There are several ways of approach in the study of problems concerning the strength of metallic materials. The strength of materials is discussed for its basis in the scope of atoms composing the materials with respect to their order. In order to eliminate the factors affecting the complex character of the strength, single crystals or specimens of extremely coarse grains of pure metals or metals of simple chemical composition have been used as the test materials in this line of works. We are amply equipped with knowledges of the strength of materials.
A great number of studies, on the other hand, have been made in application of engineering science. In this line of work, the materials to be subjected to experiments are mainly engineering metals of rather complex composition, and the strength of materials is observed or interpreted from macroscopic or submacroscopic viewpoint. This side of approach is, of course, of immense importance to machine designers and metallurgists.
Various criterions in the strength of materials have been proposed. These criterions have in general been derived from probable models of the strength of materials that have been introduced from the findings in the fundamental study in atomic order. Although some of the criterions are useful for the prediction of strength of materials, we are seldom convinced of the mechanism because of lack of vivid proof of the strength of materials on engineering materials. In this sense, the authors believs that there still remains a gap to be fulfilled between the study of strength in engineering field and those in physical aspects. It is desirable therefore to make efforts in search of practical experimental means to find the change in microstructure of engineering materials, to enable us to recognize the property of the strength of materials.
The application of X-ray diffraction is no new technique as means of experimental study. It has often been adopted for direct and non-destructive observation of changes in the micro-structure of crystalline materials in fundamental researches. It has been the plan of the authors to adopt this technique of applying X-ray diffraction to the experiment to elucidate the minute variation of micro-structure that has occuried in engineering materials.
The authors have hitherto adopted the technique of applying a series of X-ray diffraction in the study of the strength of engineering materials where X-ray stress measurement and its half-value breadth have been adopted as the measure of changes in the structure. The X-ray measurement has been applied to various kinds of stresses. Especially its application marks one of our most successful work in measuring the residual stress of cold worked metals under the conditions of various kinds of cold work by using sin²φ method. The relation of half-value breadth and number of cycles of fatigue stresses has been studied in detail for various sorts of engineering metallic materials. As the results of a number of experiments, it has been found that the variation in half-value breadth shows very regular relation with number of cycles.
The technique of X-ray diffraction that used to be employed in studies of earlier days was, however, of usual back-reflection, being a merely conventional means in industry for practical estimate of the strength of the materials, and so the findings obtained thereby were not sufficient for microscopic interpretation of the strength of the materials. In place of the ordinary back-reflection technique that is commonly used for the study of strength of engineering metallic materials, as being of insufficient resolving power, the X-ray microbeam technique has recently been introduced, whereby it is expected that engineering metallic materials will reveal more clearly the feature of variation in micro-structure, and the understanding of the findings in the early studies will be supported by the observation of the micro-structure.

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The properties of the Fourier series and the method of their application are reviewed here. The treatment of Fourier's method of analysis is not a new problem, there have been but a comparatively small number of studies that have been made using this method. These have been reported since the proposition was made by B.L. Averbach and B.E. Warren in 1949. Recently the extensive use of electronic computors has made this method popular in the field of engineering for the purpose of studying the strength of materials. The summary of the discussions on this method will be introduced here.

