Notched fatigue behavior including load sequence effects under axial and torsional loadings

Notch effects on axial and torsion fatigue behaviors of low carbon steel were investigated. Fully-reversed tests were conducted on thin-walled tubular specimens with or without a transverse circular hole. A shear failure mechanism was observed for both smooth and notched specimens and under both axial and torsion loadings. The notch effect was more pronounced under axial loading, in spite of higher stress concentration factor in torsion. The commonly used nominal S–N approach with fatigue notch factor in conjunction with von Mises effective stress resulted in overly conservative life predictions of both smooth and notched torsion fatigue lives. Neuber’s rule yielded notch root stress and strain amplitudes close to the FEA results for both axial and torsion loadings. The local strain approach based on effective strain obtained from Neuber’s rule or FEA resulted in poor correlation of the fatigue life data of smooth and notched specimens. The Fatemi–Socie critical plane parameter represented the observed failure mechanism and resulted in very good correlations of smooth and notched specimens fatigue data under both axial and torsion loadings. In block loading tests with equal number of alternating axial and torsion cycles at the same stress level, beneficial effect of axial loading was observed. Possible potential reasons for this unexpected behavior are discussed.     

Low cycle fatigue life of Ti–6Al–4V alloy under non-proportional loading

Multiaxial low cycle fatigue life of Ti–6Al–4V under non-proportional loading was studied. Strain-controlled multiaxial fatigue tests at room temperature were carried out using tubular specimens. The strain paths employed were push–pull loading, reversed torsion loading, and two kinds of 90° out-of-phase loadings. The former two loadings are proportional loading tests where the principal directions of stress and strain are fixed in the cycle. The latter two are non-proportional loading tests where there is a 90° phase difference between axial and shear loadings, and the principal directions are cyclically rotated continuously. Failure lives are reduced obviously by non-proportional loadings in comparison with those in proportional loading tests. This paper focuses on determining a suitable fatigue model for evaluating the failure lives of Ti–6Al–4V under multiaxial loading.     

Critical plane approach for the assessment of the fatigue behaviour of welded aluminium under multiaxial loading

ABSTRACT Multiaxial stress states occur in many welded constructions like chemical plants, railway carriages and frames of trucks. Those stresses can have constant and changing principal stress directions, depending on the loading mode. Latest research results on welded steel joints show a loss of fatigue life for changing principal stress directions simulated by out‐of‐phase bending and torsion compared to constant directions given by in‐phase loading. However, aluminium welds reveal no influence of changing principal directions on fatigue life compared to multiaxial loading with constant principal stress directions. This behaviour is not predictable by any conventional hypothesis. A hypothesis on the basis of local normal and shear stresses in the critical plane has been developed and applied to aluminium weldings.     

Fatigue crack growth of a welded tube–flange connection under bending and torsional loading

In this contribution the results of an experimental investigation into the fatigue crack growth of welded tube-to-plate specimens of steel StE 460 under bending, torsion, and combined in-phase and out-of-phase bending/torsion loading are presented. The tests were performed at stress ratios of R = −1 and R = 0. The residual stresses were reduced by thermal stress relief. The fatigue crack development is compared with the prediction on the crack growth rates of Paris. Individual stress intensity factors for the semielliptical surface cracks in the tube-flange specimens are approximated on a weight function analogy using the published solutions of other workers.     

Einfluss der Werkstoffzähigkeit auf das Festigkeitsverhalten unter mehrachsiger Beanspruchung am Beispiel von Schweißverbindungen aus Stahl und Aluminium

