Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

The Notch Stress Intensity Factors (NSIFs) quantify the intensities of the asymptotic linear elastic stress distributions of sharp (zero radius) V-shaped notches. When the notch tip radius is different from zero, the singular sharp-notch field diverges from the rounded-notch solution in the close neighborhood of the notch tip. Nevertheless the NSIFs might continue to be parameters governing fracture if the notch root radius is small enough. Otherwise they can be seen simply as stress field parameters useful in quantifying the stress distributions ahead of the specific notch. Taking advantage of some analytical formulations which are able to describe stress distributions ahead of parabolic, hyperbolic and V-shaped notches with end holes, the paper discusses the form and the significance of the NSIFs with reference to in-plane shear loading, considering explicitly the role played by the notch opening angle and the notch tip radius. These parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case to which they should naturally tend for decreasing values of the notch radius.     

Path independent integrals for computing stress intensity factors at sharp notches in elastic plates

A set of path independent integrals is constructed for the calculation of the generalized stress intensity factors occurring in elastic plates having sharp re-entrant corners or notches with stress-free faces and subjected to Mode I, II or III type loading. The Mode I integral is then demonstrated to enjoy a reasonable degree of numerical path independence in a finite element analysis of a test problem having an exact solution. Finally, this integral is used on the same problem in conjunction with a regularizing, finite element, procedure or superposition method. The results indicate that sufficiently accurate estimates of these stress intensity factors for engineering purposes can be achieved with little computational effort.     

A discussion on various estimations of elastic stress distributions and stress concentration factors for sharp edge notches

The elastic stress distributions in some edge-notched geometries have been estimated from Creager and Paris's and Neuber's expressions. Close to the notch root, these approximate solutions agree well with the finite element results. Further away from the notch, the approximate methods give overestimations. A simple formula derived from Creager and Paris's expression provided accurate stress concentration factor solutions for some edge-notched geometries.     

A simple method for computing the stress intensity factors for cracks at notches

This paper presents a simple method for calculating the stress intensity factors for cracks emanating from a notch under arbitrary loading. A range of examples are presented to demonstrate the accuracy of the present method.     

Elastic notch stress intensity factors for sharply V-notched rounded bars under torsion

The paper deals with the determination of analytical expressions for the mode III notch stress intensity factors for circumferentially-sharply-notched rounded bars under torsion loading, starting from the theoretical stress concentration factors of the corresponding notch problem.An exact, closed-form solution for the NSIFs is obtained for deep notches; subsequently the solution is extended also to finite notched components taking advantage of a shape function determined by a numerical best fitting procedure.     

Fracture loads for ceramic samples with rounded notches

Fracture loads of ceramic components with rounded notches cannot be computed by linear elastic fracture mechanics techniques because no stress singularity exists. We propose a procedure to estimate such fracture loads, which is based on the cohesive zone model and supported by experimental evidence with alumina, zirconia and silicon ceramics. Data from 18 ceramic materials and different notched geometries were used. The only material parameters needed were the tensile strength and the fracture toughness.     

Experimental evaluation of stress field around the sharp notches using photoelasticity

A higher order representation of the stress field around the sharp notch has been utilized for calculating notch stress intensity factors (NSIFs) as well as the coefficients of higher order terms by the technique of photoelasticity. Adding the higher order terms to the singular term makes it possible to collect the data points from a larger zone, which helps to simplify the data collection from experiments. Moreover, the effects of higher order terms in the region near the notch tip are taken into account. To utilize the advantages of whole-field photoelasticity and minimize the experimental errors, a large number of data points have been employed and the overdeterministic least squares method combined with the Newton–Raphson method have been used to solve the resulting system of nonlinear equations. The NSIFs for a laboratory specimen called V-notched Brazilian disk (V-BD) were calculated for various notch angles under pure mode I, pure mode II and mixed mode I/II loading conditions. In addition to NSIFs, the coefficient of the first non-singular term of 30° notch was calculated experimentally and the effects of this term on the stress distribution in the vicinity of notch tip were investigated. A good correlation was observed between the experimental results and the numerical results obtained from finite element analysis.     

Crack tip stress intensity factors for a crack emanating from a sharp notch

Accurate calibrations are provided for the crack tip stress intensity factor for a crack of finite length emanating from the symmetric tip of a sharp notch, of arbitrary angle, in terms of the generalised stress intensity quantifying remote loading of the notch. The solution is applied to example problems and shown to be accurate for cases where the crack is much shorter then the notch depth.     

Calculation of stress intensities at sharp notches in anisotropic media

We present a procedure to calculate mode I and II notch stress intensities in anisotropic media using the path-independent H-integral. The method is based on coupling the analysis of asymptotic stress and displacement fields near a sharp notch with a path independent integral that results from the application of Betti's reciprocal theorem to the notched solid. The approach is demonstrated for two loading/geometry combinations that arise naturally in etched single crystal silicon: mode I loading of a 70.53° notch and mixed mode I and II loading of a T-structure with a 90° notch. Results agree well with those obtained by correlating computed notch-flank displacements with the asymptotic solution.     

