A generalised solution for the crack surface displacement of mode I two-dimensional part-elliptical crack

A generalised approximate crack surface displacement solution for the two-dimensional part-elliptical mode I crack was developed. This solution includes the surface crack, corner crack and embedded crack, which is subjected to the arbitrary crack surface pressure. The crack surface displacement is derived from stress intensity factor solution and corresponding crack surface pressure distribution. Comparisons of the solution with accurate solutions showed that rather high accuracy has been achieved with the developed solution for various surface, embedded and corner crack problems. This solution can be used to derive three-dimensional weight functions as long as the stress intensity factor and the corresponding crack surface pressure are available for arbitrary mode I problems.     

A new method of crack-tip opening displacement determined based on maximum crack opening displacement

In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension.     

The approximate analytical solution for both surface and embedded cracks in cylinder with finite size

The exact solution for a penny-shaped crack in an infinite elastic body under the action of an arbitrary normal load and the trigonometric series solution for a cylinder with finite size under an arbitrary lateral surface load are taken as basic solutions. From the alternate action of the basic solutions, we have obtained the approximate analytical expressions of K_I for both the surface and embedded cracks in cylinder with finite size. The first approximate expressions of K_I for a cylinder under tensile load and pure bending respectively and some numerical results of K_I are given as an example of practical calculation.     

The crack opening displacement field of semi-elliptical surface cracks in tension for weight functions applications

Application of the weight function method for calculating energy release rates or averaged weighted stress intensity factors requires that both the stress intensity factors and the crack opening displacements are known for a reference load case. This report gives an approximative solution for the crack opening displacement field of a semi-elliptic surface crack under pure tension loading. As a practical example the energy release rates are calculated for bending and compared with results available in the literature. Also a test procedure is described for checking the quality of approximative stress intensity factors.

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Résumé Pour appliquer la méthode des fonctions pondérées au calcul des vitesses de relaxation de l'énergie ou des facteurs d'intensité de contraintes moyens pondérés, il faut que soient connus les facteurs d'intensité de contraintes et les déplacements d'ouverture de la fissure, dans un cas de sollicitation de référence. La rapport fournit une solution approximative pour le champ de COD correspondant à une fissure superficielle semi-elliptique soumise à une charge de traction pure. Comme exemple pratique, on calcule les vitesses de relaxation de l'énergie correspondant à la flexion, et on se compare avec les résultats publiés dans la littérature. On décrit également une procédure d'essai en vue de vérifier la qualité des facteurs d'intensité de contraintes approchés.

     

The effect of shallow cracks on crack tip opening displacement

Further results given in the present paper confirm that shallow cracks have larger crack tip opening displacements at initiation than deep cracks. This difference in behaviour is shown to be principally caused by the different hydrostatic stresses existing at the tips of shallow and deep cracks. A new method based on lateral crack growth across the thickness is used in this work to measure crack tip opening displacements in specimens containing machined slots rather than fatigue pre-cracks. Justification and advantages of this method are discussed and compared to the conventional technique.     

A numerical procedure for the approximate WF solution of mode I SIFs in 3D geometries under arbitrary load

A numerical procedure was developed for the approximate weigth function (AWF) evaluation of reliable stress intensity factor (SIF) for part-through Mode I cracks for general load. Different from other WF procedures which require closed form reference SIFs, this procedure requires only limited number of discrete SIF solutions directly obtained from other numerical methods as reference SIFs to compute continuous SIFs as function of both the crack size and the location along the crack front. As an implement to the general numerical methods in the Damage and Safe Life analysis, this procedure substantially increases the value of numerical SIF results. The present procedure is relative simple, with most of basic relations being analytically soved, and therefore efficient in use. Several examples were presented to demonstrate the accuracy of this procedure.     

A new method of plastic zone size determined based on maximum crack opening displacement

This paper presents a new method to determine the crack-tip plastic zone size (R_y) in the center cracked plate in tension. The maximum crack opening displacement (MCOD) is used to estimate R_y in this method. Based on the series of calculation results by finite element analysis, the explicit expression for the crack-tip plastic zone size versus MCOD is fitted by least square method. The expression enables to eliminate the influences of the yield stress of material, crack geometry, plate sizes and transverse stress. Therefore, the presented method of R_y determined by MCOD is suitable to any center crack finite plate of any material under uniaxial or biaxial tension.     

