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Showing papers on "Paris' law published in 1977"


Journal ArticleDOI
TL;DR: In this article, the influence of mean stress and microstructure on fatigue crack growth near the threshold stress intensity for crack propagation, was investigated in humid air over a very wide spectrum of growth rates from 10/sup -8/ to 10/Sup -1/ mm/cycle.
Abstract: Fatigue crack propagation behavior of an ultra-high strength steel (300-M) has been investigated in humid air over a very wide spectrum of growth rates from 10/sup -8/ to 10/sup -1/ mm/cycle. Particular emphasis has been devoted to the influence of mean stress (or load ratio R = K/sub min//K/sub max/) and microstructure on fatigue crack growth near the threshold stress intensity for crack propagation, ..delta..K/sub 0/. Increasing the load ratio from R = 0.05 to 0.70 was found to lead to increased near-threshold growth rates, and a decrease in the threshold stress intensity. Similarly, increasing material strength, by varying the microstructure through quench and tempering and isothermal transformation, resulted in higher near-threshold growth rates, and a marked reduction of ..delta..K/sub 0/. These effects are contrasted with behavior at higher growth rates. The infuence of strength on ..delta..K/sub 0/ is rationalized in terms of the cyclic hardening or softening response of the material, and hence it is shown that cyclic softening can be beneficial to fatigue crack propagation resistance at very low growth rates. The results are discussed in the light of crack closure and environmental contributions to fatigue crack growth at low stress intensities.

140 citations


Journal ArticleDOI
TL;DR: In this article, it appears from replica and scanning electron microscopic examination that the facets are comprised of three superposed features, viz cleavage-like river-line patterns, very fine striations and traces of slip lines (and slip-band cracks).
Abstract: Fatigue crack growth rates in commercial purity Ti-6A1-4V can be substantially reduced with a beta anneal from levels associated with the mill anneal, owing primarily to crystallographic crack bifurcation in the Widmanstatten packets. This microstructurally sensitive fatigue crack growth occurs when the reversed plastic zone is less than the packet size and results in a fracture surface with a faceted morphology. It appears from replica and scanning electron microscopic examination that the facets are comprised of three superposed features,viz cleavage-like river-line patterns, very fine striations and traces of slip lines (and slip-band cracks). Limited X-ray evidence suggests a facet orientation some 8 to 10 degrees off the basal plane.

122 citations


Journal ArticleDOI
TL;DR: In this article, a simple model for the demarcation of the initiation and stage I fatigue crack growth phases is introduced, and experimental cumulative damage data are used to determine the phase boundary between these two regimes, and an exponential accumulation of damage theory is invoked for each; here, damage is equated to crack length.
Abstract: A simple model for the demarcation of the initiation and stage I fatigue crack growth phases is introduced. Experimental cumulative damage data are used to determine the phase boundary between these two regimes, and an exponential accumulation of damage theory is invoked for each; here, damage is equated to crack length. Using both the model and the data, predictions are made of lifetime in double, treble and multilevel strain range tests. The theory successfully accounts for the load sequence effect, which is a consequence of the initiation period, and the effect of the difference between successive strain range levels. It is suggested that the Palmgren-Miner expression be replaced by individual expressions for the accumulation of damage in the separate phases of initiation and stages I and II fatigue crack propagation.

122 citations


Journal ArticleDOI
TL;DR: In this paper, the fatigue-crack growth (fcg) behavior of metals and alloys at low stress intensities is considered in terms of load ratio, microstructure, and environment.
Abstract: The fatigue-crack growth (fcg) behaviour of metals and alloys at low stress intensities is considered in terms of load ratio, microstructure, and environment. The behaviour of aluminium and titanium alloys and steels is examined and their mode of fcg reported. The occurrence of microstructurally sensitive fcg is considered and the conditions leading to its occurrence examined. The identity of trans granular facets formed in this region of fcg are tabulated and some of the models proposed for this phenomenon are presented. The importance of K max as a controlling influence on the growth of fatigue cracks even at low stress intensities is conveyed by the results presented.

