small residual fatigue cracks did not inhibit the effectiveness of the cold‐expansion process, indicating that it may not be essential to remove such cracks prior to hole cold‐expansion. The increase in life is primarily associated with a reduced crack propagation rate compared with that for cracks from non‐cold‐expanded holes. Cold‐expanded hole fractures displayed a marked disparity in crack depths adjacent to the two faces of the specimens. Considerable differences were evident in crack depths and fatigue crack areas at failure between cold‐expanded and non‐cold‐expanded hole specimens. These findings have ramifications in the damage tolerance assessment of aircraft structures.
FATIGUE CRACK GROWTH FROM SMALL SEMI‐ELLIPTIC HYDROGEN‐INDUCED CRACKS IN QIN STEEL
Authors: Cowling J. M. , Knott J. F.
Published: April 2007

Abstract— Small semi‐elliptic hydrogen‐induced cracks were produced in QIN (HY80) steel. Fatigue crack growth rate behaviour and threshold values for these cracks were investigated at several positive stress ratios (R= 0.2 to 0.7) and compared with results from long through‐cracks. At low R values the hydrogen‐induced cracks gave higher thresholds, and lower crack growth rates at the same nominal ΔK value in the near threshold region. At high R values the growth rates of both crack types were almost identical. The results are explained by a combination of crack tip blunting and roughness induced closure of the intergranular hydrogen crack.
THE FRACTURE BEHAVIOUR OF AN AXIAL CRACK IN A PRESSURISED PIPE
Authors: Neale B. K. , Haines A. B. , Miller A. G.
Published: April 2007

Abstract— The multiple specimen technique was developed to measure the crack growth fracture resistance of a through axial crack in a pressurised pipe and the results compared with data measured from test specimens. The comparison indicates that there is no significant difference between pipe and specimen behaviour. The results are also compared with elastic‐plastic three‐dimensional finite element analyses of the pipe and the R6 failure assessment curve. Reasonably good agreement was found between the experimental results and finite element analyses. The experimental results all lie outside the material specific failure assessment curve of the R6 structural integrity assessment procedure.
STANDARDIZED LOAD SEQUENCE FOR OFFSHORE STRUCTURES–WASH 1
Authors: Schütz W. , Klätschke H. , Hück M. , Sonsino C. M.
Published: April 2007

WASH 1 is composed of a defined series of six seastates for a yearly return period; the two lowests seastates 1 and 2 being eliminated, because they do not influence the fatigue life of offshore structures, and the three highest seastates 8, 9 and 10 were combined. The sequence and the duration of the resultant six seastates correspond also to long term observations in the North Sea. A generated load history with the power spectrum of the strain measuremnts used as a basis, is the result for each seastate. The return period of the standardized load history WASH 1 decided upon is 5 × 105 cycles coresponding to one year of wave loads. It is fixed sequence of peaks recorded on tape. Testing frequency and signal shape are optional. The basis for the derivation of standardized load histories is always formed by strain histories measured in operation. WASH 1 was derived on the basis of strain measurements on the FRIGG DP2 platform of IFREMER, Brest, supplemented by measurements of Germanischer Lloyd, Hamburg, on the Research Platform NORDSEE. As even comprehensive measurements can only be samples over a limited period of time, the strain measuremments were supported by the results of long‐term observations of seastates in the North Sea.
SMALL FATIGUE CRACK GROWTH IN A LOW CARBON STEEL UNDER TENSION–COMPRESSION AND PULSATING‐TENSION LOADING
Authors: Tokaji Keiro , Ogawa Takeshi , Aoki Tetsuya
Published: April 2007

The growth behaviour of small fatigue cracks has been investigated in a low carbon steel under axial loading at the stress ratios R of –1 (tension‐compression) and 0 (pulsating‐tension). Crack closure was measured to evaluate the effects of stress ratio and stress level on small crack growth. Except for the accelerated growth at stress levels close to the yield stress of the material, at R=–1 small cracks grow faster than large cracks below a certain crack length, but at R= 0 the crack growth rates for small cracks are coincident with those for large cracks in the whole region of crack length investigated. The critical crack length, 2cc, above which the growth behaviour of small cracks is similar to that of large cracks depends on stress ratio, being 1–2 mm at R=–1 and smaller than 0.7 mm at R=0. The 2cc value at R=–1 agrees with that obtained under rotating bending (R=–1). The small crack data are closely correlated with large crack growth rates in terms of the effective stress intensity range, ΔKeff; thus ΔKeff is found to be a characterizing parameter for small crack growth including the growth at the higher stress levels.
A COMPARATIVE STUDY OF METHODS FOR ESTIMATING BOLT FATIGUE LIMITS
Authors: Patterson E. A.
Published: April 2007

