Multiaxial Fatigue Tests Research Articles

Effect of pre-deformation on the pre-corrosion multiaxial fatigue behaviors of 2024-T4 aluminum alloy

Pre-damages which contain pre-deformation and pre-corrosion have influences on multiaxial fatigue properties. In this paper, the effect of pre-tension of 1%, 2%, 3% and 4% as well as pre-torsion of 10°, 20°, 30° and 40° on fatigue life of 2024-T4 aluminum alloy under corrosion conditions is evaluated. Multiaxial fatigue tests are performed under constant amplitude sinusoidal wave loading with tension-torsion ratio of 3 in air at room temperature. The results indicate a reduction tendency of pre-corrosion multiaxial fatigue life with the pre-deformation level in the same pre-corrosion time. With the same pre-deformation level, the pre-corrosion multiaxial fatigue life decreases as pre-corrosion time increases. Pitting caused by corrosion is observed on the surface of specimens. The observed mechanical behavior and associated phenomena are directly linked to microstructure characteristics such as surface defects, corrosion pits and micro-cracks. The analysis of mechanism reveals that the synergistic combination of pre-deformation and pre-corrosion is more detrimental than that of either one acting separately. The alternate cyclic hardening and softening appear in the axial direction. The cyclic softening in the tangential direction becomes more serious with the increase of pre-deformation. The typical morphology of corrosion fatigue can be observed on the fracture. Involving the damage factors of single pre-damage conditions, which include pre-deformation and pre-corrosion effects, the damage factor for pre-corroded multiaxial fatigue after pre-deformation is deduced. Fine results are achieved according to the above methods with most predicted life in 2× scatter band.

Simulation of the Spindle Coupled Multi-Axial Loading Fatigue Test of a Minivan Rear Axle

This study aims to establish a practical method for simulating the spindle coupled multi-axial loading fatigue test of a rear axle. A dynamic finite element model of the minivan rear axle was constructed and validated using a static calibration test. Based on the theory and methodology of the Schenck ITFC system, a simulation process was devised which includes system identification, calculation of the input loading signals for the finite element model, calculation of the response stress signals based on this model, calculation of the response strain signals from the corresponding stress signals, and finally, a comparison of the desired and achieved signals. The corresponding data processing programs were made using MATLAB, ensuring their easy reproducibility. The desired signals were measured on the Hainan proving ground for a duration of 2441.216 s, using strain gauges and rosettes placed in important stress-prone locations of the rear axle. The results indicate that the desired signals can be reproduced quite accurately, ensuring that the strain distribution of the rear axle in the field can be reasonably predicted.

Pit to crack transition behavior in proportional and non-proportional multiaxial corrosion fatigue of 304 stainless steel

Multiaxial corrosion fatigue tests with interruption were carried out on 304 stainless steel in 6wt.% FeCl3 solution at room temperature. Pit initiation, growth and pit to crack transition behavior under proportional and non-proportional loading were investigated. Under proportional loading, significant sharper pits, higher initial pit density and growth rate were observed in comparison with non-proportional loading. The pit depth growth rate under proportional loading was larger than those under non-proportional loading and without loading. Pit to crack transition mechanism was mainly controlled by mechanical assisted local dissolution under proportional loading while additional hardening under non-proportional loading.

Fatigue damage prediction in multiaxial loading using a new energy-based parameter

A new approach for the definition of the critical plane and a new energy-based multiaxial fatigue parameter are proposed in this work. The normal strain energy and shear strain energy on two orthogonal material planes are used to predict fatigue damage in multiaxial fatigue loading. The influence of the Poisson effect, mean normal strain energy and the different contribution of the compressive and tensile normal strain energies are accounted for. An energy-based parameter is defined which explains the different effects of the total strain energy on different material directions. Experimental data are used to validate the capabilities of this new multiaxial fatigue parameter, including 10 materials and 33 loading paths, which cover most of the commonly used loading conditions in multiaxial fatigue tests. The results show that the proposed multiaxial fatigue parameter gives good predictions (within a life factor of two) for most of these materials and loading paths.

