Stress intensity factors for slanted through-wall cracks based on elastic finite element analyses

Based on detailed 3‐dimensional (3‐D) elastic finite element (FE) analyses, the present paper provides stress intensity factors (SIFs) for plates with slanted through‐wall crack (TWC) and cylinders with slanted circumferential TWC. Regarding loading conditions, axial tension was considered for the plates, whereas axial tension, global bending and internal pressure were considered for the cylinders. To cover a practical range, the geometric variables affecting the SIF were systematically varied. Based on FE results, SIFs along the crack front, including the inner and outer surface points, were provided. The present results can be used to evaluate the fatigue crack growth or stress corrosion cracking behaviour of a slanted TWC and furthermore to perform detailed Leak‐Before‐Break analysis considering a more realistic crack shape.     

Successive 3D FE analysis technique for characterization of fatigue crack growth behavior in composite-repaired aluminum plate

An analytical approach using successive finite element analysis technique was conducted to characterize the fatigue crack growth behavior of pre-cracked aluminum plates reinforced with composite patches. For single-sided repairs, due to the asymmetry and the presence of out-of-plane bending, crack front shape would become skewed curvilinear started from a uniform through-crack profile, as observed from previous studies. As the stress intensity factor (SIF) calculated at the crack tip is much influenced by crack front shape, it is necessary to predict the actual crack front shape evolution and take it into account for the accurate analysis of fatigue behavior. Present procedure performed a three-dimensional geometrically nonlinear finite element analysis to determine the SIF distribution at a set of points along the crack front, and then estimated the crack growth increments at these points by invoking a fatigue crack growth rate relationship (power-law relationship). A new crack front was then established for the next step by using a relevant remeshing scheme. Through conducting this procedure successively, the crack path of the patched plate as well as the fatigue life was evaluated with sufficient accuracy. The analytical predictions of both the crack front shape evolution and the fatigue life were in good agreement with the experimental observations.     

External surface cracks in shells under cyclic internal pressure

The stress analysis and fatigue crack growth behaviour of a part‐through‐cracked double‐curvature thin‐walled shell is examined. An external surface crack is assumed to lie in one of the principal curvature planes of the shell, and to present a semi‐elliptical shape. The stress intensity factors (SIFs) along the crack front for different elementary opening stresses acting on the crack faces are determined through a three‐dimensional finite element analysis. Then approximate values of SIF in the case of a cracked pressure vessel are computed by employing the above results together with the superposition principle and the power series expansion of the actual opening stress. Finally, a numerical simulation procedure is carried out to predict the crack growth under cyclic internal pressure. Some results are compared with those of other authors.     

Extraction of stress intensity factors for 3D small fatigue cracks using digital volume correlation and X-ray tomography

This paper describes a methodology used to compute stress intensity factor values along the curved front of a fatigue crack inside a nodular cast iron. An artificial defect is introduced at the surface of a small sample. The initiation and growth of a fatigue crack from this defect during constant amplitude cycling is monitored in situ by laboratory X-ray tomography. The method for processing the 3D images in order to compute SIF values is described in detail. The results obtained show variations of the stress intensity factor values along the crack front.     

Applying strain energy density factor theory to propagation estimating of surface crack in tubular T-joints

The propagation direction of a surface crack in tubular T-joints and the surface crack profile are studied in this paper. By using Photoelasticity and Finite Element method, the distribution of Stress Intensity Factor (SIF) along the front edge of the prefabricated semi-elliptic surface cracks at the hot spots of tubular T-joints is obtained. The results show that the cracks are subjected to mix-mode loading, and the distribution of SIF along the front edge of the crack depends not only on a/T, the ratio of crack depth to the thickness of chord wall, but also largely on shape ratio a/c, the ratio of depth of the crack a to its length c. It can also be predicted that there exists a certain precedent propagation direction for a surface crack with a certain a/c. According to the Strain Energy Density Factor theory the condition of constant strain energy density factor S on the front edge of the crack will be enforced on each point of the prosective crack profile, so that the crack profile can be pre-estimated.     

