Change in geometry of Surface Cracks during alternating tension and bending

The change in geometry of surface cracks during alternating tension and bending is calculated using the stress intensity factors of Newman and Raju and of the ASME Boiler and Pressure Vessel Code. It is assumed that the crack extends at the deepest point and at the surface according to the stress intensity factors at these points. Calculations were performed with local K-values and with K-values obtained by a weighted averaging along the crack front. The obtained results were compared with results from the literature.     

Boundary element analysis of thermal stress intensity factors for interface griffith and cusp cracks

The thermal stress intensity factors for interface cracks of Griffith and symmetric lip cusp types under vertical uniform heat flow in a finite body are calculated by the boundary element method. The boundary conditions on the crack surfaces are insulated or fixed to constant temperature. The relationship between the stress intensity factors and the displacements on the nodal point of a crack-tip element is derived. The numerical values of the thermal stress intensity factors for an interface Griffith crack in an infinite body are compared with the previous solutions. The thermal stress intensity factors for a symmetric lip cusp interface crack in a finite body are calculated with respect to various effective crack lengths, configuration parameters, material property ratios and the thermal boundary conditions on the crack surfaces. Under the same outer boundary conditions, there are no appreciable differences in the distribution of thermal stress intensity factors with respect to each material property. However, the effect of crack surface thermal boundary conditions on the thermal stress intensity factors is considerable.     

Stress intensity factor at the surface and at the deepest point of a semi-elliptical surface crack in plates under stress gradients

The weight function method is used to calculate stress intensity factors for a semi-elliptical surface crack in a plate exposed to stress gradients. Starting from a reference load and stress intensity factor an approximate reference displacement field is calculated analytically. The present method allows to calculate stress intensity factors with minimal numerical effort at the deepest point and at the surface. Comparisons with FEM-results from the literature are presented to show satisfying agreement.     

Fatigue crack growth analyses of offshore structural tubular joints

This study investigated various aspects of a fatigue crack growth analysis, ranging from the stress intensity factor solutions to the simulation of a fatigue crack coalescence process of a tubular joint weld toe surface flaw. Fracture mechanics fatigue crack growth analyses for offshore structural tubular joints are not simple, because of the difficulty to calculate the stress intensity factors due to their geometric complexity. The fully mixed-mode stress intensity factors of nine weld toe surface cracks of an X-shaped tubular joint under tension loading were calculated by detailed three-dimensional finite element analyses. Using these stress intensity factor solutions, a fatigue crack growth study was performed for the X-joint until (the crack surface length grew to two times the tube thickness. Through this study, the crack shape change during the fatigue crack propagation was investigated in detail. Fatigue life calculations were also performed for a range of crack geometries using the stress intensity factor solutions of the nine flaws. These calculations indicate that the natural fatigue crack growing path for a crack is its quickest growing path. The study demonstrated that detailed fracture mechanics fatigue analyses of tubular joints can be practical using the finite element method.     

Analysis of stress intensity factors for three-dimensional cruciform cracks

The stress intensity factors for three-dimensional cruciform surface cracks in a semi-infinite body are numerically calculated by the body force method. Mindlin's point force solution is used for the derivation of basic equations to express the influence coefficient of triangular elements, into which the crack is divided. The interactions between crossed crack planes as well as contact between crack surfaces are considered in the iterative manner. Stress intensity factors for a cruciform median crack and a cruciform semicircular crack under a point force on the surface of a semi-infinite solid are analyzed. The possibility of growth of a median crack toward the free surface of the semi-infinite solid is discussed. A cruciform semicircular surface crack under remote uniaxial tension, or under combined tension and compression is also analyzed. The effect of contact of crack surfaces on stress intensity factors is discussed.     

Toughening polymeric composites using nanoclay: Crack tip scale effects on fracture toughness

Fracture behavior of vinyl ester resin and the methods that can be used to toughen vinyl ester resin were studied. Neat resin, 5% by weight nanoclay, 5% by weight core shell rubber (CSR) and hybrid system (3% nanoclay and 2% CSR by weight) were the material systems considered for comparing fracture toughness. Three types of cracks were used to determine the stress intensity factors at failure, viz., sharp crack, blunt crack and notch. The critical stress intensity factor in the case of sharp cracks improved significantly when compared to neat resin. In the case of notched and blunt cracked specimens, a reduction in stress intensity factors (at failure) was observed for reinforced systems. However, for notched and blunt cracked specimens, it was shown from the morphology of the fracture surface that the stress intensity factor calculated by assuming a notch or a blunt crack as an ideal crack was not the controlling parameter for fracture. A method for quantifying the crack tip sharpness using fracture surface roughness has been proposed.     

