Stability of arrays of multiple edge cracks

The creation and subsequent shedding of arrays of edge cracks is a natural phenomenon which occurs in heat-checked gun tubes, rapidly cooled pressure vessels and rock, dried-out mud flats, paint and concrete and in ceramic coatings and permafrost. The phenomenon covers five orders of magnitude in crack spacing and the driving mechanisms may include fast fracture, environmental cracking and fatigue crack growth. A simple model is developed which indicates that the shedding behaviour is governed by the behavior of individual cracks rather than global energy changes. The model predicts that all cracks will deepen until a crack-spacing/crack depth ratio (2h/a) of 3.0 is achieved, at which stage crack-shedding will commence. Two out of every three cracks will be shed, leading to a new (higher) crack spacing/crack depth ratio at which stage growth of all currently active cracks will be dominant. An approach based upon rapid, approximate methods for determining stress intensity provides good indications of behaviour provided near-surface stress gradients are not excessive. In cases where stress gradients are high it is shown that it is necessary to employ numerical techniques in calculating stress intensity. Two specific examples are presented, the first at very small scale (heat-check cracking in a gun tube, typical crack spacing 1 mm) and the second at very large scale (permafrost cracking, typical crack spacing 20 m). The predicted ratios for the proportion of cracks shed and for crack spacing/crack depth are in agreement with experimental evidence for gun tubes, concrete and permafrost. The ratios also appear to match experimental observations of “island delamination” in ceramic coatings and paint films.     

Generic Overlapping Cracks in Polymers: Modeling of Interaction

This paper deals with modeling of the interaction in overlapping cracks that the authors have earlier identified to be generic to a wide range of polymeric systems (Ramasamy and Lesser, J Polym Sci B Phys, 2003). A complex stress function method is used for evaluating stress intensity factors for interacting cracks. The interaction between two parallel overlapping cracks is considered first. It is shown for this case that the stress intensity factor can fall below the threshold value when there is sufficient overlap, leading to arrest of crack growth at the overlapping tip. Then the interaction in a doubly periodic infinite array of cracks is considered. The interaction in the array is found to be non-linear. However, at a given stress level, the highest density of stable cracks is related to the threshold value for crack propagation K_th though a simple set of equations. It is also shown that in an infinite array of cracks, the energy release rate criterion for crack growth is different from the stress intensity factor criterion due to a reduced stiffness of the material.     

Stress intensity factor equations for branched crack growth

Overload-induced fatigue crack branching is a well-known crack growth retardation or arrest mechanism, which can quantitatively explain such effects even when arguments based on plasticity induced crack closure cannot be applied, e.g. in high R-ratio or in plane strain controlled fatigue crack growth. However, the few results available for branched cracks cannot be used to predict the subsequent crack growth nor account for the delays observed in practice. In this work, specialized finite element (FE) and fatigue life assessment software are used to solve this problem. The crack path and associated stress intensity factors (SIF) of kinked and bifurcated cracks are numerically obtained by the FE program for several angles and branch lengths, and the companion life assessment program is used to estimate the number of delay cycles associated with them. From these results, crack retardation equations are proposed to model the number of delay cycles and the retardation factor along the crack path, allowing for a better understanding of the influence of crack deflection in the propagation life of structural components.     

The effect of crack surface interaction on the stress intensity factor in Mode III crack growth in round shafts

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interaction of the mutual fracture surfaces results in a pressure and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor.The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loading by considering a pressure distribution between mating fracture surfaces. The pressure between fracture surfaces results from climbing of asperities respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the interactions diminish beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.     

Stress Intensity Factors of partly circumferential surface cracks at the outer wall of a pipe

By means of the finite element method stress intensity factors were calculated for partly circumferential surface cracks at the outer wall of a pipe. The crack shape considered can be described as curved rectangular shape. The cracks considered have crack depths between 20 and 80 percent of the wall thickness of the pipe and crack lengths (defined by the angle of circumference φ) between φ = 10° and φ = 60°. The pipe is loaded by a constant axial tensile stress σ₀ (equal to 136 Nmm^?2 in the numerial calculations), and the wall thickness to inner radius ratio of the pipe was chosen to 0.1. A wall thickness of 20 mm was used for the numerical calculations.     

