Fatigue strength of welded joints under multiaxial loading: experiments and calculations

In reality most welded components are loaded with a combination of different variable forces and moments that often cause a state of multiaxial stress in the fatigue-critical areas. If the multiaxial loading is non-proportional, traditional deformation-based hypotheses are not able to give a reliable lifetime prediction. This investigation is a cooperation between three German research institutes to build an experimental database for the verification of different concepts of lifetime prediction. In accordance with former investigations, a flange-tube connection made of steel P460 was used. The test program was divided into constant amplitude and variable amplitude tests. The ratio between the nominal bending and shear stress is 1. For the variable amplitude tests, a Gaussian-standard is used. A lifetime prediction software for multiaxial state of cyclic stress was developed. The software has a modular structure and allows calculations with different hypotheses and methods. The calculations are based on the local elastic stresses. This is an acceptable method for high-cycle fatigue. In this work, two general types of calculation, the Integral Approach and Critical Plane Approach and a local stress-based modification of the von Mises Criterion, the hypothesis of effective equivalent stress (EESH) are shown. The damage accumulation is performed with the elementary Miner's rule ( S – N curve without fatigue limit). The statistical distributions of the damage sums are also shown.     

Fatigue strength of laser beam welded automotive components made of thin steel sheets considering size effects

The applicability of and the quality of assessment using the nominal stress, structural stress and notch stress approaches for calculating the fatigue strength of laserbeam welded components made of thin steel sheets has been investigated. For this purpose, the fatigue lives of a longitudinal carrier, an injector and two tube-flange specimens have been determined by tests under constant amplitude loading. Fatigue cracks initiated at sharp root notches on all of these components. While the nominal stress is derived by theory of structural mechanics, the determination of structural and notch stresses is performed using 3D finite element models and solid elements. The structural stress is derived by an extrapolation of surface stress to the fatigue critical notch and the notch stresses by rounding the sharp root notch with a reference radius of r_ref = 0.05 mm. For all of the concepts used, the endurable stresses have been compared to the design SN-curves recommended by the International Institute of Welding (IIW).On comparing the quality of assessment of the different concepts, the notch stress approach shows the highest scatter. The highest endurable notch stresses occur in specimens with crack initiation at weld ends. These specimens have a very small highly loaded weld length. The lowest endurable stresses are determined for specimens with a long, equally loaded weld. The reason for these findings can be explained by statistical size effects. For an improved fatigue assessment, an easily applicable method is introduced, which takes into account the highly stressed weld length.     

Fatigue assessment of laserbeam‐welded aluminium joints under multiaxial loading

This paper presents the results and evaluation of the multiaxial fatigue behaviour of laserbeam‐welded overlapped tubular joints made from the artificially hardened aluminium alloy AlSi1MgMn T6 (EN AW 6082 T6) under multiaxial loadings with constant and variable amplitudes. Several fatigue test series under pure axial and pure torsional loadings as well as combined axial and torsional proportional and non‐proportional loadings have been carried out in the range of 2·10⁴ to 2·10⁷ cycles. The assessment of the investigated thin‐walled joints is based on a local notch stress concept. In this concept the fatigue critical area of the weld root is substituted by a fictitious notch radius r_ref = 0.05 mm. The equivalent stresses in the notch, considering especially the fatigue life reducing influence of non‐proportional loading in comparison to proportional loading, were calculated by a recently developed hypothesis, which is called the Stress Space Curve Hypothesis (SSCH). This hypothesis is based on the time evolution of the stress state during one load cycle. In addition, the fatigue strength evaluation of multiaxial spectrum loading was carried out using a modified Gough‐Pollard algorithm.     

