Fatigue strength assessment of laser stake‐welded web‐core steel sandwich panels

This paper investigates the fatigue strength assessment of web‐core steel sandwich panels. The production of these structures is made possible by laser stake welding. The investigation in this study considered two series of panels, one being an empty steel structure and the other filled with in situ polyurethane foam in order to increase the panel stiffness. Both series were tested under cyclic bending loading condition (R = 0) until one of the panel joints failed completely. A 3D panel bending response was analysed using finite element method. The J‐integral values at the panel joints were obtained by means of plane strain finite element analysis and by using displacements from 3D panel response. The influence of the weld geometry on the J‐integral value was investigated. It was found that the J‐integral value is similar in the cases of the average and critical geometry. The contact between the joint plates is possible in some cases, but its influence proved to be insignificant for the fatigue strength assessment. The study further shows that by using the average geometry, the J‐integral approach was able to identify the critical panel joints and present the fatigue strength results from both panel series in a narrow scatterband. The fatigue strength at two million cycles obtained for the panels within this study was in agreement with the laser stake welds and other steel joint types from previous studies. However, the slope of the panels fatigue resistance curve was found to be shallower than in the case of joints.     

A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings

Full penetration T butt weld joints between a tube and its flange are considered, subjected to pure bending, pure torsion and a combination of these loading modes. The model treats the weld toe like a sharp V‐notch, in which mode I and mode III stress distributions are combined to give an equivalent notch stress intensity factor (N‐SIF) and assess the high cycle fatigue strength of the welded joints. The N‐SIF‐based approach is then extended to low/medium cycle fatigue, considering fatigue curves for pure bending and pure torsion having the same slope or, alternatively, different slopes. The expression for the equivalent N‐SIF is justified on the basis of the variation of the deviatoric strain energy in a small volume of material surrounding the weld toe. The energy is averaged in a critical volume of radius R_C and given in closed form as a function of the mode I and mode III N‐SIFs. The value of R_C is explicitly referred to high cycle fatigue conditions, the material being modelled as isotropic and linear elastic. R_C is thought of as a material property, independent in principle of the nominal load ratio. To validate the proposal, several experimental data taken from the literature are re‐analysed. Such data were obtained by testing under pure bending, pure torsion and combined bending and torsion, welded joints made of fine‐grained Fe E 460 steel and of age‐hardened AlSi1MgMn aluminium alloy. Under high cycle fatigue conditions the critical radius R_C was found to be close to 0.40 mm for welded joints made of Fe E 460 steel and close to 0.10 mm for those made of AlSi1MgMn alloy. Under low/medium cycle fatigue, the expression for energy has been modified by using directly the experimental slopes of the pure bending and pure torsion fatigue curves.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based on J‐integral

Load‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJ with stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effective J‐integral range was modified by ΔJ_p in order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios of R > 0.     

Plastic collapse load prediction and failure assessment diagram analysis of cracked circular hollow section T‐joint and Y‐joint

This paper concerns the validation of standard safety assessment procedure given in BS 7910 for cracked circular hollow section T‐joint and Y‐joint, using the finite element (FE) results. A robust and efficient FE mesh generator is developed to produce the 3D models of the cracked joints and to calculate the elastic J‐integral (J_e) and elastic–plastic J‐integral (J_ep) values of the crack respectively. In order to verify its accuracy and convergence, the plastic collapse loads (P_c) obtained from experimental tests and FE predictions are compared; they agree very well with each other. It is also found from experimental tests that the plastic collapse loads (P_c) predicted using the BS 7910 reduction factor (F_AR) are safe and conservative. Subsequently, the failure assessment diagrams (FADs) of five cracked T‐joints and three cracked Y‐joints are constructed using the FE results, following the J‐integral method, which is classified as Level 3C in BS 7910. Thereafter, a comparison between the constructed FAD curves and the standard Level 2A curve is carried out, and it is observed that the safety assessment results using the standard Level 2A curve might be unsafe because some parts of the constructed FAD curves fall inside of the standard one. A penalty factor of 1.15 working on both the elastic–plastic J‐integral and plastic collapse load (P_c) is proposed to move all the constructed FAD curves just outside of the standard Level 2A curve.     

