Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading

The paper contains a new algorithm for estimation of fatigue life in HCF regime under multiaxial random loading using spectral methods. Loading of Gaussian distribution and narrow‐ and broad‐band frequency spectra were assumed. Various characteristic states of multiaxial loading were considered. The equivalent stress history was determined with use of the failure criteria of multiaxial fatigue based on the critical plane. For determination of the critical plane position, the method of variance was applied. During simulation, the authors compared the results obtained by a spectral method in the frequency domain with those from the rain‐flow algorithm in the time domain. The paper also contains the results of fatigue tests for 18G2A structural steel subjected to bending and combined bending with torsion. The tests were performed in order to verify the proposed algorithms for determination of fatigue life. It has been shown that under multiaxial random loading results of fatigue life calculated according to the considered algorithms in frequency and time domains are well correlated with the results of experiments.     

Fatigue life estimation for 2017A-T4 and 6082-T6 aluminium alloys subjected to bending-torsion with mean stress

This paper proposes a model for estimating fatigue life under multiaxial stress states, based on critical plane concepts, taking into account the effect of mean shear stress. The fatigue life test results, calculated on the basis of the proposed model, are compared to the experimental ones related to 2017A-T4 and 6082-T6 aluminium alloy specimens under constant-amplitude bending, torsion and proportional combinations of bending and torsion. For the results obtained a statistical analysis is performed by comparing the calculation results with experimental data.     

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.     

Fatigue analysis of unidirectional GFRP composites under combined bending and torsional loads

Fatigue behavior of unidirectional glass fiber reinforced polyester (GFRP) composites at room temperature under in-phase combined torsion/bending loading was investigated. All fatigue tests were carried out on constant-deflection fatigue machine with frequency of 25 Hz. A 30% reduction from the initial applied moments was taken as a failure criterion in the combined torsion/bending fatigue tests of the composite materials. A series of pure torsional fatigue tests were conducted to construct the failure contour of GFRP composites using different failure theories. The obtained S–N curves from combined torsion/bending tests were compared with both, pure torsion fatigue test results and published results of pure bending fatigue tests of GFRP rods. Pictures by scanning electron microscope were used to closely examine the failure mode of the tested specimens under combined torsion/bending loading.

The results showed that, the unidirectional glass fiber reinforced polyester composites have poor torsional fatigue strength compared with the published results of pure bending fatigue strength. Endurance limit value (calculated from S–N equation at N = 10⁷ cycles) of GFRP specimens tested under combined torsion/bending loading equals 8.5 times the endurance limit of pure torsion fatigue. On the other hand the endurance limit of combined torsion/bending fatigue strength approximately half the fatigue limit of pure bending fatigue strength. The predicted values of combined torsion/bending fatigue strength at different number of cycles, using the published failure theory are in good agreement with the experimental data. For the investigated range of fiber volume fractions (V_f) it was found that higher stress levels are needed to produce fatigue failure after the same number of cycles as V_f increases.     

ESTIMATED AND EXPERIMENTAL FATIGUE LIVES OF 30CrNiMo8 STEEL UNDER IN-AND OUT-OF-PHASE COMBINED BENDING AND TORSION WITH VARIABLE AMPLITUDES

Abstract— Calculated fatigue lives, based on three criteria for multiaxial random fatigue, were compared with lives obtained from tests on cylindrical specimens of 30CrNiMo8 steel subjected to in- and out-of-phase bending and torsion at variable amplitudes. In the chosen fatigue criteria the expected position of the fracture plane, determined from a variance method for the equivalent stress, were taken into account. The equivalent stress history was related to the rain flow method and fatigue damage was evaluated from the Palmgren–Miner hypothesis. It has been shown that the expected fatigue fracture planes agree with those determined by experiments. The most realistic estimations of fatigue life were obtained by the criterion of maximum shear and normal stresses on the fracture plane using a modified shear stress.     

