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.     

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.     

Influence of non‐proportional bending with torsion on fatigue life of 10HNAP steel within the range of crack initiation and propagation

The paper presents a precise analysis of the influence of non‐proportional loading of specimens on fatigue life during initiation and propagation of fatigue cracks. Simulation of the fatigue life of specimens was based on relations describing propagation rate of the fatigue cracks. The Paris and Forman relations were applied; they were integrated after previous introduction of relationships for the equivalent range of the stress intensity factor ΔK_eq and including the phase shift angle ? between amplitudes of the bending moment and the torsional moment. Under bending with torsion, range of the equivalent stress intensity factor ΔK_eq includes ranges of stress intensity factors for loading modes I and III, i.e. ΔK_I and Δ K_III. The performed tests of 10HNAP constructional steel under cyclic bending with torsion allowed us to determine the influence of the phase shift angle ? on the fatigue life. It has been proved that increase of the phase shift angle from ?= 0° to ?= 60° and the ratio of amplitude of the bending moment M_ag to amplitude of the torsional moment M_as equal to 1.33, 2 and 4 cause increase of the fatigue life of the tested specimens. The maximum increase of the fatigue life of specimens made of 10HNAP steel was 73% (M_ag/M_as= 2, ?= 45°).     

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.     

Effect of strain ratio on cyclic deformation and fatigue of extruded AZ61A magnesium alloy

Strain-controlled fatigue experiments were conducted on an extruded AZ61A magnesium alloy at three strain ratios (R_ɛ = −∞, −1, 0) using smooth tubular specimens. As the strain ratio decreased, stronger cyclic hardening, more asymmetric hysteresis loop, smaller stress amplitude, lower mean stress, and higher initial plastic strain amplitude were observed. These phenomena were associated with twinning in the compressive phase and detwinning in the tensile phase during cyclic deformation. At the same strain amplitude, fatigue life increased with decreasing strain ratio. The strain-fatigue life curve at each strain ratio exhibited a distinguishable kink. Such a kink point represents a demarcation point above which persistent twinning–detwinning occurs under cyclic loading. Two Smith, Watson, and Topper (SWT) fatigue criteria can predict the fatigue lives of the material at all strain ratios satisfactorily.     

Multiaxial fatigue of quenched and tempered U2 steel: Testing and fatigue life prediction

Tension‐compression, tension‐tension, torsional, and 90° out‐of‐phase axial‐torsional fatigue tests were performed on a quenched and tempered U2 steel. All tests were conducted under force/torque control because macroscopic plastic strains were insignificant in the life range of interest (from 10⁴ to 2 × 10⁶ loading cycles). Stress‐based versions of the Fatemi‐Socie critical plane parameter and of the Smith‐Watson‐Topper parameter with a critical plane interpretation were evaluated using the experimental data. The Smith‐Watson‐Topper parameter was not able to correlate the test data. The Fatemi‐Socie method correlated most of the test data within factor‐of‐three boundaries. A modified Crossland invariant‐based parameter made of two interaction rules between the shear stress amplitude and the maximum hydrostatic stress, and of a definition of shear stress amplitude based on the maximum prismatic hull method, yielded fatigue life estimates in reasonable agreement with the experimental observations.     

Scaled boundary finite‐element analysis of a non‐homogeneous elastic half‐space

As a result of stresses experienced during and after the deposition phase, a soil strata of uniform material generally exhibits an increase in elastic stiffness with depth. The immediate settlement of foundations on deep soil deposits and the resultant stress state within the soil mass may be most accurately calculated if this increase in stiffness with depth is taken into account. This paper presents an axisymmetric formulation of the scaled boundary finite‐element method and incorporates non‐homogeneous elasticity into the method. The variation of Young's modulus (E) with depth (z) is assumed to take the form E=m_Ez^α, where m_E is a constant and αis the non‐homogeneity parameter. Results are presented and compared to analytical solutions for the settlement profiles of rigid and flexible circular footings on an elastic half‐space, under pure vertical load with αvarying between zero and one, and an example demonstrating the versatility and practicality of the method is also presented. Known analytical solutions are accurately represented and new insight regarding displacement fields in a non‐homogeneous elastic half‐space is gained. Copyright © 2003 John Wiley & Sons, Ltd.     