Non-proportional multiaxial fatigue of super-elastic NiTi shape memory alloy micro-tubes: Damage evolution law and life-prediction model

Based on the experimental observation to the non-proportional multiaxial fatigue tests of super-elastic NiTi SMA micro-tubes and the uniaxial damage-based fatigue failure model established by Song et al. (2015) [52], an appropriate damage variable for the multiaxial fatigue failure is introduced, and the corresponding evolution law of the multiaxial damage is also proposed to describe the damage accumulation observed in the multiaxial fatigue tests of the NiTi SMA micro-tubes with different non-proportional loading paths. From the evolution law of damage, an adequate life-prediction model is then developed for the multiaxial fatigue of super-elastic NiTi SMA micro-tubes. The simulated evolution curves of the multiaxial damage and the predicted fatigue lives are in good agreement with the experimental results of super-elastic NiTi SMA micro-tubes.

Crack initiation life in notched Ti-6Al-4V titanium bars under uniaxial and multiaxial fatigue: synthesis based on the averaged strain energy density approach

The fatigue behaviour of circumferentially notched specimens made of titanium alloy, Ti-6Al-4V, has been analysed. To investigate the notch effect on the fatigue strength, pure bending, pure torsion and multiaxial bending-torsion fatigue tests have been carried out on specimens characterized by two different root radii, namely 0.1 and 4 mm. Crack nucleation and subsequent propagation have been accurately monitored by using the direct current potential drop (DCPD) technique. Based on the results obtained from the potential drop technique, the crack initiation life has been defined in correspondence of a relative potential drop increase ?V/?V0 equal to 1%, and it has been used as failure criterion. Doing so, the effect of extrinsic mechanisms operating during crack propagation phase, such as sliding contact, friction and meshing between fracture surfaces, is expected to be reduced. The experimental fatigue test results have been re-analysed by using the local strain energy density (SED) averaged over a structural volume having radius R0 and surrounding the notch tip. Finally, the use of the local strain energy density parameter allowed us to properly correlate the crack initiation life of Ti-6Al-4V notched specimens, despite the different notch geometries and loading conditions involved in the tests.

Multiaxial fatigue property of type 316 stainless steel using hollow cylinder specimen under combined pull loading and inner pressure

Stress controlled multiaxial fatigue test was carried out using a hollow cylinder specimen of type 316 stainless steel. A newly developed fatigue testing machine which can apply push-pull loading and reversed torsion loading and inner pressure to the hollow cylinder specimen was employed. 5 types of cyclic loading paths were employed by combining zero to pull axial and hoop stresses: a Pull (only axial stress), an Inner-pressure (only hoop stress), an Equi-biaxial (equi-biaxial stress by axial and hoop stresses), a Square-shape (trapezoidal waveforms of axial and hoop stresses with 90-degree phase difference) and a L-shape (alternately axial stress and hoop stress) loading paths. Since directions of principal stresses are fixed in all the tests, all of the loading paths are classified into ‘proportional loading’. In the Pull, the Inner-pressure and the Equi-biaxial tests, fatigue lives can be correlated on a unique line by a maximum equivalent stress based on von Mises. On the other hand, fatigue lives in the Square-shape and the L-shape tests were reduced comparing with that in the other tests, which was caused by yielding of larger plastic deformation.

Notched multiaxial fatigue of Al7050-T7451: on the need for an equivalent process zone size

The aim of this work is to investigate stress gradient effects on the fatigue life estimation of notched Al 7050-T7451 specimens under combined torsion and push-pull loading conditions. Initially, simple push-pull and torsion fatigue tests in plain and notched specimens were independently conducted not only to obtain the material properties necessary to calibrate a standard multiaxial critical plane based model, but also to raise the critical distance versus life curves in tension (L? – Nf) and in torsion (L? – Nf). This latter step also required a Finite Element Elastic Stress Analysis of the notched specimens tested in the medium high-cycle fatigue regime. Then, proportional multiaxial fatigue tests were carried out using this same notched geometry. The combination of a multiaxial model with the theory of critical distance (TCD) was applied to estimate fatigue lives. For this aluminium alloy, neither the use of the L? – Nf nor L? – Nf combined with the predictive multiaxial model was able to estimate lives in an accurate way.

