Fatigue Limit Σw Research Articles

A New Approach to Estimate the Fatigue Limit of Steels Based on Conventional and Cyclic Indentation Testing

For a reliable design of structural components, valid information about the fatigue strength of the material used is a prerequisite. As the determination of the fatigue properties, and especially the fatigue limit σw, requires a high experimental effort, efficient approaches to estimate the fatigue strength are of great interest. Available estimation approaches using monotonic properties, e.g., Vickers hardness (HV), and in some cases the cyclic yield strength, only allow a rough estimation of σw. The approaches solely based on monotonic properties lead to substantial deviations of the estimated σw in relation to the experimentally determined fatigue limit as they do not consider the cyclic deformation behavior. In this work, an estimation approach was developed, which is based on a correlation analysis of the fatigue limit σw, HV, and the cyclic hardening potential obtained in instrumented cyclic indentation tests (CIT). For this, eleven conditions from five different low-alloy steels were investigated. The CIT enable an efficient and quantitative determination of the cyclic hardening potential, i.e., the cyclic hardening exponentCHT eII, and thus, the consideration of the cyclic deformation behavior in an estimation approach. In this work, a strong correlation of σw with the product of HV and |eII| was observed. In relation to an existing estimation approach based solely on HV, considering the combination of HV and |eII| enables the estimation of σw with an enormously increased precision.

Experimental Investigations and Damage Calculations of a Load Time History in the Very High Cycle Fatigue

The main focus of this investigation is to clarify the influence of variable amplitude loadings on subsurface crack initiation and crack growth. Therefore, differently reconstructed load sequences on the basis of a standardized load time history called FELIX are investigated with an R-ratio of -1. The major amount of cycles is situated beneath the fatigue strength. A new damage calculation approach considering inclusion sizes is presented. Thus, the stress amplitude in the S-N curve was normalized with a calculated fatigue limit σw(area), which is defined by Murakami. Afterward, the fatigue life depending on the inclusion size is calculated using a Palmgren/Miner rule. The largest inclusion in the measurement volume was determined using extreme value statistics. Fatigue lives for each investigated load sequence were calculated taking the scatter of inclusion sizes into account.

Fatigue Limit Evaluation of Blunt-Notched Specimen Using ΔKthValue of Small Crack

It is the big problem to evaluate the fatigue limit σw in order to safely design structures and machines. Under the condition of the fatigue crack initiation limit σw1,the present author defined the initial crack scale √area using the characteristic elastic field of the notch, the half length of the fatigue crack a and a notch depth t. Using this√area,the methods of calculating ΔKth and σw1 were proposed. In addition to it, in this condition it is made sure that ΔKth exists on the band from ΔKth prediction line of the micro fatigue crack [1] within 18% error. Using ΔKth calculated by the prediction line and the value of√area,this evaluating method of σw1 was confirmed with annealed 0.35% carbon steel. As a result, it was confirmed that this method to evaluate σw1 is within 18% error. Moreover it was also confirmed that the σw1 value by this prediction method is within 10% error when the predicted σw1 value is greater than σw2.

Fatigue Characteristic of Spheroidal Vanadium Carbides Cast Iron

The purpose of this study is to investigate the fatigue characteristic and fatigue fracture mechanism of the high V-Cr-Ni spheroidal carbide cast iron (SCI-VCrNi) with spheroidal vanadium carbide (VC) dispersed within austenitic stainless matrix microstructure. The SCI-VCrNi that has high hardness was developed by 10mass%V adding to 18-8 stainless steel with spheroidal VC is distributed in the matrix. Firstly from the plane bending, the fatigue limit σw has been found to the 358MPa of SCI-VCrNi. Secondly, fracture surface observations were performed to clarify the fatigue mechanism of SCI-VCrNi. The fracture surface of SCI-VCrNi was so rough that the beach mark could not be observed. So, SEM was employed to observe, the fatigue fracture surface which showed a particular fatigue pattern. Also, many fracture cracks of VC were observed. In addition, the secondary cracks are shown at the interface between VC and the matrix. It can be suggested that the bondability between VC and the matrix is strong, and therefore, the propagation of cracks was delayed by the breakage of VC.