109 citations


Journal ArticleDOI
TL;DR: In this article, the fracture surface characteristics of five commercially available amorphous polymers [poly(methylmethacrylate) (PMMA), polycarbonate (PC), polyvinyl chloride (PVC), polystyrene (PS), and polysulphone (PSF) were studied to determine if common mechanisms of fatigue crack propagation prevail among these glassy polymers.
Abstract: Fatigue fracture surface characteristics of five commercially available amorphous polymers [poly(methylmethacrylate) (PMMA), polycarbonate (PC), poly(vinyl chloride) (PVC), polystyrene (PS), and polysulphone (PSF)] as well as bulk-polymerized PMMA prepared over a wide range of molecular weights were studied to determine if common mechanisms of fatigue crack propagation prevail among these glassy polymers. In those polymers with viscosity-average molecular weight ¯Mv≲2×105, the macroscopic appearance of the fracture surface showed the presence of a highly reflective mirror-like region which formed at low values of stress intensity and high cyclic test frequencies (∼100 Hz). The microscopic appearance of this region revealed that many parallel bands exist oriented perpendicular to the direction of crack growth and that the bands increase in size with ΔK. In all instances, the crack front advanced discontinuously in increments equal to the band width after remaining stationary for hundreds of fatigue cycles. Electron fractographic studies verified the discontinuous nature of crack extension through a craze which developed continuously with the load fluctuations. By equating the band size to the Dugdale plastic zone dimension ahead of the crack, a relatively constant yield strength was inferred which agreed well with reported craze stress values for each material. At higher stress intensity levels in all polymers and all values of ¯Mv, another series of parallel bands were observed. These were also oriented perpendicular to the direction of crack growth and likewise increased in size with the range in stress intensity factor, ΔK. Each band corresponded to the incremental advance of the crack during one load cycle, indicating these markings to be classical fatigue striations.

96 citations



Journal ArticleDOI
TL;DR: In this article, an analysis of fatigue crack closure under variable amplitude loading was made by using the finite element technique, and the predicted fatigue crack growth behavior which was obtained analytically was consistent with the experimental results.

80 citations


Journal ArticleDOI
TL;DR: In this paper, emissions from fatigue crack growth have been examined for three steels (A533B steel, low carbon steel and H1 weld metal) using ACEMAN, a system for acoustic emission source location and analysis.

76 citations


Journal ArticleDOI
TL;DR: In this paper, a range of continuum-based crack growth laws are reviewed and it is concluded that they may be divided into those based on instantaneous values of cyclic crack-opening displacement which have a ∆K exponent of 2 and others based on damage or strain accumulation which have an exponent of 4 and predict the onset of rapid crack acceleration as K→ Ic.
Abstract: A range of continuum-based crack growth laws are reviewed and it is concluded that they may be divided into those based on instantaneous values of cyclic crack-opening displacement which have a ∆K exponent of 2 and those based on damage or strain accumulation which have a ∆K exponent of 4 and, in addition, predict the onset of rapid crack acceleration as K→ Ic. No laws showing how to introduce the effects of aggressive environments were found. A third type of law, based on energy-balance concepts within a crack tip process zone, can predict a gradient lying between 2 and 4 depending on the size of the reversed plastic zone. Comparison between theory and experiment suggests that the (∆K)4 type laws provide better agreement for data gathered in inert environments. It is thought that, when growth laws are being assessed by comparison with experimental observations, data gathered in inert environments should be used. In addition it is noted that when experimentally and theoretically determined exponen...

64 citations


Journal ArticleDOI
TL;DR: In this article, a model of fatigue crack growth is proposed based on a line plastic zone analysis, which is assumed that the effect of cycling is to reduce the craze stress to some proportion of the original value depending on the degree of unloading.
Abstract: A model of fatigue crack growth is proposed based on a line plastic zone analysis. It is assumed that the effect of cycling is to reduce the craze stress to some proportion of the original value depending on the degree of unloading. Successive loadings result in growth of the craze with a corresponding increase in crack opening displacement. At some critical value of this displacement, crack growth occurs and the rate of growth is related to the applied stress intensity factor and the critical static value. The results of the model are applied to data on several polymers and a good description of growth rate, mean stress and frequency effects is given. Finally, some fatigue lives are predicted.

