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.     

Use of a load non-proportionality measure in fatigue under out-of-phase combined bending and torsion

A load non‐proportionality measure has been developed for use with an existing critical plane fatigue criterion for the case of fatigue under out‐of‐phase bending and torsion. Use of this measure shows improved agreement with test data in the literature for this loading condition.     

Fatigue characterization and modeling of 30CrNiMo8HH under multiaxial loading

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

Area and point approaches in fatigue life evaluation under combined bending and torsion loading

We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction of stresses to representative local ones in the critical plane for fatigue life calculation. The shear and normal stresses are averaged in two overlapping areas of different sizes on the critical plane. The proposed method is compared with the point (in critical distance) method and both are verified by fatigue tests under combined bending and torsion. Verification is done for the experimental and calculated fatigue lives with use of two multiaxial fatigue failure criteria. __________ Translated from Problemy Prochnosti, No. 1, pp. 69–72, January–February, 2008.     

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 life of 2017(A) aluminum alloy under proportional constant-amplitude bending with torsion in the energy approach

We present the results obtained for 2017(A) aluminum alloy under the conditions of pure bending with constant amplitude, pure torsion, and two combinations of proportional bending with torsion. All results can be described by a single criterion based on the parameter of strain-energy density in the critical plane. The critical plane is defined as the plane where the parameter attains its maximum value. The fatigue life is affected by the sum of the densities of normal and shear strain energies in the accepted critical plane. The results are presented in a scatter band with coefficient equal to three for the case of pure bending. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 4, pp. 68–74, July–August, 2008.     

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.     

Impact strength of thin-walled composite structures under combined bending and torsion

The effect of bending and torsional stresses on the fracture characteristics of thin-walled square, rectangular and circular cylindrical structures has been investigated under static and impact loadings by use of the apparatus capable of applying bending and torsional moments in various proportions. The thin-walled structures were fabricated from glass-fiber strand, chopped strand mat and unsaturated polyester resin. Comparisons between experimentally determined strength and theoretical predictions using the failure criteria are presented. As a result of this investigation, the existence of the relation between the fracture mode and the strength was recognized and the failure criteria examined could be used successfully to predict the combined impact bending and torsional strength of thin-walled composite structures.     

Fatigue crack propagation in API 5L X‐70 pipeline steel longitudinal welded joints under constant and variable amplitudes

Fatigue crack propagation (FCP) under constant and variable amplitude loading in base metal (BM), weld metal (WM) and heat affected zone (HAZ) of longitudinal welded joints of an API X‐70 pipeline steel was investigated. Constant amplitude loading tests were performed at R = 0.1 and 0.5, whereas for variable amplitude testing single peak tensile overloads (OLs) alternating between 75 and 100% of maximum load were applied at 2.5 mm intervals in crack growth. Results of SE(B) specimens tested under constant and variable amplitude loading revealed that BM, WM and HAZ regions subjected to R = 0.5 and low ΔK‐values presented the highest crack growth rates. At higher ΔK values FCP rates in all the studied regions were similar and the R effect on FCP rate was no more observed. Crack growth retardation due to OLs was observed at the three studied regions, showing a decrease on the FCP delay with a decreasing on ΔK.     

Energy approach to fatigue under combined cyclic bending with torsion of smooth and notched specimens

We present the results of fatigue tests of smooth and notched round specimens made of 10HNAP steel under the combined action of cyclic bending and torsion. The experimental results are analyzed by using the well-known energy models proposed by Neuber and Molski-Glinka and a new model proposed by the authors and based on the analysis of the amplitude of the strain-energy density. The accumulation of fatigue damage in the stage of crack initiation was observed only in the active part of the cross section of the specimen where the level of stresses is higher than the fatigue limit. The proposed model enables one to determine the fatigue life of smooth and notched specimens under the combined action of cyclic bending and torsion by using standard characteristics of uniaxial fatigue and the relationship between cyclic stresses and strains. Department of Mechanics and Machine Design, Technical University of Opole, Opole, Poland. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 5, pp. 34–42, September–October, 1998.     

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.     

Fatigue growth behavior for surface crack in welding joints under combined compressive and bending stresses

It has been demonstrated by experiments that crack can grow under cyclic compressive loading. However, it is difficult to observe and describe accurately by mathematical methods. In addition, cracks may close under compressive loading, which also increases the complexity of the problem. The fatigue growth behavior for surface cracks under biaxial loadings was studied by fatigue tests of HTS-A steel. According to experimental evidences, it is concluded that the transverse compressive stress not only changes the fracture morphology but also affect crack propagation life. Considering the influence of the compressive stress, this paper proposed an equivalent SIF and crack growth model subjected to compressive and bending stresses on the basis of McEvily formula. Finally, comparisons are made between prediction results and experimental data.     

Fatigue life estimation of notched specimens of modified 9Cr-1Mo steel under uniaxial cyclic loading

Accuracy in the estimation of low cycle fatigue life of modified 9Cr-1Mo steel notched specimen by different analytical methods such as linear rule, Neuber’s rule, strain energy density method and numerical method such as finite element analysis have been studied in this investigation. The fatigue tests on notched specimens having notch radius of 1.25 mm, 2.5 mm and 5.0 mm were carried out at 823 K with net stress amplitudes of 250 MPa, 300 MPa and 350 MPa. The fatigue tests on smooth specimens were carried out with strain amplitudes ranging from ±0.3% to ±0.8% with a strain rate of 3 × 10^?3 s^?1 at 823 K to evaluate the fatigue life of notched specimen through strain-life approach. In order to predict the cyclic stress response of the material, Chaboche non-linear hardening model was employed considering two back stress components. Predicted hysteresis loops for smooth specimen were well in agreement with experimental results. Estimated fatigue lives of notched specimens by analytical methods and finite element analysis were within a factor ±16 and ±2.5 of the experimental lives respectively.     

The investigation of crack growth in specimens with rectangular cross-sections under out-of-phase bending and torsional loading

The paper presents the fatigue test results of rectangular cross-section specimens made of 10HNAP (S355J2G1W) steel. The specimen height to width ratio was 1.5. The tests under bending with torsion were performed for the following ratios of bending to torsional moments M_aB/M_aT = 0.47, 0.94, 1.87 and the loading frequency 26.5 Hz. Nominal stresses were chosen for the equivalent stress according to the Huber-Mises hypothesis equal to 360 MPa. The tests were performed in the high cycle fatigue regime for the stress ratio R = −1 and phase shift between bending and torsion loading equal to ϕ = 0 and 90°. Crack initiation and propagation phases were observed on the specimen surface using the optical microscope (magnification 20×) with an integrated digital camera. The test results for the fatigue crack growth rate versus the stress intensity factor range for mode I and mode III have been described with the Paris equation.     

Fatigue life evaluation for carbon/epoxy laminate composites under constant and variable block loading

This paper presents the results of current research on the fatigue life prediction of carbon/epoxy laminate composites involving twelve balanced woven bidirectional layers of carbon fibres and epoxy resin manufactured by a vacuum moulding method. The plates were produced with 3 mm thickness and 0.66 fibre weight fraction. The dog bone shape specimens were cut from these plates with the load line aligned with one of the fibre directions. The fatigue tests were performed using load control with a frequency of 10 Hz and at room temperature. The fatigue behaviour was studied for different stress ratios and for variable amplitude block loadings. The damage process was monitored in terms of the stiffness loss. The fatigue life of specimens submitted to block loading tests was modelled using Palmgren–Miner’s law and taking in to account the stress ratio effect. The estimated and experimental fatigue lives were compared and good agreement was observed.