Showing papers on "Paris' law published in 1979"
TL;DR: In this article, the average growth rate for very short cracks considerably exceed those given by conventional stress intensity-crack growth laws fitted to long crack data, by introducing an effective crack length U into the solutions for intensity factors and the J integral method of analysis, and therefore the value of k can be obtained once the threshold stress intensity factor and the fatigue limit are known.
Abstract: Previous studies have shown that both threshold stress intensity factors and fatigue crack growth rates are dependent on crack size The average growth rates for very short cracks considerably exceed those given by conventional stress intensity-crack growth laws fitted to long crack data Elastic and elastic plastic fracture mechanics solutions are modified to predict this behavior of short cracks by introducing an effective crack length U into the solutions for intensity factors and the J integral method of analysis The threshold stress at a very short crack length approaches the fatigue limit of the material, and therefore the value of k can be obtained once the threshold stress intensity factor and the fatigue limit are known The accuracy of the term k in predicting crack growth rates for short cracks is found to be independent of the applied strain level It varies linearly with the grain size of material and can be considered at surface as a measure of the reduced flow resistance of surface grains due to their lack of constraint
573 citations
TL;DR: In this paper, the authors studied the mechanical fatigue of NiTi shape memory alloys and found that the fatigue limit is lower than predicted from the phenomenological law relating growth rates to the elastic modulus.
304 citations
TL;DR: In this article, the influence of microstructure on fatigue crack growth in an AISI 1018 steel has been investigated and two distinctly different duplex microstructures were investigated.
Abstract: A study of the influence of microstructure on fatigue crack growth in an AISI 1018 steel has been carried out. Two distinctly different duplex microstructures were investigated. In one microstructure ferrite encapsulated islands of martensite; in the other martensite encapsulated islands of ferrite. The latter structure resulted in a significant increase in threshold level (18 MPa√mvs 8 MPa√m) together with an increase in yield strength. Fractographic analysis was used to investigate the influence of microstructure on the mode of fatigue crack growth.
130 citations
TL;DR: In this paper, the authors analyzed the FD growth behavior of five beta-annealed alloys and found significant effects of microstructure upon the logarithmic plot of fatigue crack growth rate (da/dN) vs stress-intensity range (ΔK).
127 citations
TL;DR: In this paper, Fatigue crack growth and threshold behavior have been examined in three commercial aluminium alloys in both air and vacuum environments, and it was observed that, in air, the threshold stress intensity range ΔKt, varied linearly with the ΔKT ratio.
Abstract: — Fatigue crack growth and threshold behaviour have been examined in three commercial aluminium alloys in both air and vacuum environments. It was observed that, in air, the threshold stress intensity range ΔKt, varied linearly with the ΔKt ratio. In contrast ΔK, in vacuum was found to be independent of R. Over the whole growth rate range examined fatigue crack growth in vacuum was ΔK controlled and failure occurred by a dimple and ductile striation mechanism. This also applied to failure in the intermediate growth rate ranges in air. However, at slow growth rates in air, fatigue crack growth was structure sensitive and crystallographic facets were formed during the crack propagation process.
110 citations
TL;DR: In this paper, the authors present an observation of fatigue crack growth in smooth specimens under biaxial loading, with particular reference to the Stage I to Stage II and Stage II to Stage I transitions.
Abstract: — Observations of fatigue crack growth in smooth specimens under biaxial loading are reviewed, with particular reference to the Stage I to Stage II and Stage II to Stage I transitions. Further results are presented for 1% Cr-Mo-V steel and AISI 316 stainless steel at various temperatures, showing that all cracks may be classed as either Stage I or Stage II. Predictive criteria are suggested for the type of crack obtained, and the mechanisms for elevated temperature crack initiation are discussed.
