Half-value Breadth Research Articles

Measurement of Residual Stress Distribution in the Depth Direction of Annealed Materials of Lapped Bearing Steel Using Weighted Averaging Analysis Method

This paper reports the results of an experimental examination using X-rays to test annealing materials for lapped bearing steel (STB2), to confirm the validity of the weighted averaging analysis method. The distribution behavior for the αψ-sin2ψ diagram and the presence or absence of differences in the peak method, half-value breadth method, and centroid method were investigated. When lapping the annealed bearing steel (STB2) material, a residual stress state with a non-directional steep gradient appeared in the surface layer, and it was found that the weighted averaging analysis method was effective. If there is a steep stress gradient, the sin2ψ diagram is curved and the diffraction intensity distribution curve becomes asymmetric, resulting in a difference between the peak method, half-value breadth method, and centroid method. This phenomenon was evident when the stress gradient was more than 2~3 kg/mm2/µm. In this case, if the position of the diffraction line is determined using the centroid method and the weighted averaging analysis method is applied, the stress value on the surface and the stress gradient under the surface can be obtained more accurately. When the stress gradient becomes a problem, since the curvature of the sin2ψ diagram appears clearly in the region of sin2ψ > 0.5, it is necessary to increase the inclination angle ψ as much as possible. In the case of a lapping layer, a more accurate value can be obtained by considering σ3 in the weighted averaging analysis method. In an isotropic biaxial residual stress state, the presence or absence of σ3 can be determined as the presence or absence of strain for sin2ψ≈0.4.

Measurement of the Effectiveness of Half Value Breadth of X-ray Diffraction Profile for Residual Stress Analysis using FEM Based on the Inherent Strain Methodology on the Cold-formed Part

Measurement of the Effectiveness of Half Value Breadth of X-ray Diffraction Profile for Residual Stress Analysis using FEM Based on the Inherent Strain Methodology on the Cold-formed Part

Quantitative Evaluation of Fatigue Strength at N=107 for Carburized Steels

The fatigue strength at N=107 for carburized steels, which indicates the fatigue strength for specimens whose fatigue origins are not at inner defects but at as-carburized surfaces in this study, is affected by a softened structure, oxidized intergranular, retained austenite and residual stress. In the early study, it was clarified that the fatigue strength at N=107 of the specimens containing the retained austenite in the structure was higher than that estimated by the √area parameter model.This study aims to quantitatively evaluate these complex influences mentioned above and predict the fatigue strength at N=107 with high accuracy. Therefore, rotating bending and three point bending fatigue tests with several stress ratios were conducted using carburized SCM420s. Since the fatigue crack of all the specimens, whose fatigue origin was at the as-carburized surface, emanated from oxidized intergranular at a non-martensitic structure, the oxidized intergranular was considered to be mechanically equivalent to a surface crack. The dependence of mean stress on the fatigue strength at N=107 was accurately arranged by the modified Goodman diagram. Furthermore, the hardness of a thin softened structure was estimated from the half value breadth of the structure. Based on these results, the prediction of the fatigue strength at N=107 for the carburized SCM420s was performed by applying the √area parameter model, and its fatigue strength was successfully estimated at an unquestionable level for practical use.

Residual Stress Distribution in the Sub-Surface Region of Shot-Peened Ceramics

The surface of silicon nitride ceramics was modified by fine particles bombarding (FPB) of high strength steel with 50 μm in diameter and by ultrasonic shot peening (USP) of tungsten carbide shots with 1.1 mm in diameter. The residual stress in the sub-surface region measured by the X-ray diffraction method was compression. For FPB surfaces, the sin2 ψ diagram was nonlinear, indicating a steep gradient of the residual stress distribution in the sub-surface region. The distribution of the residual stress was determined by the constant-penetration-depth method. The stress on the surface was a large compression of about -1.5 GPa and diminished 5 μm below the surface. The compressive stress increased with the shot pressure for FPB. For USP surfaces, the compressive stress was nearly constant with in the layer of 10 μm and increased up to -1.5 GPa with the peening time. The half value breadth of diffraction profiles increased nearly proportionally with the magnitude of the compressive residual stress. The fracture toughness measured by the Vickers indentation method also increased with the compressive residual stress.