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The authors have pointed out in their previous papers that both the accuracy and reliability of X-ray residual stress value on the samples with narrow breadth of X-ray diffraction profile were sufficiently good. However, no results on the sample whose X-ray diffraction profile is very broad have yet been obtained. As the measurement of peak position of X-ray diffraction profile, although the half-value breadth method can be employed and good results were obtained in the case of sharp diffraction profile, this method cannot be applied to the case of broad diffraction profiles, because the back ground line of the profile cannot be clearly determined. Consequently, it is considered that the accuracy of the stress value obtained is not sufficiently good. Therefore, it is necessary to develop a new method for the measurement of the peak position of diffraction profiles.
In addition to this problem, the effect of Kα₂ component on the measuring stress ought to be considered. Furthermore, the effect of the Lorentz polarization factor and the absorption factor should be taken into account when the measuring sample has a large amount of residual stress with a broad diffraction profile.
In the present study, the authors attempted to separate the Kα₁ component from Kα doublet by using Fourier analysis so that this procedure may be applied to any shape of profile, and so they discussed the effects of the Lorentz polarization factor on the stress value.
For the determination of the peak position, first, two assumptions were made as follows:-1) The intensity distribution curve actually observed Φ(x) is given by the sum of the intensity distribution curves φ₁(x)and φ₂(x) diffracted from Kα₁ and Kα₂ radiations, respectively. 2) The following relation holds between φ₁(x) and φ₂(x),
φ₂(x)=kφ₁(x-Δx)
where k is a constant and Δx is the distance between the peak positions of the intensity curves diffracted from Kα₁ and Kα₂ radiations. Next, the intensity distribution curves Φ(x) and φ₁(x) were represented by the Fourier series respectively, and φ₁(x) was separated from Φ(x), and the Lorentz polarization factor was inducted into φ₁(x). Lastly, the peak position of intensity distribution curve obtained by the above manner was determined by the parabola fitting method. These calculations were carried out by the digital computer.
By using this method, the residual stresses on the some samples were measured, and on the basis of the experimental results, the following conclusions were derived.
(1) It is considered that the effect of Kα doublet can be ignored from the view point of the accuracy of stress value even if the value of residual stress is large.
(2) It is supposed on the other hand that the effect of the Lorentz polarization factor on the measured stress is remarkable especially for the specimen which has a broad profile. However, when the half-value breadth of the profile given by Kα doublet is less than 3°, it may be considered that this effect can be neglected.
(3) By separating the Kα doublet and then correcting the Lorentz polarization factor, the X-ray residual stress on the shot peened carbon steel specimen agrees fairly well with the mechanical one, compared with the X-ray residual stress obtained by the raw data.
(4) Although the effect of Kα doublet can be neglected, it is considered that this method has the characteristic of being suitable to the measurement of the peak position of diffraction profiles with whatever shapes including broad ones.

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The accuracy of stress measurement by X-rays has recently been remarkably improved, and some studies on the accuracy of measurement are reported. In this study, for the case of the film method, several problems on the accuracy of stress measurement were investigated.
First, the effect of errors in the determination of the radius of diffraction ring on the measured stress values was examined for each case of the Glocker method, Δ method and sin²ψ method. In the Glocker method, let the error in the vertical incidence and the oblique incidence of 45° be e and e' respectively, then the incorrect stress value is given by
σ'=K{sec(1/2tan^-1l₄₅+e'/l'+e'φ)-sec(1/2tan^-1l_⊥+e/l'+eφ)} (1)
where K=sinθ₀E/1+ν1/sin²(45+η), φ=tan(π-2θ')
and l_φ, l'=radius of diffraction ring for the specimen and the standard substance, respectively. In the case of the Δ method, the erroneous stress value is expressed as
σ'=25C_⊥+(l'-l_⊥/l'+e-l'-l₄₅/l'+e') (2)
The erroneous stress values were calculated for four possible cases of combination of the signs of e and e' by taking the values of 0, ±0.03, ±0.05, ±0.07, ±0.09mm for e and 0, ±0.05, ±0.09mm for e' in Eqs. (1) and (2). These calculations were carried out for two beams of CoKα and CrKα by selecting two arbitrary stress levels of 8kg/mm² and 16kg/mm² as correct values. For the sin²ψ method, erroneous values of cosecθ'_ψ can be calculated from the correct values of cosecθ_ψ by introducing the error e. Thus two incorrect values of cosecθ'_ψ were plotted as the ordinates of corresponding sin²ψ, and from these points the maximum and minimum gradients were determined. For the purpose of comparison of accuracy among the three methods, the errors e of opposite signs were introduced into the two extreme cases of ψ=0° and 45° for the sin²ψ method. Under the same values of the error as in the Glocker and Δ methods, the incorrect stresses were determined.
Secondly, in the sin²ψ method, the influence of errors in the setting angle was studied. Assuming the error in the setting angle as ±1° in each incidence and plotting the erroneous values of cosecθ'_ψ as the ordinates of corresponding correct sin²ψ, the maximum and minimum values of σ' were calculated.
Thirdly, as experimental study, the effect of several ways for the determination of the peak position of diffraction profile was investigated. In addition to the ordinary half-breadth method at half height (1/2H), those at the heights of 3/8H and 5/8H were experimented, and the accuracy was compared among these three ways. Besides, the efficacy of the separation of Kα doublet was examined.
Lastly, the problem on the grain size of the film was dealt with as a possible factor affecting the accuracy. Two sorts of films, Fuji type 100 and 200, were used for this purpose. Adjusting the exposure time so as to obtain the same degree of blackening of diffraction ring between the two films, the values of cosecθ'_ψ and stress were compared for a stress level of 10kg/mm².
From the results of calculation and experiment, the following conclusions were obtained.
(1) The effect of errors in the radius of diffraction ring on the measured stress values may, in some instances, be appreciably large, especially when the errors are of opposite signs between vertical and oblique incidences.