Crack initiation from micro surface holes in bearings under rolling contact fatigue

Investigations concerning surface crack growth are necessary for understanding the mechanism of rolling contact fatigue (RCF) of bearings because the surface defects cause flaking failures. In the present work, micro holes were artificially made prior to the RCF tests and the initiation of the surface cracks from the micro holes was observed in order to find the key factors for understanding their features. Crack initiation directions were compared to the stress intensity factors calculated by a simple method based on the theory. The extent to which ‘contact pressure (wedge effect)’ and ‘contact stresses’ are applicable for understanding the correlations between the crack initiation directions and stress intensity factors is discussed. The crack initiation directions are strongly correlated to the stress intensity factors caused by the contact stresses alone. We concluded that the crack growth and initiation are dominated by stress intensity factors caused by contact stresses rather than the wedge effect.     

Stress Intensity Factors of a circumferential surface crack at the outside of a thermally loaded pipe

Stress intensity factors were calculated for partly circumferential surface cracks at the outside of a pipe. The pipe is loaded by internal pressure and by thermal stresses. The weight functions method is used to calculate averaged weighted stress intensity factors at the deepest point and at the surface points of the crack. The evaluation of temperatures and stresses in the pipe and the application of the weight functions method are described. Numerical results are given for an application to steam generator tubes.     

Stress intensity factors for large arrays of radial cracks in thick-walled steel cylinders

Mode I stress intensity factors for large arrays of up to 512 radial cracks emanating from the inner surface of a pressurized thick-walled cylinder are evaluated. Furthermore, for cylinders that underwent autofrettage, the negative stress intensity factors due to the compressive residual stresses are also calculated. Both stress intensity factors are evaluated, for numerous crack arrays (2–512), for a wide range of crack lengths and for a fully autofrettaged cylinder, via the finite element (FE) method. The present results accentuate the considerable influence of the number of cracks in the array, as well as that of the autofrettage on the actual stress intensity factor prevailing at the tip of these cracks.     

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.     

Fatigue Crack Propagation in cylindrical bars

Crack propagation calculations were conducted to describe a developing surface crack in a solid round bar. The theoretical basis is a stress intensity factor solution in weighted average for the center and the surface points of a so called “almond-shaped” crack under Mode 1 loading. This solution was obtained by use of approximate weight functions. With these weight functions stress intensity factors for tension and bending were calculated. Predictions for the developing crack shape and the crack growth rate can be made utilizing a da/dN-ΔK relation. Experimental results for a 42 CrMo4 steel are in excellent agreement with these predictions.     

Weight function calculation for surface cracks using the line-spring model

A numerical method for calculating weight functions for surface cracks in plates and shells is proposed. Thick-shell finite elements are used to create the discrete model of a body with a through-wall flaw. Line-spring elements transform the through-wall flaw into a surface crack. A quadratic line-spring element is presented. Weight functions for some semielliptical surface cracks in a plate have been calculated. The weight functions obtained may be used for computing stress intensity factors related to two-dimensional stress fields at the crack surface.     

Fatigue crack propagation simulation in an aircraft engine fan blade attachment

This paper discusses the computation of three-dimensional fatigue crack growth rates in a typical military aircraft engine fan blade attachment under centrifugal and aerodynamic loads. The three-dimensional crack growth simulations utilize FRANC3D, a state-of-the-art crack propagation software developed at Cornell University, which uses boundary elements and linear elastic fracture mechanics. With an existing three-dimensional finite element contact stress analysis with a prescribed coefficient of friction (COF) along the contact surface, the displacements and stress intensity factors are calculated on the crack leading edge to yield crack propagation trajectories and growth rates. Due to complex geometry of the fan blade attachment and loading conditions, all three-fracture modes are considered and the associated stress intensity factors (SIF) are calculated using the Crack Opening Displacement (COD) approach. Crack propagation trajectories under mixed-mode conditions are obtained using the planar and maximum tangential stress crack-extension criteria. The fatigue crack in the blade attachment is subjected to an over speed mission cycle that includes high cycle frequencies (i.e., spectrum load) and the crack growth rate is predicted utilizing the Forman–Newman–de Koning (FNK) model. Scanning Electron Microscope (SEM) images of a cracked component from an engine ASMET (Accelerated Simulated Mission Endurance Test) are used to evaluate and compare the simulation results. The calculated SIF's from the simulations indicate a strong Mode-I (K_I) and Mode-III (K_III) interaction at the edge of contact (EOC). However, on the free surface it is primarily a crack opening (K_I) condition only. The crack growth rates are determined using the planar extension criterion which correlates better with the test data than the maximum tangential stress extension criteria.     