62 citations


Journal ArticleDOI
TL;DR: In this article, it has been shown that the threshold stress intensity depends more on the elastic modulus rather than on any other material property in agreement with many experimental results, and that the stress intensity can be related to the stress necessary to nucleate a dislocation at the crack tip.
Abstract: It has been shown that the ratio of threshold stress intensity for fatigue crack growth to the shear modulus is nearly a constant for many materials This implies that fatigue crack growth is related to some fundamental phenomenon occurring at the crack tip In the following a dislocation model has been developed to predict the threshold stress intensity It is shown that the stress intensity can be related to the stress necessary to nucleate a dislocation at the crack tip The most important outcome of the present analysis is that the threshold stress intensity depends more on the elastic modulus rather than on any other material property in agreement with many experimental results


Journal ArticleDOI
TL;DR: In this article, the Paris equation for fatigue crack growth is explained in relation to the crack closure concept suggested by Elber, and it is concluded that the exponent parameter m reflects mainly the dependency of crack closure behavior on ΔK.
Abstract: The two parameters, C and m, which characterize the Paris equation for fatigue crack growth are explained in relation to the crack closure concept suggested by Elber. It is proposed that the range of effective incremental change in stress intensity factor (ΔK) needed for crack growth should have a second power correlation with the growth rate. The crack growth is essentially determined by cumulative damage to the material in cycled plastic zone near the crack tip, and is relatively insensitive to the applied ΔK-values and the mechanical properties of material. However, the crack closure behavior is expected to depend on both the stress range and the material properties. Thus it is concluded that the exponent parameter m reflects mainly the dependency of crack closure behavior on ΔK. For example, in the case of m=4 the crack opening level increases linearly with increase in ΔK, while in the case of m=2 it remains constant. It is suggested that the cyclic straining at the crack tip possibly varies with ΔK, thus changing primarily the crack closure behavior rather than the damage accumulation process in the plastic zone.

Journal ArticleDOI
TL;DR: In this article, the effects of specimen thickness, stress ratio and maximum stress intensity factor (K max ) on crack closure or opening were studied using a 2219-T851 aluminum alloy.

Journal ArticleDOI
TL;DR: In this paper, a study of fracture and low growth rate (near-threshold) fatigue crack propagation in 300-M high strength steel, tested in humid air, is presented.
Abstract: Interactions between hydrogen embrittlement and temper embrittlement have been examined in a study of fracture and low growth rate (near-threshold) fatigue crack propagation in 300-M high strength steel, tested in humid air. The steel was investigated in an unembrittled condition (oil quenched after tempering at 650°C) and temper embrittled condition (step-cooled after tempering at 650°C). Step-cooling resulted in a severe loss of toughness (approximately 50 pct reduction), without loss in strength, concurrent with a change in fracture mode from micr ovoid coalescence to inter granular. Using Auger spectroscopy analysis, the embrittlement was attributed to the cosegregation of alloying elements (Ni and Mn) and impurity elements (P and Si) to prior austenite grain boundaries. Prior temper embrittlement gave rise to a substantial reduction in resistance to fatigue crack propagation, particularly at lower stress intensities approaching the threshold for crack growth(x0394;Ko). At intermediate growth rates (10-5 to 10-3 mmJcycle), propagation rates in both unembrittled and embrittled material were largely similar, and only weakly dependent on the load ratio, consistent with the striation mechanism of growth observed. At near-threshold growth rates (<10−5 to 10−6 mmJcycle), embrittled material exhibited significantly higher growth rates, 30 pct reduction in threshold ΔKo values and intergranular facets on fatigue fracture surfaces. Near-threshold propagation rates (and ΔKo values) were also found to be strongly dependent on the load ratio. The results are discussed in terms of the combined influence of segregated impurity atoms (temper embrittlement) and hydrogen atoms, evolved from crack tip surface reactions with water vapor in the moist air environment (hydrogen embrittlement). The significance of crack closure concepts on this model is briefly described. ntmis]formerly with the Lawrence Berkeley Laboratory, University of California in Berkeley.

