Mixed Mode Stress Intensity Factor Determination of Multiple Cracks in Hollow Circular Pipe

Failure of pressure vessels and piping due to high temperature applications occurs due to the formation of fatigue cracks caused by cyclic load. It is well known that, the consequences of collapses of pipes causing enormous disruption of daily life. Thus there is a need to design and manufacture the pipes with precision and care. The major cause of crack nucleation in pipes is due to corrosion and internal fluid pressure. The crack-tip stresses are determined using stress intensity factor (SIF). In the present work an attempt has been made to determine the SIF for multiple cracks in a circular pipe subjected to internal fluid pressure. Two surface cracks of same size were introduced at the inner wall of the tube. The crack depth ratio (a/t) ranging between 0.1 and 0.5 and crack aspect ratio (a/c) of 0.6 and 1.0 was considered. Internal fluid pressure of 100 MPa was applied at the inner surface of the pipe and the corresponding SIF was measured. SIF values were calculated with consideration of mode-II and mode-III fracture in order to predict the exact SIF. As available SIF solutions of cracked pipes are limited to mode-I fracture, present work presents the influence of additional influence of mode-II and mode-III fracture. It is observed that, as crack depth ratio increases, SIF also increases considerably for semi-circular cracks. Higher SIF values were observed at the crack surface region [S/S ₀ = ±1] compared to crack middle [S/S ₀ = 0] region. A crossover in SIF was noted at a crack depth ratio of 0.3. At higher crack depths, SIF values decrease at the crack surface region due to additional influence of mode-II and mode-III fracture. In contrast to semi-circular cracks, SIF values are higher at the crack surface region for semi-elliptic cracks irrespective of the crack depths.     

Fatigue crack grovvth in fibre reinforced titanium MMC laminate at room and elevated temperatures

Abstract

The fatigue crack growth resistance of a [0/90°]_2S Ti-6Al-4V (wt-%) SCS-6 cross ply laminate has been assessed as a function of varying the initial nominal stress intensity factor range (?K), the test temperature, and the environment. In all cases, through thickness cracks have been grown from unbridged defects. Fatigue crack growth rates are higher at elevated temperatures of 300 and 450° C in air. However, tests carried out at a temperature of up to 450° C in vacuum have shown that crack arrest conditions are similar to those observed from specimens studied at room temperature and at a temperature of 300° C in air. In these cases, initial ?K_ini transition values between fatigue crack arrest and eventual specimen catastrophic failure are close to 10 MPa m^1/2. In contrast, at a temperature of 450°C in air, even for tests performed at a frequency of 10 Hz, the limiting value of initial ?K_ini to give crack arrest is less than 6 MPa m^1/2. This has been attributed to the action of an aggressive environment, and particularly to the attack of the carbon coating layers. In addition, correlations have been found between fibre pull out lengths and changes in both temperature and environment; these are negligible after tests at 450°C in air. Finally, for such composites, sudden increases in fatigue crack growth rates have been attributed unequivocally to the failure of bridging fi bres, which were detected using acoustic emission.     

Failure analysis of cold forged 37Cr4 alloy M10x28 bolts

This paper covers experimental and numerical studies on the crack evolution on cold forged ³⁷Cr₄ high strength steel M10x28 bolts. Numerical simulations of forging operations were prepared on SIMUFACT FORMING finite element software. Failure evolution in simulations was predicted by using Cockroft-Latham damage model. Possible surface defects on work-pieces were also considered in the study. Artificial surface defects were generated on work-pieces by using electric discharge machine to determine the effects of defects on crack formation and propagation. As followings, numerical predictions on crack evolution were verified by conducting forging experiments. It was determined that deviation of the punch during forging led formation of shear cracks on the bolt head. Artificial surface defect was found to trigger crack evolution and affect the shape and propagation of the crack. Shear cracks propagated though the head of the bolt with 52° inclination angle while cracks triggered by surface defect propagated perpendicularly though longitudinal axis of the bolt.     

