The effect of an elliptical inclusion on a crack

The interaction between an elliptical inclusion and a crack is analyzed by body force method. The investigated stress field is simulated by superposing the fundamental solutions for a point force applied at a point in an infinite plate containing an elliptical inclusion. Based on numerical results, effects of the inclusion shape on the crack tip stress intensity factor are discussed. It is found that for small cracks emanating from a stress-higher point on the inclusion interface the stress intensity factors are mainly determined by the stresses, occurring at the crack starting point before the crack initiation, and the inclusion root radius, besides the crack length. However, for the cracks occurring in a stress-lower region around the inclusion, it is difficult to characterize the effect of the inclusion geometry on the stress intensity factors of small cracks by the inclusion root radius alone. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mixed mode fatigue growth of curved cracks emanating from fastener holes in aircraft lap joints

The finite element alternating method is extended further for analyzing multiple arbitrarily curved cracks in an isotropic plate under plane stress loading. The required analytical solution for an arbitrarily curved crack in an infinite isotropic plate is obtained by solving the integral equations formulated by Cheung and Chen (1987a, b). With the proposed method several example problems are solved in order to check the accuracy and efficiency of the method. Curved cracks emanating from loaded fastener holes, due to mixed mode fatigue crack growth, are also analyzed. Uniform far field plane stress loading on the plate and sinusoidally distributed pin loading on the fastener hole periphery are assumed to be applied. Small cracks emanating from fastener holes are assumed as initial cracks, and the subsequent fatigue crack growth behavior is examined until long arbitrarily curved cracks are formed near the fastener holes under mixed mode loading conditions.     

ELASTIC-PLASTIC FINITE ELEMENT ANALYSES OF CRACKED NOTCHES IN PLATES UNDER MIXED-MODE LOADING

Plates containing inclined elliptical notches with and without cracks are analysed for five different major axis inclinations, namely, θ equal to 0, 11.25, 22.5, 33.75 and 45?. Short cracks emanating from the roots of such inclined circular and elliptical notches are analysed. Under various mixed-mode loading conditions, when cracks are present, a simple method is described for the evaluation of the Mode I and Mode II stress intensity factors, for the elastic state. Values of the J integral along three different contours are also evaluated in the elastic and elastic-plastic states, as well as the Mode I and Mode II components of the crack tip opening displacenient (CTOD), the maximum principal stresses, the maximum average equivalent plastic strains and the location of the elements in which they occur. Comparisons of the different loading conditions are presented and the implications of the effects of mixed-mode loading on fracture and fatigue crack propagation are discussed.     

Calculation of mixed mode stress intensity factors for an elliptical subsurface crack under arbitrary normal loading

Normal loading causes mixed fracture modes in an elliptical subsurface crack because of the nonsymmetrical geometry with respect to the crack face. In this paper, mixed mode weight functions (MMWFs) for elliptical subsurface cracks in an elastic semi‐infinite space under normal loading are derived. Reference mixed mode stress intensity factors (MMSIFs), calculated by finite element analysis, under uniform normal loading are used to derive MMWFs. The cracks have aspect ratios and crack depth to crack length ratios of 0.2–1.0 and 0.05 to infinity, respectively. MMWFs are used to calculate MMSIFs for any point of the crack front under linear and nonlinear two‐dimensional (2D) loadings. So, in order to evaluate the fatigue crack growth phenomenon under complicated 2D stress distributions, MMWFs can be easily used. The comparison between the MMSIFs obtained from the MMWFs and finite element analysis indicates high accuracy.     

Numerical and experimental evaluation of SIF for threaded connectors

This paper presents a methodology for fatigue crack growth analysis in tubular threaded connectors. A solution for stress intensity factor for semi-elliptical surface cracks emanating from a thread root in a screw connector is also discussed in the paper. The solution is based on a mixed approach incorporating weight function and finite element methods. The weight functions used are the universal functions for cracks in mode I and these are linked with a thread through-thickness stress distribution obtained from finite element analysis to produce a stress intensity factor for a crack at the critical tooth of a thread. The resulting crack growth data are then validated experimentally.     

