Stress intensity factors for three‐dimensional weld toe cracks using weld toe magnification factors

In welded components, particularly those with complex geometrical shapes, evaluating stress intensity factors is a difficult task. To effectively calculate the stress intensity factors, a weld toe magnification factor is introduced that can be derived from data obtained in a parametric study performed by finite element method (FEM). Although solutions for the weld toe magnification factor have been presented, these are applicable only to non‐load‐carrying cruciform or T‐butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints, the currently used weld toe magnification factors do not adequately describe the behaviour of weld toe cracks. In this study, the weld toe magnification factor solutions for the three types of welded joints such as cruciform, cover plate and longitudinal stiffener joints were provided through a parametric study using three‐dimensional finite elements. The solutions were formed with exponents and fractions that have polynomial functions in terms of a/c and a/t – that is, crack depths normalised by corresponding half crack lengths and specimen thickness. The proposed weld toe magnification factors were applied to evaluate the fatigue crack propagation life considering the propagation mechanisms of multiple‐surface cracks for all welded joints. It showed good agreement within a deviation factor of two between the experimental and calculated results for the fatigue crack propagation life.     

Fatigue analysis of non-load-carrying fillet welded cruciform joints

The goal of this investigation was to study the effect of local geometrical variations of the weld on the fatigue strength. Therefore the fatigue behaviour of non-load-carrying cruciform fillet welded joint under tensile loading has been studied parametrically. Several two-dimensional (2D) finite element models of the joint were analysed using plane strain linear elastic fracture mechanics (LEFM) calculations in order to get the magnification function M_k. A maximum tangential stress criterion was used to predict the crack growth direction under mixed mode K_I-K_II conditions. The derived M_k solution was then applied both for continuous weld toe cracks and also for semi-elliptical toe cracks at the deepest point of the crack front. An experimental crack aspect ratio development curve was used for propagating semi-elliptical cracks. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. The Paris crack growth law was used to predict the growth rate. The effects of weld toe radius, flank angle and weld size on the fatigue strength were systematically studied. Finally, predicted fatigue strength values corresponding to different assumed crack sizes were compared with the available test results.     

FATIGUE ANALYSIS OF SURFACE CRACKS AT FILLET WELDED TOES

This paper reports a study of fatigue crack growth and coalescing behaviour at semi-elliptical cracks in the stress concentration region of steel plates with fillet shoulders or fillet welds. Fatigue tests were carried out on machined plate specimens with a fillet geometry similar to a fillet welded joint. These specimens were notched and precracked to provide single and multiple coplanar semi-elliptical surface cracks at the fillet toe region. Finite element stress analysis results were used to obtain approximate Mk factors (i.e.: stress concentration magnification factors) for the fillet toe geometry with a semi-elliptical surface crack. An analytical model was developed to simulate crack shape development and growth to failure in the case of multiple coplanar semi-elliptical cracks. In this model, a simple crack coalescing procedure is applied to merge coplanar cracks when they meet by recharacterising the coplanar cracks into a single semi-elliptical crack. Alternative crack growth laws were investigated and comparisons made between actual and predicted shape developments and lives.     

The development of an accurate model for the fatigue assessment of doubly curved cracks in tubular joints

Fatigue tests on tubular joints have shown that as a crack propagates through the chord wall, it curves under the weld toe. This produces, at the brace-chord intersection, a doubly curved semi-elliptical crack emanating from the weld toe. A doubly curved crack in a tubular joint is a very complex geometry which has proved to be difficult to model. In consequence, previous work on the evaluation of stress intensity factors in tubular joints adopted a simplified approach, ignoring the crack curvature under the weld toe. However, in the absence of benchmark solutions, the effects of any modelling approximation on accuracy are impossible to quantify. To address this problem and as part of the research on fatigue assessment methodologies, a technique which is able to accurately model doubly curved cracks in tubularT-joints has been developed at University of Wales, Swansea. This paper describes a detailed account of the generation of the finite element model and the procedure for evaluating the stress intensity factor solutions. The validation results are also presented to demonstrate the reliability of the model developed.     

