Murakami Equation Research Articles

Estimating the fatigue limits for quenched and tempered steel rods treated with multifunction cavitation considering residual stress, hardness, and surface pits

AbstractIn this study, multifunction cavitation (MFC) was performed on low‐alloy steel (AISI 4140 steel) rods with different hardnesses to increase their fatigue limit. It was found that a high compressive residual stress was generated on the surface of steel rods by MFC and that the magnitude of the compressive residual stress tended to increase with increasing specimen hardness, which resulted in a higher fatigue limit. However, fatigue cracks are known to be initiated from the pits and red rust that form on the surface during MFC treatment in water. Furthermore, relaxation of the compressive residual stress was also investigated during the fatigue test to elucidate the mechanism for improving the fatigue properties. The results showed that the fatigue limit for MFC‐treated steel rods was accurately estimated by considering residual stress relaxation, hardness, and pit formation. Validation of the fatigue limit estimation was also conducted through comparison with Murakami's equation.

Effect of surface integrity on fatigue life of 2024 aluminum alloy subjected to turning

Changes in cutting parameters can cause changes in surface integrity and affect fatigue life. In this paper, the surface integrity and fatigue life of 2024 aluminum alloy were studied by surface integrity measurement, tensile fatigue test and fatigue fracture characterization with cutting speed and feed rate as control variables. The main factors affecting surface integrity and fatigue life were analyzed, and a fatigue life prediction model considering fracture surface roughness was proposed. Finally, the mapping relationship between surface integrity and fatigue life was established. The results showed that the feed rate contributes the most to the surface residual stress (σrs) and surface morphology (RaRy/Rz), and the surface residual stress (σrs) contributes the most to the fatigue life. The prediction accuracy of the fatigue life prediction model considering the fracture surface roughness is as high as 99 %. At the same time, Murakami equation can well explain the initiation and propagation mechanism of fatigue cracks. The increase of feed rate will increase the fatigue life, while the increase of cutting speed will reduce the fatigue life.

Fatigue strength assessment of high-speed railway axle EA4T steel with foreign object damage

Axle is easy to be hit by ballast and other foreign object rolled up due to aerodynamic effect to form the typical foreign object damage (FOD) on the surface, leading to deteriorate the axle structural integrity and reduction of fatigue performance. In order to evaluate the effects of surface damage and strengthening treatment on the fatigue performance, the EA4T axle steel specimens with or without shot peening (SP) were induced FOD by a compressed-gas gun. Meanwhile, the strengthening mechanism of shot peening were investigated by both nanoindentation technique and X-ray diffraction. Then the probabilistic fatigue S-N curves (P-S-N) were acquired for unSPed and SPed specimens subjected to FOD or not. In addition, the fatigue limit of FODed axle estimated by Murakami equation was corrected by size effect, surface quality, loading mode factors. Finally, the fatigue limits with 97.5% reliability were adopted to construct the modified Kitagawa-Takahashi (K-T) diagrams for FODed axle with or without shot peening treatment, which can be used in the service performance evaluation of foreign object damaged axle.

On the Use of the areaΔ and the Three-Parameter Model to Estimate High Cycle Fatigue Life

Abstract In our previous work, a parameter areaΔ was proposed to describe fatigue damage caused by micro scratch, whose validity was verified by fracture mechanics. In this article, we summarize an attempt to check the applicability of the areaΔ in the field of the classic S-N curve method. For the sake of objective verification, the experiment data used in this article are from our published work. A high cycle fatigue life model of TC17 based on micro scratches is established with the synthesis of the three-parameter model and Murakami equation modified by areaΔ. Prediction results gave accuracy to mainly fall into the scatter band of factor 2. It can be suggested that areaΔ is suitable for being used in both fracture mechanics and classic S-N curve method. Furthermore, the validity of areaΔ in fatigue behavior analysis combined with current fatigue theories and materials is summarized. The measurement method of scratch depth and width suitable for areaΔ is also introduced.