Fatigue crack growth in thick-walled cylinders under pulsating internal pressure

The stress intensity factor is derived for both single and multiple longitudinal, elliptical cracks in the wall of a pressurized thick cylinder of given geometry. For this purpose, it is found necessary to combine known solutions to the stress intensity factor for a straight longitudinal crack with the effects of a curved crack front and multiple cracking. The analysis is appraised from a number of fatigue tests reported for % Ni-Cr-Mo cylinders with diameter ratios of between 2 and 3 under repeated and fluctuating pressure cycles. When cylinders with poorly finished bores are assumed to be initially flawed, it is found that their fatigue lives under high ranges of pressure may be predicted reliably for the single crack propagation failures observed. This analysis employs published WOL or SEN fatigue crack growth data for the alloy. The enhancement in fatigue life that results from an improved surface finish has enabled that proportion of life expended during the initiation phase to be determined. It is further shown that the observed effect of mean stress and surface finish on the fatigue limit may be quantified with a change to the threshold of stress intensity for crack growth. A number of tests were conducted with two-step changes to the amplitude of the pressure cycle. In this instance, nonlinear, stress dependent, cumulative damage rules are shown to offer no advantage over Miner's rule in the prediction of fatigue life.     

Load sequence effects in fatigue crack growth of thick-walled welded C–Mn steel members

Many welded steel structures in marine, offshore, and infrastructural industries are subjected to variable amplitude (VA) fatigue loads. It is well known that the level and sequence of the load cycles can cause crack growth retardation or acceleration and thus influence the fatigue life. An important sequence effect is generated by a large stress cycle followed by smaller stress cycles. Whereas the effect of single large stress cycles in a further constant amplitude (CA) load on central through cracks in thin-walled aluminium sheet is well established, studies into the effects of practical VA loads on cracks in thick-walled welded steel structures are less common. This paper presents the results of CA tests with large stress peaks and VA tests on 70 mm C–Mn steel butt welded 4-point bending specimens with crack growth in thickness direction. It is demonstrated that loading by a sequence of accelerating and subsequent decelerating stress cycles cause significant retardation of the crack growth and that the same stress cycles but placed in random sequence hardly result in retarded crack growth. The obtained crack growth versus number of cycles for as-welded and stress relieved specimens have been simulated using two relatively simple crack rate retardation models, being the well-known Willenborg model and the Space-state model developed by Ray and Patankar. The latter model is also used to simulate crack growth of semi-elliptical surface cracks in welded steel structures tested by others. The Space-state model is able to predict experimental results with reasonable to good accuracy. A proposal is put forward for future improvement of the model.     

The applicability of leak-before-break on flooded member detection for offshore structures under fatigue

The full development of growth of a circumferential crack in a tubular member from a long deep surface crack to final failure has been investigated by carrying out fracture mechanics based fatigue analyses, including the stage of a partial through-wall crack. The influences of member size, crack configuration material properties and loading conditions on the fatigue life have also been explored. The time available to detect the presence of the crack once it has penetrated the wall thickness (the flooded life) depends particularly on the rate of accumulation of fatigue damage (S³N/year) and on the initial length of surface crack present. The analysis results have been applied to a case study of a particular offshore structure and loading situation and found to support inspection intervals of three years for flooded member detection for this case. The results of this fatigue analyses, have been compared to a conventional leak-before-break (LBB) procedure in flooded member detection. It was found that, for long deep cracks, the standard LBB procedure may underestimate the flooded life available for inspection, but for short cracks a standard LBB approach using extrapolations of standard stress intensity factor solutions would be non conservative.     

An improved image processing method for assessing multiple cracking development in Strain Hardening Cementitious Composites (SHCC)

Strain Hardening Cementitious Composites (SHCC) exhibit tension-hardening behavior accompanied by the formation of multiple cracks. To study the multiple cracking process, cracks are identified from digital images. As conventional image processing technique based on a single threshold of gray intensity cannot accurately determine the width of both fine and wide cracks, a new double-threshold algorithm is developed and its accuracy is verified by comparing with direct measurement under the microscope. Then, an additional algorithm for removing the noises and isolating individual crack regions is introduced. With the improved image processing method applied to a large number of sequential images, detailed information on the development of crack number and width is acquired. The average value and deviation of crack width at a given strain can be calculated to facilitate durability design. Also, with the stress-crack width relation obtained for various cracks, the fiber distribution among cracked sections can be estimated.     

PREDICTION OF THE FATIGUE LIMIT OF CRACKED SPECIMENS BASED ON THE CYCLIC R-CURVE METHOD

Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R -curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R -curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.     

