Semi-elliptical Surface Flaws Research Articles

Investigation for Stress Intensity Factor Solutions on Nozzle Corner Flaw (Part 2)

In order to provide a stress intensity factor (K)-solution for a nozzle corner flaw subjected to internal pressure for the Japan Society of Mechanical Engineers (JSME) Rules on Fitness for Service (FFS) for nuclear power plant, four candidates, which are the Paris and Sih based solution, the Fife’s solution, the Kobayashi’s solution and the solution of a flat plate with a semi-elliptical surface flaw in the JSME Rules on FFS, were compared with the Ks by Finite Element Method. As the result, the flat plate solution was confirmed to be the most adequate for K calculation of a nozzle corner flaw in the JSME Rules on FFS.

Studying the interaction of crack-like flaws using the MATLAB toolbox int_defects

int_defects is a free and open-source toolbox for MATLAB which uses the Abaqus finite element analysis suite to automate the analysis of interacting crack-like flaws in structures. It is designed to aid the development of flaw interaction criteria for structural integrity assessment procedures and to simplify sensitivity analysis of flaw proximity. It can also perform automatic 3D elastic, elastic-plastic or limit load analysis of elliptical embedded flaws and semi-elliptical surface flaws in plates and thick-walled pipes under a wide range of loading conditions. This technical note outlines the capabilities of int_defects and gives some examples of its use.

Discontinuous slow crack growth modeling of semi-elliptical surface crack in high density polyethylene using crack layer theory

Surface flaws in structural materials are most likely to be generated during service time. One of the most general shapes of surface flaws is the semi-elliptical surface crack. Frequently, the slow crack growth (SCG) of a crack has been fitted based on the conventional Paris–Erdogan relationship. However, in the case of engineering plastics, which generally reveal a severe unrecoverable damage zone at the crack tip, the conventional Paris–Erdogan relationship is not appropriate to describe the SCG of a crack. Especially, SCG kinetics of some engineering polymers such as high-density polyethylene (HDPE) affect the SCG characteristics, i.e. non-conventional discontinuous SCG behavior, which cannot be simulated by conventional Paris–Erdogan relationship. It is known that the crack layer (CL) theory, which deals with driving forces of crack and process zone (PZ) together, can be a good mathematical model to simulate such SCG behavior. In this study, the discontinuous SCG of a semi-elliptical surface flaw in HDPE plate under cyclic tensile stress was simulated using the CL theory. Although the CL theory has the advantage of simulating the discontinuous SCG of HDPE accurately, until now the applications have been concentrated on one-dimensional slow crack growth. In this paper, the CL model for two-dimensional surface crack growth for axial and bending loading conditions was developed for the first time. The proposed model is validated with actual test results, and the role of some key CL parameters on discontinuous SCG behavior of a semi-elliptical surface flaw is investigated by intensive parametric studies.

Prediction of Stress Intensity Factor on Precracked Composite Wing Rib Made up of Carbon-Epoxy IM7-8552

The stress intensity factor (SIF), K, is an important parameter to predict the stress state (“stress intensity”) near the tip of a crack caused by a remote load or residual stresses. It can determine the probability of crack propagation and failure of the material. To study the use of high-strength material, IM7/8552 in the crack prone region is the main focus of this present study. A semi-elliptical surface flaw in a typical Boeing-747 rib section having circular cut out and experiencing an in-plane shear loading of 10.21 MPa was considered for analysis. A parametric study on crack initiation is done by having different size of cracks at different locations across the layers. The values of SIF for all the three modes were calculated using the contour integral method. In the present study, we have considered IM7-8552/carbon-epoxy composite due to its high performance and intermediate modulus property. As there are no theoretical solutions for mixed mode loading problems, finite element packages like HYPERMESH and ABAQUS were used to obtain the SIF along the crack edge. The corresponding stress intensity factor values were compared to the fracture toughness of the material to determine the probability of crack initiation. It was observed that the mode of failure changes along with shape of the crack. The analysis results showed a high probability of failure. A comparative study on T300-5208/carbon-epoxy and IM7-8552/carbon-epoxy was performed. IM7-8552/carbon-epoxy composite showed higher resistance to failure. By modifying the fiber orientations, stress concentrations were minimized to a tangible limit.