Study on Application of the cos .ALPHA. Method to Neutron Stress Measurement

In order to study on a method of neutron stress measurement using the cos a method, a numerical simulation study was performed comparing with experimental data. The resultant diffraction profiles, which are defined as the distribution of the intensity of diffracted beams in the radial direction from the center of the diffraction ring, were calculated by summing all diffraction profiles which were diffracted at entire depth in the material. The locations of the peak points which were determined using the half value breadth method (or the centroid method) showed dent distribution with respect to the central angle of the diffraction ring even in case of stress free state. Though the stresses calculated by the cos α method showed different values from the initial stresses, the difference between the calculated and initial stresses almost kept constant for different stress level. These misfit stresses can be vanished after correcting original diffraction radius using that in stress free. The results obtained by the present simulation study agreed with those obtained in the previous experiment, which suggests the validity of the method of neutron stress measurement combining both an area detector and the cos α method.

熱サイクルを受ける銅薄膜中の内部応力の放射光によるその場測定

Copper thin films with a thickness of 600nm were sputtered on the undercoating. The top layer of the undercoating was TiN with a thickness of 50nm sputtered on SiO2 layer with the thickness of 300nm on the Si wafer. Films were subjected to heating to 500°C in vacuum followed by cooling. During heat cycling, the in-situ measurement of the X-ray profiles and the stress of the film was conducted by using X-rays from a synchrotron radiation source of SPring-8. The stress was determined from the measured strains using the two-tilt version of the sin2ψ method assuming the equi-biaxial stress state. The half-value breadth of the diffraction profiles decreased during heating and then increased during cooling. This behavior of the half-value breadth corresponded to the decrease and increase of the lattice defects during heat cycling. The lattice constant measured by X-rays was a linear function of the temperature. With respect to the stress, the heating process to 180°C decreased the stress from about 200MPa to about-100MPa, and then, at higher temperatures, the compressive stress was relaxed by creep. The stress in the film was almost zero above 400°C. In the cooling process, the tensile stress was built up with decreasing temperature. After heat cycling, the residual stress was increased to about 350MPa. The experimental data was compared with the prediction based on the model proposed by Thouless et al. The model was based on the stress relaxation by various creep mechanisms. The predicted variation of the stress during heat cycling agreed well with the experimental results.

Strength Level Dependence of Long-Life Fatigue Behavior in Interior Inclusion Induced Fracture for Bearing Steel in Rotating Bending

Cantilever-type rotating bending fatigue tests were carried out on bearing steels tempered at three different temperatures in order to clarify the strength level dependence of the long-life fatigue behavior. For the surface induced fracture, it was found that the fatigue limit tended to decrease with a decrease of the specimen hardness and it was related to the half value breadth which was a typical parameter of X-ray diffraction. On the other hand, the fatigue life in the interior inclusion induced fracture was improved as the hardness was decreased. Based on the fractography of the fracture surface, characteristic rough surface of fine granular area (FGA) was observed in the vicinity around the interior inclusion. Formation mechanism of this FGA was discussed from microscopic observations by TEM and SIM and X-ray diffraction patterns. Thus it was finally found that the martensite-lath was restructured as to give a number of microscopic subgrains and separation of the boundaries of these subgrains caused the fatigue crack producing the characteristic rough area of FGA.

Damage Evaluation of Rolling Contact Fatigue Using Ultrasonic Spectroscopy

For maintenance of the back-up roll used in iron and steel rolling, it is important to establish evaluation technique for the rolling contact fatigue damage. Thus far, progress of fatigued zone below the surface of rolls has been evaluated using profile analysis of half value breadth of X-ray diffraction line. However, the development of quantitative evaluation of the rolling contact fatigue damage is moreover expected. Therefore, in this study, we estimated the density of movable dislocation under the rolling contact fatigue process by measuring ultrasonic surface wave velocities with three-different propagating frequencies via Granato-Lucke's dislocation string theory. The comparison of changes of the loop density of movable dislocation with changes of half value breadth of X-ray diffraction line profile analysis under the rolling contact fatigue process suggests promising availability of the proposed method. As a result, the ultrasonic surface wave velocities with three-different propagating frequencies (5, 10 and 14 MHz) decrease due to increase of the rolling number of rolling contact fatigue. And, the loop density of movable dislocation estimated by Granato-Lucke model increases as the fatigue damage progresses.