Improving low-cycle fatigue properties of rolled AZ31 magnesium alloy by pre-compression deformation

The effect of pre-compression deformation on the low-cycle fatigue properties and cyclic deformation behavior of as-rolled AZ31 alloy was investigated by performing the stress-controlled low-cycle fatigue tests at room temperature. Fatigue properties and cyclic damage process should be closely related to the twins. The present work aimed to investigate the deformation mechanism and fatigue life caused by the introduced {1 0−1 2} twinning–detwinning from the viewpoint of stress amplitude. The results reveal that the twins contribute to the fatigue properties and cyclic damage process of AZ31 alloy. There were noticeable changes in hysteresis loops, microstructures and fatigue lives when the stress amplitude increased from 120 to 150 MPa. The fatigue life of pre-compressed samples was more superior to that of the as-rolled sample under different stress amplitudes, especially under the stress amplitude close to the tensile yield strength of the as-rolled sample.     

Corrosion fatigue behaviour of 304 stainless steel under proportional and non‐proportional multiaxial loading condition

Corrosion fatigue and electrochemical tests under proportional loading and non‐proportional loading were conducted on 304 stainless steel in 0.63 mol L^?1 NaCl solution at room temperature. Two biaxial loading paths were applied to study the effect of proportional loading and non‐proportional loading on corrosion fatigue behaviour. Surface and fractographic observations of multiaxial corrosion fatigue specimens were carried out by scanning electron microscopy. It was shown that proportional loading had a more significant effect on the occurrence of local corrosion compared with non‐proportional loading because the continuous rotation of the principal stress plane under non‐proportional loading inhibits the pit formation.     

Multiaxial fatigue of V‐notched steel specimens: a non‐conventional application of the local energy method

The paper deals with the multi‐axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V‐notched specimens were subjected to combined tension and torsion loading, both in‐phase and out‐of‐phase, under two nominal load ratios, R=?1 and R= 0, also taking into account the influence of the biaxiality ratio, λ=τ_a/σ_a. The notch geometry of all axi‐symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V‐notch angle of 90° and a net section diameter of 12 mm. The results from multi‐axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of non‐propagating cracks measured from some run‐out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V‐notch tip. The control volume is found to be dependent on the loading mode.     

Influence of the Al(Co,Ni) layer on the corrosion resistance of a cobalt based alloy (Mar‐M‐509®)

In the present work, the results of studies on the structure and corrosion resistance of Al(Co, Ni) layer are shown. The diffusion Al(Co, Ni) layer was created on the cobalt alloy Mar‐M‐509 substrate by chemical vapor deposition (CVD) method with aluminum trichloride (AlCl₃) under the hydrogen atmosphere. The scanning electron microscope (SEM) observations and microtomography measurements of layers were performed. Also an analysis of the chemical (energy‐dispersive X‐ray spectroscopy (EDS)) and phase (X‐ray diffraction (XRD)) composition was carried out. By the X‐ray diffraction method (sin² φ) also the residual stresses were calculated in the matrix of the material. The corrosion resistance was tested with impedance and potentiodynamic methods in 0.1 M Na₂SO₄, 0.1 M H₂SO₄ solutions and acidulous 0.1 M NaCl solution (pH = 4.2) at room temperature. The results indicate that the analyzed layer with a thickness of about 14 μm have a similar corrosion resistance compared to the base material – Mar‐M‐509^® cobalt alloy. Only in the strongly acidic environments, the corrosion resistance of the layer is remarkably decreased.     

