A theoretical analysis of the stress intensity factors varying along the front of a surface crack

Using an equivalent through-crack model (ETCM), a theoretical analysis of the stress intensity factors, K _I, along the front of semicircular and part-circular surface cracks under mode I loading is carried out to study the variation of K _I. The results of the theoretical calculation agree satisfactorily with the experimental data obtained by photoelastic stress freezing [1]. It means that the ETCM method can be used accurately to solve the surface crack problem and especially, to predict the elastic behavior of the crack on the free surface layer.     

Variation of stress intensity factor along the front of a 3D rectangular crack by using a singular integral equation method

In this paper a singular integral equation method is applied to calculate the distribution of stress intensity factor along the crack front of a 3D rectangular crack. The stress field induced by a body force doublet in an infinite body is used as the fundamental solution. Then, the problem is formulated as an integral equation with a singularity of the form of r ^–3. In solving the integral equation, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function, which expresses stress singularity along the crack front in an infinite body. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary.     

A precise computation of stress intensity factor on the front of a convex planar crack

In this paper, we consider a general integral expression for mode I stress intensity factor along the fronts of convex planar cracks. For this integral approximation, we develop a simple numerical quadrature formula on every convex set Ω which allows a precise estimation of the error. This permits the use of extrapolation techniques for the accurate computation of the integral. Copyright © 2002 John Wiley & Sons, Ltd.     

Three-dimensional stress intensity factor analysis of a surface crack in a high-speed bearing

The boundary element method is applied to calculate the stress intensity factors of a surface crack in the rotating inner raceway of a high-speed roller bearing. The three-dimensional model consists of an axially stressed surface cracked plate subjected to a moving Hertzian contact loading. A multi-domain formulation and singular crack-tip elements were employed to calculate the stress intensity factors accurately and efficiently for a wide range of configuration parameters. The results can provide the basis for crack growth calculations and fatigue life predictions of high performance rolling element bearings that are used in aircraft engines.     

Thermally induced stress intensity factor of a semi-circular surface crack in a half-space

This paper presents thermal stress intensity factor solutions for a semicircular surface crack in a semi-infinite space, i.e., as illustrated in Fig. 1, a semicircular crack of radius a in a semi-infinite space y 0. The cracked semi-infinite space is subjected to point heat sources with arbitrary time history Q(t) at any points (x, y, z) in the region of y 0.     

The stress intensity factor for a deep surface crack in a finite plate

A stress intensity factor solution has been determined for the case of a surface crack in a finite width plate. This solution is for tension or bending and includes a finite area correction factor. It has been shown that using this new stress intensity factor solution it is possible to correlate fatigue crack growth data measured on surface cracked plate specimens with conventional through crack data.     

Stress intensity in the vicinity of a surface flaw in the linear part of a pipeline

Real sharp-edted surface and subsurface flaws detected in a gas pipeline body are modeled by surface semi-elliptical mathematical cracks (cuts) in a closed cylindrical shell. A relationship is proposed that relates the geometrical dimensions of the flaws to the crack aspect ratio. Based on the line spring model, the problem of stress state and boundary equilibrium conditions of a closed cylindrical shell with a surface semi-elliptical crack is reduced to a system of singular integral equations. An algorithm was developed for computational solution of the problem, and numerical analysis was made for the dependence of stress intensity factors on loading conditions and geometrical parameters of shell and crack. For a shell subjected to internal pressure and weakened by a surface longitudinal semi-elliptical crack, a closed approximation formula is proposed that interrelates pressure level, shell/crack dimensions, and material mechanical properties in boundary equilibrium conditions. The maximal error value is indicated for the results obtained using this formula. Lvov Polytechnic State University, Lvov, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 38–47, July–August, 1999.     

Calculation of stress intensity factor from stress concentration factor

Using the general formulas of stress concentration factor, methods for calculating stress intensity factor are mentioned.These methods make use of the several known values of stress concentration and radius of curvature at the point of stress concentration to form expression of stress concentration factor. Values of stress concentration from handbooks or experiments and others can be used.This paper deals with plane elastic, longitudinal shearing and thin plate bending problem.     

