Torsional Fatigue Limit Research Articles

A continuum approach to multiaxial high-cycle fatigue modeling for ductile metallic materials

In this work we propose a generalization of the endurance function employed in the continuum approach to high-cycle fatigue modeling by Ottosen et al. (2008). The von Mises-type backstress-modified effective stress term of the original formulation is replaced by the non-quadratic Hershey-Hosford function, which introduces flexibility with respect to the predicted fatigue limit in pure shear. While the original model assumes a fixed ratio between the fatigue limits in fully reversed torsion and fully reversed bending of 0.5774 for all materials, the modification enables the ratio to take on values on the interval from 0.5 to 0.5852 by calibration to experimental data that is readily available in the literature. Like the original formulation simplifies to the invariant-based Mises-Sines fatigue limit criterion for proportional stress histories, the current proposal can be written as a Hershey-Hosford-Sines criterion. A systematic validation to experimental multiaxial infinite fatigue life data from eight different mild and semi-hard metals with fully reversed torsion and bending fatigue limit ratios lower than 0.6 demonstrates that the proposed modification increases the accuracy and reduces the number of non-conservative predictions.

Analysis of biaxial fatigue limit models for cases with circular notches

This work shows an analysis of several models of multiaxial fatigue for notches: Navarro-Rios’ model, which analyses the interaction between the crack and its associated plastic zone with the material microstructural barriers, and three models that combine a critical volume method for notches with a critical plane model for multiaxial fatigue in unnotched solids. Specifically, the application of these models for the prediction of the fatigue limit for a plate with a circular hole subjected to axial, shear and in-phase biaxial cyclic loading is studied. The effects of two parameters are analysed: the radius of the hole and the relationship between the torsional and axial fatigue limits. For all the analysed models, cases are observed in which an increase in the hole radius produces an increase in the predicted fatigue limit, that is, the evolution of the fatigue limit with an increasing hole radius is not always monotonically decreasing, as would be expected. These effects, which we have called “humps” because of their appearance on the prediction graphs, mainly occur in shear loading. No humps were observed in the studied experimental results, but the number of available experimental results is too small to assure this tendency. The results shown in the work indicate that a greater knowledge of the physics of multiaxial fatigue in notches is necessary to achieve models that are capable of providing increasingly accurate predictions.

Device for Torsional Fatigue Strength Assessment Adapted for Pulsating Testing Machines.

The torsional fatigue test determines the fatigue limit for a certain asymmetry coefficient of the cycle. The assessment of fatigue tests is performed on specialized machines. There are two types of torsion testing machines: universal machines that have the torsion component and specialized machines only for torsion testing. Nevertheless, no matter which proposed option we choose, the purchase prices for these testing machines or the values spent for self-management are quite high. This paper presented a device used for torsion fatigue testing, adaptable to a universal pulsating testing machine, designed to determine the torsion fatigue limit for different materials. The built device is simple and reliable, and therefore inexpensive. By using this device, we can determine the limit of the torsional fatigue after any stress cycle and we can use the parameters obtained from the universal machine to which it was attached. The torque and twisting angle of the test specimen during the test can be determined by calculation. The paper also presented an experimental method for determining shear strains based on calibration experiment, using a specimen on which strain gauges were mounted. The values taken from this calibration experiment were compared with those obtained from the theoretical calculation.

Influence of load ratio on torsion very high cycle fatigue of high‐strength spring steel in the presence of detrimental defects

AbstractThe influence of mean shear stress on torsion very high cycle fatigue (VHCF) for internal inclusion‐initiated fracture is investigated. Ultrasonic torsion fatigue tests are performed at load ratios R = −1, 0.1, and 0.35 with high‐strength spring steel SWOSC‐V featuring an increased number of nonmetallic inclusions. Based on Murakami and Endo's parameter model, an equation predicting the torsion fatigue limit in the presence of detrimental defects is rendered. Stress biaxiality is considered using a ratio of torsion to axial fatigue strength of τa/σa = 0.86. Considering the load ratio sensitivity according to ([1 − R]/2)α, the value for α is experimentally determined to be 0.550. A fine granular area (FGA) is generated at an artificial surface defect in a fully reversed cyclic torsion test in vacuum. Measured growth rates in the FGA were 10−14–10−12 m/cycle, and the formation of the FGA consumed 98% of the VHCF lifetime.