The approach to predicting fatigue limits from calculated stress concentration factors, using thread load distributions obtained from analytical theories is examined. In particular combinations of the methods of Shigley, Otaki, Heywood, Birger, Bluhm and Flanagan, Sopwith and a modification to Sopwith's theory are assessed against fatigue test data and photoelastic results for a range of bolt and nut geometries. The Snow‐Langer‐Cook, the Goodman and the Gerber methods of allowing for the effect of mean stress were also examined. It was concluded that mean stress effects are significant, that none of the theories are sufficiently sensitive to changes in geometry, and that they seriously overestimate the fatigue limit when the geometry is more severe than the standard. The use of Sopwith's theory of load distribution combined with Heywood's method and the Snow‐Langer‐Cook technique was found to be the safest for design purposes, but not the most accurate.
SMALL CRACK GROWTH IN THE ALUMINIUM–LITHIUM ALLOYS 8090 AND 8091
Authors: Nicholls D. J. , Martin J. W.
Published: April 2007

The relationship between microstructure and the fatigue behaviour of small cracks has been examined for the aluminium–lithium alloys 8090 and 8091 after peak ageing at 170°C. Duplex ageing and pre‐stretching were used to vary the distribution of S'precipitates and thus the distribution of slip. No effect of S'distribution an small crack growth was observed in either alloy. This is thought to be due to a combination of the lack of closure and lower overall slip reversibility in small cracks. Small cracks in 8091 were found to grow slower than in 8090 due to differences in grain shape rather than texture. Small cracks in both alloys were observed to grow much faster than long cracks for equivalent ΔKs. This difference was reduced when small crack data were compared with long crack data generated at R= 0.7 due to the reduced closure. The use of ΔJ made long and small crack growth rates still more comparable.
GEL ELECTRODE IMAGING OF FATIGUE CRACKS IN MAGNESIUM ALLOYS
Authors: Baxter W. J. , Gorkiewicz D. W.
Published: April 2007

The gel electrode technique has been modified for the detection of fatigue cracks in magnesium alloys. Prior to fatigue loading, the surface is coated with a thin (70nm) insulating anodic film of magnesium fluoride. This film is ruptured wherever a fatigue crack subsequently forms in the magnesium alloy so that current from the gel electrode flows preferentially to the crack. This current forms an image of the crack on the gel electrode probe with a resolution of 0.05 mm. The image is repeatable, permitting the early stages of growth of small cracks to be monitored.
COMPATIBLE COMPLIANCE AND STRESS INTENSITY EXPRESSIONS FOR THE STANDARD THREE‐POINT BEND SPECIMEN
Authors: Bakker A.
Published: April 2007

Available expressions for load‐line compliance and crack‐mouth opening compliance expressions for standard three‐point bend specimens (span over width ratio =4) are assessed. It is concluded that none of the available expressions are able to reproduce the source data (boundary collocation results and theoretical limits for relative crack depths equal to 0 and 1) for the entire range of relative crack depth. New expressions for example are proposed and the accuracy of each is indicated. A by‐product of the new expression for load‐line compliance is a new, fully compatible stress intensity expression that is, consistent with the load line compliance expression as known from theoretical considerations. Also inverse expressions are presented which predicting the crack length from compliance. To improve the accuracy of such inverse expressions, a correction that results in a considerable error reduction is presented.
FATIGUE ANALYSIS AND PREDICTION IN FILLET WELDED JOINTS IN THE LOW THICKNESS RANGE
Authors: Ferreira J. A. , Branco C. M.
Published: April 2007

Abstract— The paper reports the results of a comprehensive research project concerning fatigue life prediction in fillet welded joints. Geometry variables such as main plate thickness, radius of curvature at the weld toe and leg to leg distance were analysed in detail. Fatigue life computations were carried out for semi‐elliptical cracks using appropriate FE techniques. The range of results covered several types of welded joints loaded in tension and in bending. A comparison of results was made using two methods of stress intensity determination. Experimental data was also obtained and that included measurements of weld toe radius, monitoring of crack shape and S‐N curves. Correlation of results with the theoretical predictions gave generally good agreement. A set of fatigue design curves for fillet welded joints is proposed and in these the designer can introduce the geometry of the weldment.
CRACK TIP FIELDS UNDER NON‐STEADY CREEP CONDITIONS—I. ESTIMATES OF THE AMPLITUDE OF THE FIELDS
Authors: Ainsworth R. A. , Budden P. J.
Published: April 2007