Crack Initiation Study on Aircraft Composite Rib with Semi-elliptical Surface Flaw

A parametric study on crack initiation was done by having different sizes of cracks at different locations in a rib section of an aircraft using finite element techniques. A semi-elliptical surface flaw in a typical Boeing-747 rib section having circular cut-out and experiencing an in-plane shear loading was considered for the analysis. A laminated composite square plate around a centrally located cut-out was selected in the wing rib for computation purpose. A delamination has been modeled in between the composite layers in the form of a semi-elliptical surface crack using node duplication technique. As there are no theoretical solutions for mixed mode loading problems, the general purpose finite element package ABAQUS was used to obtain the Stress Intensity Factor (SIF) along the crack edge. These stress intensity factor (K C) values were further compared with the fracture toughness of the material to determine the probability of crack initiation. It was observed that the modes of failure change with the dimensions of the crack and also showed a greater tendency towards the crack initiation.

OS0815 延性破壊挙動予測のためのGURSONモデルパラメータ決定法の試験的検討

This paper introduces the application of Gurson model to simulate the ultimate ductile failure of three types of specimens with different constraints. Fracture tests were conducted using three kinds of notched round bar tensile specimens with different notch radii, a flat plate tensile specimen with a centered semielliptical surface flaw. Using the test results of the notched round bar tensile specimens, the Gurson model parameters were determined from the literatures, fracture observation and experimental design calculations. After fixing the Gurson parameters, they were applied to the flat plate tensile specimen model. As a result Gurson model could simulate the fracture behavior of the flat plate with good accuracy.

Failure Bending Moment for Pipes With an Arbitrary-Shaped Circumferential Flaw

When a flaw is detected in a stainless steel piping system, an evaluation has to be performed to determine its suitability for continued operation. The failure bending moment of the flawed pipe can be predicted by limit load criterion in accordance with Appendix E-8 in the JSME S NA-1-2008 and/or Appendix C in the ASME Code Section XI. However, in these current codes, the limit load criterion is only calculated for the case of pipes containing a single flaw with constant depth, although the actual flaw depth is variable along the circumferential direction. Particularly, geometrical shapes of stress corrosion cracks are generally complex. The objective of this paper is to propose a method by formula for predicting the load-carrying capacity of pipes containing a circumferential surface flaw with any arbitrary shape. The failure bending moment is obtained by dividing the surface flaw into several subflaw segments. Using this method, good agreement is observed between the numerical solution and the reported experimental results. Several numerical examples are also presented to show the validity of the proposed methodology. Finally, it is demonstrated that three subflaw segments are sufficient to determine the collapse bending moment of a semi-elliptical surface flaw using the proposed methodology.

任意形状の単一周方向欠陥を有する管の極限荷重評価法

When a flaw is detected in a stainless steel pipe during in-service inspection, the limit load criterion given in the codes such as JSME Rules on Fitness-for-Service for Nuclear Power Plants or ASME Boiler and Pressure Vessel Code Section XI can be applied to evaluate the integrity of the pipe. However, in the present codes, the limit load criterion is only provided for the case of a flaw with the uniform depth, although many flaws with complicated shape such as stress corrosion cracking have been actually detected in a pipe. In this paper, a limit load estimation methd is proposed considering a circumferential surface flaw with arbitrary shape, in orer to make it possible to evaluate the integrity of the pipe for general case. The plastic collapse moment and stress are obtained by dividing the surface flaw into several segmented sub-flaws. Using this method, good agreement is observed between the numerical solution and reported experimental results. Several numerical examples are also given to show the validity of this method. Finally, it can be seen that the number of the segmented sub-flaws for the semi-elliptical surface flaw is sufficient to be three from engineering judgment.

Approximation method for the calculation of stress intensity factors for the semi-elliptical surface flaws on thin-walled cylinder

A simple approximation method for the stress intensity factor at the tip of the axial semi-elliptical cracks on the cylindrical vessel is developed. The approximation methods, incorporated in VINTIN (Vessel INTegrity analysis-INner flaws), utilizes the influence coefficients to calculate the stress intensity factor at the crack tip. This method has been compared with other solution methods including 3-D finite element analysis for internal pressure, cooldown, and pressurized thermal shock loading conditions. For these, 3-D finite-element analyses are performed to obtain the stress intensity factors for various surface cracks witht/R=0.1. The approximation solutions are within ±2.5% of the those of finite element analysis using symmetric model of one-forth of a vessel under pressure loading, and 1–3% higher under pressurized thermal shock condition. The analysis results confirm that the approximation method provides sufficiently accurate stress intensity factor values for the axial semi-elliptical flaws on the surface of the reactor pressure vessel.