新的估算表面裂纹应力强度因子经验公式

该文给出了新的估算拉伸和纯弯曲载荷下表面裂纹应力强度因子的经验公式。根据疲劳裂纹扩展的数值模拟结果确定强度因子分布函数;利用按已知应力强度因子分布函数求裂纹形状及相应应力强度因子的方法计算给定尺寸的表面裂纹的应力强度因子;通过对数值结果的曲线回归得到估算表面裂纹应力强度因子经验公式。利用该公式对有限厚度和宽度平板内表面裂纹的应力强度因子进行了估算,并与已知的半椭圆形表面裂纹的应力强度因子解进行了比较。该文结果为估算表面裂纹应力强度因子提供了一种新的途径。     

Near-threshold fatigue propagation of physically through-thickness short and long cracks in a low alloy steel

In this paper, the near-threshold fatigue behavior of physically through-thickness short cracks and of long cracks in a low alloy steel is investigated by experiments in ambient air. Physically through-thickness short fatigue cracks are created by gradually removing the plastic wake of long cracks in compact tension specimens. The crack closure is systematically measured using the compliance variation technique with numerical data acquisition and filtering for accurate detection of the stress intensity factor (SIF) at the crack opening. Based on the experimental results, the nominal threshold SIF range is shown to be dependent on the crack length and the characteristic of the crack wake which is strongly dependent on the loading history. The effective threshold SIF range and the relation between the crack propagation rate and the effective SIF range after the crack closure correction are shown to be independent on crack length and loading history. The shielding effect of the crack closure is shown to be related to the wake length and load history. The effective threshold SIF range and the relationship between the crack growth rate and the effective SIF range appear to be unique for this material in ambient air. These properties can be considered as specific fatigue properties of the couple material/ambient air environment.     

Non‐planar mixed‐mode growth of initially straight‐fronted surface cracks,in cylindrical bars under tension,torsion and bending,using the symmetric Galerkin boundary element method‐finite element method alternating method

In this paper, the stress intensity factor (SIF) variations along an arbitrarily developing crack front, the non‐planar fatigue‐crack growth patterns, and the fatigue life of a round bar with an initially straight‐fronted surface crack, are studied by employing the 3D symmetric Galerkin boundary element method‐finite element method (SGBEM‐FEM) alternating method. Different loading cases, involving tension, bending and torsion of the bar, with different initial crack depths and different stress ratios in fatigue, are considered. By using the SGBEM‐FEM alternating method, the SIF variations along the evolving crack front are computed; the fatigue growth rates and directions of the non‐planar growths of the crack surface are predicted; the evolving fatigue‐crack growth patterns are simulated, and thus, the fatigue life estimations of the cracked round bar are made. The accuracy and reliability of the SGBEM‐FEM alternating method are verified by comparing the presently computed results to the empirical solutions of SIFs, as well as experimental data of fatigue crack growth, available in the open literature. It is shown that the current approach gives very accurate solutions of SIFs and simulations of fatigue crack growth during the entire crack propagation, with very little computational burden and human–labour cost. The characteristics of fatigue growth patterns of initially simple‐shaped cracks in the cylindrical bar under different Modes I, III and mixed‐mode types of loads are also discussed in detail.     

Sustained Mode I and Mode II fatigue crack growth in flat plates

This study was conducted to contribute to the understanding of fatigue crack growth under mixed mode loading. This was accomplished by developing and analyzing a flat plate specimen capable of maintaining crack growth on a plane oblique to the direction of the applied load. Several specimens were built and exposed to controlled fatigue loading in the laboratory. These specimens were then modeled using finite elements to determine the stress intensity factors (SIF). For the “Mode I/Mode II” specimens developed, the crack was forced to grow in a direction other than perpendicular to the load. The resulting crack front did not remain straight and flat, but stabilized into a curved or warped shape. Based on finite element analyses of these curved specimen cracks, it is concluded that the SIR were predominantly Mode I, with the Mode II and III SIR being negligible.     