Abstract— Under non‐steady creep conditions, the stress and strain rate fields near the tip of a stationary crack can be described by the singular fields of Hutchinson, Rice and Rosengren for power‐law creeping materials. Estimation formulae are presented for describing the amplitude of these fields under load and displacement controlled boundary conditions. For constant loading, the formulae reduce to the result of Riedel and Rice for short times after load application and to the steady state line integral C* for long times. At intermediate times, the estimate is validated by detailed finite‐element computation. For displacement‐controlled loading, the amplitude of the near‐tip fields is shown to fall rapidly, consistent with finite‐element analysis. The implications of the results for data collection and defect assessments are discussed in a companion paper.
MIXED FATIGUE FRACTURE MORPHOLOGY OF FERRITIC DUCTILE IRON
Authors: Pokluda J. , Siegl J.
Published: April 2007

Abstract— This paper presents the results of the fractographical investigation of ferritic ductile iron samples, which fractured under three‐point pulsating bending at 140 Hz and R= 0.09. The fracture morphology was of mixed inter‐transgranular character and the striations were observed on both trans‐and intergranular facets. This allowed comparisons to be made between inter‐and transgranular crack growth rates. The general conditions necessary for the creation of intergranular striations are formulated with respect to preceding sporadically published works.
A NEW APPROACH TO STRUCTURAL INTEGRITY ASSESSMENT FOR DUCTILE FRACTURE
Authors: Dong Y. M. , Yang W. , Hwang K. C.
Published: April 2007

Abstract— A new approach to structural integrity assessment based on ductile fracture is explored in the present paper. A simplified, yet more convenient methodology than the conventional EPRI elastic‐plastic fracture analysis is outlined which assesses the ductile fracture instability of structures by an intersection rather than a tangent construction. The J‐equivalence principle of crack growth is employed for tearing instability determination of single edge cracked plates. An admissible stress curve method is established with a peak value indicating instability. This approach gives reasonable predictions concerning the burst pressure of pre‐flawed pressure vessels. A theoretical J resistance curve, which is justified by experimental measurements for steels with relatively high yield strength, can be incorporated for a complete analytical characterization of the defect assessment procedure.
FRACTURE AND DEFECT ASSESSMENT OF CERAMIC COMPOSITES
Authors: de los Rios E. R. , Ando K. , Biddulph R. H.
Published: April 2007

Abstract— Industrial ceramic crucibles manufactured by hot‐pressing a mixture of ceramic powders sometimes fail by delamination when operated under extreme conditions. Results of laboratory tests under similar conditions suggest that failure may be caused by the constrained evaporation of a water rich liquid absorbed by relative large aggregate particles. Fracture mechanics test results, from specimens cut parallel and transverse to the direction of hot pressing, revealed a clear anisotropic behaviour and a large sensitivity to notch size for notches smaller than a millimetre in depth. A model based on the existence of a notch‐tip damage zone is proposed and used to present fracture curves that can be employed for failure assessment of industrial crucibles.
MARKOV APPROXIMATION TO FATIGUE CRACK SIZE DISTRIBUTION
Authors: Solomos G. P. , Lucia A. C.
Published: April 2007

The distribution of the crack size during the fatigue crack propagation phenomenon is investigated. A Markovian modeling of the crack is introduced through the fatigue crack growth law, and the associated Fokker‐Planck equation is written while special care is devoted to specifying its boundary conditions. This equation is solved by the method of separation of variables and the sought distribution function is obtained in the form of a convergent infinite series. An illustrative example, demonstrating the applicability of the approach, shows satisfactory agreement between theoretical results and experimental data.
FATIGUE CRACK GROWTH THROUGH ARALL‐4 AT AMBIENT TEMPERATURE
Authors: Davidson D. L. , Austin L. K.
Published: April 2007