Influence of Ductility on the Multiaxial Fatigue Behaviour by the Example of Welded Joints of Steel and Aluminium The multiaxial fatigue behaviour of materials with different ductility under constant and changing principal stress directions is also applicable to welded joints of different materials. For this, welded flange tube connections of the fine grained steel StE 460 and the artificially aged aluminium alloy AlSi1MgMn T6 were investigated under constant amplitude combined bending and torsion. Out‐of‐phase loading, i. e. changing principal stress directions, of the steel joints led to a decrease of fatigue life, which is observed at ductile material states. However, for the aluminium joints out‐of‐phase loading resulted same behaviour as in‐phase loading, which indicates a semi‐ductile material behaviour. The results for the welded steel joints were evaluated on basis of local stresses by the integral hypothesis of the Effective Equivalent Stress EES (WVS). This hypothesis for ductile material states takes into account the life decreasing influence of out‐of‐phase loading by considering the interaction of the shear stresses on different planes. The fatigue behaviour of the aluminium welds is described by the critical plane based combination of shear and normal stresses (KoNoS), which is valid for semi‐ductile material states.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

Fatigue strength of tubular carbon fibre composites under bending/torsion loading

Carbon fibre reinforced polymer composites have been increasingly used on structures frequently subjected to biaxial fatigue loadings. This paper studies the fatigue behaviour of tubular carbon fibre composites under in phase biaxial bending/torsion dynamic loadings. Particularly, it was analysed both the torsion stress and mean stress effects on the fatigue strength and failure mechanisms. Fatigue strength decreases significantly with increased torsional/bending stresses ratio, while the damage becomes faster. For the cases in which a torsion loading was applied the effect of the mean stress on the fatigue strength seems to be well fitted by using a quadratic equation.     

Lebensdauer von Schweißverbindungen unter mehrachsigen Belastungen mit variablen Amplituden – Schadensakkumulation und Hypothese der wirksamen Vergleichsspannung

Fatigue Life of Welded Joints under Multiaxial Variable Amplitude Loading – Damage Accumulation and the Effective Equivalent Stress Hypothesis Flange‐tube joints from fine grained steel FeE 460 with different notch factors were investigated under biaxial constant and Gaussian variable amplitude loading (bending and torsion) in the range of 10⁴ to 5 · 10⁶ cycles to crack initiation and break‐through, respectively. In order not to interfere with residual stresses they were stress relieved by a heat treatment. Damage accumulation under a Gaussian spectrum can be assessed for in‐ and out of phase combined bending and torsion using an allowable damage sum of 0.35 for weldments in the as‐welded state and 0.16 for joints with machined weldments with a lower notch factor of the critical area. For the evaluation of multiaxial in‐ and out‐of‐phase stresses the introduced hypothesis of the effective equivalent stress leads to good results. For this, the knowledge of local strains or stresses is necessary. This hypothesis considers the fatigue‐life reducing influence of out‐of‐phase loading by taking into account the interaction of local shear stresses acting in different surface planes of the material. Further, size effects resulting from the weld geometry and loading mode were included.     

Criteria of multiaxial random fatigue based on stress,strain and energy parameters of damage in the critical plane

In this paper generalized criteria of multiaxial random fatigue based on stress, strain and strain energy density parameters in the critical plane have been discussed. The proposed criteria reduce multiaxial state of stress to the equivalent uniaxial tension–compression or alternating bending. Relations between the coefficients occurring in the considered criteria have been derived. Thus, it is possible to take into account fatigue properties of materials under simple loading states during determination of the multiaxial fatigue life. Presented models have successfully correlated fatigue lives of cast iron GGG40 and steel 18G2A specimens under constant amplitude in‐phase and out‐of‐phase loadings including different frequencies.     

Fatigue crack initiation assessment of welded joints accounting for residual stress

The impact of residual stresses on the fatigue crack initiation life of welded joints is evaluated by the finite element method. The residual stresses of nonload‐carrying cruciform joints, induced by welding and ultrasonic impact treatment, are modelled by initial stresses, using the linear superposition principle. An alternative approach of using modified stress‐strain curves in the highly stressed zone is also proposed to account for the residual stress effect on the local stress‐strain history. An evaluation of the fatigue crack initiation life of welded joints based on the local strain approach is carried out. The predicted results show the effect of residual stresses and agree well with published experimental results of as‐welded and ultrasonic impact treated specimens, demonstrating the applicability of both approaches. The proposed approaches may provide effective tools to evaluate the residual stress effect on the fatigue crack initiation life of welded joints.     