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For the purpose of making precise stress measurement by means of an X-ray diffractometer an automatic focusing apparatus was devised and reported in our previous paper, together with the results of some experiments of its application to the sharp diffraction lines.
In this paper, the application of this apparatus to the broad lines obtained on the bearing steels is described in which difficulty is usually experienced in locating their diffraction peaks exactly.
The determination of location of the peaks was performed by using D.P. Koistinen's three point parabola method, and the exact peak positions were experimentally obtained by correcting the diffracted intensity curves by using two factors, namely L.P.A. factor and the factor variable for the distance between the specimen and the Geiger-tube slit which is decided by the focusing condition.

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In the stress analysis by X-rays, the detectable volume is the function of the area irradiated by X-rays and the depth of penetration of X-rays. It involves a number of crystals having the specific diffraction plane which satisfy the Bragg's diffraction condition in regard to incidental X-rays. Therefore, if the orientation of each crystal in the metal is statistically uniform, we can postulate that the macroscopic gauge length for the stress analysis equals the area irradiated by X-rays.
In the photographic method, the irradiation area is limited mainly by the optical slit system. Since the irradiation area is the gauge length for stress analysis, it is necessary that X-rays with higher intensity and better parallelity are irradiated uniformly on the area limited by the measurement purpose. But, there are no practical slits with good characteristics, which was examined closely from such a view point, on the market.
According to the geometrical condition, we classified the slit system into the following four classes;
class (1) α₀-α_i>θ_i-θ₀>α_i-α₀
class (2) α₀+α_i>θ_i-θ₀>α_i-α₀ or α₀-α_i
class (3) α_i-α₀>θ_i-θ₀
class (4) θ_i-θ₀>α_i+α₀
where α_i, α₀ are respectively the aperture angle of inlet and outlet slit at X-ray source, and θ_i, θ₀ are that of the source at inlet and outlet slit. For these four classes we calculated the dimensions of X-ray irradiation areas and their intensity distributions from the view point of geometrical optics.
We made for trial the slit systems with different geometrical conditions to provide for our experiment. By using these slit systems, we measured the dimensions of X-ray irradiation areas and their intensity distributions. The experimental results were in fairly good agreement with the theoretical calculations. From this study it was concluded that the setting of inlet and outlet slit close to the X-ray source and to the specimen respectively, was effective to obtain a uniform distribution of incident X-rays and to reduce the exposure time.

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The measurement of stress by means of X-rays has an advantage over any other methods in being more fit to measure the stress of local areas. However, we are often disappointed even by this method in such cases as where the stress has a high gradient in localized regions, such for instance as the stress field near the root of sharp notches. In the present paper a practical method of finding the stress gradient existing in a localized area by applying X-ray diffraction is discussed. It is also found that the Poisson's ratio ν can be determined by this analysis.
It is well known that the breadth of X-ray diffraction line is influenced by the micro-strain included in the material. If the microstrain is replaced by a stress field in a localized area having stress gradient, the profile of diffraction lines emanating from such an area would be likewise broadened and the breadth of the diffraction line would be affected by the stress gradient. On the basis of this consideration, it was intended to analyse the relation between the breadth of diffraction line and the stress gradient, assuming the similarity of the profile of diffraction line to the Gaussian curve.
The results of the analysis can be written as follows;
G=CM√β₂²-β₁²
where G is the stress gradient, C the constant which is decided by the geometry of slit system, M the constant given by the equation
M=Ecotθ/√π{(1+ν)sin²ψ-ν},
where E, ν; elastic constants
θ; Bragg's angle
ψ; angle between the surface normal of specimen and the diffraction plane normal,
and β₂ and β₁ are the integral breadths of diffraction lines of the specimen with and without stress gradient, respectively. In fine, the stress gradient can be determined by measuring the integral breadths before and after applying stress gradient.
The analysis is examined experimentally by measuring the integral breadth of diffraction line obtained from the side surface of a thin plate specimen subjected to bending stress. The results of the experiments show an agreement with the results of the analysis with the maximum scatter of about ±7kg/mm²/mm in stress gradient.