Threshold stress intensity factor and crack growth rate for stress corrosion cracking of simulated heat affected zone in caustic solution

The threshold stress intensity factor for stress corrosion cracking (K_Iscc) of the simulated heat affected zone (HAZ) of mild steel in caustic solution has been determined using circumferential notch tensile (CNT) technique. The HAZ microstructure produced upon manual metal arc welding of grade 250 steel was simulated over a length of 35 mm of CNT specimens, using a thermo-mechanical simulator. Inter- and trans-granular stress corrosion cracking has been confirmed using a scanning electron microscope. The results presented here validate the ability of CNT technique for the determination of K_Iscc of HAZ and Base metal. Crack growth rates have also been determined using CNT technique. Further, the effect of microstructures on K_Iscc and crack growth rate is discussed in the present study. The determined K_Iscc of Base metal and simulated heat affected zone in 30% caustic solution is 24 and 45 MPa m^1/2, respectively.     

Analyzing the mechanisms of fatigue crack initiation and propagation in CRH EMU brake discs

A significant number of high-speed electric multiple units’ (EMU) brake discs, manufactured from forged steel, showed thermal cracks during work and NDT. There exist three kinds of cracks on the friction surface; namely, the crackle, radial crack and circumferential crack. Macro-morphologies of the friction surface indicate that the cracks appeared in the interior and edges of the hotspots. Crack growth methods include the single crack propagation and multiple crack connectivity. A finite element analysis (FEA) was performed to determine temperature and stress distribution in the brake disc as well as to estimate stress distribution during braking. Simulation results indicate more significant residual, circumferential tensile stress on the external friction surface after emergency braking. The maximum residual circumferential tensile stress is 200 MPa after 300 km/h emergency braking. In addition, there is only the circumferential compressive stress on a section which is a certain distance from the exterior of the friction surface, and the distance depends on braking conditions. Therefore, not taking into account thickness reduction of the friction surface due to wear, it can be concluded that when the cracks run along the thickness direction to the specified distance, they will cease to run along this direction and begin propagating mainly in the direction of the radius. In addition, based on the simulation results, a measure was presented to prevent and inhibit the crack propagation.     

In situ observation of crack propagation in ESP (engineered stress profile) glass

Important features of the ESP (engineered stress profile) glasses are the crack arrest and multiple cracking phenomena that occur even in an unstable stress field. In this work a detailed “in situ” observation of crack observation and analysis was performed with the aim to examine crack propagation in detail and relate it to the residual stress field produced by ion exchange and to the final mechanical performances of the material. The results showed that the peculiar residual stress field with a maximum below the surface is responsible for the formation of a multitude of stable cracks on the tensile surface of the glass that evolved into through-thickness flaws. The propagation within the material is limited by the increasing compressive residual stress, which also leads to kinking of the cracks in a direction parallel to the surface. The observed fracture phenomena are also responsible for a shielding effect that makes the measured failure resistance of ESP glass larger than predicted by simplistic single crack models.     

Fatigue crack growth in a fillet welded joint

Existing theories for the growth of cracks at weld toes have proved difficult to verify because of a lack of experimental proof at short crack depths and slow growth rates. Arbitrary initial defect sizes have been employed in life calculations coupled with approximate two-dimensional stress analyses. In this study, the fatigue performance of a stress relieved fillet weld is determined by both theory and experiment. Crack growth results for shallow (less than 1 mm depth) elliptical cracks at weld toes are used to test an elastic expression for stress intensity using a correction factor from a three-dimensional stress analysis. No evidence of higher than expected growth rates, observed by others for very short cracks and cracks in notch plastic zones, is apparent. Integration of a growth law that includes the threshold stress intensity factor provides fatigue life predictions for various stress ratios and from experimentally measured defect depths. Needle peening the weld toe improves the fatigue life by retarding crack growth up to 1 mm below the weld toe.     

Fatigue crack propagation in the threshold regime after rapid load reduction

In this work, the influence of rapid load reduction on fatigue crack growth in the threshold regime of the aluminium alloy 2024-T3 has been studied. It can be shown that fatigue crack growth may be severely influenced by crack closure due to oxide formation and fracture surface roughness. After rapid load reduction, crack arrest could be observed at K_max values 10–100% above the constant amplitude threshold, depending on the environment. With measurements in different environments (humid air and vacuum), the oxide-induced crack closure effect could be recognized as being mainly responsible for an increase of the stress intensity threshold. Using high-frequency fatigue testing equipment, it was possible to show that after rapid load reduction in a vacuum, cracks may begin to grow again after crack arrest of more than 5 × 10⁷ cycles.     