Gear Root Bending Strength: A New Multiaxial Approach to Translate the Results of Single Tooth Bending Fatigue Tests to Meshing Gears

Developing accurate design data to enable the effective use of new materials is undoubtedly an essential goal in the gear industry. To speed up this process, Single Tooth Bending Fatigue (STBF) tests can be conducted. However, STBF tests tend to overestimate the material properties with respect to tests conducted on Running Gears (RG). Therefore, it is common practice to use a constant correction factor fkorr, of value 0.9 to exploit STBF results to design actual gears, e.g., through ISO 6336. In this paper, the assumption that this coefficient can be considered independent from the gear material, geometry, and loading condition was questioned, and through the combination of numerical simulations with a multiaxial fatigue criterion, a method for the calculation of fkorr was proposed. The implementation of this method using different gear geometries and material properties shows that fkorr varies with the gears geometrical characteristics, the material fatigue strength, and the load ratio (R) set in STBF tests. In particular, by applying the Findley criterion, it was found that, for the same gear geometry, fkorr depends on the material as well. Specifically, fkorr increases with the ratio between the bending and torsional fatigue limits. Moreover, through this method it was shown that the characteristics related to the material and the geometry have a relevant effect in determining the critical point (at the tooth root) where the fracture nucleates.

Influence of Crystal Structure of Nitride Compound Layer on Torsion Fatigue Strength of Alloy Steel

The demand for high-strength components for commercial vehicles has recently increased. Conventional gas nitrocarburizing has been used to increase strength and productivity of the crankshaft. A potential-controlled nitriding process was recently developed to control the crystal structure of the nitride compound layer. It has been found that this treatment improves the bending fatigue strength compared with conventional treatment, and has the potential to cope with the increase in crankshaft strength. However, the effect of torsional fatigue strength has not been studied. Therefore, in this study, the influence of the crystal structure of the nitride compound layer on torsional fatigue strength was investigated. Two kinds of test specimens with different crystal structures of the compound layer were prepared using gas nitriding treatment with controlled nitriding potential for an alloy steel bar (JIS-SCM435). Torsional fatigue tests were carried out using these test specimens. Although the compound layer of these test specimens had different crystal structures, the hardness distribution and residual stress distribution on the diffusion layer were almost the same. The relationship between stress amplitude and number of cycles to failure (S-N curve) showed that the torsional fatigue limits of the specimens were almost the same. This indicates that the crystal structure of the nitride compound layer did not affect the torsional fatigue limits, because the origin of the torsional fatigue failure is inside the specimen.

Crack path and threshold condition for small fatigue crack growth in annealed carbon steels under fully-reversed torsional loading

Torsional fatigue tests at an R of −1 were carried out near the fatigue limit, using smooth, round-bar specimens of annealed carbon steels with banded ferrite/pearlite and isotropic ferrite/pearlite structures. Precise polishing of the specimens made it possible to observe the interior geometry of fatigue cracks. While the crack-plane was macroscopically of shear-mode, it was irregular microscopically, bearing many kinked and branched cracks. Based on calculation of the stress intensity factor for propagating and non-propagating cracks, it was concluded that the torsional fatigue limit was determined by the threshold condition for continuous Mode I propagation into the ferrite/pearlite structure.

Effects of mean shear stress on the torsional fatigue strength of a spring steel with small scratches

The torsional fatigue behavior of a high-strength spring steel, SWOSC-V, was investigated. Of particular interest were the influences of small scratches and superimposed static shear stress in the very high cycle fatigue regime. To achieve the research objectives, an ultrasonic torsional fatigue testing machine was developed. S-Ncurves showed the fatigue limit for the tested material condition (i.e. with no residual stresses at specimen surface). This study revealed that a notable influence of the stress ratio, R, on the torsional fatigue behavior was not explicitly recognized. Concerning the influence of small scratches, it was found that the [Formula: see text]-parameter model can predict the lower bound of the torsional fatigue limit, irrespective of the value of R.

An alternative approach to calibrate multiaxial fatigue models of steels with small defects

In this work the authors propose a new methodology to estimate threshold loading conditions for naturally defective steels under complex stress states. In this setting, multiaxial fatigue models based on the critical plane approach and in the stress invariant approach are adapted to assess the effect of non-metallic inclusions in the material. In order to do so, it will be used a method that relates the √area parameter of a small defect and the Vickers hardness of the material Hν) with the nominal fatigue limit for this material either under uniaxial (σw) or under torsional (τw) loading. Therefore, uniaxial and torsional fatigue limits usually required to calibrate the multiaxial criteria will be calculated by the √area parameter. With this methodology the multiaxial fatigue criteria utilized are not changed. However, calibrating them is considerably cheaper and faster compared to traditional methods. To assess the new methodology, combined axial-torsional multiaxial fatigue data in DIN 42CrMo6 steel generated by the authors will be used. The proposed methodology is compared to the experiments and agreement within 5% error bands were obtained.