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A new method of Fourier analysis for analysis of X-ray diffraction pattern has been developed. By this method minute variation of profiles is expressed as changes of the phase and absolute value of Fourier transforms of the observed X-ray diffraction pattern. The phase change is related to the peak shift of the profile, and thereby stress is accurately determined. The reliability of this method is confirmed by numerical simulation. The accuracy index shows more than ten times as high as that by the usual methods. By application of this method in determining the stress in steel turbine wings its accurate value is obtained.

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Measurements and analysis of X-ray diffraction lines of high diffraction angles were first carried out on iron specimens after tensile deformation. Changes in half value width of diffraction lines with changes in tensile strain or annealing condition were observed, and further, the profiles of the lines from (211) were analyzed by the method of Fourier analysis and the result obtained was as follows. The mean particle size, often 18% elongation was 3.5×10^-5cm. and the strains in them were uniformal. The value 3.5×10^-5cm corincided well with the value that had preciously been reported by the another, using X-ray micro beam technique. At the same time the recovering process were traced.

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The distribution of residual lattice strains or lattice spacings and residual stresses in plastically extended aluminum alloys were measured by various characteristic X-rays. Then, the scattering of the distribution of the residual lattice strains vs. sin²ψ were investigated precisely in each stage of plastic strains, and the wave length and lattice plane dependency of the residual stresses were discussed.
Hot rolled sheets of Al-1.2 Mn (3003) and Al-4.5 Cu-1.5 Mg-0.6 Mn (2024) alloy were used in this experiment. The shape and dimensions of specimens are shown in Fig. 1. The chemical composition, heat treatment and mechanical properties are indicated in Table 1, 2. To prevent the diffraction lines of these specimens from becoming spotty, the specimen holder⁸⁾ was equipped with horizontally and vertically oscillating mechanism, by which sufficiently continuous diffraction patterns were obtained (Fig. 2).
In order to make sure of the wave length and diffraction plane dependency of the residual stress, the data for several planes by CuKα, CoKα and CrKα radiation were sought and obtained (Fig. 5). On the observation of the distribution of residual lattice strains by sin²ψ method, the direction of the incident X-ray beam to the specimen surface ψ₀ is devided at intervals of 5°in the range of 0°∼45°and their diffraction lines on the side of ψ₀+η were observed (Fig. 3, 4). The results obtained in this study are summarized as follows.
(1) In order to examine the detailed distribution of the lattice strains or lattice spacings, it is necessary to obtain many lattice strains vs. sin²ψ and to observe always only the sharp diffraction lines on the side of ψ₀+η precisely.
(2) It is confirmed that the distributions of the lattice strains vs. sin²ψ of annealed specimens are nearly linear, but scatter evidently in the early stage of the plastic strain about 2%, and aproach linear relation again with increase of the plastic strain. From these configuration, it is considered that the stress of a second kind⁹⁾ in terms of Heyn intergranular stress takes place in the residual lattice strain.
(3) The residual stresses are independent of the wave length but depend mainly on the lattice planes.

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In their previous paper, the authors have reported the study on the relation between the change in half-value breadth of X-ray diffraction line and the orientation factor μ of the reflecting crystals under cyclic or static stress of relatively low magnitude (σ_??_10kg/mm²). (Whereτ_s=μσ; σ is applied stress and τ_s is resolved shear stress). It was found that, under cyclic stress the half-value breadth showed great change in proportion to the values of μ of the grains, that is, slip occurred preferentially in the favourably oriented crystals. Under static stress, however, it was found that the change in half-value breadth was almost the same irrespective of the μ-values of the crystals. This may be understood from the mutual restriction of grains during the static straining.
In the present paper, then, the changes in half-value breadth are investigated under cyclic and static stresses of relatively high magnitude (σ_??_10mg/mm²). It was found that, in contrast to the previous paper, the changes in half-value breadth could be interpreted more properly in terms of the orientation dependence of the work hardening rate g of corresponding single crystal, than orientation factor μ. This suggests that the orientation dependence of the work hardening rate of crystals in polycrystalline aggregates is similar to that of single crystals. It can be concluded that; (1) the fatigue mechanism of Cu is different depending of applied stress levels, (2) the orientation dependence of the work hardening rate of the crystals must be taken into account in order to get a relevant model of polycrystalline aggregates of Cu.

