Fatigue Limit Of Smooth Specimens Research Articles

Reliability Improvement of Offshore Structural Steel F690 Using Surface Crack Nondamaging Technology

Microcracks can rapidly grow and develop in high-strength steels used in offshore structures. It is important to render these microcracks harmless to ensure the safety and reliability of offshore structures. Here, the dependence of the aspect ratio (As) of the maximum depth of harmless crack (a<sub>hlm</sub>) was evaluated under three different conditions considering the threshold stress intensity factor (ΔK<sub>th</sub>) and residual stress of offshore structural steel F690. The threshold stress intensity factor and fatigue limit of fatigue crack propagation, dependent on crack dimensions, were evaluated using Ando's equation, which considers the plastic behavior of fatigue and the stress ratio. a<sub>hlm</sub> by peening was analyzed using the relationship between ΔK<sub>th</sub> obtained by Ando's equation and ΔK<sub>th</sub> obtained by the sum of applied stress and residual stress. The plate specimen had a width 2 W = 12 mm and thickness t = 20 mm, and four value of As were considered: 1.0, 0.6, 0.3, and 0.1. The a<sub>hlm</sub> was larger as the compressive residual stress distribution increased. Additionally, an increase in the values of As and ΔK<sub>th(l)</sub> led to a larger a<sub>hlm</sub>. With a safety factor (N) of 2.0, the long-term safety and reliability of structures constructed using F690 can be secured with needle peening. It is necessary to apply a more sensitive non-destructive inspection technique as a non-destructive inspection method for crack detection could not be used to observe fatigue cracks that reduced the fatigue limit of smooth specimens by 50% in the three types of residual stresses considered. The usefulness of non-destructive inspection and non-damaging techniques was reviewed based on the relationship between a<sub>hlm</sub>, a<sub>NDI</sub> (minimum crack depth detectable in non-destructive inspection), a<sub>cr N</sub> (crack depth that reduces the fatigue limit to 1/N), and As.

Effect of Fiber Direction and Stress Ratio on Fatigue Property in Carbon Fiber Reinforced Epoxy Composites

The fatigue limit and crack growth behavior of slit specimens of carbon fiber reinforced epoxy composites were investigated. The fatigue limit was defined by the maximum stress amplitude that the specimen endured 106 times repeated stress when S-N curve was used. The highest fatigue limit was obtained when all the fiber directions were parallel to the load axis. The fatigue limits were evaluated in the cases of composites using alternately parallel and perpendicular to the load axis and compared with the result of the specimen having all the carbon fiber orientations were parallel to the load axis. When the measured value of the fatigue limit was lower, shear damage to the epoxy resin and peeling of fiber from epoxy resin occurred clearly. According to those results, it was expected that the fatigue limit of smooth specimens of carbon composites with long fibers can be evaluated from the results of the slit specimens.

255 微小き裂問題への特定位置応力法の適用

Fatigue strength evaluation for small crack structures using fracture mechanics has a disadvantage as the value of threshold stress intensity factor range must be modified. Many modification models are presented by many researchers, in these modification equations the dominant parameters is crack length. But in actual engineering fields the determination of these small crack length are difficult as the surrounding structures near these small cracks are complicated. In previous papers we introduce critical distance stress theory for fatigue limit estimation of general stress concentrate structures such as circular or elliptical hole, stress singularity structures such as sharp notch, contact edge and adhesive edge structures. All estimated results coincided well with experimental results, and the availability of this method for more wide field structures can be confirmed. In this paper we apply this critical distance stress theory for fatigue strength evaluation of small crack structures. This method need only fatigue limit of smooth specimen σ_<w0>, and threshold stress intensity factor range ΔK_<th> of materials and stress distributions of structures near crack tips. The estimated fatigue limits of small cracked specimens coincided well with experimental results. Finally these estimated and experimental results are compared with other researchers estimated results using equivalent crack length, and the superiority of this critical distance stress theory can be confirmed.

Fatigue Properties of Thermally Deformed Alloys of the TI–SI System

We study the mechanical properties of the well-known VT1 and VT6 titanium alloys and new deformed alloys of the Ti–Si system with silicon contents of 0.1–6%. It is shown that, as the amount of silicon increases, the modulus of elasticity, the fatigue limit of smooth specimens, and the calculated fatigue threshold of the specimen containing a crack determined according to the parameters of fatigue fracture increase. It is shown that the mechanical characteristics of alloys of the Ti–Si system exceed the characteristics established for extensively used VT6 alloy.