High Temperature Rotating Bending Fatigue Characteristic for SUS403 Notched Round Bar

In order to study the notch effect on rotating bending fatigue properties for SUS403 stainless steel, the rotating bending fatigue tests were carried out at room temperature, 300°C and 600°C with a frequency of 1200 cycles/min. The temperature dependence of fatigue limit and the estimation method of fatigue notch factor were investigated. The relationships between the fatigue limit σW of smooth specimen and the tensile strength σB and also σW and the Vickers hardness HV were obtained as σW=0.58σB=1.63 HV at every temperature. Furthermore the relationship between the parameter (β-1) √σ0/σB and Kt-1 was proposed to estimate the fatigue notch factor, where σ0 is the tensile strength at room temperature, β is the fatigue notch factor at a certain temperature and Kt is the stress concentration factor. Then fatigue notch sensitivity factor η was obtained as η=0.056√σB/Kt. Using these results, the estimated fatigue limit was satisfactory and the predicted accuracy was ±10%.

Study on Rotating Bending Fatigue Characteristic of Several Stainless Steels at High Temperature

The rotating bending fatigue tests were carried out at room temperature, 200°C, 400°C, 600°C and 800°C with a frequency of 1200 cycles/min. using SUS 304 solution treatment material and SUS 304-1/2 H 10% cold working material, and were carried out at room temperature, 300°C and 600°C using SUS 430 and SUS 403. The cold working material showed higher strength at finite life and fatigue limit in every temperature than the other materials did, although the difference of fatigue limit above 400°C between the cold working material and the other materials were a little. The relationships between the fatigue limit σW and the tensile strength σB were obtained as σW =0.44σB for SUS 304 at every temperature and SUS 304-1/2 H over 200°C, and σW=0.58σB for SUS 430, SUS 403 at every temperature and SUS 304-1/2 H below 200°C. Besides, the relationship between the stress ratio σa/σωR.T. and the parameter P= (10-log Nf) /T was proposed to estimate the fatigue strength at finite life, where σa is the bending stress amplitude, σωR.T. is the fatigue limit at room temperature, Nf is the cycles to failure and T is the absolute temperature.

Zr基バルク金属ガラスの疲労寿命特性に及ぼすナノ結晶分散効果

A nano-scale crystal (NC) dispersed bulk metallic glass has both high tensile strength and high ductility. The new alloy is therefore expected as a candidate of high-strength structural materials in machines and structures. However, fatigue life properties in the NC bulk glass has not been examined. In this report, effects of the nanocrystalline dispersion on fatigue was studied in a NC glassy alloy Zr55Al10Cu30Ni5 (at%). Fatigue ratio, fatigue limit σw⁄tensile strength σB, in the NC bulk glass was estimated to be about 0.13. The value was 3 times larger than that of single phase bulk metallic glasses with the same composition reported in the literature. It is considered that the inhibition of the slip initiation and growth was induced by the nanocrystal dispersion and it increased the σw.

Nanoscopic Strength Analysis of Tempered-Martensitic Steels.

The relationships between tensile strength and microstructural parameters and between fatigue limit and microstructural parameters were investigated for seven tempered-martensitic steels S45C, SMn443, SCr440, SNCM439, SCM440, SUP7 and SUP12. An optical and atomic force microscopy showed that prior-austenitic grain diameter, dγ, block width, Wblo, and precipitation spacing, λ, were 18μm, 0.7μm and 0.11∼0.24μm, respectively, as microstructural parameters. A nanoindentation showed that HV=100+Hv*dls+Hv*pre+Hv*bou, where Hv is macro-Vickers hardness, and Hv*pre and Hv*bou are micro-covered Vickers hardness due to dislocation and solid, precipitation and block boundary strengthening. Hv*pre and Hv*bou were expressed by the microstructural parameters of λ and Wblo. The constant value of 100 is base hardness of the iron. Based on these results, we proposed that tensile strength σB and fatigue limit σw, were expressed in the followings. σB=3.27{100 + Hv*dls + 1.02 × 10-2λ-1 + 3.67 × 10-4λ-1w-1/2blo}…………………………………(A-1) σw=1 .6{100 + Hv*dls + 1.02 × 10-2λ-1 + 1.15(3.67 × 10-4λ-1w-1/2blo)}…………………………(A-2)