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In their previous papers, the authors made some studies of annealed 6-4 brass, and particularly investigated its changes in residual stress, in half-value breadth and in micro-structure, during its fatigue process under constant and varying stress amplitudes, and found that its second phase showed some peculiar phenomena.
One of these results showed the dependency of the changes in diffraction line widths on its crystal lattice plane in its α-phase. The authors tentatively interpreted this phenomenon as resulting from the heterogeneity of fatigue deformation as in the case of plastic deformation.
Considering the character of fatigue fracture, however, it is questionable to ascrible the variation in the change of half-value breadth on diffraction crystal lattice planes only to the heterogeneity of plastic deformation.
The authors examined therefore, during his X-ray investigations of fatigue deformation and fracture mechanism, first, the relationship between the tensile and the fatigue deformation, and secondly, fracture as dependent on the presence of a second phase.
Heterogeneity in the tensile deformation had been commonly indicated as anisotropy of crystal, that is, orientation factor μ Accordingly, the authors attempted to make it clear whether this conception was applicable to a case of fatigue deformation or not. In case the application failed what sort of factors would be required?
Heterogeneity as due to external forces had been investigated by Laue's reflection methods in single crystals, and the presence of asterism in the Laue spots on an individual crystal lattice plane showed anisotropy in tensile deformation. The reports, of which there had been a few, that no asterism was found in fatigue deformation process, requires reinvestigation, being a merely qualitative matter. The authors made inquiries, therefore, as to in what kind of changes in Laue spots the heterogeneity in the fatigue deformation appeared, and whether the dependency on the crystal lattice plane should have anything to do with asterism.
The synopsis in this paper are as follows:
(1) The changes in half-value breadth of 6-4 brass during the stretching process showed a variance in feature. The crystal plane dependency was seen in the β-phase but not in the α-phase on (420) and (331) planes. The changes in the half-value breadth of 7-3 brass and pure copper (α-phase only) were quite similar in general feature to the α-phase of 6-4 brass. From these experimental results it is evident that the crystal lattice plane dependency of the changes in diffraction line widths of the α-phase crystals was not affected by that of the β-phase crystals.
(2) The interpretations of the dependency of the changes in the diffraction line widths on the crystal plane are based on the idea that each crystal in the polycrystalline aggregates is fit for the slip due to its orientation. Therefore, the authors adopted this idea to explain the changes in the half-value breadth. It is thought that the diffraction planes lying in parallel with the specimen surface occasioned by the experimental condition of X-rays considerably inclined up ward by some external force, and by reason of the crystals getting slips diverged broadly, while those planes of which the crystals are free from slips remained sharp.
As for the plastic deformation of crystal, what is component of the shear stress τ in the slip plane along the slip line is all that is important. This shear stress is the result of the relation τ=μ×σ_N, where σ_N represents the normal stress and μ is the orientation factor. The latter is also indicated as μ=cosφ·cosα, where φ=the angle that the slip plane normal makes with the direction of the stress, and α=the angle that the slip direction makes with the direction of the stress.

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X-ray diffraction is a useful means for the study of change in structure of materials. There have been a number of publications related to X-ray observations in creep of metallic materials. However, it is noted that these observations are not sufficiently adequate to account for the change in microstructures that occurs in the material during creep process, because of inadequacy of ordinary technique of X-ray diffraction in its resolving power.
Recently the instrumentation in the field of X-ray diffraction has achieved great progress in this country, and even exquisite techniques of X-ray diffraction have been made available, providing high resolving power, such as the X-ray micro-beam technique and the double crystal monochrometer technique. These new techniques have high resolving power to account for the change in microstructure of materials.
The authors applied the X-ray micro-beam technique to the study of the creep, and investigated the micro-structural changes in 0.06%C steel during creep at 450°C under constatnt stress of 8kg/mm² and 12kg/mm². The results obtained from the micro-beam technique are as follows:
(1) In the case of 8kg/mm², the diffraction spots were diffused slightly with increasing creep strain, and split in to small sharp spots. These results show that while with the increasing strain the cell size remains constant, the misorientation between the cells increases and the lattice distorsion within the cells decreases. The dislocation density on the cell walls increases with strain.
(2) In the case of 12kg/mm the diffraction spots are diffused in arc, with increasing strain, and in the arc many split spots are found. These split spots are diffused to parallel the radius of the Deby-Sherrer ring. These results show that while the cell size remains constant with strain, it is smaller than in the case of 8kg/mm. The misorientation between the cells increases and the lattice distorsion with in the cells also increases with strain. The dislocation density on the cell walls increases with strain more rapidly than in the case of 8kg/mm.
In addition to this, we measured the changes in half-value breadth obtained from ordinary X-ray diffraction patterns and observed the micro-structural changes of the surface of the specimens by means of an electron microscope. The findings by the X-ray micro-beam technique agree with that by the above mentioned techniques.