Low Cycle Fatigue Estimation Based on the Critical Distance Stress Theory

Generally the critical distance stress theory was applied for the fatigue limit estimation of general structures using fatigue limit of smooth specimen (σw0), and threshold stress intensity factor range (Kth). In this paper we extended this method for the estimation of low cycle fatigue life too. In this method we define the critical distance (rc) on static strength conditions, which is calculated using ultimate tensile strength (σB) and fracture toughness (KIC), in addition to the critical distance on fatigue limit condition (rc). Then the critical distances of any low cycle fatigue conditions can be calculated by interpolation of critical distance on fatigue limit (rc) with critical distance on static strength (rc). By unifying these low cycle fatigue life estimation method with high cycle fatigue limit estimation method we can estimate the full range fatigue life easily. And to confirm the availability of this estimation method we perform the fatigue test for any stress concentration specimens.s

Fatigue Strength and Life Estimation Methods Using Critical Distance Stress Theory

Generallythe critical distance stress theory was applied for the fatigue limitestimation of general structures. In thismethod, it needs only two parameters, fatiguelimit of smooth specimen (σw0), and threshold stress intensityfactor range (∆Kth). In this paper we extended this method for theestimation of low cycle fatigue lifetoo. In this improvement wedefine the critical distance (rc’) on static strength conditions,which is calculated using ultimate tensile strength (σB) andfracture toughness (KIC), in addition to the critical distance onfatigue limit condition (rc). Then the critical distances of any lowcycle fatigue conditions can be calculated by interpolation of criticaldistance on fatigue limit (rc)with critical distance on staticstrength (rc’). By unifying these low cycle fatigue life estimationmethod with high cycle fatigue limit estimation method we can estimate the fullrange fatigue life easily. And to confirm the availabilityof this estimation method we perform the fatigue test for circlehole specimens, sharp V notch specimens andfretting fatigue specimens.

OS1708 微小き裂部位の疲労強度評価

Fatigue strength evaluation for small crack using fracture mechanics has a disadvantage that the value of stress intensity factor is low than long crack. We apply the critical distance theory to that. Critical distance theory is fatigue strength evaluation that the stress is fatigue limit when stress distribution of crack specimen matches a point of a stress distribution of smooth specimen and threshold stress intensity factor. Pulsating fatigue test conditions are 20Hz of frequency and 0 of stress ratio. Based on the critical distance theory, we applied analysis of stress distribution using FEM to evaluate the fatigue strength evaluation. As the crack lengths approach small crack, stress distribution of crack tips tend to reduce. As the result of critical distance theory using stress distributions, fatigue strength evaluations for long cracks using fracture mechanics were consistent to critical distance theory. On the other hand, fatigue strength evaluation for small cracks using critical distance theory and fatigue test results were convergent to a point of fatigue limit of smooth specimen. As the result, fatigue strength evaluation based on the critical distance theory is effective in all crack lengths. However, because the results depend on the fatigue limit of smooth specimen and the threshold stress intensity factor, we need to find the accurate value based on the experiment.

영역피해모델에 의한 균열 및 노치의 피로강도평가

Inherent damage zone model is presented to explain the fatigue properties near the fatigue limit and the crack growth threshold consistently Inherent damage zone model assumes that the stress at a point which is located at a small distance, <TEX>$r_0$</TEX>, an inherent length of the material that represents the size of effective damage zone, from the crack initiation position governs the fatigue characteristics regardless of the geometric configuration of the specimen; smooth specimen, notched specimen or cracked specimens with short and long crack length. A special feature of the paper is using the exact stress distributions of notched and cracked specimens at the strength evaluations. Analytical elastic solutions by Neuber and Westergaard are employed for this purpose Relationship between fatigue limit of smooth specimen and threshold stress of cracked specimen, occurrence condition of non-propagating crack at the root of elliptic notch and circular hole and relationship between stress concentration factor and fatigue notch factor are discussed quantitatively based on the proposed model.

Fatigue Properties of Rail Steel Under Constant Amplitude Loading and Variable Amplitude Loading

In this study, fatigue growth behavior of the transverse crack, which was the most dangerous damage among the various types of rail defects, was investigated using the notched keyhole specimen under constant amplitude loadings. Fatigue limit of smooth specimen in rail steel at R=0 was 110MPa, and the fatigue crack initiation life in the region of the low stress amplitude (ie. long life) occupied the major portion of the total fatigue life. The fatigue strength under variable amplitude loading was converted to the equivalent fatigue strength based upon. Miners rule, which was estimated approximately 9% lower than that under constant amplitude loading. Also, in the low ΔK(sub)rms region (21MPa√m), fatigue crack growth rate (da/dN) under constant amplitude loading was higher than that under variable amplitude loading, whereas the tendency was reversed in the high ΔK(sub)rms region. It is believed that this behavior is due to the transition of fracture appearance.