A simplified fatigue assessment method for high quality welded cruciform joints

The primary goal of this study was to develop an equation relating the geometric parameters to fatigue strength which can be used is routine design assessment. To attain this, the influence of local geometrical weld variations on the fatigue strength of non-load-carrying cruciform fillet welded joints were systematically studied using plane strain linear elastic fracture mechanics (LEFM). The effects of weld toe radius, flank angle and weld size were considered. Both continuous weld toe cracks and semi-elliptical toe cracks with alternate pre-existing defect depths were considered. A previously developed experimental crack aspect ratio development curve was used for assessing the growth of the semi-elliptical cracks using 2D FE models. A total of 152 experimental fatigue data points from six published studies of welded cruciform joints were evaluated. Details of the actual weld toe radius, flank angle and weld size were available for these joints. For the high quality welds evaluated, an assumed initial crack depth of 0.05 mm was found to correlate best with the experimental data. Of all the geometric parameters considered analytically, weld toe radius was found to have the most dramatic influence on fatigue life. A simple equation is proposed which relates welded joint fatigue strength to the ratio weld toe radius/plate thickness for high quality welds.     

Weld magnification factors for semi-elliptical surface cracks in fillet welded T-butt joint models

The weld magnification factor method has been widely used in the determination of the stress intensity factor (SIF) for weld-toe cracks in welded structural components. Weld magnification factors M _kare normally derived from two-dimensional crack models with fillet weld profiles to take account of the effect of weld-notch stress concentration at the deepest point of the crack front. This paper presents a detailed three-dimensional analysis of weld-toe surface cracks in fillet welded T-butt joint models using the finite element method. Effects of the weld notch and the welded attachment stiffness on the SIFs of the weld-toe surface cracks have been studied quantitatively. Weld magnification factors applying to the whole surface crack fronts have been estimated. Numerical results show two contradictory effects; that the effect of weld notch increases SIF values throughout the shallow surface crack fronts which are in the region of notch stress concentration, while the effect of local structural constraint reduces the SIF values. The increase in the SIF values mainly depends upon the relative crack front depth and the decrease in the SIF values mainly depends upon the crack shape aspect ratio for a specific weld profile. Both effects on the weld magnification factors can be estimated separately. A simple approach for deriving the weld magnification factors for various weld-toe surface crack problems is proposed for engineering applications.     

An analysis of fatigue cracks in fillet welded joints

In most of the lower fatigue strength welded joints failure occurs by the propagation of a semi-elliptical surface crack which initiates at the weld toe. In order to analyse the progress of these cracks using fracture mechanics techniques, the solution for the stress intensity factor, K, is required. Fatigue cracks in most welded joints adopt shapes which give low a/2c values (up to approximately 0.3) while solutions in the literature are more applicable to a/2c values close to 0.5. Therefore, results in the literature were used to estimate the stress intensity factor for cracks with low a/2c values. Furthermore, the effect of the weld stress concentration factor was incorporated in the solution. The accuracy of the resulting solution was confirmed by using it to determine ΔK values of weld toe cracks for which crack propagation data were available. The results agreed with the expected da/dN vs. ΔK scatterband obtained from centre-notched specimens.     

Fatigue crack growth simulation in a first stage of compressor blade

A first-stage rotary compressor blade of a Model GE-F6 gas turbine failed due to vibration in early March 2008. Initial investigations showed that pitting on the pressure side of the blade caused micro cracks, leading to larger cracks due to high cycle fatigue. To assess this failure, a series of experimental, numerical, and analytical analyses were conducted. Fractography of the fractured surface of the blade indicated that two semi-elliptical cracks incorporated and formed a single crack. In this study, static and dynamic stress analyses were performed in Abaqus software. Moreover, fracture mechanics criterion was accomplished to simulate fatigue crack growth. This was carried out using a fracture analysis code for 3-dimensional problems (Franc3D) in two states. Firstly, stress intensity factors (SIFs) for one semi-elliptical surface crack and then SIFs for two semi-elliptical surface cracks were taken into account. Finally, the Paris and Forman–Newman–De Koning models were used to predict fatigue life. Since stress level and crack shape in both conditions are the same and the SIF at the crack tip reaches the fracture toughness of the blade, SIFs results indicate that insertion of a second crack has no effect on the final SIF, however, the second crack facilitates the process of reaching the critical length. So, fatigue life in two-crack condition is less than in the one-crack state.     