Fatigue life estimation for 30CrNiMo8 steel under in- and out-of-phase combined bending and torsion with variable amplitudes

Fatigue life successively calculated according to three criteria of multiaxial fatigue for randomly varying loading is compared with fatigue life obtained by Sanetra and Zenner in testing cylindrical specimens of 30CrNiMo8 steel by in- and out-of-phase bending and torsion with variable amplitudes. The position of the plane of fatigue fracture is determined using the variance method. The histories of equivalent stresses are schematically represented by the Monte Carlo method. Fatigue damage was computed using the Palmgren-Miner hypothesis. The most realistic estimates of fatigue life in the scatter band of the results with a factor of 3 are obtained on the basis of the criterion of maximum tangential stresses and normal stresses in the fracture plane with shear stresses taken into account.Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 1, pp. 31–38, January – February, 1995.     

Application of an energy model for fatigue life prediction of construction steels under bending, torsion and synchronous bending and torsion

The paper contains a mathematical model of the material’s behaviour under cyclic loading taking into account the dynamics of the fatigue process, including the number of cycles to failure, induced by the mean stress value. The coefficients in the proposed model have been obtained from experimental tests under symmetrical and nonsymmetrical loading (with the stress ratio R=0). The proposed model has been used in order to modify an energy criterion with the aim of accounting for the influence of the mean stress on the fatigue life. The fatigue tests have been performed for structural steels 10HNAP and 18G2A subjected to cyclic bending, torsion and synchronous bending with torsion, by considering different values of the mean stress. A good agreement between the calculated and experimental results has been obtained.     

Effect of cyclic hardening on fatigue performance of slide burnished components made of low‐alloy medium carbon steel

The slide burnishing process causes cyclic loading of the surface being treated, which provokes cyclic hardening. Using a forced‐controlled indentation test, the sixth “loading‐unloading” cycle was stabilised. The effect of the number of passes and the cyclic loading coefficient (CLC) on the fatigue performance of slide burnished specimens was investigated. Rotating bending fatigue tests were conducted using nine groups of hourglass shaped specimens, which were slide burnished through a different number of passes and CLC values. A stabilised cycle of the surface layer achieved with six passes, lead to largest fatigue limit, whereas the CLC exerted negligible influence on the fatigue performance. The observed phenomenon was explained through different residual stress relaxation rates, due to the rotating bending load, as well as with the obtained surface layer microstructure. The residual stress relaxation was investigated through rotating bending fatigue tests, using cylindrical fatigue specimens, followed by X‐ray stress analysis.     

Critical plane approach with two families of microcracks for modelling of unilateral fatigue damage

New multiaxial fatigue damage model based on the critical plane approach is proposed. Two different physical mechanisms of the fatigue damage development on each potential failure plane (critical plane) are considered. In general, each critical plane contains two families of a parallel microcracks. The proposed model reproduces simultaneously fatigue damage induced anisotropy, the influence of positive and negative mean stresses, unilateral fatigue damage, microcrack closure effect and fatigue behaviour under variable amplitude loading. The expression for the equivalent stress in the damage evolution equation includes the stress intensity for the amplitudes as well as joint invariants for the mean values of the stress tensor and for the vectors associated with the directions of microcracks. The theoretical predictions are compared with experimental data under uniaxial cyclic loading of brass specimens. The influence of positive and negative mean stresses on the fatigue life of brass is investigated.     

Selection of the critical plane orientation in two-parameter multiaxial fatigue failure criterion under combined bending and torsion

The present paper is focused on engineering application of the algorithm of fatigue life calculation under multiaxial fatigue loading. For that reason, simple two-parameter multiaxial fatigue failure criterion is proposed. The criterion is based on the normal and shear stresses on the critical plane. Experimental results obtained under multiaxial proportional, non-proportional cyclic loading and variable-amplitude bending and torsion were used to verify the proposed two-parameter criterion and other well-known multiaxial fatigue criteria. Elastic–plastic behaviour of the bulk material was taken into account in calculation of the stress/strain distribution across the specimen cross-section. It is shown that the proposed two-parameter multiaxial fatigue failure criterion gives the best correlation between the experimental and calculated fatigue lives.     