Journal ArticleDOI
TL;DR: The main girder of the Lafayette Street Bridge over the Mississippi River in St. Paul was discovered to be cracked on May 7, 1975 and detailed examination of the fracture was given in this article.
Abstract: A main girder of the Lafayette Street Bridge over the Mississippi River in St. Paul was discovered to be cracked on May 7, 1975. A detailed examination of the fracture is given in this paper. Fractographic examinations and analyses of crack growth showed that failure crack growth and brittle fracture both contributed to the members' failure. Fatigue cracks were found to originate at large lack of fusion areas in the lateral bracing gusset to transverse stiffener weld. After the crack had nearly penetrated the web thickness, it precipitated a brittle fracture. Subsequent intervals of fatigue crack growth and fracture were also observed. Recommendations are also provided on ways to retrofit the bridge details to prevent reoccurrence at other comparable details. In addition, a suggested detail configuration for this type of connection is recommended for future use. /Author/

Journal ArticleDOI
TL;DR: In this article, the effect of grain size on fatigue crack propagation was examined in a high strength steel (Fe-Cr-C) where grain size can be varied considerably without significant change in monotonic and cyclic strength.

Journal ArticleDOI
R.B. Scarlin1
TL;DR: In this paper, the creep and fatigue crack growth rates have been determined in a wrought nickel-base alloy (Nimonic 105) and a cast nickel base alloy (IN 738 LC) both before and after long term ageing.

Journal ArticleDOI
TL;DR: Linear elastic crack-tip solutions for twelve different shapes of cracked body of interest, are given in this article, which assist the user of fracture mechanics in that they carry out the interpolative step accurately and therefore may be usefully incorporated in other crack computational procedures.
Abstract: Linear elastic crack-tip solutions for twelve different shapes of cracked body of interest, are given. The purpose is to provide efficient “closed” formulations of data previously presented in a tabular or graphical manner. The formulae assist the user of fracture mechanics in that they carry out the interpolative step accurately and therefore may be usefully incorporated in other crack computational procedures, such as fatigue crack growth prediction, crack-tip plasticity corrections, etc. The method used to generate the formulae can be applied to other cracked body geometries.

Journal ArticleDOI
TL;DR: In this paper, the most beneficial heat treatment for improving these crack tolerance properties was found to be the beta anneal, which resulted in yield strength reductions of 9 to 14 percent, from levels associated with the original mill-anneal.
Abstract: Significant enhancement in fatigue crack propagation resistance and plane strain fracture toughness was obtained in commercial purity Ti-6Al-4V and Ti-6Al-6V-2Sn through microstructural modification. Alloys studied were in the form of 25.4 mm-thick plate with interstitial oxygen contents of 0.20 and 0.17 weight percent, respectively. Heat treatments were chosen to provide widely varied microstructures; these included a mill anneal, recrystallization anneal and a beta anneal. The most beneficial heat treatment for improving these crack tolerance properties was found to be the beta anneal. However, the beta anneal resulted in yield strength reductions of 9 to 14 percent, from levels associated with the original mill anneal. The recrystallization anneal provided significant enhancement of plane strain fracture toughness and marginal improvement in fatigue crack propagation resistance with negligible loss of yield strength.

Journal ArticleDOI
TL;DR: In this paper, the effect of single overloads on room temperature fatigue crack growth has been studied in two steels (FV 520B and Ducol W30B) of markedly different yield stresses.
Abstract: The effect of single overloads on room temperature fatigue crack growth has been studied in two steels (FV 520B and Ducol W30B) of markedly different yield stresses. For a given overload, the amount of retardation was greater for lower baseline alternating stress intensity. In Ducol, retardation increased with decreasing specimen thickness. The results suggest that overload retardation is primarily due to residual compressive stresses generated in the crack -tip region, and is associated with crack-closure effects. An attempt has been made to rationalize the results in terms of a fatigue crack growing through overload plastic zones of different shapes and sizes associated with plane-stress and plane-strain deformation.