Fatigue evaluation of TC17 titanium alloy shaft with surface scratch based on FEA and fracture mechanics

With the development of advanced mechanical equipment, more attention should be paid to the fatigue evaluation of the critical components affect by surface scratch, like the TC17 titanium alloy shaft. The designed fatigue test is carried out to reveal the negative effect of surface scratch on fatigue failure, and the fatigue limit model for TC17 titanium alloy with surface scratch is proposed based on the Murakami equation. Then, FEA with different surface scratches for TC17 titanium alloy shaft is carried out, an empirical formula is proposed to express the relationship between the stress and surface scratch. In addition, the unknown parameter related to TC17 and the specific stress intensity factor model is identified, to estimate the critical surface scratch of TC17 titanium alloy shaft. With the comprehensive application of the classic theory and new proposed models, a new fatigue life evaluation model of TC17 titanium alloy shaft with surface scratch is developed and verified, whcih is novel and essential to the maintenance of the damaged TC17 titanium alloy shaft.

Effects of Fine Particle Shot Peening Treatment on Fatigue Properties of Al-7Si-0.3Mg Alloy

In this study, two different fine particle shot peening (FPSP) treatments were performed on Al-7Si-0.3Mg alloy specimens to evaluate their effects on fatigue properties. After the treatment, the microstructure morphology of the specimens was observed, and the surface roughness and residual stress distribution were measured. Rotating bending fatigue tests were conducted, and the fatigue fracture surfaces were observed using scanning electron microscopy (SEM). The crack initiation and propagation behavior were investigated using the replica method. The results indicate that FPSP can introduce residual stress on the surface layer of the material and refine the surface microstructure, and also change the surface roughness. At low stress amplitude levels, FPSP can improve fatigue life significantly. At 5 × 107 cycles, the fatigue strength of shot-peened specimens increased by 33% compared to unpeened specimens. In unpeened and steel shot-peened (SSP) specimens, both crystal slip and casting defects can induce fatigue failure, while only casting defects can cause failure in the case of ceramic shot-peened (CSP) specimens. Moreover, FPSP can move the crack initiation site to the subsurface from the surface. The range of threshold stress intensity factor of the material can be improved significantly by this treatment. Casting defects have a significant influence on fatigue strength; the effect on fatigue strength can be well evaluated by the modified Murakami equation.

The Kitagawa-Takahashi fatigue diagram to hybrid welded AA7050 joints via synchrotron X-ray tomography

The relationship between the microstructural nature and fatigue resistance was explored for laser welded AA7050-T7451. Based on high-resolution synchrotron radiation X-ray micro computed tomography, it is found that the large surface defects are a controlling factor in fatigue crack initiation. Besides, fine equiaxed grain zone (FQZ) near the fusion line appears to the failure site of hybrid laser welded joints. Particularly for gas pores-free at the weld surface, such FQZ might play a crucial role in degrading the service strength. Research results show that the evolution in microstructure, element and defects due to welding deteriorates the hardness, tensile strength and fatigue properties. Modified Murakami equation and Kitagawa-Takahashi diagram were finally established to correlate the fatigue strength with defects, which provides an important reference to assess the joints.

A new model for predicting the gigacycle fatigue strength of high-strength steels

Three models for predicting the gigacycle fatigue strength of high-strength steels were investigated in this study: the Tanaka-Akiniwa model, the Murakami equation and a newly-formulated model. The Tanaka-Akiniwa model proved to have the drawback of overestimating the inclusion size effects. In the Murakami equation, the calculated ODA growth curve was imaginary. Our results demonstrated that the new model generated the most accurate predictions. Predictions were then derived, with each constant calculated by fitting the experimental data to each steel grade. The derived predictions were therefore not universal but different for each steel grade. The accuracy of the derived predictions varied according to the grade of steel. The worst accuracy was for JIS-S40C, the second worst was for JIS-SUJ2 and the third worst was for JIS-SCM440 under R = –1. Other than these three predictions, though, the accuracy was excellent. During the fitting of the experimental data, the existence of new fatigue limits was suggested in the gigacycle regions: these were revealed by fatigue testing up to 1011 cycles. The derived predictions indicated only minor differences between steel grades for gigacycle fatigue strength. With increasing inclusion size, the drop in gigacycle fatigue strength became less steep, and looked at in terms of the mean stress effect, a modified Goodman line could safely be used for high-strength steel.