熱サイクルを受けた多結晶Ｃｕ薄膜の残留応力と微視的損傷

Copper thin films with a thickness of 600nm were coated on the undercoating by sputtering. The top layer of the undercoating was TiN with the thickness of 50nm sputtered on SiO2 layer on Si wafers. Films were subjected to heat cycling to various temperatures ranging from 50 to 500°C. The surface topography was examined by atomic force microscopy and scanning electron microscopy, The X-ray diffraction method was used to measure the residual stress and the intensity ratio of 222 to 200 diffraction. Heating cycles to temperatures below 200°C did not induce any remarkable change in the microstructure and topography. By heating to 500°C, the crystalline size increased from 0.5μm to 1.1μm. The volume fraction of hillocks increased after heating cycles above 250°C. At the same time, the intensity ratio of 222 to 200 diffraction increased, while the half-value breadth decreased. The residual stress at room temperature was equi-biaxial tension. The residual stress increased from 270MPa before heating to 350MPa after heating cycle to 500°C. The variation of the measured residual stress with heating temperature does not agree with the prediction based on the model proposed by Thouless et al.

X-선 회절을 이용한 피로균열진전거동과 응력확대계수 예측에 관한 연구

This study verified the relationship between fracture mechanics parameters( △ K, △ K_eff, K_max) and X-ray parameters (δ_r B) for SG365 steel at elevated temperature up to 300℃. The fatigue crack propagation test were carried out and X-ray diffraction technique according to crack length direction was applied to fatigue fractured surface. The residual stress on the fracture surface was found to increase low △K region, reach to a maximum value at a certain value of K_max or △K and then decrease. Residual stress were independent on stress ratio by arrangement of △ K and half value breadth were independent by the arrangement of K_max. The equation of δ_r - △ K was established by the experimental data. Therefore, fracture mechanics parameters could be estimated by the measurement of X-ray parameters.

Ｄ．Ｃ．マグネトロンスパッタリングにより作製したＴｉＮ薄膜の機械的特性に及ぼすバイアス電圧ならびに放電電流の影響

A study on the effects of bias voltage and discharge current on the mechanical properties of TiN films deposited on carbon steel S45C by reactive D.C. magnetron sputtering was carried out. The residual stress, hardness, toughness and adhesive strength was examined by X-ray method, nano-indentation hardness test, IF method and scratch test, respectively. Quite large compressive residual stress was evaluated and it increased as the bias voltage or discharge current increased. With increasing bias voltage or discharge current, the hardness increased, but the adhesive strength decreased. The toughness increased with increasing bias voltage. The each change of these properties had a good correlation with the change of the residual stress, and was arranged as a data-band regardless of the difference of coating conditions. It was considered that these properties were mainly depended on the residual stress. The half value breadth of X-ray diffraction peak also increased with increasing bias voltage or discharge current, and the change of residual stress showed a good correlation with the change of the half width breadth. It was confirmed the residual stress was produced by the bombardments of high-energy ions toward TiN film in coating process. It was concluded that the increase of bias voltage and the increase of discharge current had a same effect to promote the ion bombardment, and the ion bombardment dominantly influenced the mechanical properties of TiN films.

Ｘ線材料強度 高マンガンオーステナイト鋳鋼の疲労き裂進展挙動とＸ線フラクトグラフィ

Fatigue crack growth tests were carried out using a high manganese austenitic cast steel under constant amplitude loading. Average crystal grain sizes of the material are 200 micro-meters and 1000 micro-meters. For this material, threshold stress intensity factor range (ΔKth) is about 8MPa√m which is quite large as compared to the ΔKth of general structural steels. The crack growth rate is lower than the general structural steels especially in the lower ΔK region. The reasons of this behaviour are crack closure due to bridging and fretting oxide, decreasing of the stress concentration near the crack tip due to secondary crack and slip on crystal plane. X-ray fractography can be applied to the fatigue fracture surface of the material which has large grain by using oscillation of X-ray beam and in-plane oscillation on the fracture surface. The half-value breadth of the diffraction profile on the fracture surface increases with increase in the effective stress intensity factor range. The relationship between the half-value breadth and the effective stress intensity factor range was represented by a narrow band regardless of the stress ratio.Therefore, the effective stress intensity factor range can be estimated from this relation in fractured surface of actual components.