Fatigue behaviour of the bond interface between carbon fibre‐reinforced polymer sheets and concrete

Externally bonded carbon fibre‐reinforced polymers (CFRPs) have been applied to retrofit and strengthen civil structures. In this study, four‐point bending beams were manufactured and tested to examine the fatigue behaviour of the CFRP–concrete interface. The results indicated that the specimens exhibited debonding failure in the concrete beneath the adhesive layer under static loading. However, when cyclic loads were imposed on the small beams, debonding failure may occur in the adhesive layer. Moreover, fitting expressions were proposed to predict the shear stress–slip relationship between the CFRP sheets and concrete and the flexural strength of the CFRP‐strengthened beams under static loads, and good agreement with the test data was obtained. Finally, a fatigue life prediction model was also presented to capture the fatigue life of the CFRP–concrete interface under cyclic loads. The calculation results showed that the fatigue strength of the CFRP–concrete bond interface was approximately 65% of the ultimate load capacity.     

Tension and fatigue behavior of 316LVM 1 × 7 multi-strand cables used as implantable electrodes

The mechanical behavior of 316LVM 1 × 7 cables were evaluated in uniaxial tension and in cyclic strain-controlled fatigue with the use of a Flex tester operated to provide fully reversed bending fatigue. The magnitude of cyclic strains imparted to each cable tested was controlled via the use of different diameter mandrels. Smaller diameter mandrels produced higher values of cyclic strain and lower fatigue life. Multiple samples were tested and analyzed via scanning electron microscopy. The fatigue results were analyzed via a Coffin–Manson–Basquin approach and compared to fatigue data obtained from the literature where testing was conducted on similar materials, but under rotating bending fatigue conditions.     

Plastic strains and the macroscopic critical plane orientations under combined bending and torsion with constant and variable amplitudes

Round cross-section specimens made of 18G2A steel were subjected to different combinations of constant- and variable-amplitude bending and torsion. The fatigue tests were performed under bending and torsion with moment control in the high cycle fatigue regime. Two approaches were used to calculate stress courses from moment histories. In one approach, stresses and strains were computed using simple elastic beam theory (nominal stresses). In the other approach, time courses of moments were used to calculate stress and strain histories taking into account plastic strains and non-linear stress distribution along the specimen cross-section on the basis of the algorithm described in the paper. The loading histories computed according the two methods were used to calculate the critical plane orientations. It was assumed that the orientation of the critical plane is controlled only by shear or tensile fatigue mechanism. Moreover, the theoretical critical plane positions were compared to the experimental macroscopic fatigue fracture plane orientations.     

Effects of machining parameters on fatigue behavior of machined threaded test specimens

The effects of machining parameters on the fatigue strength of fine-machined threaded specimens were investigated by comparing with the endurance limits of circumferentially notched specimens with the same profile. A four-point rotary bending fatigue test machine was used to obtain constant bending moment and pure alternating stress along the thread. All specimens were machined from SAE 4340 steel, the typical material used for deep well oil drilling pipes. Notched specimens were fine-machined according to ASTM standards, while the threaded specimens were machined under the optimized cutting conditions, which maximize tool life and geometric precision, as well as under selected modified conditions. Endurance limits of all specimens after 2 × 10⁶ cycles were experimentally determined and S–N curves were plotted for 90% reliability for all experiments. The effects of cutting force, radial feed, tool wear, and two thread cutting methods on the fatigue strengths of the threaded specimens were determined. Experimental results show that the fatigue strengths of threaded specimens lie within a large range, depending on machining conditions, as compared to circumferentially notched specimens. The most influential factors on the fatigue strength of threaded specimens are tool wear and cutting velocity, while the effects of cutting method and radial feed are less significant.     

Evaluation of equi-biaxial fatigue of stainless steel by the pressurized disc fatigue test

The pressurized disc fatigue (PDF) test technique was employed to obtain fatigue lives of Type 316 stainless steel under equi-biaxial stress conditions. In the PDF test, a disc-type specimen was subjected to the cyclic bulge test. The biaxial fatigue lives were successfully obtained by the PDF tests, and they were longer than those obtained by the uni-axial and plate bending fatigue tests under the same equivalent strain range. Observations of crack initiation and growth behavior during the PDF test revealed that the relatively large size of the disc-type specimens had only a minor influence on the fatigue lives. Finite element analysis results showed the PDF test was valid for evaluating the fatigue lives under equi-biaxial conditions. It was concluded that the influence of equi-biaxial condition was not necessary to be considered in the design fatigue curve.     

