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.     

The Prediction of Fatigue Crack Initiation Life in Spot Welds

Abstract: In this paper, strain‐based fatigue life prediction method has been used to estimate the fatigue crack initiation life of spot‐welded joints of Mild Steel JSC270D and Ultra‐High Strength Steel JSC980Y. To do so, the joints were simulated using three‐dimensional finite‐element (FE) models, and then nonlinear FE analysis was performed to obtain the local stress and strain ranges and finally, the Morrow equation was applied to estimate the crack initiation lives. The results have been compared with those obtained from experimental crack growth morphology. In addition, the difference between fatigue limits for smooth specimens and spot‐welded joints for mentioned materials has been briefly discussed. It has been shown that mean stress values in the Ultra‐High Strength Steel can significantly decrease the fatigue limit of spot‐welded joint because even at very low load level the stresses exceed the yield point at the root of nugget of spot‐welded joint, while the amount of mean stress in the Mild Steel for the same load level is much less than that of Ultra‐High Strength Steel. The comparison between numerical results of fatigue crack initiation lives and experimental data provided good agreement between numerical predictions and crack growth morphology observations. The results also shows that in some cases, depending on the joint type, the life spent in the nucleation phase can be an important part of the final failure lifetime.     

Fatigue life estimation of tubular joints – a comparative study

In fatigue analysis, the structural detail of tubular joint has taken great attention among engineers. The DNV/GL‐RP‐0005 is covering this topic quite well for simple and clear joint cases. For complex joint and geometry, where joint classification is not available and there is limitation on validity range of non‐dimensional geometric parameters, the challenges become a fact among engineers. The classification of joint is an important factor to consider in fatigue analysis. These joint configurations are identified by the connectivity and the load distribution of tubular joints. To overcome these problems to some extent, this paper compares the fatigue life of tubular joints in offshore jacket according to the stress concentration factors (SCF) in DNV/GL‐RP‐0005 and finite element method employed in Abaqus/CAE. The paper presents the geometric details, material properties and load history of the considered jacket structure. It then describes the global structural analysis and identification of critical tubular joints for fatigue life estimation. Hence, fatigue life is determined based on the guidelines provided in design codes. Fatigue analysis of tubular joints is conducted using the finite element employed in Abaqus/CAE as the next major step. Finally, predicted SCFs and fatigue lives are compared, and these observations tend to conclude that even though the fatigue life, which is calculated based on code given SCFs, provides more realistic prediction to the simple uniplanar joints, there is a doubt for complex joints and geometry, where joint classification is not available. Also, the study emphasized that it is very important to preciously investigate SCFs by considering accurate geometry of complex tubular joints for a good judgement of fatigue life.     

Crack growth predictions in a complex helicopter component under spectrum loading

Fatigue crack growth predictions have been made on a helicopter round‐robin crack configuration. The crack configuration was a small corner defect at the edge of a large central hole in a flanged plate made of 7010 aluminium alloy and the component was subjected to a simulated helicopter spectrum loading. The crack growth rate data and the stress‐intensity factor (K) solution for the crack configuration were provided in the round‐robin. The FASTRAN life‐prediction code was used to predict fatigue crack growth under various load histories on the aluminium alloy, such as Rotorix and Asterix, on both compact tension C(T) specimens and the complex crack configuration. A BEASY three‐dimensional stress‐intensity factor solution for the round‐robin problem was also provided for this paper and is compared with the original K solution. Comparisons are made between measured and predicted fatigue crack growth lives for both crack configurations. The predicted lives for the C(T) specimens were 15–30% longer than the measured lives; and crack growth in the round‐robin configuration agreed very well in the early stages of crack growth, but the life was 30% short of the test results at the final crack length.     

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.     

Short crack approach for multiaxial fatigue assessment

A significant part of the fatigue life is spent during short crack growth. Therefore, modelling of short fatigue crack growth offers an opportunity to improve the accuracy of numerical life assessment. Besides stating some general remarks on the short crack approach itself and on multiaxial fatigue criteria, a short crack growth based fatigue life prediction approach for multiaxial non‐proportional loading is presented. This approach accounts for the geometrical size effect by considering the geometry correction functions for semi‐elliptical surface cracks in inhomogeneous gradient stress fields. The geometrical size effect is becoming significant for notch radii smaller than four times the defined technical crack size. Additionally, life influencing factors due to the statistical size effect have been taken into account. The comparison of calculated and experimentally observed fatigue lives of shouldered shafts made of S460N with notch radii of 0.2 to 4.0 mm under non‐proportional tension and torsion loading yields a satisfying accuracy.     