Fatigue cracks were grown in the 5 layer aluminum alloy‐Aramid fiber laminate composite ARALL‐4 over the range of cyclic stress intensity factors (ΔK) from 3.5 to 91 MPa✓m. Near the threshold, crack growth rate was about the same as for unreinforced aluminum alloys, but at high ΔK, crack growth rates were significantly lower. Crack closure was measured over this range of growth rates and found to be different than for unreinforced aluminum alloys. The magnitude of closure was also dependent on crack length. Cracks opened progressively towards the tip with increasing load in much the same way as for unreinforced aluminum alloys. Removal of the aluminum outer layer and some of the epoxy revealed that fibers were intact close to the crack tip, but heavily damaged further away. By adjusting the fatigue crack growth curve of an unreinforced aluminum alloy for the closure exhibited by the composite, it was possible to approximate the crack growth rate for the composite over the lower to mid range of ΔK, but at higher values of ΔK, this model seriously overestimated measured crack growth rates. Therefore, fiber bridging affects both closure and maximum stress intensity factor at the crack tip. Standard fracture mechanics cannot be applied to describe these effects.
RATE‐DEPENDENT DEFORMATION AND FRACTURE OF α‐TITANIUM
Authors: Smith D. J. , Jones R. L.
Published: April 2007

Aspects of combined rate‐dependent deformation and crack growth in α‐titanium at room temperature are examined. Results are presented for tests carried out on pre‐cracked three point loaded single edge notch bend and compact tension specimens subjected to constant crack opening displacement rates and constant load. Curves of the ratio of the reference stress to the yield stress as a function of the ratio of the plastic displacement to specimen width are found to be different for different rates. The stress difference between continuously loaded curves and curves obtained from load relaxation tests (“relaxed” curves) is found to be similar to uniaxial results. Earlier uniaxial tests show that the “relaxed” curve represents a boundary below which no further creep takes place. The pre‐cracked specimen constant load curves cross the “relaxed” curve, even though the contribution from crack growth to the overall deformation is found to be small. Sustained load crack growth is observed to take place under contained yielding conditions and the sustained load resistance curves are found to be different for different reference stresses.
THE CONSEQUENCES OF SHORT CRACK CLOSURE ON FATIGUE CRACK GROWTH UNDER VARIABLE AMPLITUDE LOADING
Authors: Vormwald M. , Seeger T.
Published: April 2007

Opening and closure of short cracks has been examined experimentally using small strain gauges fixed to unnotched specimens very close to short fatigue cracks. The results of completely reversed tension‐compression constant amplitude tests are that crack opening stresses decrease with increasing stress amplitude and that crack closure occurs at nearly the same strain as crack opening. In variable amplitude loading the crack is subjected to a low crack opening level resulting from larger cycles. Based on the results of this experimental investigation some simple approximation formulas are proposed with which decrease as well as increase of crack opening levels can be described. Using these formulas it is possible to compute crack opening strains for any load sequence. The findings of the investigations have been merged to build an algorithm for the prediction of fatigue lives to initiation of cracks of technical sizes in case of variable amplitude loading. The improvement in accuracy of life predictions compared to results of an existing damage accumulation concept is demonstrated for two materials and two load sequences.
SHORT CRACK GROWTH AND COALESCENCE ALONG THE TOE OF A MANUAL FILLET WELD
Authors: Verreman Y. , Nie B.
Published: April 2007

An experimental study was undertaken on the early development of fatigue cracking along the wavy toe of a manual fillet weld between structural steel plates. Stress relieved and as‐welded cruciform specimens were tested under fully reversed loading at two stress amplitudes. Miniature strain gages installed along the toe were used to monitor the crack depth and crack opening level from a crack depth of 10‐20 μ. A calibration of gage response versus crack depth from a 2D finite element analysis is shown to be acceptable. The analysis of the gage responses and of the fracture surfaces including beach marks of short cracks has revealed that discontinuous straight‐fronted cracks rapidly form along the edge of the successive weld ripples. Their aspect ratio increases until some coalescence results from a progressive bridging between the adjacent crack planes. As the step of the ridge line decreases, the cracks fully coalesce into one uniform through‐crack. Faster growth rates associated with negative opening levels are recorded in as‐welded specimens. The welding residual stress distribution makes initiation and early crack propagation concentrate at the center of the specimen which results in a long semi‐elliptical crack.
BEHAVIOUR OF SHORT FATIGUE CRACKS IN A MEDIUM CARBON STEEL SUBJECTED TO BENDING
Authors: Wu X. J.
Published: April 2007