Stress intensity factors for functionally graded solid cylinders

This paper presents the mode I stress intensity factors for functionally graded solid cylinders with an embedded penny-shaped crack or an external circumferential crack. The solid cylinders are assumed under remote uniform tension. The multiple isoparametric finite element method is used. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable influence on the stress intensity factors. The influence for embedded cracks is quite different from that for external cracks.     

A study of crack growth retardation due to artificially induced crack surface contact

The contact of the cracked surfaces during a part of a loading cycle generally results in a reduced crack growth rate. A critical experiment was designed to evaluate the influence of the crack surface contact on crack growth. A round compact specimen made of 1070 steel with a round hole at the wake of the fatigue crack was designed. Two mating wedges were inserted into the hole of the specimen while the external load was kept at its maximum in a loading cycle. In this way, the wedges and the hole in the specimen were in firm contact during the entire loading cycle in the subsequent loading. Experiments showed that the addition of the wedges resulted in a reduction of crack growth rate in the subsequent constant amplitude loading. However, crack growth did not arrest. With the increase in the subsequent loading cycles, crack growth rate increased. The traditional crack closure concept cannot explain the experimental phenomenon because the effective stress intensity factor range was zero after the insertion of the wedges. The detailed stress–strain responses of the material near the crack tip were analyzed by using the finite element method with the implementation of a robust cyclic plasticity theory. A multiaxial fatigue criterion was used to determine the fatigue damage based upon the detailed stresses and strains. The crack growth was simulated and the predicted results were in good agreement with the experimental observations. It was confirmed that the stresses and strains near the crack tip governed cracking behavior. Crack surface contact reduced the crack tip cyclic plasticity and the result was the observed retardation in crack growth.     

A STUDY ON FATIGUE CRACK GROWTH UNDER OUT-OF-PHASE COMBINED LOADINGS

Abstract— Fatigue tests were performed on thin-walled tubular specimens of S45C steel under tension-compression, pure torsion, in-phase and out-of-phase axial-torsional loadings. The relationship between cracking behaviour and stress components on the crack plane was investigated. Measurement of microcrack density showed that microcracking was governed predominantly by the shear stress amplitude acting on the crack plane for all loading conditions. The failure crack was formed by coalescence of many cracks initiated near the maximum shear planes. The cracks grew turning their orientation to the direction perpendicular to the maximum normal stress. The transition of crack orientation occurred at relatively longer crack lengths at a higher stress ratio. The crack growth behaviour for all loading modes can be correlated using an equivalent strain intensity parameter based on shear and normal strains on the crack plane.     

Simulation for intergranular stress corrosion cracking based on a three-dimensional polycrystalline model

In stress corrosion cracking of stainless steel, two different schemes of analysis of crack growth should be employed for the crack initiation phase and crack growth phase. However, this distinction is not clear-cut in the crack initiation phase, since the vicinity of the pre-existing crack is a preferential area of crack initiation due to concentration of stress. Therefore, initiation of crack tends to occur at the tip of a pre-existing crack and it can be regarded as crack growth. In this study, the contribution of this type of apparent crack growth, referred to as initiation dominant growth (IDG), to crack growth was evaluated by a Monte Carlo simulation. A three-dimensional polycrystalline body was generated by Voronoi tessellation. The cracks were assumed to grow along grain boundaries. The effect of stress-concentration around pre-existing cracks was taken into account by applying the finite element method. Initiation and propagation of the cracks were modeled based on concepts of damage mechanics. The simulation could reproduce the changes in number of cracks and the sum of crack length obtained experimentally as well as preferential crack initiation at the stress-concentration zones and suppression of crack initiation in stress-shielding zones. It was shown that the contribution of IDG to crack growth was large for small cracks, and that damage by crack initiation accounted for more than 50% of total damage even when the length of a crack was 0.6 mm at the surface.     

A simulation on growth of multiple small cracks under stress corrosion

In order to keep high reliability of components in a nuclear power plant, it is important to understand the damaging process due to multiple small cracks. The growth shows random behavior because of the microstructural inhomogeneity and the interaction between cracks. The former includes the effects of crack kinking and anisotropic deformation in each crystal of polycrystalline. In this study, a Monte Carlo simulation method is developed in order to analyze the random behavior, taking into account the their influences on the stress intensity factor. The damaging process of mill-annealed alloy 600 in the primary water stress corrosion cracking (PWSCC) is numerically simulated by the proposed method. The crack size distribution obtained agrees well with the experimental observation, and the maximum crack size is statistically estimated on the basis of the Gumbel statistics.