Arbitrary branched and intersecting cracks with the extended finite element method

Extensions of a new technique for the finite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended finite element method (X‐FEM) allows the representation of crack discontinuities and voids independently of the mesh. A standard displacement‐based approximation is enriched by incorporating discontinuous fields through a partition of unity method. A methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed. Computation of the stress intensity factors (SIF) in different examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique. Copyright © 2000 John Wiley & Sons, Ltd.     

Cyclic plasticity near a cracklike elliptical flaw

An elastic-plastic analysis of a cracklike elliptical flaw under cyclic tensile loading is discussed. A highly efficient numerical approach combining aspects of the finite element and boundary collocation methods was developed to allow accurate solution detail in the root region of the flaw. Conditions of localized yielding at the flaw root is the focus of the work with applied stress levels small relative to yield stress and plastic zone dimensions comparable to the root radius of curvature. The flaw is considered isolated in an infinite sheet under plane strain constraint. Numerical results are given for the stress and strain distributions and the plastic zone changes during a constant amplitude cyclic loading. These elastic-plastic results are compared with the predictions of elastic and fully plastic analysis and also with sharp crack solutions.     

Fatigue cracks emanating from sharp notches in high-strength aluminium alloys: The effect of loading direction, kinking, notch geometry and microstructure

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches was investigated. To this purpose, an experimental campaign has been conducted on Al-7075–T651 specimens carrying notches with aperture angles of 45°, 90°, and 135°. In order to investigate the role of microstructure texture, specimens were extracted from the plates with the main axis either in the longitudinal rolling direction (L-samples) or in the transversal direction (T-samples), or 45° inclined with respect to both directions (LT-samples). The effect of stress amplitude was investigated by performing tests at two load levels. Three loading directions θ = 0°, 45° and 90° were considered. Some specimens experienced pure Mode I loading condition, whereas the remaining ones were subjected to combined Mode I and Mode II loading condition. The crack deflection induced by the variation in loading direction was determined by measuring the kinking angle. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors (SIF) of straight cracks were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. On the contrary, a finite element model has been built up to derive the SIFs at the tip of the kinked cracks. The influence of K_II on the crack propagation was discussed on the basis of theoretical and semi-empirical models. It has been found that (i) the crack initiation at the notch root occurred in mixed mode conditions, (ii) a decreasing Mode II component with growing crack length was observed under initial loading direction θ₀ = 45° and θ₀ = 90°, (iii) a crack deflection was observed after 45° rotation of the initial loading direction; a good prediction of the kinking angle was obtained using the maximum tangential stress criterion, and (iv) a fairly good rationalization of all the collected crack growth rate data is obtained if the driving force for crack propagation is expressed in terms of K_I.     

Stress intensity factors at tips of branched cracks under various loadings

Several papers have been published on branched cracks by using various analytical methods, but most of them are concerned with special crack geometries or special loading conditions, and often give unreliable values for cracks with short branches or with small branching angles. The purpose of this paper is to give reliable formulae and new results of the stress intensity factors of various branched cracks in a wide plate. The analysis is based on the body force method combined with a perturbation procedure, and the stress intensity factors at the tips of all the branches and the main crack are given by power series formulae. Numerical results for typical branched cracks are discussed.     

Stress intensity factors for cracks at the vertex of a rounded V-notch

The method of singular integral equations was applied to determine the stress intensity factors for a system of cracks emanating from the vertex of an infinite rounded V-notch subjected to symmetric loading. The numerical values were obtained for two cases—the case of a single crack and the case of a system of two cracks of equal length. The influence of the rounding radius of the vertex of the notch and its opening angle on the stress intensity factors at the crack tips was analyzed. The solution obtained as a result has a general nature—the stress intensity factors at the crack tip are expressed as a function of the V-notch stress intensity factor and, hence, this solution could be treated as an asymptotic relation for finite bodies with deep V-notches subjected to symmetric loads.     