High cycle fatigue property and fracture behavior of high-strength austempered ductile iron

The high cycle fatigue tests of high-strength austempered ductile iron of grade 1200/850/04 (ASTM 897 M-06) were conducted by the high frequency fatigue machine. The results show that the S–N curve decreases continuously and there is no conventional fatigue limit at 107 cycles. According to the fracture surface observations, at short fatigue life region the specimens fail from defects at specimen surface and at long fatigue life region the specimens fail from internal defects with fish-eye area around it. According to the defect sizes measured in the standard inspection areas of the material, the maximum defect size evaluated by the statistics of extreme values method is in accordance with that of the fatigue test results. Meanwhile, it is obvious that the fatigue strength of austempered ductile iron is influenced by the original defect size and the fatigue limit can be well evaluated by the Murakami equation.

Effect of Yttrium Content on the Ultra-High Cycle Fatigue Behavior of Mg-Zn-Y-Zr Alloys

In the super-long life regime, the fatigue behavior of as-extruded Mg-6wt%Zn-xY-0.8wt%Zr Mg alloys with Y content of 0, 1, 2 and 3 wt% have been investigated, respectively. The result indicated that for all measured S-N curves, a plateau existed in the regime of 5×106-108 cyc, and then the fatigue strength gradually decreased between 108 and 109 cycles. Therefore, only fatigue strength corresponding to 109 cycles can be determined. Compared with other alloys, the alloy with Y content of 2 wt% has the highest fatigue strength and its value is 105 MPa. SEM observations to fracture surfaces revealed that for all alloys, the fatigue crack mostly initiated at the surface or subsurface of samples failed within 106-109 cycles. Further observation indicated that the crack initiation was related with activated slip bands instead of phase particles and activated twins. Based on the measured results and Murakami equation, it demonstrates that the fatigue strength of alloys is more dependent on the hardness values.

Fatigue Limit Prediction of Large Scale Cast Aluminum Alloy A356

Casting defects such as gas pores and shrinkages typically occur during casting process. These casting defects affect fatigue crack initiation and strongly dominate fatigue strength. Particularly, in a large scale component, the molten metal flow is complicated and the cooling rate is dependent on the locations, which affect the formation of casting defects. In the present study, rotating bending fatigue tests of cast aluminum alloy A356 were conducted using the specimens sampled at three locations of a large scale component where the cooling rates were different. The fatigue limit was predicted based on the statistics of casting defect size and compared with the experimental results. Fractographic analyses revealed fatigue crack initiated from casting defect in all specimens. Murakami et al. suggested the method for predicting the fatigue limit of steel using the extreme value statistics of inclusion size (Murakami et al., 1989). Ueno et al. modified Murakami's equation and proposed the equations to predict the fatigue limit of die-cast aluminum alloy based on the defect size (Ueno et al., 2012). The present authors suggest the modified evaluation method of defect size considering the combination of the neighboring defects which exist near to each other. The predictions agree well with the experimental results but they are slightly different, which indicates the other metallurgical factors affect fatigue strength.