Effect of microstructure on the torsional fatigue limits in bainitic steels

Effect of microstructure on the torsional fatigue limits in bainitic steels

Influence of mean shear stress on the torsional fatigue behaviour of 34CrNiMo6 steel

This study provides a theoretical and experimental investigation of the effect of static shear stresses on the high-cycle fatigue behaviour of a 34CrNiMo6 high-strength steel under quenched and tempered conditions. Torsion S–N curves under different mean shear stresses were obtained. Experimental results show that an increase in mean shear stress yields a gradual reduction in shear-stress amplitude that the material can withstand without failure. The results for this steel agree well with the Smith’s hypothesis for ductile steels, which states that the effect of the torsional mean stresses on the torsional fatigue limit is negligible as long as the maximum shear stress is within the torsional yield strength. Taking into account the results collected from the literature and the experimental results on torsional fatigue of 34CrNiMo6 steel, an extension of the theory of Crossland is proposed to include the mean-shear-stress effect. Its application to the torsional fatigue case with mean shear stresses can be interpreted in terms of a balance of the energy of distortion. Macro-analyses of the specimen fracture appearance were conducted to obtain the fracture characteristics for different mean-shear-stress values under torsion fatigue loading.

Shear-mode Crack Initiation Behavior in the Martensitic and Bainitic Microstructures

Fully reversed torsional fatigue tests were conducted to elucidate the behaviour of shear-mode crack initiation and propagation in one martensitic and two bainitic steels. The relationship between the crack initiation site and microstructure was investigated by means of an electron backscatter diffraction (EBSD) technique. From the S-N diagram, two notable results were obtained: (i) the shear-mode crack was initiated on the prior austenitic grain boundary in martensitic steel, while in bainitic steels, the crack was initiated along the {110} plane; one of the slip planes of bcc metals, and (ii) the torsional fatigue limit of lower bainitic steel with finer grains was 60 MPa higher than that of upper bainitic steel with coarser grains even though the hardnesses were nearly equivalent. The mechanism determining the torsional fatigue strength in these steels is discussed from the viewpoint of microstructure morphology.

Torsional Fatigue Strength of Newly Developed Case Hardening TRIP-Aided Steel

The torsional fatigue strength of newly developed case hardening steel, i.e., transformation-induced plasticity-aided martensitic steel subjected to vacuum carburizing followed by fine particle peening, was investigated for the fabrication of downsized precision gears with high torque capacity and wear resistance. The surface-hardened layer properties—i.e., high Vickers hardness, high compressive residual stress, and a large amount of retained austenite—considerably increased the torsional fatigue limits of vacuum-carburized and fine particle peened TM and JIS-SNCM420 steels, although the notch-sensitivity to fatigue was increased. The relation between torsional and rotational bending fatigue limits for the smooth specimens was found to be between the maximum principal stress and the minimum shear strain energy criterions. On the other hand, this relation for the notched specimens was represented through the maximum principal stress criterion.

Improvement of torsional fatigue limit and rendering surface defect harmless by shot peening for spring steel

The effects of shot peening (SP) on the torsional fatigue limit of spring steel (SUP7) were investigated for specimens with Vickers hardness values of 460, 540, and 670 HV containing a semicircular surface slit. SP was conducted on smooth specimens and specimens containing a semicircular surface slit with a depth of 0.15 or 0.3 mm. Compressive residual stress was introduced into the specimens by SP. Torsional fatigue tests were carried out under a stress ratio of R = −1. The torsional fatigue limits of the shot peened specimens with Vickers hardness values of 460, 540, and 670 HV increased by 8%–67%, 33%–143%, and 36%–127%, respectively, in comparison with the non-shot peened specimens. The maximum depth of the slit that could be rendered harmless by SP was 0.15 mm for the 460 and 670 HV specimens. However, even a slit with a depth of less than 0.15 mm could not be rendered harmless by SP for the 540 HV specimen. Considering the improvement in the torsional fatigue limit and the size of the surface defect that could be rendered harmless by SP, the 670 HV specimen is optimal for practical use.

Influences of small defects on torsional fatigue limit of 17-4PH stainless steel

The sensitivity of 17-4PH stainless steel to small defects under torsional fatigue loading condition at a stress ratio of R=−1 is examined in the high-cycle fatigue regime. Fatigue crack initiation and growth behaviors are observed, and fractographic investigations are performed. As a key geometric parameter, area is used to investigate the influence of small defects on torsional fatigue limit. Further, the results are compared to the data obtained in the uniaxial fatigue tests, which allows the effect of biaxial stresses on the surface of the material to be discussed.