非熱処理型高張力ボルトの頭部成形応力と軸部強度に及ぼすバウシンガー効果と時効の影響

At the heading of high-tensile bolt with work-hardend drawing wire, Bauschinger effect appears and raises the tool life. On the other hand, this effect reduces the shank strength of bolt. This paper proposes the steel which has large Bauchinger effect at the heading of drawing wire and the aging process which reduces the Bauschinger effect in the bolt shank. Mn or Si do not raise the Bauschinger effect. Carbon raises this effect and the high cooling rate after rolling of wire is useful too. Reduction of yield strength and tensile strength of bolt shank after compression are 15-17% and 6-7%, respectively. These reductions in strength are recovered by aging. It is concluded that aging at 573K recovers the reduction of yield strength and tensile strength of bolt-shank by the compression under strain no more than 0.03. During the compression of drawing wire, X-ray diffraction half value breadth which corresponds to the dislocation density indicates constant value. This fact suggests that the number of dislocations which are newly genereted under compression is nearly equal to that which distinguishes by the Bauschinger effect.

Ｔｉ‐６Ａｌ‐４Ｖ合金の疲労破面におけるＸ線フラクトグラフィ

Fatigue tests were carried out with Ti-6Al-4V alloy CT specimens after three kinds of the heat treatments, namely, 1) solution at 1223K, aging at 813K(STA), 2) annealing at 1123K(AN850) and 3) annealing at 1373K(±β-AN). X-ray fractography, which is a technique to estimate applied stress conditions when a fracture occurs and to be used for analysing a mechanism of fracture, was applied on the fatigue fractured surface. Distributions of residual stress and half-value breadth were measured on the fractured surface along the crack propagation direction as a function of a stress intensity factor. It was found that the residual stress on the fatigue fractured surface had a peak value when maximum stress intensity factor was nearly equal to 25MPa√m. The strain induced transformation was confirmed on the fatigue fractured surface from X-ray diffraction profile pattern. Depth of monotonous plastic zone size was estimated from the distribution of the residual stress beneath fractured surface. Depth of monotonous plastic zone size ωy was expressed by following equation; ωy=α(Kmax/σy)2, where the values of α were 0.17 for STA and 0.13 for AN850. By using X-ray fractography technique on fatigue fractured surfaces of Ti-6Al-4V alloy, a value of maximum stress intensity factor Kmax where the residual stress reach maximum value can be predicted.

Ｘ線材料強度 高マンガンオーステナイト鋼の疲労破面におけるＸ線フラクトグラフィ

Fatigue tests were carried out under constant stress amplitude, using a non-magnetic high manganese Mn-Cr steel. X-ray fractography was applied on the fatigue fractured surface to investigate the relationship between stress intensity factor and residual stress or half-value breadth of the X-ray diffraction profile. The fatigue crack propagation rate of this non-magnetic Mn-Cr steel had the same tendency as in the ordinary structural ferritic steels. The relationship between stress intensity factor and the residual stress or half-value breadth of the steel was almost the same as that of the ferritic cyclic work hardening steels. No stress induced transformation was observed on the fracture surface, but the residual stress on the fractured surface was compressive in the high stress intensity factors range, which is typical in the cyclic work hardening steels. The half-value breadth on the fractured surface increased with increasing effective stress intensity factor range. The relationship between the half-value breadth and stress intensity factor range was represented by a linear line regardless of the stress ratio. Therefore, the acting stress intensity factor range at the time of fracture can be estimated from the half-value breadth. The depth of monotonic plastic zone was estimated from the distribution of half-value breadth beneath the fractured surface. The relationship between the maximum stress intensity factor and half-value breadth was expressed by the equation ωm=α(Kmax/σy)2, where the value of α was 0.025. This is about one sixth of the value for ferritic steels, and the fact shows the severe work hardening occuring in the plastic zone in this manganese steel.

X-ray Fractography on Fatigue Fractured Surface of Solution and Aging Treated Ti-6Al-4V Alloy.