Inherent Damage Zone Model for Fatigue Strength Evaluation

Inherent damage zone model assumes that the stress at a point which is located at a small distance, γ0 from the crack initiation position governs the fatigue characteristics regardless of the geometric configuration of the specimen. The distance γ0 represents the size of effective damage zone and it is an inherent length of the material. Ishibashi proposed the model to explain the difference between fatigue notch factor and stress concentration factor of notched specimen. This paper shows that the inherent damage zone model can explain several fatigue phenomena near the fatigue limit and the crack growth threshold consistently without restriction of smooth specimen, notched specimen or cracked specimens with short and long crack length. A special feature of the paper is using the exact solution of stress distributions of notched and cracked specimens. Neuber's analytical solution for notched specimen and Westergaard's stress function for cracked specimen are employed for this purpose. Relationship between fatigue limit of smooth specimen and threshold stress of cracked specimen, relationship of fatigue strength between round-shaped flaws and crack, occurrence condition of non-propagating crack at the root of sharp notch, and fatigue notch factor are discussed quantitatively based on the proposed model.

Effect of Stress Ratio on Fatigue Threshold of Cracked Components.

The propagation behavior of fatigue cracks was investigated under various stress ratios using structural carbon steel (JIS-S45C) specimens with small surface pre-cracks. The threshold condition of crack extension from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks irrespective of the stress ratio. Cracks initiated from precracks were arrested under lower stress amplitudes because of the development of crack closure with crack growth. The cyclic resistance-curve-method was used to predict the fatigue thresholds of the precracked components. The predicted values of the fatigue limit for crack extension, the fatigue limit for fracture, and the length of non-propagating cracks agreed very well with the experimental results. The effect of the mean stress on the fatigue limit of smooth specimen was successfully predicted by the cyclic resistance-curve-method.

A Simplified Method for Evaluation of Fatigue Limits of Pre-Cracked Components under Mean Stresses.

A simplified version of the cyclic resistance-curve-method for predicting the fatigue thresholds of pre-cracked components under mean stresses was proposed. The method requires one material data such as the hardness or the tensile strength for prediction. The relation between the Stage I nonpropagating crack length and the stress amplitude was unique irrespective of the stress ratio. The length of the Stage I cracks was given as a function of the applied stress and the Vicker's hardness. The fatigue limit of smooth specimens and pre-cracked specimens could be predicted from the hardness under arbitrary mean stresses by using the simplified cyclic resistance-curve-method. The fatigue limit predicted by the simplified method was larger than that by the original resistance-curvemethod. The predicted values of the fatigue limit for crack extension, the fatigue limit for fracture, and the length of non-propagating cracks agreed very wall with the experimental results.

自動車焼結部品の高付価値化 鉄系焼結材料の切欠き疲労強度の破壊力学的解析

A method of predicting fatigue strengths using fracture mechanics on noched components of ferrous sintered materials is investigated. By applying Lukas's formula for evaluation of AK and a intrinsic crack model for small crack propagation on notched components, a simple formula for predicting fatigue limits was derived. This method requires three material properties: the fatigue limit of smooth specimen, the threshold stress intensity range for long crack, and the threshold value of the effective stress intensity. For experimental verification, a notched specimen for fatigue tests as sintered was designed, and fatigue tests were conducted with notched specimens of ferrous sintered materials with two different pore sizes. The predicted fatigue limits are comparatively in good agreement with the experimental results.

球状黒鉛鋳鉄のねじり疲労強度に及ぼす人工微小欠陥と黒鉛の影響

Reversed torsion and rotating bending fatigue tests were performed on JIS FCD400 using both smooth and defect specimens containing an artificial hole whose diameter ranges from 100 to 500μm.Although this material has numerous spheroidal graphites in the structure, the effect of interaction between defects on the fatigue limit was so small that the fatigue limit of specimen containing an artificial hole was predicted from √area for the hole and the Vickers hardness of matrix by the equation that was proposed in this study assuming steels with a single defect. The fatigue limit of smooth specimens in torsion was controlled by graphites and the lower bound of the scatter was well predicted substituting the size of the maximum graphite, √areamax, for √area in the equation. The value of √areamax may correspond to the allowable defect size of this material.