Effects of shot peening on the torsional fatigue limit of high‐strength steel containing an artificial surface defect

PurposeThe purpose of this paper is to clarify the effects of shot peening (SP) on the torsional fatigue limit of high‐strength steel specimens containing an artificial small defect.Design/methodology/approachSpecimens containing a drilled hole 0.1‐0.4 mm deep or a semi‐circular slit 0.15 or 0.3 mm deep were subjected to SP. Torsional fatigue tests were then carried out.FindingsThe torsional fatigue limits of specimens containing a drilled hole and those with a semi‐circular slit were increased 25‐64 per cent and 156‐186 per cent by SP, respectively. The torsional fatigue limits of the specimens subjected to SP and containing a drilled hole less than 0.1 mm in depth or a semi‐circular slit less than 0.15 mm in depth were almost equal to those of SP specimens without a defect. Based on these results, it can be concluded that a drilled hole less than 0.1 mm in depth and a semi‐circular slit less than 0.15 mm in depth could be rendered harmless by SP.Practical implicationsThe proposed method can be applied to mechanical parts subjected to cyclic torsion, such as coil springs, crank shafts and drive shafts.Originality/valueThis is the first paper to investigate the torsional fatigue limits after SP in materials containing a surface defect. In this paper, the effect of SP on the torsional fatigue limit having a surface defect is investigated.

Analysis of the Kart Frame Twisting Characteristics in Comparison with Torsion Working Stress and Torsion Fatigue Limit

Analysis of the Kart Frame Twisting Characteristics in Comparison with Torsion Working Stress and Torsion Fatigue Limit

Relationship between Torsional Fatigue Strength and Rotating Bending Fatigue Strength for High Strength Spring Steel with Shot Peening

To study fatigue strength design method for suspension coil springs for automobile, especially as the fundamental study of fatigue strength for spring steel, torsional fatigue and rotating bending fatigue tests were conducted for shot-peened spring steel of SUP7 having various Vickers hardness through tempering temperature variation. The effect of shot peening on the torsional fatigue strength and rotating bending fatigue strength were studied. Furthermore, the difference between the morphology of torsional fatigue failure and rotating bending fatigue failures were also studied. As a result, following findings came to light. (1) The torsional fatigue limit of peened specimen exceeded that of non-peened one in any hardness condition. On the other hand, as for rotating bending fatigue limit, there was no difference between non-peened and peened specimen, with the exception of specimen with maximum hardness. (2) The relationship between torsional fatigue limit and rotating bending fatigue limit for non-peened specimen was well explained by the shear strain energy theory. On the other hand, as for peened specimen, the relationship was explained by the combination of the maximum principal stress and the shear strain energy theories. (3) The fatigue failure morphology for non-peened specimen due to torsional fatigue indicated that shear fatigue failure initiated parallel to the axial line and then the failure propagated toward principal stress direction. As for peened specimen, the fatigue failure initiated along the 45 degree direction to the axial line (principal stress direction), and then propagated. On the other hand, as for all specimen due to rotating bending fatigue tests, the fatigue failure initiated toward principal stress direction, and then propagated.

Effect of Hardness and Shot Peening on Torsional Fatigue Strength of High Strength Spring Steel

Torsional fatigue tests were conducted for both shot-peened and non-peened spring steel, SUP7, with different Vickers hardness by changing tempering temperature. As a result, the torsional fatigue strength of shot peened specimen exceeded that of non-peened ones for the whole hardness level. Furthermore, higher Vickers hardness leads to higher torsional fatigue strength. Also, for the shot peened specimen with the hardness of 620HV, there was no decrease in fatigue limit, as seen in the non-peened specimen. In addition, the results of the measured residual stress for pre-fatigue and post-fatigue tests indicated that there was decay of residual stress after 107cycles fatigue test. The quantity of decay can be predicted by the residual stress before fatigue test and applied stress and yield strength of the specimen. Finally, we proposed the estimating equation for torsional fatigue limit of shot peened specimen. According to our estimation formula for torsional fatigue limit, we can predict accurately the torsional fatigue strength of shot -peened specimen with a hardness of up to 550HV by using the slope of the approximation curve in the modified Goodman diagram and values of residual stress for both specimens after 107 cycles fatigue test.

A study on combined torsion and axial load fatigue limit tests with stresses of different frequencies

The aim of this paper is to investigate the high cycle fatigue behaviour of metals in the case of multiaxial loading where the stresses are of different frequencies. In particular, combined axial load and torsion fatigue tests were performed on specimens made of quenched and tempered steel. This material has been chosen because it is commonly employed for the production of mechanical components intensively stressed under lengthy fatigue loads. Two frequency ratios between the shear stress and the normal stress are examined and the resulting fatigue limits from these tests are compared to the results from tests where the shear and normal stress are of the same frequency and in-phase. Moreover, different multiaxial fatigue limit criteria, based on the critical plane concept and on the so-called integral approach, are used to analyse the obtained experimental results. In general, better agreement between predictions and experimental results is achieved by the criteria of the integral approach category.