FATIGUE CRACK GROWTH IN D16T A1-ALLOY SHEET SUBJECTED TO BIAXIAL OUT-OF-PHASE LOADING

Abstract— Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under out-of-phase biaxial tension and tension-compression. In the range of the biaxial load ratios λ from ?0.5 to +0.5 and an R-ratio of 0.3, fatigue striation formation took place beyond a crack growth rate near to 4 × 10^?8 m/cycle. The striation spacing and the crack growth rate increase as the φ-angle of the out-of-phase biaxial loads increases in the range of φ-angles from 0° to 180°. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1 to 1 when da/dN is greater than 4 × 10^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 10^?6 m/cycle (N_d), and the crack growth period, N_P, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ ratios and φ angles. The value of N_d decreases as the φ angle is increased in the range from 0° to 1807deg;. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF₁(λ, R)F₂(φ). The values of F₂(φ) were determined. The calculated fatigue crack growth period, N_c, applicable up to and including the stage of fatigue striation formation (predicted by using both of the F₁(λ, R) and F₂(φ) functions) is correlated with the experimental data and the error is of the order of 15%.     

The in-plane and out-of-plane stress constraint factors and K-T-Tz description of stress fields near the border of a quarter-elliptical corner crack

The elastic T-stress and stress intensity factor K for quarter-elliptical corner cracks have been investigated in elastic plates by detailed three-dimensional finite-element calculations. The distributions of normalized K and T-stress have been obtained along the crack front with aspect ratios (a/c) of 0.2, 0.3, 0.4, 0.5, 0.6, 0.8 and 1.0, and far-field tension and the effect of Poisson's ratio have also been considered. The normalized K increases and the normalized T-stress decreases with the increase of Poisson's ratio v. For v= 0.3, the normalized K gradually increases in the range of crack-face angle φ≥ 22.5° and decreases in the range of φ≤ 22.5° with the increase of a/c. The normalized T-stress increases in the beginning and then decreases with increasing φ except for a/c= 0.2 and a/c= 0.3. By fitting the numerical results with the least squares method, empirical formulae have been given for the convenience of engineering applications. Combining with the corresponding out-of-plane constraint factor T_z, the three-parameter K-T-T_z approach has been provided, which can accurately describe the stress field around the crack front.     

Mode III interlaminar fracture characterization of composite materials

An experimental project was undertaken to develop two interlaminar Mode III tearing test methods. The first was a split cantilever beam test. A laminate, containing a starter crack, was bonded between aluminum bars. The ends of the bars were then loaded in opposite directions, parallel to the plane of the crack and normal to the beam length. Stable crack growth was achieved in carbon fiber material. Unidirectional carbon fiber composites showed Mode III critical strain energy release rates in the range 1·1–1·3 kJ/m². The effects of laminate thickness, beam depth, and data reduction method were investigated. In addition, testing was conducted on angle-ply laminates. Unsuccessful tests were conducted on a tougher matrix thermoplastic composite.An edge delamination specimen was also investigated. [15° _i/ – 15° _i]_S angle-ply laminates were fabricated with four implanted edge starter cracks. Both tension and compression tests were conducted. Difficulties in interpreting the results are discussed. The split cantilever beam and edge delamination results are compared.     

Stress-intensity factors for circular hollow section V-joints with a rack-plate chord

This study investigates the fatigue crack‐driving force, measured by the linear‐elastic stress‐intensity factors (SIFs), for a surface crack at the root of the welds in a thick‐walled, circular hollow section (CHS) V‐shape joint, typically installed in modern offshore jack‐up platforms. The primary (chord) member of the V‐joint consists of two half CHSs welded to both sides of a thick rack plate, while the secondary (brace) member adopts thick‐walled CHSs. The surface‐breaking crack considered in this study locates at the interface between the rack plate and the weld metal joining the half CHS, and represents an initial flaw introduced by lack of penetration in the welding procedure. The finite‐element model incorporates a very detailed, local crack‐front mesh in a global continuous mesh through a mesh‐tying procedure, which ensures displacement continuity between the independent master surface and the dependent slave surface. A simple plate model verifies the mesh‐tying procedure in computing the linear‐elastic stress‐intensity factors for two remote loading conditions. The computation of the stress‐intensity factors employs a linear‐elastic interaction integral approach. The comparison of the computed SIF values with a previous experimental measurement for a CHS T‐joint verifies the accuracy and feasibility of the interaction integral approach in computing SIF values for surface cracks in welded tubular connections. Subsequent numerical analysis on the gapped V‐joints examines the mixed‐mode SIF values for different loading conditions and includes an array of practical joint geometric parameters and crack sizes. The nondimensional mode I stress‐intensity factors generally increases with the following variations in the joint geometric parameters: an increase in the chord radius to the wall thickness ratio (γ=d₀/2t₀) , an increase in the brace diameter to the chord diameter ratio (β=d₁/d₀) , a decrease in the crack depth ratio (a/t) or an increase in the crack length c. The current study identifies a practical group of V‐joints that requires detailed treatment in the fatigue assessment procedure. These V‐joints adopt a large β ratio and demonstrate high mode‐mixity angles [ψ= tan^?1(K_II/K_I)] with correspondingly high mode I and mode II stress‐intensity factors.     

