FATIGUE CRACK GROWTH FROM TWO-DIMENSIONAL SURFACE DEFECTS

Abstract The growth of semi-elliptical cracks emanating from single surface defects under cyclic bending loading conditions has been investigated. Experiments to determine crack shape development during fatigue have been conducted on specimens containing spark-machined starter defects of various shapes and sizes. The results appear to indicate that the size and shape of the initial starter defect only affects the developing crack shape until the crack depth is approximately 20% of the specimen thickness; upon reaching this depth, all crack shapes (independent of initial size and shape) appear to be very similar. A mathematical model, based on the Newman and Raju stress intensity solution for semi-elliptical cracks, has been utilised to predict effectively the shape of the cracks developing from the various single starter defects with aspect (a/c) ratios as large as 3.     

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.     

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.     

Stress intensity factors in shafts subjected to torsion and axial loading

The finite element method has been used to determine stress intensity factors (SIFs) of surface cracks in plain and fillet notched shafts subjected to torsion and axial loadings. The SIFs were obtained as part of a simulation of surface crack growth under fatigue conditions. The shape of the crack front was also predicted and compared to the crack front shapes observed on several test specimens.     

ANALYSIS OF FATIGUE CRACK GROWTH IN ROTARY BEND SPECIMENS AND RAILWAY AXLES

Fatigue crack growth tests have been carried out on pre-cracked specimens of steel AFNOR XC 38 under rotary bending conditions. The semi-elliptical surface crack shape evolution was determined and the results were analyzed by da/dN =f(ΔK) using a stress intensity factor solution for semi-elliptical surface cracks in round bars subjected to a bending stress modified to take into account the rotatary bending conditions. Results show a very good correlation with fatigue crack growth data obtained in standard centre cracked tension specimens of the same steel. An application to the sensitivity of design parameters to an analysis of cracked railway axles is proposed, allowing an improvement in maintenance procedures.     

A new method for modelling the coalescence and growth of two coplanar short cracks of varying lengths in AA7050-T7451 aluminium alloy

The growth, interaction and coalescence of two coplanar short cracks of varying lengths in AA7050-T7451 aluminium alloy were studied under low amplitude cyclic loading. Fractographic studies showed that the way in which the fracture surfaces developed was dependent on the relative crack sizes, however interactions between the cracks did not significantly affect the crack growth rates before the tips of the cracks touch to form a single crack. Subsequently, the longitudinal growth rates of the crack were retarded for a period which appeared necessary for the newly coalesced crack to form a single semi-elliptical shape before resuming growth rates of a single crack. A new mathematical model was developed to account for this behaviour.     

THE PROPAGATION OF NON-COPLANAR SEMI-ELLIPTICAL FATIGUE CRACKS

Abstract— The results of fatigue tests on specimens containing parallel offset and parallel collinear configurations of multiple non-coplanar cracks are presented. The fatigue growth of parallel collinear cracks is shown to be significantly affected by crack-tip shielding and parallel offset cracks are shown to grow almost independently before their adjacent tips overlap. Subsequent growth in the region of overlap results in coalescence which begins when the deviating crack tips come into contact below the surfaces of the specimens. Simplified predictions of the propagation of offset non-coplanar semi-elliptical cracks are also presented and their implications for the prediction of fatigue lives in structures containing offset coplanar cracks are assessed.     

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.     

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.     

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.     

Interacting dissimilar semi-elliptical surface flaws under tension and bending

Stress intensity factors for two dissimilar interacting semi-elliptical coplanar surface flaws (cracks) in a semi-infinite elastic body are obtained under overall tension and bending. First the basic equations for a general planar crack normal to the free surface are established, using the method of equivalent eigen- or transformation strains (the body force method). Then the results are specialized for application to elliptical cracks. Numerical values are obtained for various configurations and crack shapes. Results are compared with those of two-dimensional collinear cracks. Finally, an approximate procedure for estimating the stress intensity factors for a general three-dimensional crack is suggested.     

Effect of specimen geometry on fatigue crack growth rates for the railway axle material EA4T

This paper presents experimental results on fatigue crack growth propagation for the EA4T steel widely employed in the manufacturing of railway axles. Apart from standard M(T) and C(T) specimens, the investigations include bending tests on cylindrical bars and rectangular plates containing semi-elliptical surface cracks, geometries representative of surface flaws in components. The results give an evidence of the crack growth rate dependency upon the geometry and loading conditions of cracked specimens. The paper also concludes that fatigue crack growth rates correlate with crack tip plasticity, even within low and middle stress intensity factor ranges. Some remarks are provided with respect to the significance of the results for assessing residual lives of railway axles under in-service conditions.     