The mathematical framework and an approximate solution of surface crack propagation under hydraulic pressure loading

Material degradation and failure in rolling contact components are often caused by surface microcrack initiation and propagation. Experimental evidence shows that surface crack growth rate is higher with the presence of lubricating fluid than without, possibly due to high fluid pressure within the crack. The mathematical framework to analyze a surface crack under hydraulic pressure loading is established. A surface crack filled with incompressible, Newtonian viscous fluid is considered. The solid is considered to be linear elastic. A pressure loading history is prescribed at the mouth of the crack. The governing equations are found to be two coupled non-linear integral equations of pressure distribution and crack opening displacement distribution. An approximate solution is obtained by assuming a local pressure-opening displacement constitutive law, and by using the method of separation of variables. The results indicate that upon a sudden decrease of pressure loading at the crack mouth, the crack-tip stress intensity decreases rapidly at the beginning followed by a long tail of diminishing decreasing rate; whereas upon a sudden increase of pressure loading, an incubation time exists before the pressure can be transmitted deep into the crack. A very important parameter, the characteristic penetration time, is identified and can be used to determine whether hydraulic pressure has significant influence on surface crack propagation.Presented at the Far East Fracture Group (FEFG) International Symposium on Fracture and Strength of Solids, 4–7 July 1994 in Xi'an, China.     

An approximate solution of the annular crack problem

A method is presented for the approximate solution of the axisymmetric problem of an annular crack Embedded in an infinite elastic solid and subjected to a normal internal pressure. The numerical results Obtained for the stress intensity factors are in good agreement with those obtained by Smetanin².     

A closed-form solution to the equivalent through-crack model for surface cracks

Summary A closed-form solution for plates containing surface cracks is obtained by using an equivalent through-crack model, which reduces the three-dimensional problem of the surface cracked plates to a two-dimensional Hilbert problem. The effect of surface crack is replaced by a continuous distribution of forcesN(x, 0) and momentsM(x, 0) applied along the crack face of the equivalent through-crack model. A convenient form of expressing these forces and moments is by using power polynomials. Then the singular integral equation, expressing the solution of the Hilbert problem can be readily integrated.According to this model we assumed that the crack depth at extremities, where the crack intersects the free surface of the plate, is not zero. This assumption, corroborated by experimental evidence, means that a singularity exists at the extremities of the crack. The experimental evidence was achieved by using the method of caustics and photoelasticity. The results of the evaluation of the stress intensity factor for elliptical cracks were compared well with the solutions of the respective 3-D problem solved by applying the finite-element method, the line-spring model based on the Reissner plate theory, the finite-element alternating method and the benchmark estimate. The distribution of the stress intensity factor along the crack lips, as calculated in this paper, was dropping off rapidly in the surface layer and it was very close to the results given by the approximate 3-D theory.With 7 Figures     

A new constraint based fracture criterion for surface cracks

A new methodology for predicting the location of maximum crack extension along a surface crack front in ductile materials is presented. Three-dimensional elastic-plastic finite element analyses were used to determine the variations of a constraint parameter (α_h) based on the average opening stress in the crack tip plastic zone and the J-integral distributions along the crack front for many surface crack configurations. Monotonic tension and bending loads are considered. The crack front constraint parameter is combined with the J-integral to characterize fracture, the critical fracture location being the location for which the product Jα_h is a maximum. The criterion is verified with test results from surface cracked specimens.     

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.     

Analytical solution for embedded elliptical cracks,and finite element alternating method for elliptical surface cracks,subjected to arbitrary loadings

The complete solution for an embedded elliptical crack in an infinite solid and subjected to arbitrary tractions on the crack surface is rederived from Vijayakumar and Atluri's general solution procedure. The general procedure for evaluating the necessary elliptic integrals in the generalized solution for elliptical crack is also derived in this paper. The generalized solution is employed in the Schwartz alternating technique in conjunction with the finite element method. This finite element-alternating method gives an inexpensive way to evaluate accurate stress intensity factors for embedded or elliptical cracks in engineering structural components.     

Variation of stress intensity factor and crack opening displacement of semi-elliptical surface crack

In this paper a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3D surface crack. Stress field induced by body force doublet in a semi infinite body is used as a fundamental solution. Then the problem is formulated as an integral equation with a singularity of the form of r ^-3. In solving the integral equations, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function; that is, the exact density distribution to make an elliptical crack in an infinite body. The calculation shows that the present method gives the smooth variation of stress intensity factors along the crack front and crack opening displacement along the crack surface for various aspect ratios and Poisson's ratio. The present method gives rapidly converging numerical results and highly satisfactory boundary conditions throughout the crack boundary.