Influence of Inclusion on Crack Initiation in Wheel Rim

Speed increase and heavy haul of the railway freight car are the effective measures to raise the transport ability of railway, and they have been the new trend for railway freight car development. The increase of speed and axle load will lead to the increase of wheel-rail contact stress, which will make a great change of stress distribution in the whole wheel rim. Goodier equation was employed to analyze the stress state around inclusion and cavity. In the operation of wheel-rail contact stress, stress concentration occurred in the pole of Al 2O 3 spherical inclusion, while it appeared on the equator of cavity. The critical inclusion sizes of 250 kN axle load freight car wheel at different velocities, a certain distance away from the tread, were calculated by Murakami equation. Comparing the inclusion in cast steel wheel with that in rolled steel wheel, it is found that the inclusion in cast steel wheel has much more excellent crack resistance than that in rolled steel wheel. In the meantime, in order to reduce the probability of rim crack, some suggestions were put forward.

Vers une optimisation de la tenue à la fatigue de pièces forgées intégrant l’histoire mécanique des matériaux

Forging of metal components induces grain flow orientation, which gives rise to anisotropic mechanical properties. Our study deals with the definition and the use of this grain flow anisotropy into fatigue life calculation. We have focused on high cycle fatigue, and we deal with steels containing malleable inclusions above a critical size. A new multiaxial criterion has been developed on the basis of the Murakami equation. This criterion has been implemented in the finite element code Forge 3®. This computational tool uses a new variable to represent the grain flow orientation provided by forging simulation to account for subsequent fatigue anisotropic behaviour. Moreover, residual stresses resulting from forging are also taken into account to perform the fatigue calculation. Finally, a virtual simulation chain, including Forging and Fatigue calculation is carried out. The final goal is to improve fatigue properties by modifying forging conditions.

THE EFFECT OF COATING THICKNESS ON FATIGUE PROPERTIES OF STEEL THERMALLY SPRAYED WITH Ni-BASED SELF-FLUXING ALLOY

The Thermal spraying is one of the most popular surface coating techniques. To achieve the most efficient use of this technique in practice, it is very important to clarify the fatigue properties of steel coated with a thermal spray coating. In this study, to clarify the effects of coating thickness on the fatigue properties of the steel substrate, three types of sprayed specimens with different coating thickness (0.2, 0.5 and 1.0mm) were prepared and fatigue tests were carried out. Coating thickness strongly affected the fatigue properties; the thinner the coating thickness, the higher the fatigue strength. Fatigue crack propagation behaviors were observed. Accordingly the fatigue cracks propagated through many defects on the coated surface. The sizes and number of the coating defects were determined by coating thickness; the thicker the coating thickness, the larger the defect and number. Therefore, the sprayed specimens with thinner coatings indicated higher fatigue strength. Furthermore, estimations of the fatigue strength were performed by using Murakami's equation. The fatigue strengths of thermal spray coated specimens were estimated by three parameters; (i) maximum size of coating defects estimated by statistics of extreme value, (ii) hardness of the matrix and (iii) volume fraction of coating defects.

Quantitative analysis of the impact of forging operations on fatigue properties of steel components

Forging of metal components induces grain flow orientation, which leads to anisotropic mechanical properties. Therefore, it is critical to describe and take into account this grain flow anisotropy into fatigue life calculation. A new state variable to represent the grain flow orientation is defined and implemented in the finite element code Forge 3® so that forging can be simulated to predict the grain flow in a forged part. When focusing on steels containing malleable inclusions above a critical size, the Murakami equation can be used for describing high cycle fatigue. This criterion is extended to multiaxial fatigue analysis for materials with a grain flow. Therefore, the output of forging simulations in terms of grain flow can be used in anisotropic fatigue analysis. Moreover, residual stresses resulting from forging should also be taken into account to obtain accurate fatigue calculations. Once this integrated simulation tool is developed, a global optimization loop including Forging and Fatigue calculation can be carried out.

1352 Ti-6Al-4V合金の疲労特性における応力比効果(S22-3 非鉄合金・試験装置,S22 ギガサイクル疲労)

Fatigue tests were conducted for Ti-6Al-4V alloy under sress ratios of R=-1, 0 and 0.3, and under the condition fixing the maximun stress at the yield stress(σ_<max>=σ_y test). Internal fracture tended to occur under high stress ratios. The fatigue strength determined at 10^8 cycles in the R=0 and 0.3 tests was below a modified Goodman relationship. The experimental gradient on log-log relationships between fatigue limit σ_ w and stress ratio (1-R) higher than that estimated by the Murakami's equation.