Advances in J‐integral estimation of circumferentially surface cracked pipes

This paper describes enhanced J‐integral estimation schemes for pipes with circumferential semi‐elliptical cracks subjected to tensile loading, global bending and internal pressure. These schemes are given in two different forms to cover the wide ranges of geometries and material parameters; the modified GE/EPRI method and the modified reference stress method. In the former method, new plastic influence functions for fully plastic J‐integral estimation are developed based on extensive three‐dimensional finite element calculations. In the latter method, new optimized reference loads are suggested and utilized to predict the J values. To verify the feasibility of these two schemes, J‐integral values obtained from further detailed FE analyses are compared to those from the proposed schemes. Because the estimated J‐integrals agree fairly well with the detailed FE analysis results, the new solutions can be applied for accurate structural integrity assessment of different size pipes with a circumferential surface crack.     

Elastic–plastic fatigue crack growth in 18G2A steel under proportional bending with torsion loading

The paper presents the results of fatigue crack growth on low‐alloy 18G2A steel under proportional bending with torsion loading. Specimens with square sections and a stress concentration in the form of external one‐sided sharp notch were used. The tests were performed under the stress ratios R=?1, ?0.5 and 0. The test results were described by the ΔJ‐integral range and compared with the ΔK stress intensity factor range. It has been found that there is a good agreement between the test results and the model of crack growth rate, which includes the ΔJ‐integral range.     

A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.     

Low‐cycle fatigue/high‐cycle fatigue interactions in notched Ti‐6Al‐4V*

Combined low‐cycle fatigue/high‐cycle fatigue (LCF/HCF) loadings were investigated for smooth and circumferentially V‐notched cylindrical Ti–6Al–4V fatigue specimens. Smooth specimens were first cycled under LCF loading conditions for a fraction of the previously established fatigue life. The HCF 10⁷ cycle fatigue limit stress after LCF cycling was established using a step loading technique. Specimens with two notch sizes, both having elastic stress concentration factors of K_t = 2.7, were cycled under LCF loading conditions at a nominal stress ratio of R = 0.1. The subsequent 10⁶ cycle HCF fatigue limit stress at both R = 0.1 and 0.8 was determined. The combined loading LCF/HCF fatigue limit stresses for all specimens were compared to the baseline HCF fatigue limit stresses. After LCF cycling and prior to HCF cycling, the notched specimens were heat tinted, and final fracture surfaces examined for cracks formed during the initial LCF loading. Fatigue test results indicate that the LCF loading, applied for 75% of total LCF life for the smooth specimens and 25% for the notched specimens, resulted in only small reductions in the subsequent HCF fatigue limit stress. Under certain loading conditions, plasticity‐induced stress redistribution at the notch root during LCF cycling appears responsible for an observed increase in HCF fatigue limit stress, in terms of net section stress.     

Residual strength at −40 °C of a precracked cold‐formed rectangular hollow section made of ultra‐high‐strength steel – an engineering approach

This study investigated the residual strength of a precracked cold‐formed rectangular hollow section made of novel ultra‐high‐strength steel. The primary goal was to experimentally discover the residual strength of the structure when used in low temperature service conditions. The secondary goal was to predict the residual strength by using a J‐integral approach with nonlinear finite element calculations and to compare these predictions with measured results. The experimental tests were carried out with a beam in four‐point bending loading. The test specimens were taken from a cold‐formed rectangular hollow section fabricated from direct quenched (untempered) ultra‐high‐strength steel S960 QC omitting the annealing in the fabrication process. The tests for final failure were carried out at ?40 °C, with the exception of the first pilot test. There were two kinds of tests: (1) the beam was cyclically loaded until the final fracture or the fatigue precrack was first introduced and (2) the specimen was then subjected to a quasistatic bending loading condition until it failed. The new experimental results matched well with our predictions, and both confirmed the high toughness of ultra‐high‐strength steel in beam construction studied, even at a low ambient temperature.     

