Mean Stress Intensity Factor Research Articles

Effects of Loading Spectra on High pH Crack Growth Behavior of X65 Pipeline Steel

The effects of mechanical factors on crack growth behavior during the second stage of high pH stress corrosion cracking in pipeline steel were investigated by applying several loading scenarios on compact tension (CT) specimens. The main mechanism for stage 2 of intergranular crack propagation is anodic dissolution ahead of the crack tip which is highly dependent on crack-tip strain rate. The maximum and minimum crack growth rates were 3 × 10−7 mm/s and 1 × 10−7 mm/s, respectively. It was observed that several factors such as mean stress intensity factor, amplitude, and frequency of loading cycles determine the crack-tip strain rate. Low R-ratio cycles, particularly high-frequency ones, enhance secondary crack initiation, and crack coalescence on the free surface. This mechanism accelerates crack advance on the free surface which is accompanied with an increase in mechanical driving force for crack propagation in the thickness direction. These findings have implications for pipeline operators and could be used to increase the lifespan of the cracked pipelines at stage 2. For those pipelines, any loading condition that increases the strain rate ahead of the crack tip enhances anodic dissolution and is detrimental. Additionally, secondary crack initiation and coalescence could be minimized by avoiding internal pressure fluctuation, particularly rapid large pressure fluctuations.

A threshold formula for fatigue crack growth with mean stress intensity factors

From the fatigue limit condition of crack front, a threshold formula has been derived with respect to mean stress intensity factors. Examinations with experimental results show that this formula can express threshold quantitatively and uniformly. It is found that threshold varies with mean stress intensity factor just as that fatigue limit varies with mean stress if the mean stress intensity factor is smaller than a critical value, while if the mean stress intensity factor is larger than the critical value, plastic deformation at crack front would affect threshold greatly. It has also been investigated that why there would be such a critical mean stress intensity factor behavior. The reason lies on that whether damage induced by plastic deformation at crack front could be neglected or not. A formula to estimate the critical mean stress intensity factor has also been derived.

Evaluation of three current methods for including the mean stress effect in fatigue crack growth rate prediction

AbstractThe fatigue crack growth rates curves of engineering materials depend on two parameters. In addition to the dependence on the classical stress intensity factor (SIF) range ΔK, there is a dependence on the mean load (or mean SIF), mainly in the near‐threshold region. The present paper provides some useful suggestions and good practices for using three of the current available methods to reduce this second dependence through the use of tuning constants. The methods considered here are the Elber, Walker and Vasudevan (or unified approach). For each approach, multiple regression analyses are performed on experimental data from the literature, and the correlations in two and three dimensions are graphically analyzed. Numerical examples of crack growth analysis for cracks growing under nominal stresses of constant amplitude in single‐edge and notch/hole geometries are performed, assuming an identical material component to that of the available experimental data. The resulting curves of crack size versus number of cycles (a versus N) are then compared. All three models gave approximately the same (a versus N) curves in both geometries. Differences between the behaviors of the (a versus N) curves in both geometries are highlighted, and the reasons for these particular behaviors are discussed.

FATIGUE CRACK GROWTH OF SILICON NITRIDE WITH CRACK WEDGING BY FINE FRAGMENTS

Abstract— Fatigue crack growth tests of silicon nitride Si3N4 were carried out under four‐point bending using square bar specimens at room temperature. A pre‐crack was introduced by a bridge indentation method. Decreasing K‐type tests at stress ratios of R= 0.1 and 0.6 and also under static load were first carried out, and after observing the cessation of crack growth, K‐increasing tests were performed except for the case of a static load. Crack closure was observed on most specimens by the elastic compliance method. Furthermore, SEM observations of the crack paths were made to see what was happening during crack growth. The threshold and the region of steady crack growth were observed more clearly under cyclic loading, and an effect of load cycling certainly existed which became more evident when the maximum stress intensity factor Kmax approached the threshold. A wedge effect, caused by fine fragments on the crack surface, played an important role in crack closure behaviour of each specimen, and it is suggested that the crack growth rate is controlled by both the effective stress intensity range ΔKeff and the effective mean stress intensity factor Km,eff at least as a first approximation.

