Actual Crack Length Research Articles

Stress intensity factors for central cracked circular disk subjected to compression

The series expressions of σ θ , τ rθ and σ r in the uncracked circular disk under diametral-compression loading is given in the present paper. Also, the general expressions of the coefficients A ji corresponding to the stress components are derived. For central cracked circular disk subjected to diametrical forces or pressures, the explicit expressions of the stress intensity factors, K I and K II, are proposed by use of the fracture mechanics weight function. Under the pressure loading, the deviation of the stress intensity factors from those under force loading increases with increasing the load distribution angle. The advantage of the present formulae is that the stress intensity factors for any arbitrary relative crack length, loading angle and load distribution angle can be obtained explicitly and easily. The conditions for pure mode I loading do not vary depending upon the relative crack length and load distribution angle. However, the conditions for pure mode II loading are not only dependent on the relative crack length but also load distribution angle. Based on the present solution, the actual critical loading angle for pure mode II crack can be easily calculated according to the actual relative crack length and load distribution angle in the pure mode II fracture test.

The use of DCPD method for measurement of growth of cracks in large components at normal and elevated temperatures

The paper deals with problems of measurement of initiation and growth of cracks in pipes and in some full-scale models––the connection of pipes to pressure vessels during experiments at room and elevated temperatures. A modification of a direct current potential drop method was used to compensate influences of (i) non-uniform cross-section of pipes, (ii) complicated shape and (iii) high temperatures. It is shown that different temperatures are not a limiting factor. A comparison between measured and actual crack length and front in complicated specimens is presented, as well as results of the method of an evaluation of subcritical crack initiation in pipes and their connections.

On the effect of the residual stresses on the crack opening displacement in a cracked sheet

The residual stress and displacement fields caused by localized plastic flow near a mode I crack tip in a sheet under plane stress conditions are investigated. The present study founds on the classical Dugdale scheme of the plastic flow localization. The residual stress field is considered to be induced by reversed plastic flow near the crack tip caused by an unloading. As it is found the residual stresses around the crack compress the crack tip, while the residual tensile stresses in a distant from the crack tip zone occur. It is shown the maximum residual tensile stresses can reach the significant value of the one third of the yield limit. The length of the compressed plastic zone and the residual displacement distributions are obtained. The exact formula for the residual crack opening displacement to estimate the crack closure is found. Then the next loading of the cracked plate is considered. It is shown that the second loading causes the origin of two plastic zones localized near the crack tip and at the point, where the maximum residual tensile stresses are concentrated. Again, according to the Dugdale scheme of the plastic localization, both the plastic flow zones are modelled as narrow stripes on the line extending the crack. To determine three non-dimensional parameters, characterizing the position of the segment-like plastic flow zones, a non-linear system of equations is obtained and analyzed. The exact formula for the crack opening displacement after a loading–unloading cycle is obtained. An asymptotic analysis (as the linear dimension of the distant plastic flow zone compared with the actual crack length is small) is given. It shows that the effect of the distant plastic flow zone appears as some complementary crack closure.

Correction methods of an apparent negative crack growth phenomenon

It often occurs in J−R testing that some initial crack extension (Δa) data points have anomalous negative values. The reason for the apparent negative crack growth is due to the analysis method. The phenomenon as a possible source of error in determining JIC or J−R curve from partial unloading compliance experiments may be eliminated by the compliance correction equation or the offset technique. In this study, new correction methods based on compliance correction and blunting behavior are proposed and verified by the measurement of the actual crack length and JIC analysis.

Calibration of DC Potential Technique Using an Optical Image Processing System in LCF Testing

AbstractThe direct current electrical potential drop (DCPD) technique is applied to monitor fatigue crack growth in plate specimens with central circular holes at room and high temperatures. The application of the calibration curves obtained from replica specimens to both room and high-temperature fatigue testing conditions is studied. The actual fatigue crack length is measured using a video-camera with image processing to assess the reliability of the DCPD technique. The use of two pairs of DCPD probes across the hole and the introduction of a special reference voltage have eliminated the dependence of the potential drop on the hole size and shape as well as the material resistivity and the notch plastic zone size prior to crack initiation. At high temperature, however, the calibration curve should be corrected to take into account the shifting in the potential ratio due to the increases in crack tip plastic zone and crack opening displacement. The effect of the temperature difference between the different potential probes is also examined.By analyzing the results given by the DCPD in connection with the image processing technique, a criterion is suggested to define the interface between the crack initiation and propagation periods.

