Stress intensity factors of sickle-shaped cracks in cylindrical bars

The stress intensity factor at the deepest point of sickle-shaped cracks is calculated for a constant, a linear and a quadratic locally varying stress distribution by use of a weight function derived from finite element results.     

Stress intensity factors for three‐dimensional surface cracks using enriched finite elements

The analysis of three‐dimensional crack problems using enriched crack tip elements is examined in this paper. It is demonstrated that the enriched finite element approach is a very effective technique for obtaining stress intensity factors for general three‐dimensional crack problems. The influence of compatibility, integration, element shape function order, and mesh refinement on solution convergence is investigated to ascertain the accuracy of the numerical results. It is shown that integration order has the greatest impact on solution accuracy. Sample results are presented for semi‐circular surface cracks and compared with previously obtained solutions available in the literature. Good agreement is obtained between the different numerical solutions, except in the small zone near the free surface where previously published results have often neglected the change in the stress singularity at the free surface. The enriched crack tip element appears to be particularly effective in this region, since boundary conditions can be easily imposed on the stress intensity factors to accurately represent the correct free surface condition. Copyright © 2002 John Wiley & Sons, Ltd.     

An assessment of stress intensity factors for surface flaws in a tubular member

In the safety assessment of pressure vessels and pipes with circumferential surface cracks, it is often necessary to consider fatigue crack propagation and fracture among the possible modes of failure. The stress intensity factors at crack tips are important parameters for estimating residual life and criticality. The purpose of this paper is to present a method to calculate the mode I stress intensities for semi-elliptical cracks in pipes. This method uses the finite element technique to analyse a crack but does not require the crack to be modelled explicitly. This method is ideal for use with either fatigue life calculations or use with structural optimisation processes. Accurate results are obtained using only a relatively small number of degrees of freedom without the need to explicitly mesh cracks. In this paper a range of examples are presented to demonstrate the accuracy of this method.     

Stress intensity factors for edge-cracked plates under arbitrary loading

Stress intensity factors for edge-cracked plates are commonly available for long plates with height-to-width ratios H / W  > 1. In the present note, stress intensity factor solutions are reported for short plates in tension and bending. In order to allow the computation of stress intensity factors under arbitrary loadings, two possibilities are considered. For the treatment of known stress distributions in the uncracked plate, the weight function is an appropriate tool. For arbitrarily prescribed tractions at the plate ends, a superposition method based on sectionally constant tractions is described and illustrated by examples.     

Stress intensity factors for cracked I-beams

We present simple, closed-form expressions for stress intensity factors for cracked I-beams subjected to a bending moment. The estimates are based on the elementary strength theory for cracked beams forwarded by Herrmann and co-workers, coupled with dimensional considerations and a finite element calibration. The expressions given here are valid for the case when the crack has propagated through the flange and into the web of the beam. The simple expressions are accurate to within 5% of detailed finite element calculations for the range of practical applicability. To further demonstrate the validity of the stress intensity factor expression, we measured fracture loads for cracked polymethyl methacrylate (PMMA) I-beams in four-point flexure. Using the failure loads and our expression for the stress intensity factor, we deduce the fracture toughness. The fracture toughness so-obtained results in excellent fracture correlation for the cracked I-beams.     

Stress intensity factors for tunnelling corner cracks under mode I loading

Stress intensity factors (SIFs) presented in the literature for corner cracks are limited to ideal quarter-circular and quarter-elliptical crack shapes. This paper presents SIF solutions for corner cracks that exhibit tunnelling, extending the range of corner crack shapes illustrated in the literature. Solutions were developed in a parametric form, obtained by empirically fitting polynomials to numerical values of SIF obtained from the FEM. A parameter was defined to quantify the extent of tunnelling. It was observed that crack shape has a significant effect on the SIF, so the consideration of equivalent quarter-circular cracks can produce inaccurate results when significant tunnelling occurs. SIF solutions for quarter-circular cracks are also presented and compared with those quoted in the literature.     

Stress intensity factors for cracks in thin plates

This paper presents stress intensity factor solutions for several crack configurations in plates. The loadings considered include internal pressure, and also combined bending and tension. The dual boundary element method is used to model the plate and mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. Several cases including centre crack, edge crack and cracks emanating from a hole in finite width plates are presented.     