窒化ケイ素の疲労亀裂成長とき裂開口に及ぼす破砕粉のくさび効果

Fatigue crack growth tests of silicon nitride Si3N4 were carried out under four point bending load using the square bar specimens of 12×16×40mm at room temperature. A pre-crack was introduced by the bridge indentation (BI) method. K-decreasing tests under cyclic load with the stress ratio R=0.1 and 0.6 and also under static load were first carried out, and after observing the cease of the crack growth, K-increasing tests were performd excepting the case under static load. Crack closure was detected on most specimens by the elastic compliance method, and furthermore, SEM observations of crack paths were made to see what had happned during the crack growth.The threshold and the region of steady crack growth were observed more clearly under cyclic load, and the effect of load cycling obviously existed, which became more evident when the maximum stress intensity factor Kmax approached the threshold. The wedge effect caused by fine fragments left on the crack surface played an important role to the crack closure behavior of each specimen and it was suggested that the crack growth rate was controlled by both of the effective stress intensity range ΔKeff and the effective mean stress intensity factor Km, eff' at least as a first approximation.

Fatigue crack propagation in unplasticized poly(vinyl chloride): 1. Effect of mean stress

Abstract The effect of mean stress on fatigue crack growth in an unplasticized poly(vinyl chloride) (uPVC) pipe material was investigated using single-edge-notched (SEN) specimens and the results analysed in terms of fracture mechanics. Three series of experiments were conducted. In the first the fatigue crack growth rates d a d N were collected as a function of the applied stress intensity factor range ΔK (= K max − K min ) by keeping the stress ratio R(= K min K max ) constant. In the second series of experiments d a d N were obtained as a function of ΔK when the mean stress intensity factor K m was constant; and in the third series ΔK was maintained constant, d a d N were obtained with increasing K m . All experimental results were obtained and processed using computerized data acquisition systems. When the data were analysed in terms of the conventional log d a d N versus log ΔK and log K m plots the effects of R and K m on fatigue crack growth rate were insignificant. However, there was a strong dependence of d a d N on R when analysed in terms of Williams' line zone model for fatigue crack growth.

Crack growth properties of nuclear graphite under cyclic loading conditions

Crack growth properties of four kinds of nuclear graphites under cyclic loading conditions were investigated at room temperature, 373, 673 and 975 K, using double cantilever beam (DCB) specimens. The crack growth rates can be expressed as a function of the stress intensity factor range at the constant mean stress intensity factor ( K mean ) and the constant minimum stress intensity factor ( K min ): that is, da/ dN = CΔK 1 n , where the constants C and n depend upon the kind of graphite and its coke grain size. The crack growth rate at the constant K mean becomes smaller than that at the constant K min . For the fine-grained graphite tested at higher temperatures, the crack growth rate increases with increasing temperature. Also cracks in the coarse grained coke graphites extend at a higher rate than that in the fine-grained high strength graphites. It seems that cracks in graphites run mostly along the coke grain boundaries.

Effect of Side Grooves on Fatigue Crack Propagation

In this report, the authors pointed out the fact that the second stage fatigue crack propagation rate of a side grooved specimen becomes lower than that of a non-side grooved one. And also, they explained above phenomenon using three dimensional finite element method(3D-FEM). Namely, the reduction of the mean stress intensity factor by the addition of the side grooves is the main reason for this phenomenon. Therefore, it is possible to estimate the crack propagation behaviour of the side grooved specimen from that of the non side grooved one using the 3D-FEM without the experimental results of side grooved specimens. Further, the authors propose three simple methods to get the stress intensity factor for the side grooved specimen and show the merit of them. The methods are based on the methods of two dimensional finite element analysis (2D-FEM), the crack opening displacement and the theory of the mechanics of materials.

Influence of environment on threshold in fatigue crack growth

Abstract The linear elastic fracture mechanics approach has been applied in the investigation of the influence of 3.5%NaCI solution in distilled water on the fatigue crack growth in two aluminium alloys, high-strength RR58 and cast LM30. The effects of mean stress intensity factor and frequency have been studied also. Specially developed double cantilever beam (DCB) specimens were used and the corrosion fatigue results compared with those determined in air. It was found that, in general, at low frequencies (≃0.2 Hz) fatigue crack growth was accelerated in the solution in comparison to a laboratory air environment, but for higher values of the maximum stress intensity factor, this effect was negligible. Also, threshold values, ∆Kth, decreased in the solution in comparison to air. In particular, threshold values for RR58 appeared to be rather low and decreased still further with higher frequency. Finally, the substantial effect of the corrodent was observed only at low values of ∆K.

An Analysis of the Influence of Mean Stress Intensity and Environment on Fatigue Crack Growth in a New High Strength Aluminum Alloy

Abstract The effects of the mean stress intensity factor Km and the range of the stress intensity ΔK on fatigue crack propagation during wholly tensile loading cycles in the aluminum (Al) alloy RR58 in laboratory air and in a 3.5% NaCl solution have been studied using contoured double-cantilever beam specimens. In general the fatigue crack growth rate in NaCl solution was greater than in air under similar conditions except for tests in which high values of the maximum stress intensity factor were used when no significant difference was observed. Based on the experimental data a relation between the cyclic crack growth rate da/dN and the tensile loading levels has been proposed. The threshold value of ΔK, ΔKth, is approximately 12% higher in air than in the 3.5% NaCl solution, and its value decreases linearly with increasing values of Km.