Three finite element analysis of semi-elliptical crack in high density poly-ethylene pipe subjected to internal pressure

The principal objective of this work is to analyze the severity of semi-elliptical crack defects and to study the degree of damage in the equipment under internal pressure during the crack propagation. The semi-elliptical cracks are considered in this work located in different position in the wall of poly-ethylene pipe. The tree finite element method based on the computation of the J integral was used to analyze the fracture behaviour of these structures. The effect of the position shape and size of the crack on the J integral was highlighted. The effects of strain rate and the temperature on the J integral values were also examined. The obtained results show that, whatever the material (strain rate) for a semi-elliptical crack, the J integral value has not an important variation with respect to the crack size. However, the energy for axial crack is more important compared to circumferential crack. The effect of the depth of the crack becomes important when the ratio (a/t) reaches a critical value of 0.6 (a/t = 0.6), especially when the ratio a/c is weak (semi-elliptical crack). We recall finally, that the temperature effect on circumferential cracks behaviour is more important compared to the axial cracks. It is also shown that in the wall of pipe, the internal cracks are more dangerous than the external cracks.     

Estimating working life for aircraft gas turbine engine disks at the stage of fatigue crack development. Part 2

It is shown that the cyclic cracking resistance in turbine disk materials is substantially affected by temperature, frequency, loading-cycle shape, and specimen thickness. Formulas describing fatigue crack growth rates are considered and calculations are done on the periods needed for fatigue cracks to grow to critical sizes from stress concentrators at various temperatures. Deceased. Translated from Problemy Prochnosti, No. 12, pp. 3–15, December, 1994.     

The T-stress solutions for through-wall circumferential cracks in cylinders subjected to general loading conditions

The elastic T-stress is a parameter used to define the level of constraint at a crack tip. It is important to provide T-stress solutions for practical geometries to apply the constraint-based fracture mechanics methodology. In the present work, T-stress solutions are provided for circumferential through-wall cracks in thin-walled cylinders. First, cylinders with a circumferential through-wall crack were analyzed using the finite element method. Three cylinder geometries were considered; defined by the mean radius of the cylinder (R) to wall thickness (t) ratios: R/t = 5, 10, and 20. The T-stress was obtained at eight crack lengths (θ/π = 0.0625, 0.1250, 0.1875, 0.2500, 0.3125, 0.3750, 0.4375, and 0.5000, θ is the crack half angle). Both crack face loading and remote loading conditions were considered including constant, linear, parabolic and cubic crack face pressures and remote tension and bending. The results for constant and linear crack face pressure were used to derive weight functions for T-stress for the corresponding cracked geometries. The weight functions were validated against several linear and non-linear stress distributions. The derived weight functions are suitable for T-stress calculations for circumferential cracks in cylinders under complex stress fields.     

On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

J integral solution for semi-elliptical surface crack in high density poly-ethylene pipe under bending

The goal of this work is to analyse the severity of semi-elliptical crack defects and to study the degree of damage in the poly-ethylene pipe in bending during the crack propagation. The semi-elliptical cracks are considered in this work located in different position in the wall of the pipe. The three finite element method based on the computation of the J integral was used to analyse the fracture behaviour of these structures. The effect of the position, shape and size of the crack on the J integral values was highlighted. The effects of strain rate and the temperature on the J integral values were also examined. The obtained results show that the strain rates have a strong influence on the J integral values especially for circumferential crack at higher bending moment. However, the energy for circumferential crack is more important compared to axial crack. The effect of the depth of the crack becomes important when the ratio (a/t) reaches a critical value of 0.6 (a/t = 0.6), especially when the ratio a/c is weak (semi-elliptical crack, a/c = 0.2) where the J integral values becomes independently of the crack depth, this conclusion is opposite to the above for the poly-ethylene pipe subjected to internal pressure. We recall finally, that the temperature effect on circumferential cracks behaviour is more important compared to the axial cracks at critical crack size (a/c = 0.2 and a/t = 0.6). It is also shown that in the wall of pipe, the internal cracks are more dangerous than the external cracks.     