Numerical and experimental validation of residual stresses of laser‐welded joints and their influence on the fatigue behaviour

In this work laser‐welded tube‐tube specimens made of aluminium alloys AlMg3.5Mn and AlSi1MgMn T6 were experimentally tested under constant and variable amplitude loading, under pure axial and pure torsion loading. In order to evaluate the influence on fatigue behaviour of the residual stresses, because of the welding process, some specimens were subjected to postweld heat treatment and then were tested. The numerical analyses, using finite element (FE), were carried out to obtain a reliable estimation of the residual stress in the specimen. The numerical results were in a good agreement with experimental ones obtained by means of hole‐drilling method. Finally, the residual stress distribution was superimposed to stress distribution because of fatigue loads obtained by FE analyses applying local concept, to calculate the stresses in the crack initiation zone and to understand the different types of failure that occurred in as‐welded and relieved specimens.     

Multiaxial fatigue of rubber: Part II: experimental observations and life predictions

Fatigue experiments were conducted with an axial‐torsion specimen covering a wide range of stretch biaxiality and a range of fatigue lives between 10³ and 2 × 10⁶ cycles. These experiments include combined torsion–compression, pure torsion, combined torsion–tension and pure axial tension. Both in‐phase and out‐of‐phase combinations of axial and torsion loading were considered. The multiaxial fatigue experiments described provide empirical evidence from which an understanding of the mechanics of the fatigue process in rubber can be developed. Each of the four equivalence parameters described in Part I has been applied to the axial‐torsion fatigue experiments described in this paper (Part II). These results provide the basis for an analysis of the effects of multiaxial loading on fatigue life, and an assessment of the degree to which the various equivalence parameters are able to rationalize the results in a unified way. For the combined axial and shear strain histories in this study, the maximum principal strain criterion gave the best correlation to fatigue life. Strain energy density gave the worst correlation. The cracking energy density criterion was generally found to give good correlation of fatigue crack nucleation lives from combined axial‐torsion tests. Because it provides a plane‐specific analysis, this criterion appears to be particularly well suited for use in crack nucleation analyses of multiaxial strain histories.     

Fatigue life assessment of welded joints under sequences of bending and torsion loading blocks of different lengths

In this work, the nominal stress concept, the notch stress approach and two critical plane approaches are used to analyse the fatigue endurance of a pipe‐to‐plate welded joint subjected to complex loading histories. Both the pipe and the plate were made of S355JR steel. Starting from already known fatigue endurance curves obtained for the same specimens under pure bending and pure torsion, a first series of tests was conducted, in which specimens were loaded in bending for a given fraction of the estimated life and then in torsion until failure. A similar series of tests was then carried out by changing the loading order: specimens were firstly loaded in torsion for a given fraction of the estimated endurance and then in bending until failure. The whole test campaign was repeated for two different fractions of the estimated life, that is, 0.3 and 0.45, respectively. After that, additional three series of tests were carried out, in which the specimens were subjected to consecutive sequences of bending and torsion blocks of different lengths (short, medium and long, respectively); the relative length of the bending and torsion block in each series was determined in order to produce the same damage. The experimental results, in terms of total damage at failure, were analysed using the Palmgren–Miner hypothesis. For all the assessment methods, the characteristic endurance curves were firstly calibrated on the basis of finite element (FE) analyses and of the experimental results obtained under pure bending and pure torsion loadings. The observed damage at failure resulted always greater than 0.5 for all the employed methods and greater than 1 for most of the tests. The different methods gave similar results, with the critical plane methods giving a slightly more stable damage at failure and a correct determination of the failure location. For all the methods, the damage at failure slightly reduces as the block length shortens.     