Effect of vertex singularities on stress intensities near plate free surfaces

The stress intensity factor (SIF) distribution along the front of a through‐the‐thickness crack is significantly influenced by the presence of the 3D corner (vertex) singularities. All past 3D finite element studies indicated that for mode I, SIF rapidly decreases near the free surface and for mode II, it sharply increases. From the previous numerical simulations, it is unclear what the limiting values of SIF near the surface are and whether these values are infinite or bounded at the vertex point. In this paper, we conduct a careful finite element study and propose a theoretical equation, which describes the SIF behaviour near the vertex. We demonstrate that the asymptotic behaviour of SIF near the surface is governed by the difference in the strength of the corner and edge singularities. Furthermore, we validate our numerical approach and calculations by utilising the invariant properties of J‐integral.     

Weld root crack propagation under mixed mode I and III cyclic loading

This study examined fatigue propagation behaviour and fatigue life of weld root cracks under mixed mode I and III loading. Fatigue tests were performed on butt-welded joints with a continuous lack-of-penetration (LOP) inclined at angles of 0°, 15°, 30° or 45° to the normal direction of the uniaxial cyclic load. Branch and/or co-planar crack propagation was observed, depending on the initial mode I stress intensity factor (SIF) range. Co-planar crack propagation predominated when the SIF range was large. The fatigue crack propagation mode affected fatigue life; the life of branch crack propagation was longer than that of co-planar crack propagation. Using an initial equivalent SIF range based on a maximum strain energy release rate criterion, the results obtained from the 0°, 15°, 30°, and 45° specimens indicated almost the same fatigue lives, despite the different inclination angles.     

Stress intensity factor estimation for unbalanced rotating cracked shafts by artificial neural networks

The knowledge of the stress intensity factor (SIF) values along a crack front is essential to calculate the crack growth rate and the remaining life of a mechanical component. In the case of a rotating shaft, usually it presents disalignments, which modify the SIF data with regard to a balanced one. This paper presents the use of an artificial neural network (ANN) for estimating the SIF at the crack front in an unbalanced shaft under rotating bending, previously, a quasi‐static numerical (finite element) model, which simulates a rotating shaft, has been developed to create the training cases for the ANN. The obtained results allow to study the influence of the unbalance of rotating shafts in the crack breathing mechanism and will allow to predict the influence of this behaviour on the values of the SIF and in the propagation of cracks.     

Crack closure in fibre metal laminates

GLARE is a fibre metal laminate (FML) built up of alternating layers of S2-glass/FM94 prepreg and aluminium 2024-T3. The excellent fatigue behaviour of GLARE can be described with a recently published analytical prediction model. This model is based on linear elastic fracture mechanics and the assumption that a similar stress state in the aluminium layers of GLARE and monolithic aluminium result in the same crack growth behaviour. It therefore describes the crack growth with an effective stress intensity factor (SIF) range at the crack tip in the aluminium layers, including the effect of internal residual stress as result of curing and the stiffness differences between the individual layers. In that model, an empirical relation is used to calculate the effective SIF range, which had been determined without sufficiently investigating the effect of crack closure. This paper presents the research performed on crack closure in GLARE. It is assumed that crack closure in FMLs is determined by the actual stress cycles in the metal layers and that it can be described with the available relations for monolithic aluminium published in the literature. Fatigue crack growth experiments have been performed on GLARE specimens in which crack growth rates and crack opening stresses have been recorded. The prediction model incorporating the crack closure relation for aluminium 2024-T3 obtained from the literature has been validated with the test results. It is concluded that crack growth in GLARE can be correlated with the effective SIF range at the crack tip in the aluminium layers, if it is determined with the crack closure relation for aluminium 2024-T3 based on actual stresses in the aluminium layers.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

Crack retardation equations for the propagation of branched fatigue cracks

The stress intensity factors (SIF) associated with branched fatigue cracks can be considerably smaller than that of a straight crack with the same projected length, causing crack growth retardation or even arrest. This crack branching mechanism can quantitatively explain retardation effects even when plasticity induced crack closure cannot be applied, e.g. in high R-ratio or in some plane strain controlled fatigue crack growth problems. Analytical solutions have been obtained for the SIF of branched cracks, however, numerical methods such as Finite Elements (FE) or Boundary Elements (BE) are the only means to predict the subsequent curved propagation behavior. In this work, a FE program is developed to calculate the path and associated SIF of branched cracks, validated through experiments on 4340 steel ESE(T) specimens. From these results, semi-empirical crack retardation equations are proposed to model the retardation factor along the crack path. The model also considers the possible interaction between crack branching and other retardation mechanisms.     