Low‐cycle fatigue life behaviour of BS 460B and BS B500B steel reinforcing bars

This paper investigates the low‐cycle fatigue resistance of BS 460B and BS B500B steel reinforcing bars and proposes models for predicting their fatigue life based on plastic‐strain (?_ap) and total‐strain (?_a) amplitudes. Constant‐amplitude, strain‐controlled low‐cycle fatigue tests were carried out on these bars under cyclic load with a frequency of 0.05 Hz. The maximum applied axial strain amplitude (?_s,max) ranges from 3 to 10% with zero and non‐zero mean strains. The strain ratios (R = ?_s,min/?_s,max) used are R =?1, ?0.5 and 0. Hysteresis loops were recorded and plastic and total strain amplitudes were related to the number of reversals (2N_f) to fatigue failure and models for predicting the number of reversals to fatigue failure were proposed. It is concluded that the predicted fatigue life of these bars is very accurate when compared with the measured experimental fatigue life results for wide range of values of strain ratios. It is also observed that based on plastic‐strain amplitude, BS B500B consistently has a longer life (higher number of cycles to failure) than those of BS 460B for all R values; however, at low plastic‐strain amplitudes they tend to behave similarly, irrespective of R value. Other observations and conclusions were also drawn.     

A critical plane‐energy model for multiaxial fatigue life prediction

A new critical plane‐energy model is proposed in this paper for multiaxial fatigue life prediction of metals. A brief review of existing methods, especially on the critical plane‐based and energy‐based methods, is given first. Special focus is on the Liu–Mahadevan critical plane approach, which has been shown to work for both brittle and ductile metals. One potential drawback of the Liu–Mahadevan model is that it needs an empirical calibration parameter for non‐proportional multiaxial loadings because only the strain terms are used and the out‐of‐phase hardening cannot be explicitly considered. An energy‐based model using the Liu–Mahadevan concept is proposed with the help of the Mróz–Garud plasticity model. Thus, the empirical calibration for non‐proportional loading is not needed because the out‐of‐phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature, and the proposed model is shown to work for both proportional and non‐proportional multiaxial loadings without the empirical calibration.     

Multiaxial fatigue of a short glass fibre reinforced polyamide 6.6 – Fatigue and fracture behaviour

The multiaxial fatigue behaviour of a short glass fibre reinforced polyamide 6.6 (PA66-GF35) is investigated on hollow tubular specimens in the range of fatigue lives between 10² and 10⁷ cycles. Fatigue experiments included pure tension, pure torsion, combined tension–torsion at different biaxiality ratios and phase shifting angles between the stress components. Tests were carried out with load ratio R = 0 and R = −1 at room temperature as well as at 130 °C. The influence of biaxiality ratio, phase angle between load components and load ratio is discussed.An extensive analysis of the fracture behaviour is performed on the specimens to recognise the crack nucleation and propagation mechanisms; failure modes were evaluated via optical and scanning electron microscopy.     

Low‐cycle fatigue behavior of a newly developed cast aluminum alloy for automotive applications

The drive for increasing fuel efficiency and decreasing anthropogenic greenhouse effect via lightweighting leads to the development of several new Al alloys. The effect of Mn and Fe addition on the microstructure of Al‐Mg‐Si alloy in as‐cast condition was investigated. The mechanical properties including strain‐controlled low‐cycle fatigue characteristics were evaluated. The microstructure of the as‐cast alloy consisted of globular primary α‐Al phase and characteristic Mg₂Si‐containing eutectic structure, along with Al₈(Fe,Mn)₂Si particles randomly distributed in the matrix. Relative to several commercial alloys including A319 cast alloy, the present alloy exhibited superior tensile properties without trade‐off in elongation and improved fatigue life due to the unique microstructure with fine grains and random textures. The as‐cast alloy possessed yield stress, ultimate tensile strength, and elongation of about 185 MPa, 304 MPa, and 6.3%, respectively. The stress‐strain hysteresis loops were symmetrical and approximately followed Masing behavior. The fatigue life of the as‐cast alloy was attained to be higher than that of several commercial cast and wrought Al alloys. Cyclic hardening occurred at higher strain amplitudes from 0.3% to 0.8%, while cyclic stabilization sustained at lower strain amplitudes of ≤0.2%. Examination of fractured surfaces revealed that fatigue crack initiated from the specimen surface/near‐surface, and crack propagation occurred mainly in the formation of fatigue striations.     