MIXED-MODE FATIGUE THRESHOLDS

Abstract— Near threshold fatigue crack growth under mixed-mode loading and elastic plane-strain conditions has been studied in 316 stainless steel in laboratory air at room temperature. Particular emphasis was placed on the influence of the mode II component. Crack growth from the starter crack, although initially coplanar, branches to be perpendicular to the maximum normal stress. However the threshold for the branched crack growth is controlled not only by mode I displacement, but also by the mode II component. Upper and lower bound curves are obtained for the threshold condition and discussed in terms of crack tip reversed plastic deformation, crack surface rubbing and oxide-induced closure. A theoretical method for predicting the lower bound curve is proposed and compared with the maximum normal stress and strain energy density criteria. The new theory shows the best agreement with experimental results, giving a safe prediction for design purposes.     

Stochastic XFEM fracture and crack propagation behavior of an isotropic plate with hole emanating radial cracks subjected to various in-plane loadings

In this article, the statistics of fracture response in terms of the mean and coefficient of variation of mixed mode stress intensity factor (SIF) of an isotropic plate with hole emanating radial cracks and crack growth subjected to in-plane mechanical tensile, shear, and combined loading is evaluated. The random system parameters, such as normalized crack length, crack angle, and normalized radius of hole, are assumed as uncorrelated random variables. The basic formulation is based on the extended finite-element method with level set method combined with second-order perturbation method. The effects of the normalized radius of the hole, normalized crack length, crack angles, different positions of the hole with cracks, and in-plane loadings on the statistics of mixed mode SIF with input random system parameters are analyzed.     

Cracks emanating from a circular hole under biaxial load

The principle of linear superposition has been employed in studying cracks emanating from a circular hole in a finite sheet under biaxial loading. The series type analytical solution around the crack tip has been combined with numerical analysis for the purpose of this investigation. The method presented here makes it possible to demonstrate both analytically and numerically, the effects of applied load biaxiality on the stress intensity factor. The ratio of the hole-radius-to-crack-length (R/c) is shown to determine the effect of the applied load biaxiality on the crack emanating from a circular hole in a finite sheet.     

Determination of crack surface displacements for cracks emanating from a circular hole using weight function method

Cracks emanating from a circular hole are of significant engineering importance, especially in aerospace industry. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue life predictions. The purpose of this paper is to provide an efficient and accurate closed‐form weight function approach to the calculation of crack surface displacements for radial crack(s) emanating from a circular hole in an infinite and finite‐width plate. Results were presented for two loading conditions: remote applied stress and uniform stress segment applied to crack surfaces, and extensively compared to recent studies using other methods in the literature. Both single and double radial cracks were considered, and also the effect of finite plate width on crack surface displacements has been investigated. A brief assessment was made on an engineering estimation of displacements based on a correction of stress intensity factor ratio. It has been demonstrated that the Wu‐Carlsson closed‐form weight functions are very efficient, accurate and easy‐to‐use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

Weight function,stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

Periodic collinear edge hole cracks and arbitrary small cracks emanating from collinear holes, which are two typical multiple site damages occurred in the aircraft structures, are studied by using the weigh function method. An explicit closed form weight function for periodic edge hole cracks in an infinite sheet is obtained and further used to calculate the stress intensity factor and crack opening displacement for various loading cases. Compared to finite element method, the present weight function is accurate and highly efficient. The interactions of the holes and cracks on the stress intensity factor and crack opening displacement are quantitatively determined by using the present weight function. An approximate weight function method is also proposed for arbitrary small cracks emanating from multiple collinear holes. This method is very useful for calculating the stress intensity factor for arbitrary small cracks.     

Superposition method for calculating singular stress fields at kinks, branches and tips in multiple crack arrays

A method is developed for calculating stresses and displacements around arrays of kinked and branched cracks having straight segments in a linearly elastic solid loaded in plane stress or plain strain. The key idea is to decompose the cracks into straight material cuts we call `cracklets', and to model the overall opening displacements of the cracks using a weighted superposition of special basis functions, describing cracklet opening displacement profiles. These basis functions are specifically tailored to induce the proper singular stresses and local deformation in wedges at crack kinks and branches, an aspect that has been neglected in the literature. The basis functions are expressed in terms of dislocation density distributions that are treatable analytically in the Cauchy singular integrals, yielding classical functions for their induced stress fields; that is, no numerical integration is involved. After superposition, nonphysical singularities cancel out leaving net tractions along the crack faces that are very smooth, yet retaining the appropriate singular stresses in the material at crack tips, kinks and branches. The weighting coefficients are calculated from a least squares fit of the net tractions to those prescribed from the applied loading, allowing accuracy assessment in terms of the root-mean-square error. Convergence is very rapid in the number of basis terms used. The method yields the full stress and displacement fields expressed as weighted sums of the basis fields. Stress intensity factors for the crack tips and generalized stress intensity factors for the wedges at kinks and branches are easily retrieved from the weighting coefficients. As examples we treat cracks with one and two kinks and a star-shaped crack with equal arms. The method can be extended to problems of finite domain such as polygon-shaped plates with prescribed tractions around the boundary.     