Creep crack growth behavior of type 316L steel

The creep crack growth behavior of a 316L type stainless steel was studied at 600°C and 650°C using widely different specimen geometries. A strong emphasis was laid on crack initiation, early crack growth, and slow crack growth rates (a). The applicability of four load parameters, the stress intensity factor, the nominal stress, the reference stress, and the contour integral C^*, was investigated. Finite element calculations were made to compare the experimental load line displacement rates with the calculated values.It is shown that it is possible to correlate time to initiation (T_i) with C^*. The obtained experimental relation is not in full agreement with a theoretical expression derived from models for creeping solids. The reasons for this discrepancy are discussed. Furthermore, it is observed that there is no unique correlation between a and any of the four investigated load parameters, especially at low crack growth rates (a0^?3mm/h). At large crack growth rates (a?10^?2 mm/h) the apparent correlation between a and C^* is essentially due to the fact that the displacement rate is controlled by crack growth and not by the overall creep behavior of the specimens. A simple model based upon the data on crack initiation and the creep ductility exhaustion concept is shown to give results in reasonable agreement with the experiments.     

Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to K _II and non-singular T-stresses T _x and T _y parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0° to 90°. A compressive T _y increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T _x decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2T _x  = T _y  ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model.     

Non-linear fracture mechanics analyses of part circumferential surface cracked pipes

This paper provides engineering estimates of non-linear fracture mechanics parameters for pipes with part circumferential inner surface cracks, subject to internal pressure and global bending. Solutions are given in the form of two different approaches, the GE/EPRI approach and the reference stress approach. For the GE/EPRI approach, the plastic influence functions for fully plastic J solutions are tabulated based on extensive 3-D FE calculations using deformation plasticity, covering a wide range of pipe and crack geometries. The developed GE/EPRI-type fully plastic J estimation equations are then re-formulated using the concept of the reference stress approach for wider applications. The proposed reference stress based estimates are validated against detailed 3-D elastic-plastic and elastic-creep FE results. For a total of 26 cases considered in this paper, agreement between the proposed reference stress based J and C ^* estimates and the FE results is excellent. An important aspect of the proposed estimates is that they not only are simple and accurate but also can be used to estimate J and C ^* at an arbitrary point along the crack front.     

Thermal-shock-induced crack arrest of two low-alloy steels

Tests were performed on a C-Mn-Nb steel (E 36) and a C-Mn-Ni-Mo steel (A 50B) to determine the fracture toughness either at crack initiation, K_1c or at crack arrest, K_1a, under a very severe thermal shock. The experimental set-up was designed in such a way that it could provide enough flexibility to investigate various factors, including the specimen size effect in brittle fracture and the variations of K_1c or K_1a with temperature.

The thermal shock experiments were carried out either on small discs (thickness 19 mm) or on larger cylinders (height 220 mm) with an inner diameter and an outer diameter of 46 or 50 mm and 150 mm respectively, containing at their external periphery either a longitudinal sharp notch (0.04 mm) for the cylinders or a fatigue crack for the discs. These specimens are cooled to liquid nitrogen temperature until a homogeneous temperature distribution is reached. Then they are heated up by an induction coil set in the centre of the inner hole. The induction coils were designed to maintain purely radial heating of the specimens in order to induce axisymmetric thermal stresses. Typically, the experimental set-up is able to develop radial temperature gradients as large as 250°C in 20 s in the large cylinders and 500°C in 5 or 10 s in the thinner discs. Under the influence of these thermal gradients, which produce tensile hoop stress at the external periphery of the specimens, a crack is initiated from the notch or the initial fatigue precrack, which propagates very rapidly (-100 j1s) over a distance of a few centimetres and then stops.

The temperature distribution measured continuously during the experiments is used as the input for the numerical calculations. Finite element method calculations were performed to determine the variations of the hoop stress and those of the stress intensity factor across the wall thickness. Results obtained on both materi.als are given. In A50B steel it is shown that the apparent fracture toughness K_1c determmed on these large test pieces is smaller than the toughness measured on smaller convsntional specimens. This size effect is explained in terms of a local approach of brLttle cleavage fracture based on Weibull statistics.     