Fatigue growth of a surface crack in a welded T-joint

Structural component failures due to fatigue loading often occur in welded T-joints, the geometry of which gives raise to a local stress increase that makes them preferential sites for crack initiation and propagation. In the present paper, the fatigue behaviour of a T-jointed blade in a hydraulic turbine runner is analysed both experimentally and numerically. For relatively small cracks, it is shown that the structural component geometry does not remarkably influence the stress-intensity factor (SIF) values, provided that the stress field in the vicinity of the crack is approximately the same. Therefore, in order to simplify the problem, a cracked finite-thickness plate is examined instead of the actual T-jointed blade. The SIFs along the front of a semi-elliptical surface flaw in such a plate are determined through a finite element analysis for different elementary loading conditions that can be employed to model the actual stress field at the expected crack location in the examined T-joint. Then, by applying the superposition principle and the power series expansion of the actual stress field due to the load applied to the T-joint being considered, an approximate SIF for the cracked T-joint is evaluated and used for fatigue crack growth simulations by also employing a two-parameter model based on the Paris law. The numerical results deduced are compared with those obtained from experimental tests. The agreement between the different results is quite satisfactory.

A numerical analysis on the interaction of twin coplanar flaws

In several practical situations, structural components present more than one crack. Such multiple cracks should be considered simultaneously since the interaction phenomenon could produce higher stress-intensity factor (SIF) values with respect to the case of a single crack. In the present paper, the influence of two identical coplanar semi-elliptical surface flaws in a plate with finite width and thickness under various stress distributions perpendicular to the crack faces is numerically analysed. Then the results for such elementary stresses are used to obtain the SIFs for real load cases. Due to the interaction effect, the SIF distribution along the crack front is asymmetric and dependent on the distance δ between the two surface cracks. The distance of non-interaction is evaluated as a function of the crack shape and the crack depth.

Simulation of plasticity-induced fatigue crack closure in part-through cracked geometries using finite element analysis

The part-through semi-elliptical surface flaw is commonly encountered in engineering practice. Proper characterization of plasticity-induced crack closure is necessary to predict both flaw growth and flaw shape evolution under cyclic loading. Three-dimensional elastic–plastic finite element analyses are used to model the plasticity-induced closure developed along the surface flaw crack front, and the subsequent crack opening behavior under constant amplitude loading. Resulting crack opening stresses are compared with results from a strip-yield model and with experimentally measured values reported in the literature. It was found that the computed values were larger than those measured.

Compliance measurements for assessing structural integrity

The phenomenon of aging structures has focused attention on the problems of multiple-site damage (MSD) and widespread fatigue damage (WFD). In Australia, the problem was highlighted by the November 1990 failure of a Royal Australian Air Force (RAAF) Macchi aircraft which suffered a port wing failure whilst in an estimated 6 g maneuvre and by the September 1998 explosion at the EXXON gas plant in Victoria. To assist in the understanding and the management of this problem the present paper uses the newly developed finite element alternating technique, for an arbitrary number of interacting three dimensional cracks, which we refer to as the MSD FEAT algorithm, to evaluate whether compliance measurements are useful in assessing continuing airworthiness. Traditionally the MSD FEAT and the FEAT analysis tools, i.e. the analysis methodology for a single crack, have been used only to analyse the stress intensity factor distributions around crack faces. The new work described in this paper enables the displacement field, and hence the compliance, to be calculated at any given location within the structure. Initial results confirm that this technique produces correct displacements and is capable of determining the crack tip opening displacement to within ∼0.7% for semi-elliptical surface flaws. Earlier work conducted on two dimensional MSD problems found that when using compliance measurements to evaluate cracking there was an optimal sensor length for monitoring crack interaction effects. The present paper extends this study to three-dimensional flaws via a combined analytical and experimental research program. The experimental work focuses on specimens containing two interacting quarter elliptical cracks. Here the changes in compliance of the specimen under monotonic loading, and fracture load, were measured and were found to be in good agreement with those predicted using the newly developed MSD FEAT algorithm. Results of this analysis indicate that placement of sensors in an optimal position is crucial.