Fatigue behaviour of die‐casting aluminum alloy suspension arms for scooters

The aim of the paper is at qualifying a methodology for the fatigue life assessment of structural components obtained by die‐casting for vehicle applications. Full‐scale fatigue tests were conducted on the back suspension arms of mid‐size scooters. Two loading conditions, i.e. bending and combined bending plus torsion, were considered as representative of typical operating conditions. Fatigue tests showed that the locations of failure initiation is different for the two loading configurations. Material was characterized by means of small size standard specimens extracted from the components in order to be representative of the effective material conditions, particularly of the surface. Both static (tensile) and fatigue tests were conducted, making use of three different R‐ratios. A finite element (FEM) model of the suspension arm, representative of full‐scale test conditions was set‐up in order to interpret the tests. The sub‐modelling approach was adopted in order to get accurate evaluations of the stress–strain fields with reasonable computing resources and elaboration time. Combined elastic and elastic–plastic analyses were necessary to estimate the stress cycles in the regions critical for fatigue damage. Employing the material properties given by small‐size specimens and the proposed FE analysis technique, predictions of either the locations of failure initiation and the fatigue strength of the component were obtained, in quite good agreement with full‐scale tests.     

Low and high‐cycle fatigue properties of an ultrahigh‐strength TRIP bainitic steel

The scope of this study is to characterize the mechanical properties of a novel Transformation‐Induced Plasticity bainitic steel grade TBC700Y980T. For this purpose, tensile tests are carried out with loading direction 0, 45 and 90° with respect to the L rolling direction. Yield stress is found to be higher than 700 MPa, ultimate tensile strength larger than 1050 MPa and total elongation higher than 15%. Low‐cycle fatigue (LCF) tests are carried out under fully reverse axial strain exploring fatigue lives comprised between 10² and 10⁵ fatigue cycles. The data are used to determine the parameters of the Coffin–Manson as well as the cyclic stress–strain curve. No significant stress‐induced austenite transformation is detected. The high‐cycle fatigue (HCF) behaviour is investigated through load controlled axial tests exploring fatigue tests up to 5 × 10⁶ fatigue cycles at two loading ratios, namely R = ?1 and R = 0. At fatigue lives longer than 2 × 10⁵ cycles, the strain life curve determined from LCF tests tends to greatly underestimate the HCF resistance of the material. Apparently, the HCF behaviour of this material cannot be extrapolated from LCF tests, as different damage, cyclic hardening mechanisms and microstructural conditions are involved. In particular, in the HCF regime, the predominant damage mechanism is nucleation of fatigue cracks in the vicinity of oxide inclusions, whereby mean value and scatter in fatigue limit are directly correlated to the dimension of these inclusions.     

A new proposal for assessment of the fatigue strength of steel butt‐welded joints improved by peening (HFMI) under constant amplitude tensile loading

Experimental fatigue data for butt‐welded joints in as‐welded condition and under constant amplitude tensile loading were analysed using the effective notch stress system and a new master curve analysis that takes the local stress ratio, R_local, into account. The local stresses needed for computation of R_local are calculated with the notch strain approach in conjunction with the reference radius concept. The main focus was to predict with the derived master curve the fatigue strength of peened butt‐welded joints. The lowest surface residual stresses after peening were first estimated based on reported measurements and an analytical lower bound result. The predictions showed quite similar strength dependences and FAT values as reported for high‐frequency mechanical impact treated welds for applied stress ratio R = 0.1. The benefits of peening reduce faster for higher strength steels when R increases. When R = 0.5, the FATs are practically the same for all steel grades.     