Modellierung des Ermüdungsrisswachstums in Schweißverbindungen unter Berücksichtigung von Schweißeigenspannungen

The present paper contains research results determined within the framework of a project called IBESS (?Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“) by the Materials Mechanics Group of the Technische Universität Darmstadt [1]. Aim is to calculate the fatigue life of welded joints by taking into account the effect of residual stresses and the influence of the weld toe geometry. Here, the fatigue life is regarded as period of short fatigue crack growth. Two and three dimensional finite element models, with cracks as initial defects, are constructed for this purpose. Fatigue crack growth analyses are performed by using the node release technique together with the finite element program ABAQUS. The welding residual stresses as well as the plasticity induced crack closure effects are considered. Structural calculations are performed in order to introduce residual stress fields in finite element models. The calculated compressive residual stress field matches the measured one especially in the weld notch area. The effective cyclic J‐integral (ΔJ_eff) is used as crack tip parameter in a relation similar to the Paris equation for the calculation of the fatigue life. For this purpose, a Python code was written for the determination of ΔJ_eff at every crack length phase. The calculated fatigue lives were compared with experimental data and a good accordance between both results was achieved. The impact of welding residual stresses on ΔJ_eff as well as on the fatigue life during short crack growth was investigated. As expected, results revealed that at lower stress amplitude, a compressive residual stress field is favorable to the fatigue life, whilst a tensile residual stress field is unfavorable. The influence of residual stresses can be neglected only for large load amplitudes.     

Fatigue life prediction based on equivalent stresses for laser beam welded 6156 Al‐alloy joints under variable amplitude loading

In the present work, a simple fatigue life prediction approach is proposed using fracture mechanics for laser beam welded Al‐alloy joints under variable amplitude loading. In the proposed approach, variable amplitude loading sequence is transformed into an equivalent constant amplitude loading using the root mean square model. The crack growth driving force K^* is chosen to describe the fatigue crack growth rate. The influences of residual stress and its relaxation on fatigue life are taken into account in the proposed approach. The fatigue lives are also predicted using the traditional approach based on the S‐N curves and the rainflow counting method. The predicted results show that the proposed approach is better than the traditional approach.     

A modification of UniGrow 2‐parameter driving force model for short fatigue crack growth

In this paper, a modification of the UniGrow model is proposed to predict total fatigue life with the presence of a short fatigue crack by incorporating short crack propagation into the UniGrow crack growth model. The UniGrow model is modified by 2 different methods, namely the “short crack stress intensity correction method” and the “short crack data‐fitting method” to estimate the total fatigue life including both short and long fatigue crack propagations. Predicted fatigue lives obtained from these 2 methods were compared with experimental data sets of 2024‐T3, 7075‐T56 aluminium alloys, and Ti‐6Al‐4V titanium alloy. Two proposed methods have shown good fatigue life predictions at relatively high maximum stresses; however, they provide conservative fatigue life predictions at lower stresses corresponding high cycle fatigue lives where short crack behaviour dominates total fatigue life at lower stress levels.     

Fatigue crack growth in 7249‐T76511 aluminium alloy under constant‐amplitude and spectrum loading

Fatigue crack growth tests were conducted on compact, C(T), specimens made of 7249‐T76511 aluminium alloy. These tests were conducted to generate crack growth rate data from threshold to near fracture over a wide range of load ratios (R). Four methods were used to generate near threshold data: (1) ASTM E‐647 load reduction (LR), (2) compression pre‐cracking constant‐amplitude (CPCA), (3) compression pre‐cracking LR, and (4) constant crack mouth opening displacement LR method. A crack closure analysis was used to develop an effective stress‐intensity factor range against rate relation using a constraint factor (α = 1.85). Simulated aircraft wing spectrum tests were conducted on middle crack tension, M(T), specimens using a modified full‐scale fatigue test spectrum. The tests were used to develop the constraint‐loss regime (plane strain to plane stress; α = 1.85 to 1.15) behaviour. Comparisons were made between the spectrum tests and calculations made with the FASTRAN life prediction code; and the calculated crack growth lives were generally with ±10% of the test results.     