Sickle-shaped crack in a round bar under complex Mode I loading

A sickle‐shaped surface crack in a round bar under complex Mode I loading is considered. First, the stress‐intensity factor (SIF) along the front of the flaw is numerically determined for five elementary Mode I stress distributions (constant, linear, quadratic, cubic and quartic) directly applied on the crack faces. The finite element method and linear elastic fracture mechanics concepts are employed. Then, a numerical procedure to calculate approximate values of SIF for a complex Mode I stress distribution on the crack faces is proposed based on both the power series expansion of the function describing such a stress distribution and the superposition principle. In order to validate the results obtained through the above procedure, a comparison with numerical data available in the literature is made.     

SIFs of CCT plate repaired with single‐sided composite patch

Constant amplitude load fatigue tests are performed to obtain crack propagation data for LF2‐aluminium centre crack tension (CCT) plates un‐repaired and repaired with single‐sided composite patches. Then, the James–Anderson method, an experimental method, is used to obtain the stress intensity factor (SIF) formula for the repaired CCT plates with carbon–fibre composite patches. At last, crack propagation life prediction and finite element (FE) calculation are carried out to validate the experimental SIF formula. It is shown that the present SIF formula can exactly predict the fatigue‐crack propagation life of the patched CCT plates and is close to the FE results, which implies the effectivity of the experimental SIF formula in the present paper.     

A modelling technique for calculating stress intensity factors for structures reinforced by bonded straps. Part II: Validation

In this second part of the two-part paper validation of the 2D FE modelling technique described in the first part is presented for a range of test configurations. Each mechanism that influences crack growth behaviour of strap reinforced structures is modelled for different substrate geometries, strap materials and dimensions in order to test the accuracy and robustness of the methodology. First, calculated through-thickness strain energy release rate distribution is compared with the result of a 3D FE model to validate this 2D model. Second, calculated disbond areas, thermal residual stresses and their redistribution with crack propagation are validated against experimental measurements. Third, influence of geometric nonlinearity and the need to use the alternate analysis method described in part I are demonstrated by examples, and errors generated by not following this analysis rule are given. Finally, using the 2D model calculated stress intensity factors, fatigue crack growth rates and lives are predicted for different specimens, strap materials and applied stress levels and are compared with the experimental tests. Good or acceptable agreement has been achieved for each case.     

Stress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimen

Stress intensity factor solutions for semi-elliptic surface and quarter-elliptic corner cracks emanating from a semi-circular notch in a tension specimen are presented. A threedimensional finite-element analysis in conjunction with the equivalent domain integral was used to calculate stress intensity factors (SIF). SIF solutions for surface or corner crack (crack length to depth ratio of 2) at a notch are presented for a wide range of crack sizes and notch radii. Results showed that the SIF are larger for larger crack lengths and for larger notch radii. The SIF are nearly constant all along the crack front for deep surface cracks and for all corner cracks analysed.     

Sickle-shaped cracks in metallic round bars under cyclic eccentric axial loading

In the present paper, the fatigue propagation of an initial sickle-shaped surface crack in a metallic round bar under eccentric axial loading acting perpendicular to the crack plane is examined. Firstly, the stress-intensity factor (SIF) along the crack front is determined through a three-dimensional finite element analysis and the one-quarter point displacement method, for different values of the loading eccentricity. Then, the fatigue behaviour of the cracked bar is numerically analysed by a step-by-step procedure based on the Paris–Erdogan law. The results are plotted in terms of crack paths, intersection angle and crack depth evolution, by varying the loading eccentricity.