Estimations of the T-stress for small cracks at notches

The T-stress is increasingly being recognized as an important additional stress field characterizing parameter in the analyses of cracked bodies. Using T-stress as the constraint parameter, the framework of failure assessments including the constraint effect has been established; and the effect of T-stress on fatigue crack propagation rate has been investigated by several researchers. In this paper, a simple method for determining the T-stress for small notch-emanating cracks is presented. First, the background on the T-stress calculation using the superposition principle and the similarities between the elastic notch-tip stress fields described by two parameters: the stress concentration factor (K_t) and the notch-tip radius (ρ), are summarized. Then, the method of estimating T-stress for both short and long cracks at the notches is presented. The method is used to predict T-stress solutions for cracks emanating from an internal hole in a wide plate, and cracks emanating from an U-shaped edge notch in a finite thickness plate. The results are compared to the T-stress results in the literature, and the T-stresses solutions obtained from finite element analysis. Excellent agreements have been achieved for small cracks. The method presented here can be used for a variety of notch crack geometries and loading conditions.     

STRESS INTENSITY FACTORS FOR SURFACE CRACKS AT A HOLE BY A THREE-DIMENSIONAL WEIGHT FUNCTION METHOD WITH STRESSES FROM THE FINITE ELEMENT METHOD

Stress intensity factors for semielliptical surface cracks emanating from a circular hole are reported in this paper. The three-dimensional weight function method with three-dimensional finite element solutions for the uncracked stress distribution is used for the analysis. Two different loading conditions, i.e. remote tension and wedge loading, are considered for a wide range of geometrical parameters. Both single and double surface cracks are studied and compared with other solutions available in the literature. Typical crack opening displacements are also provided.     

Dissolution driven crack branching in polycarbonate

Stress corrosion, in the form of chemically assisted crack growth, in polycarbonate is examined with focus on crack branching characteristics. Cracks with finite width are observed; this is to be expected for dissolution driven cracking. The cracks branched repeatedly and crack widths before and after branching are measured. Both symmetric and asymmetric branching is found. The dissolution rate is assumed to be a linear function of the strain along the crack surface. In the literature, it is proposed that the crack width is proportional to the square of the mode I stress intensity factor. Energy considerations lead to that the sum of branch widths must equal the width of the unbranched crack. The results from this study correspond fairly well with this assumption. The branching angle is found to be 32°± 12°, which is in line with results for sharp cracks reported in the literature. The mean growth direction of the branches is found to deviate slightly from the expected straight. No significant correlation between angles and crack widths is found. The scatter in results is mainly addressed to the inherent perturbation sensitivity of stress corrosion cracking. Also numerically simulations of crack branching is performed. These results show promising agreement with the experiments.     

Strong interactions of morphologically complex cracks

Previous works on crack morphology have focused on such cracks as a kinked crack, a branched crack, and an inclined array of identical branched cracks. In this paper, the strong interactions between two cracks in two-dimensional solids under remote tension are investigated. Three morphological types are considered: kinks, branches and zigzags. The method of analysis follows the singular integral equation approach in which the deviations from the main cracks are modeled by distributions of dislocations. Investigations are made on the dependence of the stress intensity factors on the asymmetry of the crack configuration, the crack separation, and the shape of the cracks. The results show that (i) strong interactions can have significant effects on the mode mixity of the stress intensity factors, (ii) a small asymmetry of the crack configuration can cause significant changes to the stress intensity factors, and (iii) zigzag cracks with rectangular steps reduce the stress intensity factors more efficiently than those with triangular or trapezoidal steps.