New specimen and horn design for combined tension and torsion ultrasonic fatigue testing in the very high cycle fatigue regime

Fatigue damage has special relevance on the life span of mechanical components and structures, as it takes responsibility for the majority of the registered structural failures. Although its mechanisms have been the subject of continuous research, the growing need for greater lifespans forced the understanding of the behavior of materials under the very high cycle regime, also known as Very High Cycle Fatigue. This field of research, which studies the mechanical behavior of materials for fatigue lives beyond 1E7 cycles, only recently gained notoriety, largely due to the appearance of ultrasonic fatigue testing machines, working at 20kHz and due to the acquisition and control equipment capable of handling signals at very high frequencies. On the other hand the behavior of materials under multiaxial fatigue has been the subject of research and development, but not in the region of very high cycles, due to the inexistence of appropriate testing machine to perform these tests. The authors of this work have already a large experience on the performance of multiaxial fatigue tests under axial/torsion loading under servo-hydraulic fatigue testing machines and on very high cycle fatigue tests. In this paper, and using a new developed multiaxial fatigue testing machine operating at 20kHz frequency, experimental results, using strain gauges and axial and shear stresses determined by finite element modelling on a new specimen design tested with biaxial loadings, tension/torsion at 20kHz, are discussed and analyzed. Results show that it is possible to carry out multiaxial (axial/torsion loading) fatigue tests at very high frequencies which will allow to perform reliable very high cycle multiaxial fatigue tests.

Evaluation of multiaxial fatigue life prediction criteria for Ni-based superalloy GH4169

Fatigue tests under multiaxial loading were conducted on Ni-based superalloy GH4169 tubular specimens. The microstructures of fracture surfaces under different loading paths were compared. Several multiaxial fatigue criteria were reviewed and evaluated with multiaxial fatigue test data. The criteria of equivalent strain, maximum shear strain and Kandil–Brown–Miller provided unsatisfactory results for GH4169. Fatemi–Socie and Wu–Hu–Song parameters showed better life prediction abilities for this material. Minor modification has been introduced in Wu–Hu–Song parameter. The material constants of modified Wu–Hu–Song criterion are only dependent on torsional fatigue tests. The satisfactory prediction results based on modified Wu–Hu–Song model were obtained for GH4169.

Multiaxial fatigue: From materials testing to life prediction

Fatigue damage has special relevance on the life span of mechanical components and structures, as it takes responsibility for a large majority of the registered structural failures in service. The continuous need for the weight reduction and improved design optimization of components and a growing need for greater lifespans of equipment, forced the understanding of the fatigue behavior of materials either under multiaxial loading cycles or under increased number of loading cycles. Fatigue tests were always performed under uniaxial fatigue loads. However, it is generally recognized that multiaxial stresses occur in many full-scale structures, being rare the occurrence of pure uniaxial stress states. In the following, a wide range of multiaxial fatigue failure criteria have been developed that may be applied to different metallic materials. These failure criteria may be classified as strain based for high strain loading conditions or stress based for higher lifespans in the elastic loading regime. These criteria are nowadays used in design optimization also contributing to the weight reduction and improved lifespans of modern equipment. Present manuscript is a review of the main specimens and equipment where research can be carried out for performing multiaxial fatigue tests under bi-axial stress states. Being a personal view, it will be based on the author experience on the performance of multiaxial fatigue tests under axial/torsion loading using mechanical actuated or servo-hydraulic fatigue testing machines or biaxial fatigue tests using electromagnetic actuators in cruciform specimens. Further research is needed and is being carried out concerning multiaxial very high cycle fatigue in order to achieve better improvements in weight reduction of components and structures and also in complex variable amplitude loading with adequate damage accumulation models.

Multiaxial low cycle fatigue life of Ti-6Al-4V under non-proportional loading with mean strain

The mean strain effect on the multiaxial low cycle fatigue behavior of Ti-6Al-4V was investigated. Strain-controlled multiaxial low cycle fatigue tests at room temperature were carried out using a tubular specimen in tension and torsion loadings. Strain paths employed were four types of proportional and non-proportional loadings. Failure lives are affected by not only the non-proportionality of stress and strain histories but also the mean stress and strain. This study discusses the failure life properties based on the test results obtained and also shows strain parameters for the life evaluation under non-proportional loading with mean strain. The proposed strain parameters, where Findley and Walker models were applied within a non-proportional strain range, were suitable parameters to evaluate the life for Ti-6Al-4V under non-proportional straining with mean strain.