Journal ArticleDOI
TL;DR: In this paper, the growth rates of three solid solution strengthened superalloys were measured at 25°C and from 538 to 871°C over a range of frequencies varying from 0.01 to 10.0 Hz.
Abstract: The fatigue crack growth rates of three solid solution strengthened superalloys were measured at 25°C and from 538 to 871°C over a range of frequencies varying from 0.01 to 10.0 Hz. The three alloys were respectively nickel base, cobalt base and iron base alloys with approximately the same chromium content. The plots of crack growth ratevs AK, the range of the stress intensity factor, show three different regimes. At low ΔAK the crack growth rates are frequency independent and the fracture is strongly crystallographic. In the medium range of ΔK the fatigue crack growth rates are frequency and waveform dependent, indicating a strong creep-oxidation time dependent fracture mechanism. At high ΔK, nearKc, the growth rates are again frequency independent and fracture proceeds by a void coalescence mechanism. The correlations between the fractographic features as seen in the SEM and the measured crack growth rates provide a good basis for the understanding of fatigue crack growth at elevated temperatures in the elastic-plastic range.

Journal ArticleDOI
TL;DR: In this paper, a technique for estimating fatigue crack propagation in notched plates subjected to variable amplitude loading is outlined, where an elastic-plastic finite element model is used to determine the effect of notch geometry and the residual plastic deformations.


Journal ArticleDOI
TL;DR: In this paper, a methodology for the quantitative prediction of crack-growth behavior of cracks emanating at cold-worked fastener holes under fatigue cyclic loading has been developed, which is based on an 4'effective stress field'1 concept that accounts for the amount of the compressive residual stress existing at the edge of the cold worked hole.
Abstract: A methodology for the quantitative prediction of crack-growth behavior of cracks emanating at cold-worked fastener holes under fatigue cyclic loading has been developed. The proposed prediction technique is based on an 4'effective stress field'1 concept that accounts for the amount of the compressive residual stress existing at the edge of the cold-worked hole. Stress-intensity factor ranges (A/0 and crack-growth rates (da/d/i) are all formulated in terms of the effective stress field. An existing fatigue-crack-growth analysis computer program has been modified to account for these changes. This program was subsequently used to study the fracturemechanics design development test data. Good correlations have been obtained.

Journal ArticleDOI
TL;DR: In this article, a new continuum mechanics model is developed for predicting fatigue crack propagation rates using a fracture mechanics approach, which demonstrates the critical dependence of fatigue crack growth on the fatigue ductility exponent, the fatigueductility coefficient, the elastic modulus and the fracture toughness; it is related to the stress intensity range.

Journal ArticleDOI
TL;DR: In this article, a crack-opening-displacement (COD) technique has been successfully employed to measure crack length in compact tension specimens for the determination of fatigue crack growth rate (FCGR).

Journal ArticleDOI
TL;DR: In this paper, the influence of tensile overloads on fatigue crack growth in polycarbonate polycarbonates has been investigated and it was shown that tensile loads may significantly retard subsequent fatigue crack expansion.
Abstract: Results are presented from a recent study of the influence of tensile overloads on fatigue crack growth in polycarbonate. Fatigue cracks were grown under conditions of constant range in stress intensity factor in four-point bend specimens. The data presented here indicate that tensile overloads may significantly retard subsequent fatigue crack growth in polycarbonate. The period of delay in crack growth was shown to increase with the magnitude of the overload. Recovery of stable crack extension following the overload appeared to involve reinitiation of separate crack growth sites at the tip of the blunted crack tip, similar to the original crack initiation at sharp V-notches.

Journal ArticleDOI
TL;DR: In this paper, the pre-and post-irradiation fatigue and flow properties of molybdenum-base alloy TZM have been determined at 427°C.

Journal ArticleDOI
TL;DR: In this paper, the effect of stress ratio (mean stress) on crack growth is illustrated through the use of plots analogous to constant-lifetime fatigue diagrams, and some of their limitations are noted.
Abstract: Empirical relations for describing constant-amplitude crack-growth behavior are reviewed. The effect of stress ratio (mean stress) on crack growth is illustrated through the use of plots analogous to constant-lifetime fatigue diagrams. Experimentally observed load-sequence effects, such as crack retardation due to tensile overloads, acceleration due to compressive overloads, the interaction between tensile and compressive overloads, etc. are summarized. The crack-closure phenomenon is reviewed, since it seems to provide a plausible physical explanation for many sequence effects. Methods of predicting crack growth under variable-amplitude loading (including irregular loadings representative of actual service) are reviewed and some of their limitations noted.