The effect of microstructure on fatigue behaviour of a Ti-6Al-4V alloy: Tokaji, K., Ogawa, T. and Ohya, K. J Soc Mater Sci Jpn (Feb. 1993) 42 (473), 169–175 (in Japanese)

Models predicting the effects of defects, inclusions and inhomogeneities on the fatigue strength of metals are reviewed. Their historical development is discussed, from the Isibasi model and the Frost model to recent models based on fracture mechanics. The method of application of existing models and the data necessary for prediction are explained. Fracture mechanics models mostly employ the value of threshold stress intensity factor range ΔKth 1c for a long crack as the basic data but usually apply only to two-dimensional cracks or two-dimensional defects. Furthermore, a careless assumption of the value of ΔKth 1c will result in a large prediction error of fatigue limit σw. Models that do not use ΔKth 1c are also introduced and discussed. Several models that consider the effects of non-metallic inclusions and inhomogeneities are also introduced, and the difficulties of prediction are indicated. The importance of understanding the fatigue limit phenomenon for the accurate prediction and choice of relevant models is emphasized, with regard to the existence of small non-propagating cracks and the statistical nature of the behaviour of small cracks and microstructures.

Ｔｉ‐６Ａｌ‐４Ｖ合金の回転曲げ疲労におけるき裂発生および初期き裂伝ぱ過程

Characteristics of crack initiation and propagation in rotating bending fatigue tests were investigated on Ti-6Al-4V alloy. Successive observations were made by the plastic replica method to determine the physical meaning of fatigue limit σw, and crack propagation behavior was studied using a small crack growth law. The main results obtained are summarized as follows.(1) When σ is over σw, microcracks appear at α phase.(2) The fatigue life is determined by the crack propagation period except for the stress near the fatigue limit.(3) When σ is equal to σw, no microcracks are observed on the specimen after 107 cycling of stress under a metallurgical microscope. Therefore, the fatigue limit is determined by the limiting condition for the initiation of microcrack.(4) The relation dl/dN∝σnl holds when σ/σ0.2>0.6, and the relation dl/dN∝ΔKm holds when σ/σ0.2<0.5.

Quantitative evaluation of effects of nonmetallic inclusions on fatigue strength of high strength steel.

First, the effects of nonmetallic inclusions on the fatique strength of metals are reviewed and the influential factors are revealed. Next, it is emphasized that the effects of nonmetallic inclusions must be analyzed from the viewpoint of small defects or small cracks, because the threshold condition at the fatigue limit is not the condition for crack initiation but the condition for the non-propagation of a crack emanating from defects or inclusions. Finally. from this point of view, the equation for the prediction of the threshold stress intensity factor range ΔKth and fatigue limit σw for defects and small cracks was applied to predict those for inclusions contained in high strength steels. It is demonstrated that the square root of the projected area of inclusions and the Hv of the matrix are the crucial parameters to predict the fatigue limit of metals containing inclusions. The predictions by the proposed equations were in very good agreement with the experimental results obtained from the fracture surface showing fish-eye patterns. The reasons why the fatigue limit σw of high strength steels does not increase linearly with increasing hardness, and why the scatters of fatigue limit are so large are made clear.