塑性締めボルトの疲労強度 再使用時の疲労強度保証

In reusing, a bolt is repeatedly tightened and loosened. In this study, the reusing properties of a shank-elongation bolt and a thread-elongation bolt tightened in plastic region were investigated from a viewpoint of fatigue strength. The fatigue tests were carried out on both types of bolts which were subjected to 10-cycle tightening in plastic region. As a result, the 10-cycle tightening had little influence on the fatigue limit of the bolts. However, on the thread-elongation bolt, the microcracks (about 7μm length) appeared at the thread root after repeated tightening in plastic region. Then, the fatigue limit of a cracked bolt was predicted by using the fracture mechanics method. The threshold stress intensity factor range (ΔKth) of the bolt material was determined from the fatigue crack propagation tests with pre-strained smooth specimens under a high stress ratio. The stress intensity factor range (ΔK) of the thread root was calculated by using the equation for a single edged crack without considering a stress concentration. In this equation, the crack length made of the actual and latent crack length was used as the effective crack length. The fatigue limit predicted from the above mentioned ΔKth and ΔK agreed approximately with the fatigue limit of a cracked bolt. This prediction clarified that the microcracks of about 7μm length had little influence on the fatigue limit of bolts but that the fatigue limit decreased with increasing the crack length beyond 7μm.

Creep Life Prediction Based on Stochastic Model of Microstructurally Short Crack Growth

A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitary time, G(a,t), and that of the time when a crack reaches an arbitary length, F(t,a), are obtained numerically by means of a Monte Carlo method. G(a,t) and F(t,a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. Taking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.

An ultrasonic technique for nondestructive testing of butt-welded steel plate in ship hulls

This paper proposes an ultrasonic nondestructive testing (NDT) method for underwater-diver inspection of shiphull welds. The specimens used were prepared with various induced cracks in the vicinity of the welds. The type of flow considered is a transverse crack in the heat-affected zone in a butt-welded seam. An automated data analysis is developed to scan, locate and characterize cracks using the pulse-echo technique with a single focus transducer. Specimens and probes were submerged in sea water as an additional exercise in simulating operating conditions. Calibration of the NDT characterization was established by first heat tinting to register the size of the induced crack and subsequently to load the specimen to failure so as to examine the crack. The results show that the actual crack length and the maximum load to failure for each cracked specimen were comparable with the test data obtained from the NDT.

Approximate Linear Analysis of Concrete Fracture by R‐Curves

Using linear elastic fracture analysis, the energy consumed per unit length of fracture (fracture energy) varies with the crack length, as described by the resistance curve (R‐curve). This concept, originally proposed for metals, is developed here into a practical, applicable form for concrete. The energy release rate is determined by an approximate linear elastic fracture analysis based on a certain equivalent crack length, which differs from the actual crack length, and is solved as part of structural analysis. It is shown that such an analysis, coupled with the R‐curve concept, allows achieving satisfactory fits of the presently existing fracture data obtained with three‐point and four‐point bent specimens. Without the R‐curve, the use of an equivalent crack length in linear analysis is not sufficient to achieve a satisfactory agreement with these data. The existing data can be described equally well with various formulas for the R‐curve, and the material parameters in the formula can vary over a relatively broad range without impairing the representation of test data. Only the overall slope of the R‐curve, the initial value, and the final value are important. A parabola seems to be the most convenient shape of R‐curve because the failure load may then be solved from a quadratic equation. For the general case, a simple algorithm to calculate the failure load is given. Deviations from test data are analyzed statistically, and an approximate relationship of the length parameter of the R‐curve to the maximum aggregate size is found.

Fracture Toughness of Rocks under Bending

Although natural cracks such as fatigue cracks are favourable as a pre-crack for fracture toughness testing of rocks, it is very difficult to measure the exact length of natural cracks because of the opaque nature of rock and the unevenness of the crack-front.In this paper, by measuring the compliance of the crack opening displacement under bending, the effective length of fatigue cracks was estimated for two kinds of rocks; Ogino tuff and Tohoku marble, and the result was compared to the actual crack length on the side of the specimen. Furthermore, in order to know the fracture toughness of the rock containing natural cracks by using an artificial notch, the fracture toughness of rock specimens with a chevron-notch was measured and compared with those with another types of pre-cracks including fatigue crack and straight-through notch.The main results obtained are as follows:(1) The relationship between the observed length and the effective length of the fatigue crack depended on the texture of the rock. The effective crack length of the marble was mostly smaller than the observed one while the effective crack length of the tuff is larger than the observed one. The stable values of the fracture toughness were obtained from the effective crack length.(2) The fracture toughness obtained from the chevron-notch was nearly equal to that from the fatigue crack using the effective crack length.(3) The fracture toughness obtained from the natural cracks of chevron-notch and fatigue crack was considerably larger than that from the artificial straight-through notch because of the unevenness of the crack-front.