89 citations
01 Jan 1979
89 citations
Abstract: — This work was conducted to study the significant increases in fatigue crack growth rates at low frequencies commonly observed at high temperature. Creep tests and fatigue tests at 0·01, 0·1 and 1·0 Hz were conducted at 650°C in air and in helium on samples of INCONEL alloy 718 in two different heat treatments. Creep crack growth rates were 50–100 times greater in air than in helium. Fatigue tests in helium showed little sensitivity to frequency, but tests in air showed considerable increases in crack growth rates at lower frequencies. The results indicate the air environment played a predominant role in both the creep and the fatigue tests. Oxygen diffusion into grain boundaries appeared responsible for the accelerated crack growth in air. An overaging heat treatment reduced the crack growth rates.
79 citations
TL;DR: In this article, Fatigue crack growth rate measurements were made on Inconel alloy 718 samples at 650°C in fourteen different gaseous environments and showed that minor amounts of either oxygen or sulfur bearing species in the environment produced large increases in crack growth rates.
Abstract: Fatigue crack growth rate measurements were made on Inconel alloy 718 samples at 650°C in fourteen different gaseous environments. Minor amounts of either oxygen or sulfur bearing species in the environment produced large increases in crack growth rates. Aggressive environments promoted intergranular crack growth. Kinetic factors rather than thermodynamic ones appear to be the variables dominating the effects of an environment on crack growth. Environments that markedly increased the crack growth rate did not produce significant corrosion attack on unstressed samples. Thus conventional high temperature corrosion tests may not be useful for predicting service performance of stressed components.
79 citations
TL;DR: In this paper, the effects of stress ratio on fatigue crack growth thresholds and low and intermediate fatigue crack rates were examined on steels with ferrite-pearlite and tempered martensite microstructures, tested in air.
77 citations
TL;DR: In this article, a fracture mechanics model is developed to describe crack growth in a low cycle fatigue test specimen, which involves a J integral analysis and a growth rate hypothesis in terms of ΔJ.
Abstract: A fracture mechanics model is developed to describe crack growth in a low cycle fatigue test specimen. The model involves a J integral analysis and a growth rate hypothesis in terms of ΔJ. A relationship for low cycle fatigue is derived that has strain energy density as the controlling variable. This relationship reduces to well-known low cycle fatigue equations in terms of elastic and plastic strains for the limiting conditions of fully elastic and fully plastic strain fields. These equations in turn define relationships between the material properties commonly employed to describe low cycle fatigue and fatigue crack growth rate data. The latter are used to demonstrate the facility of predicting fatigue crack growth rate curves from standard low cycle fatigue properties.
TL;DR: In this paper, a stress intensity factor solution for the case of a surface crack in a finite width plate was determined for tension or bending and included a finite area correction factor, which was shown to correlate fatigue crack growth data measured on surface cracked plate specimens with conventional through crack data.
TL;DR: In this article, the morphology of fatigue fracture facets which contain more than one α platelet colony in Ti-11 and IMI-685 titanium alloys was investigated, and it was found that most α/β traces on the basal fracture facets, intersect at angles approximately 50, 60 and 70 deg.
Abstract: To better understand the correlation between fatigue failure and prior β-grain size, in β-annealed microstructures, the morphology of fatigue fracture facets which contain more than one α platelet colony in Ti-11 and IMI-685 titanium alloys was investigated. It was found that most α/β traces on the basal fracture facets, intersect at angles approximately 50, 60 and 70 deg. These angles can be predicted by the Burgers relation that allows α platelet colonies to have a common basal plane within the same prior β-grain. This commonality promotes shear related faceted fracture through more than one colony and increases the effective colony size. The increased effective colony size can cause more fatigue crack branching and, therefore, reduces fatigue crack growth rates in β-annealed microstructures.
TL;DR: In this paper, the authors define the threshold in terms of the fatigue limit of cracked specimens, defined as the critical value of AKIIIt, the range of the shear mode stress intensity factor necessary to cause growth with leads to failure, even though crack growth is not in the plane of the initial crack.