過小応力を含む２段繰返し疲労試験の寿命予測における微小き裂の役割

The effect of understress in two-step stress fatigue tests on fatigue life was investigated with emphasis on the behavior of small cracks.In fatigue under variable amplitude loading, two critical stresses play important roles in fatigue damage prediction. One is the fatigue limit σw defined by the failure of a specimen containing a small crack, and the other is the critical stress σwi which is the threshold value for fatigue crack initiation from the small crack. It should be noted that both σw and σwi are the function of crack size and accordingly the degree of contribution of understress σL to fatigue damage varies at every moment with the variation of crack size, i.e. crack propagation. The equations to predict σw and σwi were derived here as the function of crack size.If the value of σL is lower than σwi defined on the basis of crack length l, the repetition of σL does not contribute fatigue damage. However, if the crack propagates due to the repetition of overstress σH and the value of σwi decreases below σL, σL starts to contribute to fatigue damage. This fact explains the reason for a wide scatter of the values of cumulative fatigue damage D of modified Miner's rule obtained in previous studies. A method is also discussed to predict the lower limit of D.

Influence of matrix structure on fatigue strength of nodular iron with high tensile strength.

The rotating fatigue tests were carried out on nodular irons with 7 types of matrix structures prepared by heat treatments, and effects of matrix structure on the fatigue limit σw were examined. In order to study the crack initiation and growth, the fracture surface was observed by SEM. The results obtained were as follows : (1) The effect of matrix structure on σw was remarkable. (2) Among irons with ferrite-pearlite duplex structures, the iron with the finest spheroidal graphite prepared by the metal mold had the highest fatigue limit. (3) Among irons with hardened matrix structure prepared by cooling of high rate, the iron with upper bainite had the highest fatigue limit. (4) The matrix structure influenced the metallurgical factor that initiated the crack, because increasing Hv of the matrix structure induced the high notch sensivity of micro-porosity. This fact caused the effect of matrix structure on σw.

亜共析黒鉛鋼の疲労限度におよぼす組織学的因子の影響

The fatigue limit of hypo-eutectoid graphitic steels was studied in connection with microstructural factors such as the mean ferritic grain size dF (mm), the volume fraction of graphite f, the mean graphite nodule diameter dG (mm), and the mean ferrite path between graphite nodules λ.By the multiple regression analysis the fatigue limit σW (MPa) was expressed as follows:(This article is not displayable. Please see full text pdf.) The effect of dG was smaller than that of dF.Non-propagating microcracks were observed on the surface of smoothed specimens subjected to the repetition of 107 cycles at the stress of the fatigue limit, and furthermore, the criterion as to whether non-propagation of a microcrack can occur or not was found to be related to the microcrack length, the cyclic stress and the mean ferritic grain size. Thus it was concluded that the fatigue limit is not the critical stress for crack initiation but is the maximum stress below which the microcrack can not grow continuously.Aspects of fatigue fracture surface depended on the microstructure of graphitic steels, and the amount of facet type fractures increased with decrease in mean ferrite path between graphite nodules.The endurance ratio of the graphitic steels was in the range from 0.52 to 0.60.

Effect of Overstress on the Fatigue Behavior of a Heat-treated 0.54% C Steel under the Stress of Fatigue Limit

The effect of definite cycles of overstress σos (&cong; 1.5 σw, σw : fatigue limit) which was applied periodically during the repetitions of the stress of fatigue limit σw was investigated through the behavior of micro-crack. The main results obtained are as follows ; 1) When σos is repeated in nos cycles at every 107 cycles of σw and the value of nos is within a limited range, the specimen is broken at a small value of the accumulated cycle ratio Σ(n/N). This phenomenon seems to be due to an increase in crack opening ratio under the repetitions of over-stress. In that case, the crack propagates only under the repetitions of σw. 2) The value of Σ(n/N) depends on the size of a non -propagating microcrack formed by the first 107 cycles of σw. 3) The repetition of 107 cycles of σw increases the fatigue life of the specimen under σos.