STRESS INTENSITY FACTOR SOLUTIONS FOR SEMI-ELLIPTICAL WELD-TOE CRACKS IN T-BUTT GEOMETRIES

Abstract— Weld toe magnification factors are widely used in the evaluation of stress intensity factors for cracks in welded structures. Traditionally, the weld magnification factor has been determined from 2-D plane strain models containing edge cracks. However, it has long been recognised that a semi-elliptical weld toe crack cannot be accurately represented by a 2-D approximation due to the 3-D nature of the geometry. As a consequence, some recent research has been carried out using 3-D numerical modelling, which highlights the limitations of the 2-D approach. Nevertheless, 3-D solutions are still scarce and are of limited validity due to the difficulties associated with creating the numerical models. This paper reports the most extensive 3-D numerical investigation of semi-elliptical cracks in T-butt geometries to date. Based on the numerical results, new and accurate equations for weld magnification factors were derived, which quantify the 3-D effects present and emphasise the importance of the attachment. The results obtained from these equations are then used in an assessment of existing solutions.     

The measurement and analysis of semi-elliptical surface fatigue crack growth

Fatigue tests in which the development of crack shape was studied with the a.c. field measurement technique have been conducted on semi-elliptical cracks growing in flat plate specimens under tension and bending stresses. The a.c. field measurement technique, which was used to measure the cracks, exploits the fact that high frequency alternating current tends to flow in a thin skin along the metal surface and the crack depths can be interpreted from the changes in the voltage distribution produced by the presence of a crack. In order to interpret the measured voltages so as to provide accurate estimates of the crack length and depth, a theoretical analysis of the a.c. field around a semi-elliptical crack is required. This analysis was used to interpret the measured voltages in terms of the changes in the crack shape. Finally the interpreted data on the changes in crack shape were then used to test the accuracy of various stress intensity factor solutions.     

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.     

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.     

Stress intensity factors for coalescing and single corner flaws along a hole bore in a plate

The objective of this paper is to describe the effects of crack interaction on stress intensity factors for two symmetric coplanar corner flaws located along a hole bore. This numerical analysis employes the Finite Element-Alternating Method to determine Mode I stress intensity factors for single and coalescing corner flaws. Using single flaw stress intensity factors as a reference, analysis of crack size and shape effects on $\text{K}{}_{\mathrm{I}}$ for coalescing corner flaws indicates the stress intensity factor for crack points along the hole bore increases as the crack tip separation distance decreases. Interaction effects are not experienced by hole bore crack points when the crack tip separation distance is equal to or greater than half of the largest corner flaw dimension.     

Subcritical Crack Growth of semi-elliptical surface cracks in a turbine rotor

The subcritial growth of semi-elliptical surface cracks in the front face of a cylindrical disk was calculated. The disk represents a part of a turbine rotor. The stress intensity factors, which are the basis for the calculations presented here, were given in a former paper [1]. The loads steps considered consist of an inhomogeneous hoop stress distribution, which occurs at a distinct time-step of the start – up procedure of the turbine, and of the stress free state, respectively. By use of a Paris-law the growth of different initial cracks was evaluated under the assumption that the crack geometry remains semi-elliptic.     

Growth evaluation of multiple interacting surface cracks. Part II: Growth evaluation of parallel cracks

In Part I of the current work, experiments on fatigue crack growth from notches and crack growth simulation for a coalesced crack with re-entrant portion were conducted. It was revealed that the growth rate in area is the same for the same applied stress and area of crack face. The main conclusion was that a crack with a re-entrant portion can be replaced with a semi-elliptical crack of the same area for the growth prediction. In this study, the influence of the interaction on the growth of semi-elliptical/semi-circular surface cracks in the parallel position was investigated. The stress intensity factor for various relative positions and shapes was evaluated by finite element analyses, and the magnitude of the interaction was quantified. Then a crack growth simulation for parallel surface cracks was developed. It was revealed that the magnitude of the interaction increases continuously during the crack growth and that, for a growth prediction, the parallel surface cracks can be replaced with a single crack of the same size on the projected plane when the relative spacing is close enough. It was concluded that the simulation can estimate the crack growth of interacting cracks and the replacement can be carried out when the offset distance is less than the crack depth.     

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.