The fatigue process of a 0.45% carbon steel was studied with hour‐glass shaped specimens under rotatary bending. The plastic replication technique was applied to observe surface short fatigue cracks. Fatigue cracks initiated continuously with increasing number of cycles. The failure of a specimen largely depended on the number and distribution of these short cracks. The relationship of surface fatigue crack density to both stress amplitude and number of cycles was determined.
PREDICTION OF REMAINING LIFE OF HIGH TEMPERATURE COMPONENTS USING NON‐LINEAR FRACTURE MECHANICS
Authors: Smith D. J.
Published: April 2007

Procedures developed by Ainsworth and Smith and Webster to assess the remaining life of high temperature engineering components containing cracks are presented and applied to a practical example of a °CrMoV steel pressure vessel operating at 565°C. The general principles of the procedures are similar. Net section creep rupture is described in terms of the reference stress method and creep crack initiation and growth is predicted using the non‐linear (creep) fracture mechanics parameter C*. However, the details of each procedure are shown to differ. The main differences lie in the predicted times for net section creep rupture and creep crack initiation. Ainsworth's method predicts shorter creep rupture times than Smith and Webster's procedure. The initiation time using the Smith and Webster procedure is predicted to occur shortly after loading while Ainsworth's estimate is about 40% of the life of the vessel. Both procedures predict similar times for failure by creep crack initiation and crack growth.
FINITE ELEMENT MODELLING OF FATIGUE CRACK SHAPES
Authors: Gilchrist M. D. , Smith R. A.
Published: April 2007

This paper describes a versatile finite element technique which has been used to investigate the fatigue growth and stability of a wide range of structural defects of practical importance. The procedure automatically remeshes the three‐dimensional finite element model during the stages of crack growth. Problems analysed to date include the subsurface and breakout growth of internally initiated elliptical defects, the growth of semi‐elliptical surface cracks in leak‐before‐break situations, the development of quarter‐elliptical corner defects, the interaction and coalescence of two adjacent coplanar semi‐elliptical surface defects and the fatigue growth of a defect in a round bar.
NUMERICAL RESULTS FOR VOLUME, SURFACE AND CONTOUR INTEGRALS AROUND CRACK TIPS
Authors: Blackburn W. S.
Published: April 2007

The repair or replacement of defective structures can be avoided if it can be shown that the defects will grow a negligible amount in service. The most robust parameters for correlating the onset of crack growth between test and service conditions can be defined as contour integrals around the crack tip. For many years, integrals of this type have been available in the post processing part of the stress analysis program BERSAFE. The new release BERSAFE 90 will include the options of evaluating these parameters by replacing most or all of the contour integration by surface or volume integration. This method known as the g function method makes them equivalent to virtual crack extension methods for an elastic material. To obtain experience of the relative accuracies of the new and old options, calculations have been carried out on coarse meshes for elastic‐plastic materials with two dimensional, axisymmetric and three dimensional geometries under both mechanical and thermal loading for various tolerances and numbers of Gauss points. It is concluded that

The quantity J*w can often be calculated more accurately by using the g function than by taking a contour integral through nodes. However further experience is required before final guidelines can be issued.

Use of 27 rather than 8 Gauss points per element did not improve the accuracy in the case considered.

For uniform tensile loading of a central cracked block, both the g function method and the contour integration method give satisfactory accuracy even with only one element through the thickness. However displacement substitution produces values which are dependent on the number of Gauss points when there is only one such element.

A close tolerance is required for thermal problems in order to obtain path independent results when using either the contour integration or the g functions.
EVALUATION OF FATIGUE CRACK PROPAGATION PROPERTIES UNDER RANDOM LOADING AVOIDING CRACK CLOSURE
Authors: Suzuki Naoyuki , Takeda Harumasa , Ohta Akihiko , Ohuchida Hisasi
Published: April 2007

Abstract—Fatigue crack propagation rates and the fatigue threshold of HT80 steel were measured by maintaining the maximum load during the whole period of random loading in order to prevent fatigue crack closure. The random loading pattern involved 62 level block loadings in which the waveform was approximated to the Rayleigh distribution of peaks. The fatigue crack propagation rates under random loading were well predicted from those obtained from constant amplitude loading and assuming a linear cumulative damage law. That is, da/dn =C{ΔKmeq−ΔKmth} where the equivalent stress intensity factor, ΔKeq={=niΔKmi/dni}1/m, whereni= 0 for ΔKi≤ΔKth, orni=nifor ΔKi> ΔKth.
COMPARISON BETWEEN TWO ASSESSMENT METHODS FOR DEFECTS IN THE CREEP RANGE
Authors: Piques R. , Molinie E. , Pineau A.
Published: April 2007