Fatigue strength and cyclic crack resistance of titanium alloy VT3-1 in different structural states. Communication 2. Procedure for considering the effect of structure on fatigue limit

On the basis of experimental results presented in communication 1 for a study of the fatigue strength of two-phase titanium alloy VT3-1 in different structural states it is shown that the fatigue limit for the alloy increases with a reduction in the average size of a structural element critical for cyclic strength. A numerical model is developed by means of linear fracture mechanics approaches which makes it possible from available data about the size of structural parameters for the alloy to predict the fatigue limit of smooth specimens.

Effect of Prestrain on the Fatigue Strength of a Haet-Treated 0.45% C Steel.

Many studies concerning the effect of prestrain have been performed using mainly annealed steels. However, such studies involving heat-treated steels are very few. In this paper, the effect of prestrain on the fatigue strength of heat-treated 0.45% carbon steel is investigated. Results show that the fatigue limit of smooth specimens decreases (about 5%), although the slight increase in yield stress and tensile strength after prestrain is recognized. Prestrain makes the crack initiation life decrease, but its decrease is not so remarkable. On the other hand, the growth rate of a small crack is fairly accelerated and it is determined uniquely by the term σnal.

Propagation threshold and crack closure of small fatigue cracks.

The propagation behavior of fatigue crack from pre-cracks in smooth or notched specimens of a low-carbon steel was studied. The development of crack closure with crack growth was measured through the compliance method. An interferometric displacement gage was used to measure the opening displacement of surface cracks. All cracks started to grow from the pre-cracks at the maximum stress intonsity factor equal to the threshold value of the effective stress intensity range ΔKeffth∞ for long cracks. As a crack grew, the crack closure developed and the effective stress intensity range ΔKeff decreased. The crack stopped growing when ΔKeff dropped below ΔKeffth∞. The relation between the crack propagation rate and the effective stress intensity range was unique, irrespective of the crack length or the atress level, and agreed well with that for leng cracks. Non-propagating cracks made under the fatigue limit in smooth specimen were mostly Stage I cracks, and the fatigue limit of smooth specimen was determined by the propagation threshold of these Stage I cracks.

Notch sensitivity of structural steels in different structural states

1. The notch sensitivity of structural steels increases (practically linearly) when the proportion of high-strength structural components (sorbite and pearlite) in their structure increases; this is determined by their suitability for more intense piling up of dislocations at obstacles. 2. The greater notch sensitivity of the high-strength structural components is the reason why the fatigue limit of specimens with stress raiser increases less with increasing tensile strength than the fatigue limit of smooth specimens, and from some value of σu onward it remains practically unchanged (and in isolated cases even decreases). The use of high-strength steel, especially temper hardened one, is therefore not always expedient. 3. The rate of increase of the fatigue limit of specimens due to increased σu slows down when the stress concentration increases and also under the effect of the scale factor. 4. For making parts subjected to fatigue in operation, it is best to use steels with high static strength and to apply surface plastic strain (SPS) to them. The effectiveness of strengthening by SPS increases with increasing σu of the steels.

Fatigue resistance of aluminum and magnesium alloys at high loading frequencies

1. Within the range 500–10,000 Hz the cyclic loading frequency has practically no effect on the fatigue resistance of the IMV-2 alloy, while for the AMg6N alloy at an increase of loading frequency to 10 kHz the fatigue limit of smooth specimens increases monotonically. 2. The effective stress intensity coefficients and the coefficients of the welding effect do not change during transition to higher loading frequencies which permits them to be determined from the results of high-frequency tests on the required loading bases. 3. On each of the investigated loading frequencies the scatter of fatigue life values of broken welded specimens and of specimens with stress concentrators is greater than that of smooth specimens of the initial material. This must be taken into account in calculating and predicting the cyclic fatigue life of structural elements and machine components.

A method for the prediction of fatigue limits of notched members.

A method for predicting the fatigue thresholds of notched components proposed by Tanaka and Nakai was modified to obtain a simpler formulation. The method requires three material data for prediction : the fatigue limit of smooth specimens, the threshold stress intensity range for long cracks, and the threshold value of the effective stress intensity range. For notched components, the fatigue limit for crack initiation, the fatigue limit for fracture, and the length of non-propagating cracks are predictable as functions of the applied stress and notch geometry. The fatigue tests were conducted with center-notched plates of low-carbon steel with two different grain sizes and the results were compared with the prediction. Good agreement was obtained for the fatigue limit for the nucleation of a Stage II crack. The prediction was slightly conservative for the fatigue limit for fracture. Agreement in the length of non-propagating cracks between prediction and experiment was fairly good. Several simple formulae were derived for easy application for practical purposes.