Fatigue behaviour of tubular AlMgSi welded specimens subjected to bending–torsion loading

This paper is concerned with an experimental and numerical study of the fatigue behaviour of tubular AlMgSi welded specimens subjected to biaxial loading. In‐phase torsion–bending fatigue tests under constant amplitude loading were performed in a standard servo‐hydraulic machine with a suitable gripping system. Some tests in pure rotating bending with and without steady torsion were also performed. The influence of stress ratio R and bending–torsion stress ratio were analysed. Correlation of the fatigue lives was done using the distortion energy hypothesis (DEH), based on the local stresses and strains. The applicability of the local strain approach method to the prediction of the fatigue life of the welded tubular specimens was also investigated. Static torsion has only a slight detrimental influence on fatigue strength. The DEH (von Mises criterion) based on local stresses in the weld toes was shown to satisfactorily correlate fatigue lives for in‐phase multiaxial stress–strain states. The stress–strain field intensity predictions were shown to have less scatter and are in better agreement with the experimental results than the equivalent strain energy density approach.     

High‐cycle and very‐high‐cycle fatigue behaviour of a titanium alloy with equiaxed microstructure under different mean stresses

The fatigue behaviour of a titanium alloy Ti‐6Al‐4V with equiaxed microstructure (EM) under different values of tensile mean stress or stress ratio (R) was investigated from high‐cycle fatigue (HCF) to very‐high‐cycle fatigue (VHCF) regimes via ultrasonic axial cycling. The effect of mean stress or R on the fatigue strength of HCF and VHCF was addressed by Goodman, Gerber, and Authors' formula. Three types of crack initiation, namely, surface‐with‐RA (rough area), surface‐without‐RA, and interior‐with‐RA, were classified. The maximum value of stress intensity factor (SIF) at RA boundary for R < 0 keeps constant regardless of R in HCF and VHCF regimes. The SIF range at RA boundary for R > 0 also keeps constant regardless of R in VHCF regime, but this value decreases linearly with the increase of R for surface RA cases. The microstructure observation at RA regions gives a new result of nanograin formation only in the cases of negative stress ratios for the titanium alloy with EM, which is explained by the mechanism of numerous cyclic pressing.     

Stress‐Strength Reliability Analysis with Extreme Values based on q‐Exponential Distribution

When dealing with practical problems of stress–strength reliability, one can work with fatigue life data and make use of the well‐known relation between stress and cycles until failure. For some materials, this kind of data can involve extremely large values. In this context, this paper discusses the problem of estimating the reliability index R = P(Y < X) for stress–strength reliability, where stress Y and strength X are independent q‐exponential random variables. This choice is based on the q‐exponential distribution's capability to model data with extremely large values. We develop the maximum likelihood estimator for the index R and analyze its behavior by means of simulated experiments. Moreover, confidence intervals are developed based on parametric and nonparametric bootstrap. The proposed approach is applied to two case studies involving experimental data: The first one is related to the analysis of high‐cycle fatigue of ductile cast iron, whereas the second one evaluates the specimen size effects on gigacycle fatigue properties of high‐strength steel. The adequacy of the q‐exponential distribution for both case studies and the point and interval estimates based on maximum likelihood estimator of the index R are provided. A comparison between the q‐exponential and both Weibull and exponential distributions shows that the q‐exponential distribution presents better results for fitting both stress and strength experimental data as well as for the estimated R index. Copyright © 2016 John Wiley & Sons, Ltd.     

General time‐dependent C(t) and J(t) estimation equations for elastic‐plastic‐creep fracture mechanics analysis

This paper presents equations for estimating the crack tip characterizing parameters C(t) and J(t), for general elastic‐plastic‐creep conditions where the power‐law creep and plasticity stress exponents differ, by modifying the plasticity correction term in published equations. The plasticity correction term in the newly proposed equations is given in terms of the initial elastic‐plastic and steady‐state creep stress fields. The predicted C(t) and J(t) results are validated by comparison with systematic elastic‐plastic‐creep FE results. Good agreement with the FE results is found.     