Synchrotron diffraction measurement of residual stresses in friction stir welded 5383-H321 aluminium butt joints and their modification by fatigue cycling

This paper presents two‐dimensional information on the residual stresses in 8 mm 5383‐H321 aluminium plates joined by double pass (DP) friction stir welding (FSW). It considers the inherent variability in residual stress magnitudes along 0.5 m lengths of weld pass, and their modification under a sequence of applied fatigue loads. This represents one of a planned series of experiments aimed at illuminating the effects of fatigue cycling on residual stress fields. In this particular case, the magnitudes of the bending fatigue loads (R= 0.1) were chosen to correlate with the measured proof strengths of the weld metal (approximately 160 MPa) and the parent plate (approximately 260–270 MPa). In four‐point bend S–N tests at R= 0.1 on 40 mm wide FS welded specimens of this alloy and plate thickness, these peak stress levels correspond to lives of around 10⁵ cycles and 10⁷ cycles, respectively. Results from the work indicate that significant variability exists among welded plates in peak compressive stress magnitudes (a range of perhaps ?50 MPa to ?140 MPa), although peak tensile stresses were relatively low and more consistent (from around 0 to 30 MPa). Fatigue loading accentuates the peak‐to‐valley stress change and causes an overall translation of the stresses to become more positive. Peak tensile stresses increase several‐fold during fatigue cycling.     

Verhalten gekerbter Biegeproben aus der Aluminiumlegierung AA7075 im Kurzzeitermüdungsbereich

Prediction on Fatigue Life of Notched Specimens under Cyclic Bending Loading Pulsating 3P‐bending fatigue tests are conducted on edge‐notched specimens of AA7075. Measurements of electrical potential drop across notches were used to determine the number of cycles up to crack initiation. Cyclic material data determined from strain–controlled constant amplitude loading are use in FE‐analyses to the determination time functions of the local stresses and strains at the notch root using non‐linear material model according to Chaboche and Lemaitre. Using these FE computations, the fatigue life is predicted by the equivalent strain approach of the “ASME Boiler and Pressure Vessel Code” and compared with the results of the plastic strain energy approach. It is found that both approaches lead to relatively good predictions.     

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.     

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.     

How to reduce the duration of multiaxial fatigue tests under proportional service loadings

This paper deals with a technique to transform a multiaxial stress and strain-time sequence (in service recorded) in a simplified sequence. This simplified sequence is shorter than the original one and equivalent in terms of damage and lifetime: the number of simplified sequences to crack initiation is equal to the number of original sequences. The proposal is based on an energy threshold, below which no micro-crack can initiate or grow in the material. This technique was validated with real loading sequences recorded by strain gauges pasted on a car suspension arm. Fatigue tests were carried out on smooth specimens made of spheroidal graphite cast iron loaded in bending, in torsion and in combined bending and torsion. Experimental fatigue lives under the original sequence and under the simplified one are in very good correlation. Fatigue test duration is reduced up to a factor of 10 for the severe stress–strain sequences tested in this study.     

在多轴载荷下45钢的循环特性

通过多轴疲劳试验，研究了在多轴加载条件下45钢的循环特性变化规律，分析了非比例附加强化、多轴循环软化/硬化特性及疲劳寿命对加载路径参数的依赖性，结果表明，相位角主要影响非比例附加强化程度，幅值比主要影响多轴循环软化/硬化特性，二者都影响多轴疲劳寿命。     

Numerical analysis of low cycle fatigue for welded joints considering welding residual stress and plastic damage under combined bending and local compressive loads

The numerical analysis of low cycle fatigue of HTS‐A steel welded joints under combined bending and local compressive loads are implemented using the damage mechanics approach. First, a finite element numerical simulation of the welding process is employed to extract the welding residual stresses, which are then imported as initial stresses in the subsequent fatigue analysis. Second, a multiaxial fatigue damage model including damage coupled elasto‐plastic constitutive equations and plastic damage evolution formulation is applied to evaluate the mechanical degradation of the material under biaxial fatigue loads. Further, the fatigue lives of the HTS‐A steel welded joints are computed and compared with the experimental results from literature. A series of predicted load‐life curves clearly illustrates the variation of fatigue lives along with the combined loadings. Finally, the effects of local compression on accumulated plastic strain and fatigue damage are studied in detail. It is revealed that the local compression induces a damage competition between two critical zones.