SHEAR FATIGUE CRACK GROWTH: A LITERATURE SURVEY

A fatigue crack is often initiated by a localized cyclic plastic deformation in a crystal where the active slip plane coincides with the plane of maximum shear stress. Once a crack is initiated, the crack will propagate on the maximum shear plane for a while and, in the majority of the cases, will eventually change to the plane of the applied tensile stress. The “shear” and “tensile” modes of fatigue crack propagation are termed stage I and stage II fatigue crack growth. They are also known as mode II and mode I fatigue crack growth. However, the mechanism of the tensile mode fatigue crack propagation is shear in nature. Considerable progress has been made recently in the understanding of mode II fatigue crack growth. This paper reviews the various test methods and related data analyses. The combined mode I and mode II elastic crack tip stress field is reviewed. The development and the design of the compact shear specimen are described and the results of fatigue crack growth tests using the compact shear specimens are reviewed. The fatigue crack growth tests and the results of inclined cracks in tensile panels, center cracks in plates under biaxial loading, cracked beam specimens with combined bending and shear loading, center cracked panels and the double edge cracked plates under cyclic shear loading are reviewed and analyzed in detail.     

Simulation investigations of the position of Fatigue Fracture Plane in materials with biaxial loads

In the paper three methods of determination of the expected fatigue fracture plane position under random triaxial stress state have been presented. They are: weight function method, variance method and damage cumulation method. The weight function method for biaxial cyclic loadings has been analysed with digital simulation. The fatigue fracture plane position has been determined with mean values of the direction cosines of principal stress axes. Averaging has been done at angle values with use of weights. Eleven various weights have been presented and their usability has been analysed on the basis of experimental results obtained by Rotvel, and Nishihara-Kawamoto. The weights with good agreement of results of simulation tests and experiments have been shown.     

Transverse tension fatigue life characterization through flexure testing of composite materials

The transverse tension fatigue life of S2/8552 glass–epoxy and IM7/8552 carbon–epoxy was characterized using flexure tests of 90-degree laminates loaded in 3-point and 4-point bending. The influence of specimen polishing and specimen configuration on transverse tension fatigue life was examined using the glass–epoxy laminates. Results showed that 90-degree flexure specimens with polished machined edges and polished tension-side surfaces had lower fatigue lives than unpolished specimens when cyclically loaded at equal stress levels. The influence of specimen thickness and the utility of a Weibull scaling law were examined using the carbon–epoxy laminates. The influence of test frequency on fatigue results was also documented for the 4-point bending configuration. A Weibull scaling law was used to predict the 4-point bending fatigue lives from the 3-point bending curve fit and vice versa. Scaling was performed based on maximum cyclic stress level as well as fatigue life. The scaling laws based on stress level shifted the curve fit S–N characterizations in the desired direction, however, the magnitude of the shift was not adequate to accurately predict the fatigue lives. Furthermore, the scaling law based on fatigue life shifted the curve fit S–N characterizations in the opposite direction from measured values. Therefore, these scaling laws were not adequate for obtaining accurate predictions of the transverse tension fatigue lives of heterogeneous, fiber reinforced, polymer matrix composites.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Determination of the critical plane by a weight-function method based on the maximum shear stress plane under multiaxial high-cycle loading

A weight function method for the determination of the critical plane is here proposed for the case of specimens under combined bending and torsion in the high cycle fatigue regime. The critical plane is assumed to be coincident with the mean maximum absolute shear stress plane, which is calculated by averaging the instantaneous angle between the specimen axis and the normal to the maximum absolute shear stress plane. Two kinds of weight functions are proposed to determine such a plane. The proposed method to determine the critical plane is verified by employing fatigue data available in the literature in terms of experimental fracture planes, and the multiaxial fatigue life is also predicted by a reformulation of the criterion proposed by Carpinteri et al. to verify the determined critical plane. The results show that the proposed method can be applied to determine the critical plane under both constant and variable amplitude loading.