Size effects in the fatigue behavior of welded steel tubular bridge joints

Tubular space trusses for bridge applications use thick‐walled tubes. The reduction in fatigue resistance due to geometrical size effects is thus an important issue. In order to carry out a thorough study, both fatigue tests on large‐scale specimens and advanced 3D crack propagation modelling were carried out at ICOM/EPFL. The study is limited to circular hollow sections (CHS) K‐joints. An alternate current potential drop (ACPD) system is used to measure crack depth on nodes of the tested truss specimens. The results obtained from the tests are given in the paper in terms of S‐N data, crack depth versus number of cycles and deduced crack propagation rates. The numerical model was developed using the dual boundary elements method (DBEM), software BEASY?, and was validated with fatigue tests data. The stress intensity factors (SIF) along the doubly curved crack front at different crack depths were obtained. With this model, a parametric study investigates the influence of geometry, size and load case on fatigue life. The results of both proportional and non‐proportional sizing effects on fatigue strength are presented. The paper shows that size effects (proportional and non‐proportional) can be expressed as a function of the non‐dimensional parameters and chord thickness.     

Variable amplitude fatigue of autofrettaged diesel injection parts

Experimental and analytical investigations of constant and variable amplitude fatigue life of not autofrettaged and autofrettaged components have been performed. In variable amplitude loading the new standardised CO mmon‐ RA il‐ L oad sequence CORAL has been used as well as two‐level‐tests with small cycles at high mean stresses interrupted by large cycles for the evaluation of load sequence effects. The results of the two level tests show that small cycles with amplitudes far below the fatigue limit cause fatigue damage. Life calculations have been performed according to the nominal stress approach with S‐N‐curves and improved Miner’s Rule, linear‐elastic fracture mechanics with 3D‐weight functions, elastic‐plastic fracture mechanics applying an extended strip yield‐model, and explicit 3D‐FE‐simulation of fatigue crack growth with predefined crack fronts. All approaches are appropriate for predicting realistic variable amplitude lives. From a practical point of view the explicit 3D‐FE‐simulation of fatigue crack growth is too time‐consuming. However, such simulations show that the approaches based on linear‐elastic fracture mechanics and elastic‐plastic fracture mechanics with extended strip yield‐model capture the essential physics of fatigue crack growth in a realistic way.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

Fatigue crack growth and life prediction of a single interference fitted holed plate

To understand the different aspects of fatigue behaviour of complex structural joints it will be much helpful if the effects of different parameters are studied separately. In this article, to study the isolated effect of interference fit on fatigue life a pined hole specimen is investigated. This specimen is a single‐holed plate with an oversized pin which force fitted to the hole. The investigation was carried out both experimentally and numerically. In the experimental part, interference fitted specimens along with open hole specimens were fatigue tested to study the experimental effect of the interference fit. In the numerical part, three‐dimensional finite element (FE) simulations have been performed in order to obtain the created stresses due to interference fit and subsequent applied longitudinal load at the holed plate. The stress distribution obtained from FE simulation around the hole was used to predict crack initiation life using Smith–Watson–Topper method and fatigue crack growth life using the NASGRO equation with applying the AFGROW computer code. The predicted fatigue life obtained from the numerical methods show a good agreement with the experimental fatigue life.     

含多处损伤宽板螺接搭接件疲劳寿命研究

对含多处损伤（Multiple Side Damage,MSD）宽板搭接件做了等幅疲劳试验和断口分析,得到搭接件的疲劳寿命和孔边MSD裂纹的形成特点、裂纹前沿形状及扩展历程。结果表明,搭接件的疲劳破坏具有一定的隐蔽性,其疲劳寿命的绝大部分消耗在螺栓头下裂纹扩展阶段,当孔间裂纹出现首次连通时,搭接件剩余寿命约为总寿命的0.7%~9.4%。基于有限元软件FRANC2D/L和裂纹扩展分析软件AFGROW,建立了考虑钉载、第二弯矩和孔间裂纹干涉等影响因素的含MSD宽板搭接件疲劳寿命计算模型,并对孔边多裂纹的扩展寿命进行了计算分析。计算结果与试验结果的对比表明,该文所建寿命计算模型具有一定的精度,能满足工程需要,计算结果和结论可作为该类结构损伤容限设计的参考依据。     