Stress intensity factors for surface fatigue crack in a round bar under cyclic axial loading

In this paper, the surface fatigue crack growth shape for an initial straight-fronted edge crack in an elastic bar of circular cross-section is determined through experiments under pure fatigue axial loading. Three different initial notch depths are discussed. The relations of the aspect ratio (b/c) and relative crack depth (b/D) are obtained, and it is shown that there is a great difference in the growth of cracks with different initial front shapes and crack depths. Further, using the three-dimensional finite element method, the stress intensity factors (SIFs) are determined under remote uniform tension loading. Since the relationship of b/c and b/D changes during the fatigue crack growth, the SIFs are determined for different surface crack configurations.     

Stress intensity factors of a surface crack near an interface end

Due to the singular behavior of the stress field near the interface edge of bonded dissimilar materials, fracture generally initiates near the interface edge, or just from the interface edge point. In this paper, an edge crack near the interface, which can be considered as being induced by the edge singularity and satisfying two conditions, is analyzed theoretically, based on the singular stress field near the interface edge and the superposition principle. It is found that the stress intensity factor can be expressed by the stress intensity coefficient of the edge singular stress field, the crack length, the distance between the interface and the crack, as well as the material combination. Boundary element method analysis is also carried out. It is found that the theoretical result coincides well with the numerical result when the crack length is small. Therefore, the theoretical representation obtained by this study can be used to simply evaluate the stress intensity factor of an edge singularity induced crack for this case. However, when the crack length becomes larger than a certain value, a significant difference appears, especially for the case with large edge singularity.     

Stress intensity factors for a surface-breaking crack in a half-plane subject to contact loading

Modes I and II stress intensity factors are derived for a crack breaking the surface of a half-plane which is subject to various forms of contact loading. The method used is that of replacing the crack by a continuous distribution of edge dislocations and assume the crack to be traction-free over its entire length. A traction free crack is achieved by cancelling the tractions along the crack site that would be present if the half-plane was uncracked. The stress distribution for an elastic uncracked half-plane subject to an indenter of arbitrary profile in the presence of friction is derived in terms of a single Muskhelishvili complex stress function from which the stresses and displacements in either the half-plane or indenter can be determined. The problem of a cracked half-plane reduces to the numerical solution of a singular integral equation for the determination of the dislocation density distribution from which the modes I and II stress intensity factors can be obtained. Although the method of representing a crack by a continuous distribution of edge dislocations is now a well established procedure, the application of this method to fracture mechanics problems involving contact loading is relatively new. This paper demonstrates that the method of distributed dislocations is well suited to surface-breaking cracks subject to contact loading and presents new stress intensity factor results for a variety of loading and crack configurations.     

Mode I stress intensity factors for curved cracks in gears by a weight functions method

The most recent trend in power transmission design considers the damage-tolerant approach as one of the methods to obtain safe, reliable and light systems. This means that components containing cracks must be considered and analysed to understand the conditions that cause critical cracks and defects and their dimensions.
In this paper a cracked tooth of an automotive gearwheel is considered. A numerical procedure (based on the slice synthesis weight function method) to calculate the stress intensity factors of curved cracks due to bending loads is illustrated. The results are compared with those obtained by expensive finite element calculations. The agreement is satisfactory and the proposed technique proves to be very attractive from the point of view of time saving.
One example of an application to fatigue design practice is provided, namely the analysis of fatigue crack propagation in surface-treated gears. The results show the role played by residual stresses induced by carburizing and shot peening.     

Stress intensity factors and weight functions for deep semi-elliptical surface cracks in finite-thickness plates

ABSTRACT Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi-elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with a/t -values of 0.9 and 0.95 and aspect ratios ( a/c ) from 0.05 to 2. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for surface cracks with a/t = 0.6 and 0.8 to derive weight functions over the range 0.05 ≤  a/c  ≤ 2.0 and 0.6 ≤  a/t  ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.     

Stress intensity factors for surface cracks at countersunk holes

Fatigue crack growth from countersunk fastener holes loaded in remote tensile loading was studied using the transparent polymer PMMA. A single edge corner crack at the bottom of the plate and a single internal surface crack at the sharp intersection between the bore and the countersink were induced in the PMMA specimens by pre-cracking. The specimens were then fatigue tested under constant amplitude remote tensile loading and the ‘back-calculation’ method was used to determine stress intensity factors at several crack front locations. When variations in fatigue crack closure were taken into account, the experimental stress intensity factors agreed well with the computational results at selected crack fronts.     