On the uniqueness of the stress intensity factor — crack velocity relationship

Experimental results due to several different investigators on the K _I – a relationship are reviewed and the apparent differences in results leading to questions regarding the uniqueness of this relationship are discussed. The influence of the errors due to the three dimensional state of stress at the crack tip, the effects of non-singular stresses, velocity, transient loading and velocity measurement is presented. These errors have obscured resolution of the uniqueness question and an experiment is described to resolve the issue.

---

Résumé On passe en revue les résultats expérimentaux obtenus par différents chercheurs sur la relation K _I – a et l'on discute des différences apparentes dans les résultats qui conduisent à des questions en ce qui regarde l'unicité de cette relation. On présente l'influence des erreurs dues à l'état tridimensionnel des tensions à l'extrémité de la fissure, les effets des contraintes non singulières de la vitesse de la mise en charge transitoire et de la mesure de la vitesse. Ces erreurs ne contribuent pas à éclaircir la question de l'unicité et, en vue de la résoudre, on décrit une expérience possible.

     

Stress intensity factor for semi-elliptical surface cracks loaded by stress gradients

The stress intensity factor at the deepest point of a semi-elliptical surface crack is calculated for stress gradients in direction of depth. The method is based on weight functions. The crack opening displacement for the reference problem is calculated with a method proposed by Petroski and Achenbach. The results are compared to finite element solutions given in the literature. As an example, the stress intensity factor is calculated for a crack in a thermally shocked pipe.     

On the calculation of crack opening displacement from the stress intensity factor

For the application of the weight function method the crack opening displacements for a reference case have to be known. An approximate method to derive the crack opening field from the stress intensity factor was proposed by Petroski and Achenbach [Engng Fracture Mech. 10, 257 (1978)]. The limited accuracy of their method becomes evident in cases where the stresses differ strongly from the homogeneous loading case (σ = const.). By expanding the crack opening displacement field in a power series it is demonstrated here how the approximative solutions can be improved by simple additional conditions.     

Variations of stress intensity factor of a semi-elliptical surface crack subjected to mixed mode loading

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of corner point singularity. It is known that the stress singularity at a corner point where the front of 3 D cracks intersect free surface is depend on Poisson's ratio and different from the one of ordinary crack. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3-D semi-elliptical surface crack in a semi-infinite body under mixed mode loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r ⁻³ using the stress field induced by a force doublet in a semi-infinite body as fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures with varying the elliptical shape and Poisson's ratio.     

On the use of quarter-point boundary elements for stress intensity factor computations

This communication studies a procedure for stress intensity factor computations using traction singular quarter-point boundary elements. Opening mode stress intensity factors are computed from the tractions' nodal values at the crack tip. A comparison is made between the factors calculated using this procedure and those obtained by previously recommended methods which made use of the nodal values of the displacements. The proposed procedure was seen to be less discretization sensitive than any other of the considered methods. Accurate results were obtained even in the case of coarse meshes.     

Computation of the weight function from a stress intensity factor

A simple representation for the crack-face displacement is employed to compute a weight function solely from stress intensity factors for a reference loading configuration. Crack face displacements given by the representation are shown to be in good agreement with analytical results for cracked tensile strips, and stress intensity factors computed from the weight function agree well with those for edge cracks in half planes, radial cracks from circular holes, and radially cracked rings. The technique involves only simple quadrature and its efficacy is demonstrated by the example computations.     

Analytical calculation of the stress intensity factor in a surface cracked plate submitted to thermal fatigue loading

A stainless steel specimen with a pre-existing surface notch is exposed to a convective medium of cyclic temperature. The history of stress intensity factor of the cracked body for different crack lengths is obtained by a closed-form integration of the stress field, using Duhamel’s theory with principle of superposition and appropriate weight functions. The obtained results are compared with numerical simulations performed with ABAQUS and they appear to be in very good agreement. The stress intensity factor history shows that fatigue behavior does not depend only on temperature amplitude ΔT=T_max-T_min, quenching rate, and duration of thermal shock but also on heating rate and duration.