Stress intensity factors around a crack parallel to a free surface of a half-plane

In this paper, stress intensity factors for a crack in a half-plane are considered. The crack is parallel to the stress-free surface of the half-plane and subjected to internal gas pressure. By using Fourier transforms, the mixed boundary value problem is reduced to the solution of a pair of dual integral equations. To solve the equations, the crack surface displacements are expanded in a series of functions which are zero outside the crack. The unknown coefficients in that series are solved with the aid of the Schmidt method. The stress intensity factors are calculated numerically and the results are compared with those given in other papers.     

Behaviour of sub-clad and through-clad cracks under consideration of the residual stress field

Aim of the present study is an assessment of the behaviour of cracks in the ferritic base metal of components supplied with an austenitic welded cladding under special consideration of the residual stress field caused by the welding and heat treatment processes. For this purpose, an experimental and numerical investigation has been performed. The experimental study consisted of two component tests at low temperature using large-scale specimens with sub-clad and surface cracks. Subsequently, the experiments were analyzed numerically where the residual stress field was determined in an advanced numerical simulation of the welding and heat treatment processes. Based on the results, a fracture mechanics assessment of the ferritic and austenitic material zones on crack initiation and arrest was performed. The experimental and numerical results reveal that fracture was initiated in the ferritic range whereas the austenitic cladding remained intact even in the case of a limited crack extension in the base metal underneath the cladding.     

Stress intensity factors for cracks emanating from a triangular or square hole in an infinite plate by boundary elements

This paper concerns stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure calculated by means of a boundary element method, which consists of constant displacement discontinuity element presented by Crouch and Starfied and crack tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Numerical examples are included to show that the method is very efficient and accurate for calculating stress intensity factors of plane elasticity crack problems. Specifically, the numerical results of stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure are given.     

Stress intensity factors for long axial surface cracks at the outer wall of a pipe loaded by stress gradients

By means of the finite element method crack opening displacements were calculated for long axial surface cracks at the outer wall of a pipe. The wall thickness to inner radius ratio of the pipe was 1 to 10. Following a procedure introduced be Mattheck et al. weight functions were evaluated by means of the finite element results. Using these weight functions it is possible to calculate stress intensity factors for arbitrary radially varying stress distributions. In this paper stress intensity factors were evaluated for a constant hoop stress loading as well as for stress distributions with a linear and a quadratic dependence on the radius.     

A fracture mechanical treatment of free edge stress singularities applied to a brazed ceramic/metal compound

The theoretical fracture mechanical treatment of craek problems in regular stress fields is extended to account for singular stresses as occur in bi-material systems whenever a discontinuity in material properties and geometry exists. The singular stress fields are derived for arbitrary material combination and geometry and the global stress state as occurs in a real compound is obtained by Finite Element (FE) calculations. Then especially the mode I stress intensity factors are calculated for semi-elliptical surface cracks in the ceramic component of a brazed ceramic/metal joint. Critical crack sizes are determined for failure analysis of the compound.     

Analysis of surface cracks using the line-spring boundary element method and the virtual crack extension technique

The authors have developed a new line-spring boundary element method which couples the line-spring model with the boundary element method to deal with the problem of a surface cracked plate. However, the drawback of the line-spring model is that a reliable stress intensity factor could not be directly obtained near the free surface intersection. Therefore, the virtual crack extension technique is employed in a post-processor of the line-spring boundary element method to obtain the stress intensity factor at the crack front-free surface intersection. Theoretical analysis is described. Stress intensity factors for surface cracks are calculated to verify the proposed method. The interaction of two surface cracks is also investigated. The solutions obtained by the line-spring boundary element method show that the method proposed is efficient and reasonably accurate.     

An edge dislocation of constant velocity near a static internal crack

An edge dislocation of constant velocity near a static internal crack was investigated. The dislocation slip and climb and dislocation source were considered. The crack surface was simulated with static continuous dislocations. After obtaining the distribution of static dislocations in the crack, we calculated the stress field in the entire space. Using the stress distribution, we then computed the stress intensity factors at both crack tips and the image force on the edge dislocation. Numerical results are provided to describe in detail the effect of velocity and crack length on toughness and image force.