Abstract: Fatigue cracks grow perpendicular to the maximum principal applied tensile stress, or put more precisely into fracture mechanics terms, in mode I. Like most generalizations this one has its exceptions, but it does mean [I] that fatigue crack growth data can conveniently be analyzed in terms of the range of mode I stress intensity factor, AK I. A threshold value of AKI, AKIt must be exceeded before a crack will propagate. Various techniques can be used to determine AKIt ; a simple approach is to define the threshold in terms of the fatigue limit of cracked specimens. Conventional specimens used to determine fatigue crack growth behaviour have the initial crack oriented perpendicular to the applied stress. In practice components fail by fatigue from crack-like flaws that are not necessarily at right angles to the maximum principal stress, and crack growth will be in general not be in the plane of the initial crack. Definition of threshold behaviour in terms of the fatigue limit of cracked specimens extends naturally to such combined mode situations; for example, AKIIIt may be defined as the critical value of AKIIIt , the range of the shear mode stress intensity factor necessary to cause growth with leads to failure, even though crack growth is not in the plane of the initial crack. It has recently been found [2] that the fatigue crack growth thresold behaviour of mild steel for pure mode II and combined mode I and II loadings depends on two separate factors: firstly, whether or not a mode I branch crack forms at or near the precrack tip under the loading being applied, and secondly, whether the loading is sufficient to cause continued crack growth from the branch. If such a branch forms easily, or is already present, threshold behaviour is controlled by AK I for the branch crack. If for some reason branch crack formation is suppressed, higher apparent threshold values are obtained. It follows that, for the understanding of mode Ill threshold behaviour, the stress intensity factor for a mode I branch at a mode III crack is required. Two dimensional cases involving small branch cracks have been extensively discussed, for example, [3]. The problem of a mode I branch at a mode III crack is more difficult because of its three dimensional nature. Approximate solutions to branched crack problems in the two dimensional case can be obtained [3] by solving the problem of an application of the prior traction on the branch, but merely ensuring that the "extended branch" (Fig. I) is traction free. Application of this method to a mode III branch at a mode III crack gives KIII (branch) = KIII [main), and is independent of the branch angle @. For an element of a mode I branch (Fig. 2), K I [branch) = KIII (main), but geometrical incompatabilities prevent assembly of these elements into a crack. Consideration of various possible configurations suggests [4] K I (branch) =
TL;DR: In this paper, the authors measured the crack growth rate and crack closure during fatigue of type 304 stainless steel with an optical microscope and television camera, and calculated the effective stress intensity range ΔK eff.
TL;DR: In this paper, the cumulative failure probability of an inhomogeneously stressed structure may be estimated when the material contains N different types of defect, each having its own fracture criterion.
Abstract: It is shown how the cumulative failure probability of an inhomogeneously stressed structure may be estimated when the material contains N different types of defect, each having its own fracture criterion. The theory is applied to:
It is also shown how to account for defects which grow in size because of fatigue and/or creep mechanisms. As an example the fatigue crack growth of defects, in a material having an inhomogeneous distribution of fracture toughness, is discussed. A method of accounting for defect nucleation during service is described.
TL;DR: In this article, a structural sheet steel crack growth under biaxial tensile load conditions is reported for real-time testing required for threshold investigations; specimens are of the cruciform type.
Abstract: Fatigue crack growth under biaxial tensile load conditions is reported for a structural sheet steel. The new test facility can operate at high frequency (0–40 Hz) thereby permitting real-time testing required for threshold investigations; specimens are of the cruciform type.
It is found that crack growth rate is affected by a cyclic tensile load applied in the direction of growth which decreases as the said load increases. The rate however increases if the biaxial loads are increasingly out of phase.
Within the test conditions reported LEFM can be applied to crack growth under biaxial load conditions. The threshold stress intensity range is shown to be a function of load biaxiality, phase difference and stress ratio.
TL;DR: In this paper, fatigue crack growth experiments have been carried out on a 2 1/4Cr-1Mo (ASTM A542, Class 2) steel in hydrogen, water vapor, and hydrogen sulfide at low pressures (below 133 kPa).