Effect of Grain-size on Fatigue Strength of Low Carbon Steel at Elevated Temperatures

Rotating beam fatigue tests over the temperature range 20-450°C were made on low carbon steel in annealed and low-temperature-quenched conditions. The relationship σw=Cw+kwd-1/2 which describes the dependence of the fatigue limit σw on the grain diameter d has been proved in this series of experiments to apply up to about 400°C. Both of the two constants Cw and kw reached the maximum at 350-375°C and the minimum at about 200°C. The existence of the maximum in the values Cw and kw is found to be caused by a rapid strain ageing. The fatigue strength at 450°C was independent of the grain size. Below 400°C, σw is increased by quenching. The increase in σw is induced by an increase in Cw, not in kw, which is little influenced by quenching. The increase in Cw only may be explained as the consequence of precipitation hardening due to quench-ageing developed prior to fatigue stressing .

Features of fatigue fracture strength and the failure of iron specimens at 77�K after cyclic preloading at room temperature

1. It was shown that the structure of low-temperature fatigue fractures depends significantly on the modes of cyclic preloading at 293°K. A stable dislocation structure in iron, created by cyclic loading at 293°K at fatigue limit σw to 107–2·107 cycles — in contrast to the unstable structure formed by loading at σa=σw or σa=σw * 3–4 kgf/mm2 to 104–3·104 cycles — leads to a reduction in the plastic strain of the iron in the event of cyclic deformation at 77°K and to the appearance of shear-type, crystallographic, ductile fracture sections in the stable crack growth zone (as in annealed material). 2. A scheme was proposed for the propagation of fatigue cracks at the stable growth stage by means of the shear mechanism of failure. It is proposed that the impeding of plastic strain at the crack tip and the initiation of submicrocracks in front of the macrocrack by the shear mechanism lay conditions for the development of shear-type, ductile, crystallographic fracture sections. 3. Reduction of the test temperature from 293 to 77°K is accompanied by a substantial decrease in stable crack length (from ∼2 to ∼0.35 mm). The investigated modes of cyclic strain at 293°K have almost no effect on stable crack length at 77°K, although the low-temperature fracture toughness of iron in which a stable substructure has been created at room temperature is 16% greater than that of iron having a relatively unstable dislocation structure. 4. It was established that in polycrystalline iron at 77°K, fatigue failure in the zone of stable crack growth occurs partially by the mechanism of the formation of fatigue microbands.

タフトライド処理鋼の疲労限に及ぼす焼もどしの影響について

The authors proposed previously the method for predicting the fatigue limit of smoothed specimens made of tufftrided steel from the hardened depth h and the distance from surface to center of specimen a. It was expected that the linear relation should hold between the improvement ratio of fatigue limit σw·t/σw·nt and h/(a-h) according to the prediction method. In case of the tufftrided steel supersaturated with nitrogen in the matrix, the linear relation was observed between these two quantities as expected and the validity of the method was clarified.On the other hand, it has been already reported that the fatigue limit of tufftrided steel decreases with the precipitation of nitrides of Fe4N. In this paper, the applicability of this prediction method is investigated on the tufftrided steel which has the nitrides of Fe4N.The results obtained are summarized as follows:(1) The fatigue limit of tufftrided steel decreases with the increase of nitride, and the decrease stops when the precipitation of nitride is perfectly completed. Its fatigue limit is still larger than that of non-tufftrided steel.(2) The linear relation is also observed between σw·t/σw·nt and h/(a-h) on the tufftrided steel which contains nitrides. Consequently, it is concluded that the prediction method proposed by the authors can be applied regardless of the condition of nitrogen. However, the linear relation equations differ depending upon the condition of nitrogen.

Fatigue Limit of Steel with Cracks

Fatigue tests were carried out on mild steel plate specimens with various lengths of cracks. The relation between the alternating fatigue limit σw and the crack length was well expressed by following equation. Rp(c)w = αe(sec πσw/2σy - 1 ) = const. where, Rp(c)w is the cyclic plastic zone size at fatigue limit, αe is the equivalent crack length of an infinite plate, and σy is the yield strength of the material. The size of the persistent slip band zone on the fatigue limit is about one tenth of Rp(c)w and is nearly equal to the measured mean grain size of the material. Rp(c)w has close relations with the crack length corresponding to the fatigue limit of a plain specimen, the material constant which was already obtained in the criteria of fatigue crack initiation at notch roots, and the critical notch root radius at the branch point.