Strip-yield and finite element analysis of part-through surface flaws

A slice synthesis methodology is developed and used to construct a weight function based strip-yield model for a semi-elliptical part-through surface flaw in an elastic–perfectly plastic body under monotonic loading. The model enables rapid approximate computation of the crack surface displacements and the crack front plastic zone size in the crack plane. A detailed mathematical description of the model is presented. Crack surface displacements from the model are shown to compare well with results from detailed three-dimensional elastic–plastic finite element analyses. From the finite element analyses, the crack plane plastic zone is shown to give an unrealistic perspective of overall crack front plasticity.

Fatigue shape analysis for internal surface flaw in a pressurized hollow cylinder

Fatigue crack shape is simulated through a theoretical model for part-through cracks in a hollow cylinder under cyclic pressure. The defect is assumed to have an elliptical-arc shape. The propagation path of the surface flaw is obtained as a diagram of aspect ratio ϵ against relative depth b/ t. The numerical procedure calculates the local growth increments at a set of points defining a crack front by employing a fracture damage zone size model, that can directly predict the shape development of propagating cracks. The aspect ratio changes during crack growth are obtained and compared with the limited experimental data found in the literature. Thick- and thin-walled cylinders, and also semi-elliptical internal surface flaws are considered. The influence of the elasto-plastic characteristics of the steels’ different properties, related to test temperature, on the aspect ratio variation is studied.

The effects of weld mismatch on J-integrals and Q-values for semi-elliptical surface flaws

Three-dimensional finite element analysis of shallow semi-elliptical surface flaws in the centre of rectangular welds was undertaken, and the effects of varying weld mismatch and weld width on J-integrals and Q-values were investigated. An interesting relationship between weld width and the applied load at failure, as predicted from a J–Q failure locus, was observed. The practicalities of modifying the J- and Q-estimation schemes developed for homogeneous plates to include mismatch effects were investigated using a limited parametric study.

Further studies into interacting 3D cracks

The phenomenon of ageing structures has focused attention on the problem of multiple-site damage (MSD) and wide spread fatigue damage (WFD). In isolation each flaw or crack may be safe. However, the cumulative effect of multiple, interacting cracks may significantly degrade the damage tolerance of the structure. This paper presents an overview of a new finite element alternating technique algorithm suitable for calculating mode I stress-intensity factors for an arbitrary number of coplanar interacting three dimensional cracks. This new algorithm has been evaluated for a variety of crack aspect ratios and crack separation ratios for fully embedded elliptical cracks, semi-elliptical surface flaws and for quarter elliptical cracks. In each instance, test cases have been studied for both finite and infinite geometries. Results of three of these cases are presented in this paper. These results indicate an agreement to within 4% for all cases checked.

Composite repairs to cracks in thick metallic components

This paper presents a series of experimental and numerical studies into the repair of cracks in thick structural components. To this end, after first summarising the design guidelines for repairs to thin structural components, a variety of problems are considered; semi-elliptical surface flaws, interacting surface flaws, cracked fastener holes, and cracked lugs.

Effects of biaxial loading on crack driving force and constraints for shallow semi-elliptical surface flaws

Three-dimensional, elastic-plastic finite element analyses have been carried out to investigate the effects of biaxial loading on J-integrals and Q-values for shallow semi-elliptical surface flaws in wide plates. Direct tension and pure bending loading of up to about 10 times the yield strain were applied to models with linear elastic-power hardening and tripartite material behaviours. Crack depths were limited to 15 percent of the plate thickness. Differences were observed between the effects of biaxiality on J-strain behaviour for cracks in semi-infinite plates and those in finite width plates. The cracked semi-infinite geometry was considered more representative of structural applications. In this case, biaxial loading gave a large increase in J-integrals compared to uniaxial loading, but had negligible effect on constraint, as measured using the Q-value.

A MODIFIED STRIP‐YIELD MODEL FOR PREDICTION OF PLASTICITY‐INDUCED CLOSURE IN SURFACE FLAWS

A slice synthesis methodology is developed and used to construct a modified strip‐yield model for the semielliptical surface flaw, enabling prediction of plasticity‐induced closure along the crack front and subsequent fatigue crack growth. A mathematical description of the model is presented. Slice synthesis methodologies have previously been limited to stress intensity factor and elastic crack displacement computation. Predictions of flaw shape evolution under cyclic loading are compared with experimental data for aluminium alloy specimens under uniform constant amplitude loading with R = 0.1, 0.3 and 0.6. Model predictions are shown to correlate well with experimental data. An empirical correlation of relative crack opening stress with applied R ratio from the literature is shown to underestimate the level of closure at the deepest point of penetration when compared with the model predictions.