Abstract: Steels used in coal gasification vessels and piping (externals) can be exposed to mixtures of hydrogen, water vapor (steam), hydrogen sulfide, methane, carbon monoxide, carbon dioxide, and other gases at temperatures and pressures up to 600/sup 0/K and 10 MPa. Such mixtures, under certain operating conditions, can either enhance or inhibit crack growth in these steels. As a part of a program to identify thermodynamic conditions for this enhancement or inhibition, fatigue crack growth experiments have been carried out on a 2 1/4Cr-1Mo (ASTM A542, Class 2) steel in hydrogen, water vapor, and hydrogen sulfide at low pressures (below 133 kPa). The results indicate considerable enhancement of fatigue crack growth by some of these environments and also indicate that the apparent immunity of this material to stress corrosion cracking does not imply the same immunity to corrosion fatigue. The results will be discussed in terms of the influences of temperature, gas pressure and loading variables, and will be interpreted in terms of chemical reaction kinetics.
01 Jan 1979
TL;DR: In this paper, the Paris law parameters of polystyrene in air at different mean stress conditions and also over the temperature range−60 to 60°C using notched specimens were analyzed using a two-stage line plastic zone model.
Abstract: Fatigue tests have been conducted on polystyrene in air at different mean stress conditions and also over the temperature range−60 to 60°C using notched specimens. In addition, some tests were performed with the specimens immersed in a detergent and in a corn oil. The data were first represented on a conventional log ΔK-log da/dN plot to determine the Paris law parameters and how these varied with mean stress, temperature and environment. Considerable variations were noted but no useful pattern could be discerned. The data were then analysed using a recently proposed two-stage line plastic zone model so that a crack tip zone stress and a fatigue damage factor could be found. These stresses were found to be very high in air and to increase with increasing mean stress, and this is attributed to a high degree of constraint at the crack tip. There was an abrupt change in σc at about 20° C which, it is suggested, is caused by the onset of crazing due to the presence of a loss peak. Associated changes in Kc were also noted. In environments, the stresses were much smaller and agreed with those obtained in static fracture, suggesting that crazes are formed in environments prior to, and not during, fatigue crack growth. The stress reduction factor, α, remained constant at about 0.2 with both temperature and environment.
TL;DR: In this article, a self consistent procedure has been developed for the determination of the J- integral parameter under load-controlled fatigue and is shown to be compatible with data based on the stress intensity factor.
TL;DR: In this article, a simple algorithm of hysteresis loop counting is presented to make on-line data processing much easier, which involves a modification of the range pair counting method and the rain flow method and yields practically the same result as these methods.
Abstract: This paper presents a simple algorithm of hysteresis loop counting to make on-line data processing much easier. It involves a modification of the range pair counting method and the rain flow method and yields practically the same result as these methods. In addition, the applicability of the present method to cumulative damage estimation is examined in experiments on fatigue crack growth rates under stationary random loads and low cycle fatigue lives under stationary random loads together with non-stationary random loads such as seismically excited loads.
TL;DR: In this article, the influence of stress ratio and the loading frequency on fatigue crack growth rates in BS 4360-50C steel was investigated in laboratory air, and it was suggested that this frequency influence may be associated with environmental effects, due to the embrittlement caused by hydrogen from the moist air.
Abstract: The influence of stress ratio and the loading frequency on fatigue crack growth rates in BS 4360–50C steel was investigated in laboratory air.
Fatigue crack growth tests were performed on compact tension specimens (CTS) made in two thicknesses 12 and 24 mm. Tests were conducted at two frequencies of 0·25 and 30 Hz, applying a stress ratio R varying from – 0·7 to 0·7. The results were analysed using the linear elastic fracture mechanics approach. They showed that the increase in both positive and negative R caused increased fatigue crack growth rates. Also an empirical effective stress intensity factor range, ΔKeff, was found more appropriate to correlate the fatigue crack growth data than the ΔK factor frequently used in crack growth studies.