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.     

Compliance and stress intensity coefficients for short bar specimens with chevron notches

For the determination of fracture toughness especially with brittle materials, a short bar specimen with rectangular cross section and chevron notch can be used. As the crack propagates from the tip of the triangular notch, the load increases to a maximum then decreases. To obtain the relation between the fracture toughness K _ic and maximum load P _max, calculations of Srawley and Gross for specimens with a straight-through crack were applied to the specimens with chevron notches. For the specimens with a straight-through crack, an analytical expression was obtained. This expression was used for the calculation of the K _ic–P _max relation under the assumption that the change of the compliance with crack length for the specimen with a chevron notch is the same as for a specimen with a straight-through crack.Comparative compliance calibrations with specimens of different geometries agreed very closely with the analytical results for the K _ic–P _max relation. For the first part of crack extension before reaching maximum load, the dimensionless quantity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaCa% aaleqabaGaaiOkaaaakiabg2da9iaadUeadaWgaaWcbaGaaeysaiaa% bogaaeqaaOGaamOqamaakaaabaGaam4vaaWcbeaakiaac+cacaWGqb% aaaa!3EBE!\[Y^* = K_{{\text{Ic}}} B\sqrt W /P\]where B and W are the specimen thickness and width, and P the applied load, is greater for the analytical approach than that obtained from the experimental results. This difference can be explained by applying the slice model proposed by Bluhm.

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Résumé Pour déterminer la tenacité à la rupture dans le cas particulier de matériaux fragiles, une éprouvette en forme de barreau court avec section droite rectangulaire et entaille à chevron peut être utilisée. Lorsque la fissure se propage à partir de l'extrémité de l'entaille triangulaire, la charge s'accroît jusqu'à un maximum et ensuite décroît. Pour obtenir la relation entre la tenacité à la rupture K _Ic et la charge maximum P _max, les calculs de Srawley et Gross pour des éprouvettes comportant une fissure droite traversante ont été appliqués aux éprouvettes comportant des entailles en chevron. Pour les éprouvettes à entailles droites traversantes, une expression analytique a été obtenue.Cette expression a été utilisée pour le calcul de la relation de K _Ic–P _max sous l'hypothèse que le changement de compliance avec une longueur de fissure correspondant à l'éprouvette à entailles en chevron est la même que dans le cas d'une éprouvette comportant une fissure droite traversante.Des calibrages comparatifs de la compliance à l'aide d'éprouvettes de géométries différentes se sont montrés en très bon accord avec les résultats analytiques correspondant à la relation K _Ic–P _max. Pour la première partie de l'extension de la fissure avant d'atteindre la charge maximum, la quantité sans dimension % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaCa% aaleqabaGaaiOkaaaakiabg2da9iaadUeadaWgaaWcbaGaaeysaiaa% bogaaeqaaOGaamOqamaakaaabaGaam4vaaWcbeaakiaac+cacaWGqb% aaaa!3EBE!\[Y^* = K_{{\text{Ic}}} B\sqrt W /P\]où B et W sont respectivement l'épaisseur et la largeur de l'éprouvette, et P la charge appliquée, est supérieure dans le cas de l'approche analytique à la valeur obtenue lors des résultats expérimentaux. Cette différence peut être expliquée en appliquant le modèle de découpage en tranches proposé par Bluhm.

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Work done under NASA-DOE Interagency Agreement number EC-77-A-31-1040.     

A simplified method for predicting the stress concentration in notches from experimental stress data

This paper describes a simple procedure to obtain very reliable estimates of the stress concentration at the root of a notch using only data from points beneath the notch root along its axis of symmetry. The advantages of the method are (i) data from only a few points are needed, (ii) the necessary computations require only a hand held calculator, (iii) inaccurate data becomes quite apparent to the analyst, and (iv) random experimental errors are largely compensated.     

Theoretical stress concentration factors for short flat bars with opposite U-shaped notches subjected to in-plane bending

The values of existing theoretical stress concentration factors for rectangular uniform thickness plates, with opposite U-shaped notches, subjected to in-plane bending do not include the effect of length as a significant parameter. This work demonstrates that below a threshold value, defined as transition length, these stress concentration factors cease to be valid and, notably, also demonstrates that below this threshold the magnitude of the stated factors may be significantly larger than existing values; a fact that may have important consequences for the accurate estimates of fatigue life. The finite element determined, theoretical stress concentration factors for the stated geometry and loading, including length as a parameter, for the existing range of the notch radii values, as well as an extended range of these values are reported and are presented in the standard graphical form. The corresponding values of the transition lengths were computed and are reported as well.