Studies on crack growth rate under high temperature creep, fatigue and creep-fatigue interaction—II: On the role of fracture mechanics parameter [formula omitted

For high temperature creep, fatigue and creep-fatigue interaction, several authors have recently attempted to express crack growth rate in terms of stress intensity factor K I = α aσ g , where a is the equivalent crack length as the sum of the initial notch length a 0 and the actual crack length a ∗ , that is, a = a 0 + a ∗ . On the other hand, it has been shown by Yokobori and Konosu that under the large scale yielding condition, the local stress distribution near the notch tip is given by the fracture mechanics parameter of aσ gƒ(σ g ), where a is the cycloidal notch length, σ g is the gross section stress and ƒ(σ g ) is a function of σ g . Furthermore, when the crack growth from the initial notch is concerned, it is more reasonable to use the effective crack length a eff taking into account of the effect of the initial notch instead of the equivalent crack length a. Thus we believe mathematical formula for the crack growth rate under high temperature creep, fatigue and creep-fatigue interaction conditions may be expressed at least in principle as function of a effσ g , σ g and temperature. In the present paper, the geometrical change of notch shape from the instant of load application was continuously observed during the tests without interruption under high temperature creep, fatigue and creep-fatigue interaction conditions. Also, the effective crack length a eff was calculated by the finite element method for the accurate estimation of local stress distribution near the tip of the crack initiated from the initial notch root. Furthermore, experimental data on crack growth rates previously obtained are analysed in terms of the parameter of a eff σ g with gross section stresses and temperatures as parameters, respectively.

Fracture Mechanics Analysis for Short Fatigue Cracks

AbstractElastic and elastic-plastic fracture mechanics solutions are modified to predict the growth of short fatigue cracks by introducing an effective crack length, which is equal to the actual crack length increased by an amount l 0, into the solutions for intensity factors and the J integral method of analysis. Since the threshold stress approaches the fatigue limit of the material as the crack length tends to zero the value of l 0 can be obtained from the threshold stress intensity factor and the fatigue limit. Crack growth results for short cracks, in both elastic and plastic strain fields of smooth specimens, when interpreted in terms of the modified solutions, show excellent agreement with elastic long crack data. The accuracy of the term l 0 in predicting crack growth rates for short cracks is found to be independent of the applied strain level. It varies linearly with grain size for low carbon steels and can be considered at the surface as a measure of the reduced flow resistance of surface grain...

Application of statistical linear elastic fracture mechanics to pressure vessel reliability analysis

An evaluation of the failure probability for a pressure vessel is made on the basis of linear elastic fracture mechanics (LEFM). Failure is identified by actual crack length equal to critical crack length. The probability of failure is the joint probability that there exists a crack (i.e. K I) greater than a given crack (i.e. K) and that the critical crack (i.e. K IC) is smaller than that same crack, where K I and K IC are considered for same time and location. K IC as well as K I are treated as statistical variables with probability density functions (p.d.f.), which are functions of material, location and time. The variability of K IC (that is the p.d.f. of K IC) is a result primarily of the statistical nature of the material properties and to a lesser degree of the increasing neutron-done experienced by certain parts of the pressure vessel. The variability of K I (that is the p.d.f. of K I) is a result of the following parameters: 1. (1) initial distribution of cracks (that is the crack distribution at the start-up of the reactor) regarded as a statistical variable, because of the uncertainty in the non-destructive testing of the pressure vessel prior to start-up. 2. (2) stresses, regarded as a statistical variable because of the uncertainty in the stress analysis and the geometry of the vessel. 3. (3) crack growth by fatigue, which is a result of the normal (with probability equal to 1.0) and abnormal (with a p.d.f.) operational transients. The statistical nature of the crack growth is due to the statistical variation of the abnormal operational transients. 4. (4) material properties (that is K IC, yield strength and the factors governing the fatigue crack growth) regarded as statistical variables. The p.d.f.s of the abovementioned parameters are evaluated on the basis of the available literature. The integrated calculations of failure probability are performed by a computer program utilizing the Monte Carlo technique with importance sampling, which gives a greater freedom in selection of p.d.f.s. Calculations of failure probability for existing reactors are presented.

Studies on the Fatigue Crack Initiation and Propagation : Report 1, Effects of Crack Length, Stress Range and Minimum Stress on Fatigue Crack Propagation

The fatigue crack propagation behaviors were investigated on HT80 steel plates under net section stress control in which stress range and minimum stresses were widely varied. The fatigue crack growth rates were proportional to the effective crack length 2ae which was an actual crack length 2a modified by the finite width effect of the specimen. When minimum stress δmin was in compression side, the growth rate depended on maximum stress δmax and in tension side, it depended on stress range Δδn. As the result, the effects of crack length, stress range and minimum stress on the fatigue crack propagation can unifyingly be shown such that the crack growth rate is proportional to the cyclic plastic zone size at a crack tip[numerical formula]. Where, δy is yield strength of material and δn is δmax when δmin≤0 and is Δδn When δmin≥0