The loading frequency had only a little influence on crack growth rates at low R. However, at high R, growth rates were significantly higher at lower frequencies. It is suggested that this frequency influence may be associated with environmental effects, due to the embrittlement caused by hydrogen from the moist air, while the crack was fully open.
TL;DR: In this paper, the fastest crack growth was observed for artificial cracks, which appear to be a worst case as compared to natural cracks, and the K-values derived from crack growth results were in good agreement with K-value proposed in the literature, whereas considerable scatter applied to the natural cracks as a result of multiple crack initiation at different times and locations.
Abstract: Crack growth in aluminium alloy lugs was recorded during constant-amplitude loading (R = 1/3). Observations were made both for artificial cracks started by a small saw cut and natural cracks started by fretting corrosion between hole and pin. Scatter was low for artificial cracks, whereas considerable scatter applied to the natural cracks as a result of multiple crack initiation at different times and locations. The fastest crack growth was observed for artificial cracks, which appear to be a worst case as compared to natural cracks. K-values derived from crack growth results were in good agreement with K-values proposed in the literature.
TL;DR: In this paper, a comparison of the corrosion fatigue behavior of a low-alloy rotor steel in aqueous and hydrogen environments was made, and it was shown that the magnitude of the environmental cracking component and the morphology of cracking is the same in the two environments, indicating that a hydrogen embrittlement mechanism also operates in water.
Abstract: A comparison has been made of the corrosion fatigue behaviour of a low-alloy rotor steel in aqueous and hydrogen environments. Cracks were grown under conditions of constant alternating stress intensity and stress ratio, and fatigue crack growth rates were determined as a function of temperature, cyclic frequency, and waveform. These were found to be up to seven and fourteen times faster in water and hydrogen than in air. It is shown that the magnitude of the environmental cracking component and the morphology of cracking is the same in the two environments, indicating that a hydrogen embrittlement mechanism also operates in water.
TL;DR: In this article, fatigue tests of crack growth rates and transmission electron microscopy in the immediate vicinity of crack tips were performed on specimens of copper and 70/30 brass, and an interpretation was put on the effect of stacking fault energy on fatigue crack growth.
Abstract: Fatigue tests of crack growth rates and transmission electron microscopy in the immediate vicinity of crack tips were performed on specimens of copper and 70/30 brass. In brass, very dense dislocations accumulated on the primary and the conjugate slip planes were observed just ahead of the crack tips, and they appeared to be not easy to move because of the difficulty of cross slip. In copper, well-defined cells were observed around the crack tips and there were frequently found cracks propagating along or across cell boundaries. On the basis of these observation results, an interpretation is put on the effect of stacking fault energy on fatigue crack growth.
TL;DR: In this article, a wide variety of materials from four basic α + β titanium alloy systems were cyclically loaded with a haversine waveform and a load ratio, R = 0.10, and the results indicated that at a constant value of stress-intensity range (ΔK), the width of the da/dN data band exceeds an order of magnitude.
Abstract: Fatigue crack growth rates (da/dN) in ambient laboratory air have been determined for a wide variety of materials from four basic α + β titanium alloy systems. Each material was cyclically loaded with a haversine waveform and a load ratio, R = 0.10. The results indicate that, at a constant value of stress-intensity range (ΔK), the width of the da/dN data band exceeds an order of magnitude. For example, at ΔK = 21 MPa·m1/2 , a 50-fold difference in fatigue crack propagation rates is observed. Analysis of the crack growth rate data at this point indicates a systematic dependence on grain size (l ), viz. that da/dN decreases with increasing l . An interpretation of this effect is offered in terms of reversed (cyclic) plastic zone size considerations.
TL;DR: In this paper, the effects of the stress biaxiality factor (B) on the growth rate of PMMA and rigid PVC are investigated on a fracture mechanics basis, and it is shown that the regime of true fatigue crack growth in PMMA is limited at its upper end by a sharp transition to a slow-growth dominated crack extension mode.