Ultrasonic Fatigue Properties of High-strength Steel Under Tensile Mean Stress

Ultrasonic fatigue tests at 20 kHz were conducted under R=-1 and R=0 for a low-temperature-tempered JIS-SCM 440 low-alloy steel, together with 50 Hz tests using a servo-hydraulic fatigue testing machine. The ultrasonic fatigue testing machine, with which tensile mean stress could be applied, were specially prepared in this research. In these fatigue tests, fish-eye fracture occurred both under R=-1 and R=0. Although the fatigue test results were scattered, difference between the 20 kHz and 50 Hz results were little in case of fish-eye fracture. The origins of fish-eye fracture were mostly an Al2O3 inclusion, whose sizes ranged from 5 to 35μm. ODAs, i.e. optically dark areas, were observed on the fracture surfaces of fish-eye fracture both under R=-1 and under R=0. The ODA sizes under R=0 were, however, smaller than those under R=-1. The scattering of fatigue test results in the fish-eye fracture region were caused by difference of the inclusion sizes and could be reduced in the modified S-N diagrams in which stress amplitudes were normalized with fatigue limits estimated by Murakami's equation. In the modified S-N diagram, the results at 20 kHz showed good agreements with those at 50 Hz under R=0, as well as R=-1. These results supported the validity of the ultrasonic fatigue testing under tensile mean stress in case of fish-eye fracture.

高強度鋼のギガサイクル疲労における介在物寸法と種類の重要性

Fatigue tests were carried out up to 108 cycles for a series of 1800 MPa-class spring steels in order to investigate the relation between inclusions and fatigue properties. The fatigue tests were carried out both for billets and bars rolled from the billets and, in case of billets, the tests were both for RD and TD directions.Al2O3rich inclusions were undeformable and not lengthened in rolling. On the other hand, SiO2 rich inclusions were divided into small pieces and the effective sizes for the axial direction were little reduced in rolling although the inclusions were deformable. In turn the difference of fatigue strength between billets and bars was not so large in most cases. The TD direction fatigue tests showed fish-eye fractures with the origins of large and lengthened MnS inclusions and the fatigue strengths were about a half of those in the RD direction.The fatigue data plotted on a modified S-N diagram, in which stress amplitude were normalized by fatigue limits estimated by Murakami's equation, were divide into two groups. One consisted of large and lengthened MnS inclusions and large artificial notched defects. The other consisted of small defects such as Al2O3 and TiN inclusions and matrix cracks. The result showed that the effects of the lengthened MnS inclusions were almost equal to artificial notches and apparently different from relatively small defects. Moreover, the small defect group was also divided into Al2O3 inclusion group and others, suggesting the effect of properties of defects on the fatigue strengths.

712 20kHz 及び 600Hz でのギガサイクル疲労試験

Fatigue tests were carried out at frequencies of 20kHz, 600Hz and 100Hz for low-temperature-tempered SNCM439 steel. Ultrasonic, high-speed servohydraulic and electromagnetic fatigue test machines were used for 20kHz, 600Hz and 100Hz tests, respectively. The fatigue tests showed that fatigue properties were independent of the frequencies, while fatigue lives were scattered on the S-N diagram. Almost all specimens were broken from internal Al_2O_3 inclusions of various sizes between 9 and 82μm. ODAs were observed in all specimens broken over (10)^7 cycles. ODA sizes were also independent of the frequencies. The scattered S-N diagram was found to be expressed by an unique curve by normalizing stress amplitudes σ_a with fatigue limits σ_w estimated by Murakami's equation. The modified S-N diagram showed a clear fatigue limit between (10)^9 and (10)^<10>cycles.