In‐phase and out‐of‐phase thermomechanical fatigue behavior of 4Cr5MoSiV1 hot work die steel cycling from 400 °C to 700 °C

The hysteresis loops, stress and strain behavior, lifetime behavior and fracture characteristic of 4Cr5MoSiV1 hot work die steel at a wide range of mechanical strain amplitudes (from 0.5% to 1.3%) during the in‐phase (IP) and out‐of‐phase (OP) thermomechanical fatigue (TMF) tests cycling from 400 °C to 700 °C under full reverse strain‐controlled condition were investigated. Stress‐mechanical strain hysteresis loops of 4Cr5MoSiV1 steel are asymmetric, and stress reduction appears at high‐temperature half cycles owing to a decrease in strength with increasing temperature. 4Cr5MoSiV1 steel always exhibits continuous cyclic softening for both types of TMF tests, and the cyclic softening rate is larger in OP loading condition. OP TMF life of 4Cr5MoSiV1 steel is approximately 60% of IP TMF life at the same mechanical strain amplitude and maximum temperature. Lifetime determined and predicted in both types of TMF tests is adequately described by the Ostergren model. Fracture surfaces under IP TMF loading display the striation and tear ridge, showing quasi‐cleavage characteristics, and the cracks are less but longer. However, fracture surfaces under OP TMF loading mainly display the striation and dimple characteristics, and the cracks are more and shorter.     

In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

Full‐field three‐dimensional (3D) numerical analyses was performed to determine in‐plane and out‐of‐plane constraint effect on crack‐front stress fields under creep conditions of finite thickness boundary layer models and different specimen geometries. Several parameters are used to characterize constraint effects including the non‐singular T‐stresses, the local triaxiality parameter, the T_z ‐factor of the stress‐state in a 3D cracked body and the second‐order‐term amplitude factor. The constraint parameters are determined for centre‐cracked plate, three‐point bend specimen and compact tension specimen. Discrepancies in constraint parameter distribution on the line of crack extension and along crack front depending on the thickness of the specimens have been observed under different loading conditions of creeping power law hardening material for various configurations of specimens.     

Fatigue thresholds of holed components under in‐phase and out‐of‐phase torsional and axial loadings

The resistance‐curve (R‐curve) method was applied to the prediction of the fatigue thresholds of notched components under in‐phase and out‐of‐phase combinations of cyclic torsion and axial loadings. The prediction was compared with the experimental data obtained from thin‐walled tubular specimen of medium‐carbon steel with a hole. The stress was completely reversed and the mean stress was zero. The crack was nucleated at the position of the maximum range of the circumferential stress on the periphery of a hole, and propagated almost straight for all cases examined. The experimental data of the thresholds for crack initiation and fracture agreed well with the predictions for in‐phase and for out‐of‐phase loadings with 45° phase difference. For out‐of‐phase loading with 90°, the threshold for fracture was close to the crack initiation limit, because of the reduction of crack closure due to crack face rubbing by mode II shear cycling.     

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.     

Microstructure and superplasticity of Mg–Al–Ca electromagnetic casting alloys after hot extrusion

Microstructure and superplastic properties of the plates extruded from the Ca containing Mg alloy (1 wt.% Ca–AZ31) billets fabricated by electromagnetic casting (EMC) without and with electromagnetic stirring (EMS) were examined. The linear intercept grain sizes of the extruded materials were 3.7 μm and 2.1 μm, respectively. The material extruded from the EMC + EMS billet exhibited good superplasticity at low temperatures as well as at high strain rates, including the tensile elongations of 370% at 1 × 10⁻³ s⁻¹, −523 K and 550% at 1 × 10⁻² s⁻¹, −673 K. These values largely exceeded those of the AZ31 alloys with the similar grain sizes. The superior superplasticity of the extruded EMC + EMS billet could be attributed to fine grains and high grain stability at elevated temperatures by the presence of finely dispersed particles of thermally stable (Al,Mg)₂Ca phase. The constitutive equations were developed for describing the high-temperature deformation behavior of the fine-grained 1 wt.% Ca–AZ31 alloys with different grain sizes in wide range of temperature and strain rate.