Fatigue strength of notched specimens made of 40CrMoV13.9 under multiaxial loading

The work deals with multiaxial fatigue strength of notched round bars made of 40CrMoV13.9 steel and tested under combined tension and torsion loading, both in-phase and out-of-phase. The axis-symmetric V-notches present a constant notch root radius, 1 mm, and a notch opening angle of 90°; the notch root radius is equal to 4 mm in the semi-circular notches where the strength in the high cycle fatigue regime is usually controlled by the theoretical stress concentration factor, being the notch root radius large enough to result in a notch sensitivity index equals to unity. In both geometries the diameter of the net transverse area is 12 mm.The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. Altogether more than 120 new fatigue data are summarised in the present work, corresponding to a one-year of testing programme.All fatigue data are presented first in terms of nominal stress amplitudes referred to the net area and then re-analysed in terms of the mean value of the strain energy density evaluated over a given, crescent shape volume embracing the stress concentration region. For the specific steel, the radius of the control volume is found to be independent of the loading mode.     

Local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading

In the notch stress intensity approach to the fatigue assessment of welded joints, the weld toe is modelled as a sharp V-notch and the local stress distributions in plane problems are given on the basis of the relevant mode I and mode II notch stress intensity factors (N-SIFs). These factors quantify the magnitude of asymptotic stress distribution obeying Williams’ solution. If the V-notch opening angle at the weld toe is constant and the mode II is not singular, the mode I N-SIF can be directly used to summarize the fatigue behaviour of welded joints. In all the other cases, varying the V-notch angle or including multiaxial loading conditions (where typically both Mode I and Mode III stress distributions are singular), the synthesis can be carried out on the basis of the mean value of the strain energy density over a well-defined volume surrounding the weld toe or the weld root. By using this scalar quantity, two fatigue scatterbands are obtained for structural steels and aluminium alloys, respectively. The material-dependent radius R_C of the control volume (area) is carefully identified with reference to conventional arc welding processes.Sometimes the weld toe radius is found to be very different from zero. The local strain energy approach can be extended as it stands also to these cases, providing a gradual transition from a N-SIF-based approach to a K_t-based approach.     

Fatigue strength investigations of welded details of stiffened plate structures in steel ships

Ships are prone to fatigue due to high cyclic loads mainly caused by waves and changing loading conditions. Therefore, fatigue is an important criterion during design. Different approaches are applied to the fatigue strength assessment. However, the results are varying and the validity of results from small-scale fatigue tests for real structures is sometimes unclear. Therefore, deeper fatigue strength investigations were performed within a German industry-wide joint research project aiming at the harmonization of the approaches. Regarding ship structures, two types of structures were selected for the investigations. The first concerns web frame corners being typical for ro/ro ships from which three models were tested. The associated small-scale specimen is a cruciform joint. The second type is the intersection between longitudinals and transverse web frames, which recently showed fatigue failures in containerships. Five models were tested, three under constant and two under variable amplitude loading. The associated small-scale specimen is a longitudinal attachment on a stiffener top. All large-scale tests showed a relatively long crack propagation phase after first cracks had appeared, calling for a reasonable failure criterion. For the numerical analysis, the nominal, the structural hot-spot as well as the effective notch stress approach have been applied. The latter allows the consideration of the weld shape which could partly explain differences in the observed and calculated failure behaviour. The applicability of the different approaches is quite good if some specific aspects are observed. Insofar the investigations give a good insight into the strength behaviour of complex welded structures and into current problems and opportunities offered by numerical analyses.     

Fatigue strength CAE system for three-dimensional welded structures

ABSTRACT Fatigue strength assessment methods are applied to practical arc-welded structural features that have complex three-dimensional geometry. Two methods are investigated in the present research. The criterion of the first method is cyclic plastic zone size, which is calculated from stress singularity parameters. The criterion of the second method is hot spot stress. These fatigue strength criteria are proved to be applicable to the fatigue strength assessment of practical arc-welded structural features. These criteria enable a critical point at which fatigue cracks are most likely to initiate to be specified for each type of welded joint and load. Consequently, the critical point simplifies the classification of various welded joints. Furthermore, a fatigue strength computer-aided engineering system, which includes functional engines for the evaluation of the fatigue strength of a designed shape, is proposed.     