Stress intensity factors of semi-elliptical surface cracks in pressure vessels by global-local finite element methodology

In the present study the problem of calculation of the stress intensity factors (SIF) of semi-elliptical cracks located in the stress concentration areas of a pressure vessel is numerically solved by advanced global-local finite element (FE) analysis. The common characteristic of the cases solved is that the stress field at the crack area varies along the axial, the circumferential, as well as, the through-the-thickness directions. SIF solutions for such problems are not available, neither analytically, nor numerically, as the currently existing solutions in the literature (numerical results, Newman-Raju empirical equations, weight function solutions, etc.) are only valid for uniform stress distribution along the axial and circumferential directions of the pressure vessel and allow variation only through-the-thickness. The crack locations considered are the intersection of the cylinder to a nozzle and the connection of the cylinder with its hemi-spherical ends. The stress intensity factors are presented in a suitable table format for various geometrical configurations of both the pressure vessel and the semi-elliptical crack, thus providing a useful tool for the fracture mechanics design of cracked pressure vessels. The modeling details of the sub-structuring methodology, employed in the analysis, are extensively discussed and the numerical approach is proven to be very efficient for the SIF calculation of pressure vessel semi-elliptical cracks.     

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates

Surface cracks are among the more common flaws in aircraft and pressure vessel components. Accurate stress analyses of surface-cracked components are needed for reliable prediction of their crack growth rates and fracture strengths. Several calculations of stress-intensity factors for semi-elliptical surface cracks subjected to tension have appeared in the literature. However, some of these solutions are in disagreement by 50–100%.

In this paper stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension are presented. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the number of degrees of freedom in the models from 1500 to 6900. The 6900 degrees of freedom used here were more than twice the number used in previously reported solutions. Also, the stress-intensity variations in the boundary-layer region at the intersection of the crack with the free surface were investigated.     

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.     

WEIGHT FUNCTIONS AND STRESS INTENSITY FACTORS FOR SEMI-ELLIPTICAL CRACKS IN T-PLATE WELDED JOINTS

Weight functions were derived for the deepest point and surface point of a semi-elliptical surface crack in T-plate joints with weld angles between 0 and 45°. These weight functions were derived from reference stress intensity factor solutions obtained from three-dimensional finite element calculations, and verified using stress intensity factors for different non-linear stress fields and for far-field tension and bending cases. The differences between the weight function predictions and the finite element data were less than 10%. They are suitable for semi-elliptical surface cracks with aspect ratios in the range 0.05 ≤ a/c ≤ 1, together with relative depths 0 ≤ a/t ≤ 0.6 and weld angles 0 ≤ φ ≤ 45°.     

Determination of stress intensity factors for surface cracks using fatigue crack growth data

The fatigue growth of semi-elliptical surface cracks in a structural steel under constant amplitude tensile cycling loading is investigated. The AC potential technique is used for sizing and monitoring the profile development of the cracks. The data are used to determine the stress intensity factors along the entire crack front at different stages of crack growth where the effects of front face, finite thickness and finite width are continuously changing. Various numerical solutions are compared with the experimental results     

FATIGUE ANALYSIS AND PREDICTION IN FILLET WELDED JOINTS IN THE LOW THICKNESS RANGE

Abstract— The paper reports the results of a comprehensive research project concerning fatigue life prediction in fillet welded joints. Geometry variables such as main plate thickness, radius of curvature at the weld toe and leg to leg distance were analysed in detail. Fatigue life computations were carried out for semi-elliptical cracks using appropriate FE techniques. The range of results covered several types of welded joints loaded in tension and in bending. A comparison of results was made using two methods of stress intensity determination. Experimental data was also obtained and that included measurements of weld toe radius, monitoring of crack shape and S-N curves. Correlation of results with the theoretical predictions gave generally good agreement. A set of fatigue design curves for fillet welded joints is proposed and in these the designer can introduce the geometry of the weldment.     