Reliability of Cu wire bonds in microelectronic packages

In this study the thermo-mechanical response of 25μm Cu wire bonds in an LQFP-EPad (Low Profile Quad Flat-Exposed Pad) package was investigated by numerical and experimental means. The aim was to develop a methodology for fast evaluation of the packages, with focus on wire bond fatigue, by combining finite element analysis (FEA) and mechanical fatigue testing. The investigations included the following steps: (i) simulation of the warpage induced displacements in the encapsulated LQFP-176-Epad package due to temperature changes, (ii) reproducing the thermally induced stresses in the wire bond loops in an unmolded (non-encapsulated) LQFP package using an accelerated multiaxial mechanical fatigue testing set-up under the displacement amplitudes determined in case (i) and determination of the loading cycles to failure (Nf), (iii) FEA of the experiments performed in (ii) based on the boundary conditions determined in (i) to calculate the states of stress and strain in the wire bonds subjected to multiaxial mechanical cyclic loading. Our investigations confirm that thermal and mechanical cyclic loading results in occurrence of high plastic strains at the heat affected zone (HAZ) above the nail-head, which may lead to fatigue failure of the wire bonds in the packages. The lifetime of wire bonds show a proportional relation between the location and angle of the wire bond to the direction of loading. The calculated accumulated plastic strain in the HAZ was correlated to the experimentally determined Nf values based on the volume weighted averaging (VWA) approached and presented in a lifetime diagram (∆d - Nf) for reliability assessment of Cu wire bonds. The described accelerated test method could be used as a rapid qualification test for the determination of the lifetimes of wire bonds at different positions on the chip as well as for related improvements of package design.

Multiaxial fatigue strength assessment of welded joints using the Peak Stress Method – Part I: Approach and application to aluminium joints

The notch stress intensity factor (NSIF) approach for the fatigue strength assessments of welded joints assumes the weld toe as a sharp V-notch with tip radius equal to zero and the weld root as a pre-crack. The Peak Stress Method (PSM) is an approximate, FE-oriented application of the NSIF-based approaches to fatigue design of welded joints and it is based on the singular linear elastic peak stresses calculated from FE analyses carried out by using a proper mesh pattern; more precisely, the element type is fixed, the average element size is kept uniform in the mesh pattern and before running the mesh generation algorithm the size can be chosen arbitrarily within a given range. The PSM allows to adopt rather coarse FE meshes if compared to those required for the NSIFs evaluation from the local stress fields. While originally the PSM was validated for pure axial or bending loadings as well as pure torsion loadings, here the PSM is extended for the first time to analyse the fatigue strength of welded joints subjected to in-phase as well as out-of-phase multiaxial fatigue loadings. By adopting the averaged Strain Energy Density (SED) as a fatigue strength criterion, a so-called equivalent peak stress is defined and it is adopted to assess either weld toe and weld root fatigue failures in conjunction with a properly defined design curve. Some multiaxial fatigue test data taken from the literature and relevant to welded joints made of aluminium alloys are analysed using the Peak Stress Method. The equivalent peak stress has shown to correlate with good approximation all the experimental data.

Multiaxial fatigue strength assessment of electroslag remelted 50CrMo4 steel crankshafts

This work investigates the fatigue strength of multiaxially-loaded gas engine crankshafts incorporating electroslag remelted 50CrMo4 steel. Uniaxial fatigue tests with small-scale round specimens before and after performing the ESR process are conducted. The results reveal that the high-cycle fatigue strength at the run-out region significantly decreases by 21% if no ESR-treatment is performed. Multiaxial fatigue tests under proportional normal and shear stress loading demonstrate that the elliptical model by Gough and Pollard leads to a minor underestimation of 5% compared to the test results. An application of several state-of-the-art equivalent stress hypotheses utilizing the critical plane approach is presented and the estimated results are compared to the experiments in terms of high-cycle fatigue resistance and crack initiation angle.