Stress intensity factors for a mixed mode center crack in an anisotropic strip

An approach based on the continuous dislocation technique is formulated and used to obtain the Mode I and II stress intensity factors in a fully anisotropic infinite strip with a central crack. First, the elastic solution of a single dislocation in an anisotropic infinite strip is obtained from that of a dislocation in an anisotropic half plane, by applying an array of dislocations along the boundary of the infinite strip, which is supposed to be traction-free. The dislocation densities of the dislocation array are determined in such a way that the traction forces generated by the dislocation array cancel the residual tractions along the boundary due to the single dislocation in the half plane. The stress field of a single dislocation in the infinite strip is thus a superposition of that of the single dislocation and the dislocation array in the half plane. Subsequently, the elastic solution is applied to calculate the stress intensity factors for a center crack in an anisotropic strip. Crack length and material anisotropy effects are discussed in detail.     

Stress intensity factors of cracks emanating from a surface square hole in infinite body in tension

This paper deals with such a kind of surface crack problem with a same depth (called a liked‐plane crack problem for short). Based on the previous investigations on an internal rectangular crack and a surface rectangular crack in an infinite solid in tension and the hybrid displacement discontinuity method, a numerical approach for the liked‐plane crack problem is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the stress intensity factors (SIFs) of the liked‐plane crack problem. Specifically, SIFs of a pair of cracks emanating from a surface square hole in an infinite body in tension are investigated in detail.     

Weight functions and stress intensity factors for quarter-elliptical corner cracks in fastener holes

Approximate weight functions for a quarter‐elliptical crack in a fastener hole were derived from a general weight function form and two reference stress intensity factors. Closed‐form expressions were obtained for the coefficients of the weight functions. The derived weight functions were validated against numerical data by comparison of stress intensity factors calculated for several nonlinear stress fields. Good agreements were achieved. These derived weight functions are valid for the geometric range of 0.5 ≤a/c≤ 1.5 and 0 ≤a/t≤ 0.8 and R/t= 0.5; and are given in forms suitable for computer numerical integration. The weight functions appear to be particularly suitable for fatigue crack growth prediction of corner cracks in fastener holes and fracture analysis of such cracks in complex stress fields.     

Evaluating stress intensity factors of a surface crack in lubricated rolling contacts

The three-dimensional finite element method and the least-squares method were used to find the stress intensity factors (SIFs) of a surface crack in a lubricated roller. A steel roller on a rigid plane was modeled, in which a semi-elliptical surface crack is inclined at an angle ψ to the vertical axis. A distance c is set between the crack base and the roller edge. The results indicate that the mode-I SIF reaches the maximum value when the angle θ is equal to 0° (on the roller surface), and the mode-II SIF reaches the absolute maximum value when the angle θ is near or equal to 90° (inside the roller), where θ is the angle of the semi-ellipse from 0° to 180°. The influence of mode-III SIFs in this model is minor since they are much smaller than the mode-I and mode-II SIFs. The SIFs increase greatly when the crack location approaches the uncrowned edge. At this time, a crowned profile can be used to significantly reduce the SIFs near the roller edge. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computing a-posteriori bounds for stress intensity factors in elastic fracture mechanics

This paper mainly focuses on computing the lower and upper bounds on stress intensity factors in elastic fracture mechanics with an efficient finite element output bound procedure on quantities of interest in engineering. The bounds procedure is obtained by minimizing the quadratic energy functional of output with constraints of equilibrium conditions of mechanics and continuity conditions of finite element space. The computation is based on solving the elemental Neumann residual problems for the bounds on energy norm of error in finite element solutions. The lower and upper bounds on the intensity factors of an open mode and a shear mode elastic fracture problems are computed in this paper.     

Stress intensity factor solutions for finite body with quarter-elliptical flaws emanating from a notch

This paper presents a new simple engineering method for estimating the stress-intensity factor around a quarter-elliptical cracks emanating from a notch. Several examples will be used to highlight some of the advantages of the present method and several comparisons are made with other existing approaches. Stress-intensity factors produced by the present method are in good agreement with other published solutions. The present technique based on finite element analysis does not require the crack to be explicitly modelled. Making this technique ideal for studying fatigue crack growth and or shape optimisation with damage tolerance constraints.