Accounting for constraint effects in fracture mechanics analysis of floating production, storage and off-loading vessels and ships

Research has been performed to study the effect of constraint dependent fracture toughness of parent metal and HAZ for steels applied for fabrication of oil and gas floating production, storage and off-loading (FPSO) vessels and ships. A test method was employed to study the HAZ crack tip opening displacement (CTOD) fracture toughness at various levels of constraint avoiding excessive scatter usually associated with conventional HAZ CTOD testing, which may obscure effects of constraint.The objective of the research was to determine the material dependent constraint parameters in Ainsworth and O'Dowd's constraint modified fracture assessment approach and to develop a method based on information from the literature pertaining to the structural constraint in plates with semi-elliptical surface cracks. Results due to Wang and Parks and Nakamura and Parks computed using line-spring and FE analyses were used to establish polynomial expressions for the structural constraint in tension and bending applicable to fracture assessment of shallow fatigue cracks initiated at weld toes in floating offshore structures such as FPSOs.The results of the analyses clearly show that fracture assessment of semi-elliptical surface cracks in tension would be overly conservative if constraint effects are not accounted for in the Option 1 or Option 2 fracture assessment curves or in fracture toughness. It was also found from the tests conducted on specially prepared wide-plate test specimens, that the constraint modified Option 1 curve was conservative for fracture assessment of semi-elliptical surface cracks located in the HAZ of a 500 MPa minimum specified yield strength quenched and tempered steel for offshore application.     

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.     

Fatigue life prediction model for laser clad AISI 4340 specimens with multiple surface cracks

Fatigue test on laser clad AISI 4340 steel specimens show that multiple surface cracks initiate from the clad-toe region due to clad bead overlap features deposited in a raster scan pattern. A fatigue crack growth modeling algorithm capturing the observed fatigue behavior of periodic multiple co-planar semi-elliptical cracks initiating from these features was developed based on crack closure concepts for small cracks to predict the fatigue S–N curve of laser clad AISI 4340 steel specimens. New solutions for stress intensity factor and clad-toe magnification factor (Mk-factor) are presented for surface cracks propagating from the laser clad-toe region. The fatigue life prediction model is able to start from multiple clad-toe surface cracks propagating from the clad-toe region which coalesce into a dominant surface crack or edge crack before final failure. The fatigue life prediction result was compared to the experiment S–N curve test data and gave good agreement.     

A novel weight function for RMS stress intensity factor determination in surface cracks

This paper discusses the problem of stress intensity factor determination in surface cracks. In particular, the concept of root mean square stress intensity factors (RMS SIF) is discussed for the general class of semi-elliptical surface cracks. The weight function SIF derivation method is considered, problems with the existing techniques are highlighted, and a novel technique for the derivation of the RMS SIF weight functions for surface cracks is presented and results are compared with numerical solutions for a variety of loadings and geometries.     

Time-dependent fundamental solutions for homogeneous diffusion problems

This paper describes the applications of the method of fundamental solutions (MFS) for 1-, 2- and 3-D diffusion equations. The time-dependent fundamental solutions for diffusion equations are used directly to obtain the solution as a linear combination of the fundamental solution of the diffusion operator. The proposed scheme is free from the conventionally used Laplace transform or the finite difference scheme to deal with the time derivative of the governing equation. By properly placing the field points and the source points at a given time level, the solution is advanced in time until steady state solutions are reached. Test results obtained for 1-, 2- and 3-D diffusion problems show good comparisons with the analytical solutions and some with the MFS based on the modified Helmholtz fundamental solutions, thus the demonstration present numerical scheme of MFS with the space–time unification has been demonstrated as a promising mesh-free numerical tool to solve homogeneous diffusion problem.     

Effect of biaxial loads on elastic-plastic <Emphasis Type="Italic">J</Emphasis> and crack tip constraint for cracked plates: finite element study

Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE) analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plastic J and crack tip stresses for a plate with a through-thickness crack and semi-elliptical surface crack under positive biaxial loading. For the plate with a through-thickness crack, plate thickness and relative crack length are systematically varied, whereas for the plate with a semi-elliptical surface crack, the relative crack depth and aspect ratio of the semi-elliptical crack are systematically varied. It is found that the reference stress based approach for uniaxial loading can be applied to estimate J under biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected for positive biaxial loading, and thus elastic-plastic J for a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front.