基于微观结构的热喷涂WC/Co涂层裂纹生长模拟

涂层微观结构特征直接影响涂层的寿命,基于涂层微观结构研究涂层裂纹扩展特征成为评价热喷涂层性能的重要问题.本文基于WC/Co涂层微观结构建立了有限元模型,并采用XFEM方法研究了单应力状态预存裂纹行了模拟,获得了涂层微观裂纹扩展的损伤规律.研究表明:在拉应力作用下,沿着WC-Co边界产生的应力集中是涂层裂纹产生的根源;WC/Co涂层浅表面(0.125b,b为涂层厚度)的水平裂纹对垂直拉应力敏感、吸收能量快,0.78b处的裂纹扩展后对应力响应迅速,因此0.125b与0.78b是WC/Co涂层裂纹生长的关键深度;在0.78b处,当初始裂纹角度0°～45°时,扩展位移逐渐减小,扩展偏转角增大,45°时存在能量积累导致角度快速偏转.在周期应力作用时,WC/Co涂层的疲劳周期随应变幅值增加而减小;应变幅值相同时,WC/Co涂层的疲劳周期随频率增加而增加.     

FATIGUE CRACK GROWTH FROM TWO-DIMENSIONAL SURFACE DEFECTS

Abstract The growth of semi-elliptical cracks emanating from single surface defects under cyclic bending loading conditions has been investigated. Experiments to determine crack shape development during fatigue have been conducted on specimens containing spark-machined starter defects of various shapes and sizes. The results appear to indicate that the size and shape of the initial starter defect only affects the developing crack shape until the crack depth is approximately 20% of the specimen thickness; upon reaching this depth, all crack shapes (independent of initial size and shape) appear to be very similar. A mathematical model, based on the Newman and Raju stress intensity solution for semi-elliptical cracks, has been utilised to predict effectively the shape of the cracks developing from the various single starter defects with aspect (a/c) ratios as large as 3.     

Quantitative Evaluation of Corrosion in a Thin Small-Bore Piping System Using Bobbin-Type Magnetic Camera

Nondestructive testing (NDT) methods have been developed to ensure the integrity of heat exchanger pipes. NDT systems can be used to not only locate cracks on the pipes but also evaluate the size and position of the cracks. A bobbin-type magnetic camera (BMC), an electromagnetic NDT system, was developed to inspect both the inner and outer diameters (ID and OD, respectively) for stress corrosion cracking on a small-bore piping system with a high spatial resolution at high speeds. In this paper, an algorithm that discriminates the ID cracks from the OD cracks and estimates the crack volume is proposed. Artificial ID and OD hole-type cracks which have diameter of 1–4.5 mm and depth of 0.3–27 mm were used to imitate the corrosions on a 1.27 mm thickness and 16.56 mm inner diameter copper alloy pipe to verify the proposed algorithm. The inspection results of the BMC with respect to excited frequencies from 1–9 kHz are presented. 100 % of the ID and OD cracks were discriminated, and their volumes were estimated with a standard deviation of 1.132 mm³ for volume from 1.00–9.01 mm³.     

Crack propagation in thick cylinders of 1/2 CrMoV steel during thermal shock

Cylinders of 1/2 CrMoV turbine casing steel of external diameter 92 mm and bore diameters of 53 and 19 mm were subjected to repeated thermal shock by internal quenching from 550° with water in order to determine growth characteristics for longitudinal and circumferential cracks. It was found that somewhere between 3000 and 10000 cycles cracks became dormant when about halfway through the wall thickness in as-cast material (ferrite +5% pearlite). This was due to a relatively high threshold for crack arrest (~12 MPa √m) together with the influence of multiple cracking. Coarse grained bainite, however, had a much lower threshold and behaved unstably, a single circumferential crack from a starter groove breaking through by ~ 1600 cycles. Tempering the bainite delayed complete penetration in the case of a single crack and caused crack arrest at ~3/4 of the wall thickness when multiple cracking occurred.

These results are interpreted in terms of the stress intensity profile developed at the peak temperature gradient and the effects of multiple cracking using previously published correction factors. In addition, cyclic crack growth history was examined using oxide dating, striation measurement and DC potential drop techniques. These measured growth histories were compared with those predicted by integrating a known crack growth law (from isothermal tests) along the stress intensity profile. Because crack depths were underestimated, the law requires modification, as ‘wet’ conditions prevail at the crack tip in the early stages.