Fatigue tests of notched specimens made from butt joints at steel

The weld toe as well as the weld root of joints acts as a geometrical notch, which decreases the fatigue strength of welded components. Local approaches used for fatigue assessment account for the local stress concentration when referring to the notch stress as a fatigue parameter. This applies also to the approaches based on the notch stress intensity factor like, for example, the averaged strain energy density, neglecting the actual notch radius and considering a sharp notch as a simplification. A uniform S‐N curve valid for different types of welded joints and failure locations was derived from re‐analyses of fatigue test results as documented in literature. The fatigue tests described in this paper aimed at validating that energy‐based S‐N curve by dedicated tests on artificially notched specimens. At first, four parameters were investigated in order to estimate their influence on the fatigue strength and to select appropriate notch geometries for the final step of the test campaign. The advantages of these tests are that both the exact notch geometry and the local stress range at the notch, including misalignment effects, were identified and considered in experimental data analysis. This paper presents the results of the rather comprehensive testing activities and comparisons with the design‐S‐N curve mentioned, yielding unexpected fatigue behaviour. This can be explained by the short crack propagation life.     

Fatigue life estimation of ultrasonic spot welded Mg alloy joints

Lightweight magnesium alloys are increasingly used in automotive and other transportation industries for weight reduction and fuel efficiency improvement. The structural application of magnesium components requires proper welding and fatigue resistance to guarantee their durability and safety. The objective of this investigation was to identify failure mode and estimate fatigue life of ultrasonic spot welded (USWed) lap joints of an AZ31B-H24 magnesium alloy. It was observed that the solid-state USWed joints exhibited a superior fatigue life compared with other welding processes. Fatigue failure mode changed from interfacial failure to transverse-through-thickness crack growth with decreasing cyclic load level, depending on the welding energy. Fatigue crack initiation and propagation occurred from both the notch tip inside the faying surface and the edge of sonotrode indentation-footprints due to the presence of stress concentration. A life prediction model for the spot welded lap joints developed by Newman and Dowling was adopted to estimate the fatigue lives of the USWed magnesium alloy joints. The fatigue life estimation, based on the fatigue crack growth model with the global and local stress intensity factors as a function of kink length and the experimentally determined kink angle, agreed fairly well with the obtained experimental results.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Investigation of small fatigue crack initiation and growth behaviour of nickel base superalloy GH4169

Surface replication method was utilized to monitor the small fatigue crack initiation and growth process of single‐edge‐notch tension specimens fabricated by nickel base superalloy GH4169. Three different stress levels were selected. Results showed that small fatigue cracks of nickel base superalloy GH4169 initiated from grain boundaries or surface inclusions. The small fatigue crack initiation and growth stages took up about 80–90% of the total fatigue life. Multiple major cracks were observed in the notch root, and specimen with more major cracks seemed to have smaller fatigue life under the same test conditions. At the early growth stage, small crack behaviour might be strongly influenced by microstructures; thus, the crack growth rates had high fluctuations. However, the stress level effect on the small fatigue crack growth rates was not distinguishable for the three different stress levels. And no clear differences were found among the crack initiation lives by using replication technique.     

Development of fatigue cracks from mechanically machined scratches on 2024‐T351 aluminium alloy—part I: experimentation and fractographic analysis

Clad and unclad 2024‐T351 aluminium alloy sheets, weakened by mechanically machined scratches, were fatigued to investigate the effect of small surface damage, like scribe marks, on aircraft fuselage joints. The role of scratch cross section geometry on fatigue life of scribed components was analysed. Scratches between 25 and 185 µm deep, with 5, 25 and 50 µm root radii, were cut on sample surface by using diamond‐tipped tools. After testing, fracture surfaces were examined using a scanning electron microscope, and crack growth rates were measured by striation counting. Scratches reduced aluminium fatigue life under tensile and bending load up to 97.8% due to multiple crack nucleation at their roots. Short cracks nucleated from sharp scratches coalesced to form unique elongated cracks growing through sample thickness. Cracks initiated from scratches were typical short cracks, growing faster than conventional long cracks. Despite the different scribing process, fatigue data of regular diamond tool cut scribes can be used to conservatively predict life reduction owing to ploughed in‐service scribe marks on fuselage joints. Finite element analyses on scribed samples and the fatigue life prediction models are described in Part II of this paper.