Effect of residual stresses on crack behaviour in single edge bending specimens

Residual stresses due to manufacturing processes, such as welding, change the load bearing capacity of cracked components. The effects of residual stresses on crack behaviour in single edge bending specimens were investigated using Finite element analyses. Three parameters (J, Q and R) were used to study the crack behaviour. The J‐integral predicts the size scale over which large stresses and strains exist, the constraint parameter Q describes the crack‐tip constraint as a result of geometry, loading mode and crack depth and the constraint parameter R is used to describe the constraint resulting from residual stresses. To carry out a systematic investigation on the effect of residual stresses on the J‐integral and crack‐tip constraints, models under different combinations of residual stresses and external loads with different crack depths were analysed. It has been shown that the crack‐tip constraint R increased by tensile residual stresses around the crack‐tip. On the other hand, the constraint parameter R decreased and tended to zero at high external load levels.     

J-integral-based approach to fatigue assessment of laser stake-welded T-joints

The aim of this paper is to investigate the influence of the plate thickness on the fatigue strength of laser stake-welded T-joints under the tension loading condition. Fatigue tests were conducted on specimens with plate thicknesses below 5 mm subjected to tension loading with the load ratio R = 0. The statistical analysis of the weld geometry showed a normal distribution of the each parameter that was measured. In addition, the parameters had similar proportions in comparison to the specimens with plate thicknesses above 5 mm. FE analysis was performed with the aim of determining the stress state in the joint along with the J-integral. If the square root of the J-integral, √ΔJ, is used as the fatigue strength assessment parameter, the fatigue strength obtained at five million cycles is similar as in the case of other steel welded joint types. The investigation concluded that the stress state changes with the reduction of the plate thicknesses and the contribution of fracture mode II becomes significant. However, using √ΔJ as a fatigue strength assessment parameter ensures that the complex state of the mixed fracture mode loading is accurately accounted for. This fact further enables the fatigue strength of laser stake-welded T-joints of any plate thicknesses to be described by means of a narrower scatterband than the one obtained by the nominal stress approach.     

EURAXLES – A global approach for design,production and maintenance of railway axles: WP1 – Advances in fatigue load analysis and reliability assessment of railway axles

The work presented in this paper was led within the collaborative project “Euraxles” of the FP7 program of the European Commission. It aimed at developing processes and methods that contribute to the minimization of the risk of fatigue failure of railway axles in service. This paper focuses on the development of a method to assess the reliability of axles according to fatigue damage. The proposed approach is mainly based on the stress strength interference analysis (SSIA) and the fatigue‐equivalent‐load (FEL) methods. It aims at calculating the axles’ probability of fatigue failure, by characterizing the variability of real in‐service loads and the scatter of the axles fatigue strength, and at evaluating more accurately the actual design margins. First of all, the main lines of the stress strength interference analysis method are recalled. This method aims at evaluating the in‐service reliability of components for their design or their homologation. It is used in many industries for various applications (mechanical components or systems, electronic elements, etc.). In the second part, the fatigue load analysis method that is proposed for railway axles is described. It starts with a post‐processing of an axle load measurement: from a time signal of forces applied to both wheels fitted on the axle, fatigue cycles of bending moment applied to the axle are identified and transformed into a cyclic equivalent load, the M_eq, which is a measurement of the severity of the initial variable load. Then, virtual but realistic load spectra are generated, thanks to a classification operation followed by a random draw of elementary load data that considers the operation and maintenance conditions of the axle. All the spectra are then analysed thanks to the fatigue‐equivalent‐load method in order to build the distribution of in‐service load severities that gives a picture of the stress to which the axles are submitted. In the third and last part of the paper, the methods are applied to real data of “Société nationale des chemins de fer français” (SNCF), the French national railway operator. Sensitivity analyses are performed in order to quantify the effect on the M_eq of variations of parameters and to verify the convergence and robustness of the process. Finally, results obtained for a passenger coach are given. The comparison between the distribution of load severities and the normative load, defined as according to european standards EN13103, shows that, for the studied axle, the normative load is very conservative. Using the axles fatigue limits identified on full‐scale tests, a stress strength interference analysis is performed to calculate the probability of failure of the axle.