The theoretical strength of fcc crystals under multiaxial loading

Atomistic modeling of a special triaxial loading of six perfect fcc crystals is performed by means of pseudopotential density functional method. The triaxial stress state is simulated as a superposition of axial pressure and transverse biaxial stresses. The transverse stresses are treated as adjustable parameters and their influence on the theoretical compressive strength is evaluated for the 〈1 0 0〉 and the 〈1 1 1〉 crystallographic orientations of the loading axis. The obtained results revealed that the compressive strengths are increasing linear functions of the transverse compressive stresses. On the other hand, the tensile transverse stresses lower the compressive strength. This implies that the compressive strengths of individual crystals approach a zero value when some critical (characteristic) levels of tensile biaxial stresses are reached. These stresses are then considered to be the theoretical tensile biaxial strengths.     

Fatigue of welded steel joints under wideband loadings

Fatigue tests were conducted on high-strength welded steel cruciform-shaped specimens subjected to random loadings to investigate the effects of loading intensity, nonnormality and frequency bandwidth on the rate of fatigue damage accumulation. The test result are compared with predictions made using the Rayleigh approximation and rainflow analysis in terms of cycles and times to failure. Results indicate that nonnormality can significantly increase the rate of fatigue damage accumulation and result in nonconservative fatigue life estimates if it is effect is not accounted for properly. Likewise, frequency content was also found to influence the rate of fatigue damage accumulation, but to a lesser extent than nonnormality.     

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.     

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.     

Fatigue strength prediction of ultra high strength steel butt‐welded joints

First, fatigue tests were performed on butt‐welded joints made of novel direct quenched ultra high strength steel with high quality welds. Two different welding processes were used: MAG and Pulsed MAG. The weld profiles, misalignments and residual stresses were measured, and the material properties of the heat‐affected zone were determined. Fatigue tests were carried out with constant amplitude tensile loading both for joints in as‐welded condition and for joints after ultrasonic peening treatment. Finally, in fatigue strength predictions, the crack initiation phase was estimated using the procedures described by Lawrence et al. [Lawrence F V, Ho N J and Mazumdar P K (1981) Predicting the fatigue resistance of welds. Annu. Rev. Mater. Sci, 11, 401–425]. The propagation phase was simply estimated using S–N curves for normal quality butt welds, which may contain pre‐existing cracks or crack‐like defects eliminating the crack initiation stage.     

Fatigue strength of welded butt joints in thin and slender specimens

This paper investigates the geometrical properties of the butt-welded thin and slender specimens and their influence on the fatigue strength. The fatigue tests and the finite element analysis are used to investigate the influence. The weld shape, axial misalignment and angular misalignment and the actual shape of the specimen are studied by the extensive optical geometry measurements. The structural hot spot and the notch stress method are used for the fatigue strength assessment. The results reveal that for thin and slender specimens the straightening under the axial loading is significant and thus the relationship between the structural and the nominal stress is highly nonlinear. The straightening effect is influenced by the slenderness and by the curved shape of the plate near the weld. If these effects are included by applying the geometrically nonlinear analysis the fatigue strength of thin and slender welded specimens in notch stresses at two million load cycles corresponds to that of thick welded specimens. The relationship between the structural and the notch stress is however constant regardless of the specimen straightening.     

Fatigue assessment of metallic components under uniaxial and multiaxial variable amplitude loading

In the present paper, the fatigue lifetime of metallic structural components subjected to variable amplitude loading is evaluated by applying 2 different multiaxial high‐cycle fatigue criteria. Such criteria, proposed by some of the present authors, are based on the critical plane approach and aim at reducing a given multiaxial stress state to an equivalent uniaxial stress condition. In particular, the procedure employed by both criteria consists of the following 3 steps: (1) definition of the critical plane; (2) counting of loading cycles; and (3) estimation of fatigue damage. Finally, the previous criteria are validated by comparing the theoretical results with experimental data related to smooth metallic specimens subjected to uniaxial and multiaxial variable amplitude loading.     