Multiaxial Fatigue Life Prediction of Metallic Materials Based on Critical Plane Method under Non-Proportional Loading

The critical plane method is widely discussed because of its effectiveness for predicting the multiaxial fatigue life prediction of metallic materials under the non-proportional loading conditions. The aim of the present paper is to give a comparison of the applicability of the critical plane methods on multiaxial fatigue life prediction. A total of 205 multiaxial fatigue test data of nine kinds of metallic materials under various strain paths are adopted for the experimental verification. Results shows that the von Mises effective strain parameter and KBM critical plane parameter can give well predicted fatigue lives for multiaxial proportional loading conditions, but give poor prediction lives evaluation for multiaxial non-proportional loading conditions. However, FS parameter shows better accuracy than the KBM parameter for multiaxial fatigue prediction for both proportional and non-proportional loading conditions.

Analysis of multiaxial low cycle fatigue of notched specimens for type 316L stainless steel under non-proportional loading

The paper analyzes multiaxial low cycle fatigue tests of notched specimens under proportional and non-proportional loading conditions. Strain controlled multiaxial low cycle fatigue tests were carried out using circumferentially notched round-bar specimens of type 316L stainless steel, with different stress concentration factors. The experimental results show that the crack initiation site is shifted from the notch tip. Based on this finding, a new model for life evaluation is proposed by taking into account the strain gradient in the proximity of the notch tip and the effective maximum strain range. The new model allows evaluating the fatigue life in a narrow scatter band.

Multiaxial fatigue behaviors of 2024-T4 aluminum alloy under different corrosion conditions

In order to study multiaxial fatigue behavior of 2024-T4 aluminum alloy with an aircraft in-service environment, fatigue tests of multiaxial pre-corrosion and alternate corrosion are carried out. With the extension of pre-corrosion time, the multiaxial fatigue life decreases under the same equivalent stress. Pitting caused by corrosion is observed on the surface of specimens. While pre-corrosion time increases, the number and size of pits become larger and connection between adjacent corrosion pits becomes more obvious. For the multiaxial fatigue tests with alternate corrosion, for the same unit corrosion time, the fatigue life decreases with the increase of unit loading cycles. Under the same unit loading cycles, the fatigue life decreases as the unit corrosion time increases. The cyclic hardening appears in both axial and tangential directions at the initial loading stage. Cyclic softening trend becomes obvious as the number of alternation increases. It is shown that cracks initiate at specimen surface and gradually extend to inside. Exfoliation corrosion morphology can be observed on specimen surface. Based on Miner’s rule and data of pre-corroded multiaxial fatigue test, the alternate corrosion-multiaxial fatigue lives are predicted.

多軸一定応力振幅下の高サイクル疲労寿命予測

Multiaxial high cycle fatigue life prediction under constant stress amplitude is proposed. This new criterion, which extends the proposed fatigue limit criterion by the authors in the previous papers, uses the unified equivalent shear stress amplitude. The material properties for the proposed criterion are the axial fatigue limit and the true fracture strength. The multiaxial high cycle fatigue tests for life prediction accuracy verification was carried out with S45C and SCM440. The fatigue tests were conducted under combined axial and torsion stresses with mean stress and phase difference. The criterion error is better than that of the Susmel criterion. The proposed criterion predicted the experimental fatigue life to be within a factor of 3.

An Energy-Critical Plane Based Fatigue Damage Approach for the Life Prediction of Metal Alloys

This paper presents a new energy-critical plane based fatigue damage approach for the assessment of the fatigue life under uniaxial and multiaxial proportional and non-proportional fatigue loading. The proposed approximate method, based on Farahani's multiaxial fatigue damage model, takes into account the critical plane orientations during a loading cycle and the values of the respective damage parameters on them. The uniqueness of the proposed method lies on the fact that it considers a weighted contribution of each critical plane orientation to the material damage. The relative weighting factors depend on the declination of each critical plane with respect to the critical plane, where the damage parameters exhibit their maximum values during a fatigue loading cycle. Herein, several low, mid and high-cycle fatigue loading cases are being investigated. The induced elastic-plastic stress-strain states are approximated by means of respective finite element analyses (FEA). Several experimental fatigue data derived from uniaxial and multiaxial fatigue tests on StE460 steel alloy thin-walled hourglass-type specimens have been used to verify the model's calculation accuracy. Comparison of experimental and calculated fatigue lives confirm remarkable fatigue life calculation accuracy in all cases examined.