In recent years considerable effort has been made to understand the behaviour of creep defects at elevated temperature. A large number of experimental studies have been devoted to creep crack growth behaviour. In Europe, both in U.K. (CEGB) and in France (EMP), attention is focussed not only on crack growth but also on creep crack initiation behaviour in the assessment of defects at high temperature. This paper describes and applies both methods, first to laboratory test results and then to a cracked component. The comparison with test data is made with three materials, a ferritic 1 Cr‐1Mo‐0.25 V steel and two austenitic stainless steels, while the application to a cracked pressure vessel deals with a ½ Cr‐Mo‐V steel. For these materials which are creep ductile, the relevant load‐geometer parameter for stationary creep cracks is the C* parameter, which relies on the concept of reference stress and reference length. The expressions used for these parameters in both procedures are compared. Then the methods used for calculating the time for incubation prior to crack extension, t1, the time for subsequent growth, tg, and the time to failure, tF=ti+tg are compared. This comparison is made not only for laboratory test data but also for a cracked pressure vessel. It is shown that, in spite of different approaches, especially in the assessment of tg, both methods provide comparable t1 ‐ C* and tF=C* diagrams. The reasons for this situation are briefly discussed.
SENSITIVITY ANALYSIS OF THE DOUBLE CLIP GAUGE METHOD
Authors: Manzione P. , Ipiñta J. E. Perez
Published: April 2007

During fracture toughness testing, the stable crack growth measurement is necessary for the construction of the R‐curves of J vs Δa or CTOD vs Δa. One possible measurement technique uses the Double Clip Gauge Method, which is based on the assumption that the specimen is deformed like two rigid arms that rotate around an apparent centre of rotation located in front of the crack tip. This apparent centre moves as the crack grows in a stable way, and its position can be estimated through the measurement of two crack opening displacements located at different heights. As a consequence the crack growth can be calculated. In this paper the behaviour of the equations that govern the Double Clip Gauge Method are described, and the zones of greatest sensitivity for the location of the clip gauges are determined. A sensitivity analysis of the most influential intervening variables is also made.
FRACTURE MECHANICS ANALYSIS OF FATIGUE RESISTANCE OF SPOT WELDED COACH‐PEEL JOINTS
Authors: Wang Pei‐Chung , Ewing K. W.
Published: April 2007

Resistance spot welding is the most widely used joining method in automobile manufacture. The number, location, and quality of welds are some of the factors that influence the performance of welded subassemblies, and body panel structures. Therefore, design optimization requires knowledge of not only sheet metal behavior, but also weld behavior under service loadings. A linear elastic fracture mechanics approach was employed in this study to estimate the fatigue lives of spot welds subjected to tearing loads in a coach‐peel specimen. Using a finite element method (FEM), the initial J‐integral values for five coach‐peel joints, each with different geometries, were calculated. Fatigue tests conducted on the same weld geometries provided life data. The experimental data were used to derive a relationship between the initial elastic J‐integral values (ΔJe) and the fatigue life. It was found that the total fatigue life (Nf) of a weld at one applied stress range is related to its range of J‐integral value such that a ΔJe vs Nf log‐log plot gives a straight line relationship. This relationship can be used to evaluate the effects of geometrical variables on the fatigue life of coach‐peel joints. The results show that, within the dimension range studied here, the effects of geometrical variables on the fatigue resistance can be ranked in the following decreasing order: weld eccentricity, sheet thickness and weld nugget diameter.
ACCELERATION OF CRACK GROWTH UNDER INTERMITTENT OVERSTRESSING IN DIFFERENT ENVIRONMENTS
Authors: Koterazawa Ryoichi , Nosho Takayoshi
Published: April 2007