Fatigue characterization and modeling of 30CrNiMo8HH under multiaxial loading

Fatigue of 30CrNiMo8HH steel alloy has been studied thoroughly. Uniaxial cyclic tension-compression, cyclic torsion, proportional tension-torsion, and non-proportional tension-torsion at various strain ratios have been considered. Tests were performed at standard laboratory conditions on solid and tubular specimens machined from an actual driveline component. Fractography was conducted on the tested samples to investigate the fatigue mechanisms involved. Under torsion, large numbers of early micro cracks were found to emanate from the sample's surface, with a few propagating into very long longitudinal cracks. In biaxial tests, cracks tend to propagate into the gauge reducing the cross section area. A strain energy density fatigue parameter has been employed for life prediction of the material under uniaxial and biaxial loading. The life prediction method is based on two different cracking mechanisms that agree with the observed cracking mechanisms in torsion and biaxial loading of 30CrNiMo8HH steel alloy studied here. Energy-based properties are obtained and the predicted lives are compared to experimental results. The results obtained agree well with experiments.     

Fatigue strength of CFRP strengthened welded joints with corrugated steel plates

This paper presents an experimental and numerical research on the carbon fibre reinforced polymer (CFRP) strengthened welded joints with corrugated plates. The effectiveness of the strengthening in the improvement of fatigue strength has been examined experimentally on the test joints through varying the number and the layout of the CFRP laminates. The test results show that the joints with transition curvature region reinforcement and single side reinforcement produce slightly lower rigidity but longer fatigue life in contrast to those with full width reinforcement on the double side of the main plate. Furthermore, a simplified two dimensional analytical model which allows for the geometric characteristics of the joint has been proposed to investigate the stress intensity factor of mode I. The proposed analytical model has been simulated by finite element technique and its solution result is compared with previously reported theoretical calculation. Parametric studies have been performed to investigate the effects of the number of CFRP layers and the moduli of carbon fibre & adhesive on the stress intensity factor. The combined influence of the corrugation angle and crack depth has also been considered. It has been found that these effects on the stress intensity factor are more significant for the joints with smaller corrugation angle.     

Fatigue crack growth property of laser beam welded 6156 aluminium alloy

Fatigue crack growth behaviours in different welding zones of laser beam welded specimens were investigated using central crack tension specimens for 6156 aluminium alloy under constant amplitude loading at nominal applied stress ratio R = 0.5, 0.06, ?1. The experimental results showed that base metal (BM) exhibited superior fatigue crack resistance compared to weld metal (WM) and heat‐affected zone (HAZ). Crack growth resistance of WM was the lowest. The exponent m values for BM and HAZ at different stress ratios are close and around 2.6, while m for WM at different stress ratio is around 4.7. The discrepancy between crack growth rates for WM and BM is more evident with increasing stress ratio, while it is a little change for HAZ and BM. Change of the microstructure in WM deteriorates the resistance of fatigue crack growth compared to BM. It was mainly due to grain boundary liquation and dissolving of second‐phase particles in the weld region. It was also found that the variety of fatigue crack resistance for different welding zones is in conformity with the change of hardness. BM with the highest hardness exhibited the maximum resistance for fatigue crack, and WM with the lowest hardness exhibited the minimum fatigue crack resistance.     

Fatigue strength of steels under multicycle impact loading

The functional dependence of the fatigue limit under impact loading on the fatigue limit in harmonic loading was derived for structural steels, together with the dependence of the coefficient of the effect of impact on impact toughness. The impact toughness values at which multicycle impact loading is detrimental are determined.Translated from Problemy Prochnosti, No. 3, pp. 87–93, March, 1994.