Fatigue tests were carried out under two kinds of stress ratios in constant amplitude loading of Ti-6Al-4V alloy after heat treatment of solution at 1223K and aging at 813 K (STA). Retardation behavior of fatigue crack propagation was observed. It is considered that this retardation is caused a stress relieving at front of crack tip by growth of secondary cracks. X-ray fractography, which is a technique to estimate the stress conditions and to be used for analysing a mechanisms when a fracture of structures occurs, is applied on fractured surface. Distributions of residual stress and halfvalue breadth by X-ray technique on the fractured surface along the crack propagation direction as a function of a stress intensity factor. It was found that the residual stress on the fatigue fractured surface had a peak value when maximum stress intensity factor was nearly equal to 25MPa√(m). Strain induced transformation was observed on the fatigue fractured surface from X-ray diffraction pattern. The half-value breadth on fractured surfaces increased with increasing maximum stress intensity factors. Depth of monotonous plastic zone size was estimated from a change of the distribution of the residual stress in direction of depth near fractured surface. Depth of monotonous plastic zone size ωy was expressed by following equation ; ωy=a(Kmax/σy)2, where the value of a was 0.17. By using X-ray fractography, maximum stress intensity factor Kmax in fatigue crack propagation of Ti-6Al-4V alloy can be predicted.

軸受鋼の疲労による漏洩表面弾性波の音速変化

The bearing used for the axle of Shinkansen train and the #6206 bearing were subjected to a fatigue test, and the V(z) curves were measured by a scanning acoustic microscope. Discussions are made on the detection of bearing damage in terms of residual stress, half-value breadth of X-ray diffraction, by comparing the results of hardness test and metallographic observation (SEM, TEM).The conclusions are as following;(1) The variation in sound velocity of elastic surface waves in the measured V(z) curve can be applied for estimation of bearing damage due to fatigue.(2) When the increase in dislocation is limited, the sound velocity of elastic surface waves corresponds to the variations in residual stress and half-value breadth very well. But when the dislocation increases and a cell structure is formed, the sound velocity tends to drop gradually.(3) When thermal deformation and large stress develop, the sound velocity of elastic surface wave becomes lower regardless of presence of residual stress.

Statistical Analysis of Fatigue Damage in Cr-Mo-V Steel Forging.

In this study, an attempt to analyze the fatigue damage in Cr-Mo-V rotor steel based on a probability theory or statistical mechanics was made. The following results were obtained: (a) A model of distributed "driving force" with uniform "fracture resistance" is applicable for the analysis of two phenomena, i.e., the fatigue crack initiation and the decrease of half value breadth of X-ray diffraction profiles with an increase of fatigue damage in Cr-Mo-V steel forging (b) The driving force shows an exponential distribution. The mean value of the distribution appears to be a monotonic function of the nominal strain of fatigue test. (c) It is reasonable to consider that the change of half-value breadth of X-ray diffraction profiles corresponds to the accumulation of fatigue damage before crack initiation.

X-ray Fractographic Study on TiAl Alloys with Various Types of Microstructures

Abstract The fracture toughness test was conducted on γ + α2 two-phase TiAl alloys with lamellar, duplex and near-y structures. The x-ray fractographic technique was applied to the fracture, surfaces. The plastic zone size my was determined on the basis of the distributions of the residual stress and the half-value breadth beneath the fracture surfaces. Although the fracture mode shows microstructure dependence, ωγ is related to the fracture toughness value KIC and the yield stress σY as: ωy=α(KIC/σY) where α is 0.13.

衝撃破壊破面のＸ線フラクトグラフィ手法とその損傷解析への適用

To study the plastic zone size of dynamic fracture surface, instrumented Charpy impact tests of high carbon bearing steels were conducted. The plastic zone size beneath the fracture surface was evaluated by the X-ray diffraction parameters. The results gave the following three experimental conclusions. The first, a good correlation exists between the plastic zone size and the dynamic stress intensity factor as ωy=α(Kd/σY)2, and the values of α depend on materials. The second, α can be calculated from the equation α=0.15[(B0+2.12)/(BF+2.12)]2, where B0 is the average half-value breadth of the base material and BF is the maximum half-value breadth beneath the fracture surface. The third, both ωy and α can be simultaneously measured on the fracture surface, and Kd can be evaluated by using the above two equations.This technique was applied to an actual fracture surface and confirmed to be very effective for failure analysis. It is advantageous over other test methods and it will find wider application in the industry.