Fatigue crack growth behaviour under intermittent overstressing was investigated in moist air, dry air, nitrogen and vacuum with low carbon steels under tension‐compression loading with a few tests under compression‐tension loading. A very small number of cycles of overstress applied intermittently during a very large number of cycles of understress below threshold caused significant acceleration, of about one hundred times, in crack growth rate as compared to the case of steady cyclic stress in the cases of moist air, dry air and nitrogen. In the region of low understress, the acceleration in moist air was appreciably less than that in dry air and nitrogen due to oxide‐induced crack closure. The acceleration in vacuum was smaller than that in other environments over all understress levels, possibly because of rewelding. There was no effect of an overstress sequence on the acceleration.
A MODIFIED FRACTURE MECHANICS APPROACH TO METAL FATIGUE
Authors: DuQuesnay D. L. , Abdel‐Raouf H. , Topper T. H. , Plumtree A.
Published: April 2007

The fatigue lives, the fatigue limit stress ranges and fatigue notch factors for metallic specimens can be predicted using a modified fracture mechanics model for short cracks based on the combination of solutions for the non‐uniform strains at the surface of a metal and the development of crack closure. The resulting local stress intensity factor exceeds that indicated by linear elastic fracture mechanics at short crack lengths. The model predicts a smooth and continuous variation of the fatigue notch factor with notch size between a lower bound of unity and an upper bound equal to the theoretical notch stress concentration factor. The model is verified using experimental data for a 2024‐T351 aluminium alloy for smooth and notched specimens tested at various stress ratios.
CTOD FOR SLOW STABLE CRACK GROWTH CONDITIONS
Authors: Ipiña J. E. Perez
Published: April 2007

A procedure for CTOD calculation under slow stable crack growth conditions is presented in this work. This procedure gives more accurate CTOD values than those obtained using existing standards, and can be used in tests in which the slow stable crack growth is measured. An analysis of the errors made, when the traditional ([I], ASTM STP 668, pp. 307‐333) or the European Group of Fracture equations are used, is also made. A weighting factor on Δa is proposed for tests without crack growth measurement.
STRESS SINGULARITIES IN BI‐MATERIAL WEDGES WITH ADHESION AND DELAMINATION
Authors: van Vroonhoven J. C. W.
Published: April 2007

The order of the stress singularity at corners in bi‐materials is calculated by means of a local approximation of the stresses. This is performed for interfaces with adhesion and for interfaces which show delamination. It is demonstrated that the singular behaviour is less severe in the case of adhesion, i.e. when delamination is prevented. This result provides an explanation for the phenomenon that cracking at comers of bi‐material wedges only occurs in the presence of delamination. This conclusion is confirmed by experiments on micro‐electronic devices using scanning acoustic tomography, Fracture of the plastic encapsulation and failures of the electrical circuits are only observed in areas where the plastic has delaminated from the chip surface.
CRACK TIP BEHAVIOUR AND CRACK PROPAGATION IN DUCTILE MATERIALS
Authors: Li G. C. , Liu H. Q. , Du M. L. , Hong Y. S. , Zhang X.
Published: April 2007

Dilatational plastic equations, which can include the effects of ductile damage, are derived based on the equivalency in expressions for dissipated plastic work. Void damage developed internally at the large‐strain stage is represented by an effective continuum being strain‐softened and plastically dilated. Accumulation of this local damage leads to progressive failure in materials. With regard to this microstructural background, the constitutive parameters included for characterizing material behaviour have the sense of internal variables. They are not able to be determined explicitly by macroscopic testing but rather through computer simulation of experimental curves and data. Application of this constitutive model to mode‐I cracking examples demonstrates that a huge strain concentration accompanied by a substantial drop of stress does occur near the crack tip. Eventually, crack propagation is simulated by using finite elements in computations. Two numerical examples show good accordance with experimental data. The whole procedure of study serves as a justification of the constitutive formulation proposed in the text.
CONVERSION OF SHORT FATIGUE CRACKS INTO A LONG CRACK
Authors: Hyspecký P. , Strnadel B.
Published: April 2007

This paper presents a method for the statistical processing of results of initiation and propagation of short fatigue cracks. The distribution of the lengths of these cracks followed a Weibull distribution function. The value of the size parameter of this distribution grows with the number of cycles, but the value of the shape parameter declines as the number of cycles increases. A study of the modal value of fatigue crack lengths as a function of the number of cycles yielded a statistical criterion defining the conversion of the short fatigue crack initiation and propagation stage into the long fatigue crack propagation stage. One condition for this conversion is a zero magnitude of the first derivative of the modal value of fatigue crack lengths by the number of cycles. When the dependence of the Weibull distribution shape parameter and size parameter upon the number of cycles was inserted in this condition, solution of the resultant expression revealed the critical number of cycles that is necessary for the formation of a long fatigue crack.