Influence of Mean Stress Intensity on Fatigue Crack Growth in an Aluminium Alloy

The effects of the mean stress-intensity factor, Km, and the range of the stress intensity, Δ K, on crack propagation phenomena in the Al-alloy RR 58 have been studied using contoured double-cantilever beam specimens providing a constant stress-intensity factor for all crack lengths. Based on the experimental data available, a relationship of the following form, between the cyclic crack growth rate, d a/d N, and the tensile loading levels, has been proposed: where Δ K = ( Kmax - Kmin); Kmax, Kmin and Km are the maximum, minimum and mean values of the stress-intensity factor; Δ Kth is the threshold value of Δ K for crack propagation; K1C is the critical fracture toughness in plane strain conditions; A and α arc constants. In tests at room temperature (21 °C) in laboratory air and at a loading frequency of 0.15 Hz, it was found that Δ Kth decreased with increasing values of K m, α was equal to 1.36 and A equalled 3.16 times 10-5(in/cycle).

Growth of fatigue cracks in metals and polymers

Empirical data on the propagation of tensile fatigue cracks in metals and thermoplastics have been examined. It was found that a cyclic crack propagation relationship, based on the stress intensity factor concept, exists which can be successfully utilised for both types of materials. The proposed equation has a form /.a x = MA n where A is a function of ΔK and mean K. The analysis of results suggests that this equation incorporating the influence of mean stress intensity factor provides an excellent fit to the investigated data. The possible modified forms of such a relationship in terms of strain energy release rate, the crack tip yielding and the crack opening displacement concepts are also indicated.

Fatigue Crack Propagation in Epoxy Resin Containing Plasticizer

Fatigue crack propagation in epoxy resins containing 0 wt% to 45wt% plasticizer was examined. In this experiment, double-cantilever type specimens were used. The stress intensity factor was adopted to express the stress near the crack tip. When specimen was cyclically loaded, not only the range of stress intensity factor ΔK but also the maximum stress intensity factor Kmax or the mean stress intensity factor Kmean were taken into consideration. Under the assumption of dl/dN=A(Kmax)α1(ΔK)α2 or dl/dN=B(Kmean)β1(ΔK)β2(dl/dN means the fatigue crack propagation rate) as the fatigue crack propagation law, dl/dN was measured for several combinations of ΔK and Kmax or Kmean and the values of constants A, α1, α2, B, β1 and β2 were evaluated from the values of log(ΔK) and log(Kmax) or log(Kmean) by means of least squares analysis.As the results, it was found that as the percentage of plasticizer increases, A and B increase by two orders, α1 and β1 decrease by 40%, and α2 and β2 decrease slightly. For the specimen without any plasticizer, both α1 and α2 are equal to about 5, and for the specimen with 40 wt% of plasticizer, both β1 and β2 are equal to about 4. It is interesting that the exponent of ΔK remains constant in spite of the decrease in exponent of Kmax or Kmean. The mechanical properties vary widely from the brittle fracture type to the ductile fracture type as the percentage of plasticizer increases, and it seems that the above interesting results about the fatigue crack propagation behavior in epoxy resins containing plasticizer are principally attributed to the difference in their mechanical properties.

Ni-Cr-Moマルテンサイト鋼の水中疲労き裂伝ぱ則

The effect of delayed failure on the fatigue crack propagation rate in water of Ni-Cr-Mo martensitic steel was investigated. The results obtained are as follows:(1) The relation between the fatigue crack propagation rate da⁄dN in air and the stress intensity factor range ΔK is expressed as da⁄dN=C1(ΔK)m1, and m1 increases with increase of Km⁄ΔK, where Km is the mean stress intensity factor.(2) The relation between the crack propagation rate da⁄dt in delayed failure and the static stress intensity factor KD is expressed as da⁄dt=C2(KD)m2.(3) The fatigue crack propagation rate (da⁄dN)w in water is expressed as the addition of both fatigue crack propagation rate in air and crack propagation rate in delayed failure, and the following equation holds:(This article is not displayable. Please see full text pdf.) where f is the frequency (cpm); β is a coefficient of addition and depends mainly on f and Km⁄ΔK. Under the condition in this experiment (f=55∼345 cpm, Km⁄ΔK=0.5∼4), β is 0.2∼0.4.(4) Physical meaning of β is considered to be the ratio of the time in which the tri-axial tensile stress state region at the crack tip meet a cluster of hydrogen atoms during one cycle.