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In the previous paper we analyzed the relations between the skin-pass reduction rations and the surface residual stresses at various skin-pass ratios from 0.3% to 2.5% using different rolling mills on steel sheets of various kinds and thickness. We have found that they showed the same inclination.
In the present paper we have analyzed the interrelations between the skin-pass reduction ratios and the surface residual stresses and some of their main mechanical properties (especially the yield point elongations) at various skin-pass reduction ratios from 0.5% to 2.5% on the specimens made with the same rolling mill of steel sheets of the same kind and thickness.
By the results of our experiments concerning the relation between the skin-pass reduction ratios and the surface residual stresses we have been confirmed of the same inclination as before. We have found also that there are considerable deviations in the relation curves of these specimens. But clear relation is recognized between the surface residual stresses and the yield point elongations of the cold-rolled steel sheets; i, e., if the sign of the surface residual stresses of the cold rolled steel sheets is positive, their yield point elongation is less than 1% and there is but little apparent stretcher strain.

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Sachs' boring-out method is used for determining the residual stresses in a cylinder. When a test piece that is separated from a longer cylinder -solid or hollow- is too short, the boring-out test will not yield the same residual stresses that would have been observed in the original cylinder. Bühler has stated, from his experimental investigation, that the residual stresses in the separated specimens are roughly the same as those in the original longer specimens, provided the ratio of length to diameter remains greater than about 2.
One of us studied theoretically the influence of end faces of the separated specimen, proving that for any arbitrary distribution of longitudinal, the tangential and radial stresses over a cross section, Bühler's experimental conclusion is always valid.
In the present study, experiments have been carried out to find the influence of the end effect of detached specimens by X-ray stress measurement, that is, the residual stress distributions of the longitudinal (σ₁) and the trangential (σ₂) stresses on the specimen surface are determined by shifting the specimen from end to mid-length.
In the X-ray measurements, “Twin-counter method”is employed together with an ordinary film method. The twin-counter method enables us directly to read out a small shift in the position of X-ray reflection line which is caused by lattice strain; then (σ₁+σ₂) are continuously recorded from end to mid-length. The difference of σ₂ between end and mid-length zone is negligibly small, and σ₁ is zero at the end, then σ₁ in the mid-length can be determined without using the sin²ψ method which is a well known method in the X-ray stress measurement, the result showing a good agreement with the ordinary Sachs' boring-out method.
The residual stress distributions are suddenly changed within the distance comparable to the radius of the cylinder from the end. However, they are gradually changed in the same direction for the distance of the same radius. Beyond the point at the distance of the diameter from the end, the stress distributions are almost kept constant, and it appears that the residual stresses of this zone are the same that would have existed in the original cylinder.
These experimental results can lead us to the conclusion that the residual stresses in the original cylinder remain unchanged in the vicinity of mid-length of the separated specimen, provided the ratio of length to diameter exceeds 2.

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The research was carried out in order to find the effect of preheat treatment, such process as annealing, quenching and tempering, on the effect of induction hardening of steel, and their difference in effects according to the kind of steel.
The steel used for the test is of four kinds; namely, carbon steel S40C, Mn steel SAE 1340, Cr steel SCr4 and CrMo steel SCM4.
As preheat treatment before induction hardening these steels were annealed at 880°C and 720°C, water quenched in case of carbon steel, oil quenched in case of other steels both from 850°C and after that tempered at 180°C, 400°C, 480°C, 540°C, 600°C, 650°C, 700°C and 730°C, respectively. Then they were all subjected to progressive and one shot heatings.
In those cases, all the test specimens were quenched under the same condition as that which yielded the thickness of hardened layer of 1.5mm (up to Micro Vickers 500), when S40C steel annealed at 880°C for two hours, was hardened by induction.
As the measure hardening effect, hardness, thickness of hardened layer, and residual stress by means of X-rays, were measured.
The effects of induction hardening are as follows:
(1) They vary with the conditions of carbide caused by the preheat treatment, reduced in proportion to the increase in the size of carbide particles.
(2) Steel not containing Cr and Mo such as S40C and SAE 1340 is subject to smaller influence than that containing those elements such as SCr4 and SCM4.
(3) As for S40C and SAE 1340, annealing at 880°C and tempering in the range from 180° to 400°C showed a good result.
As for SCr4 and SCM4, tempering in the range from 400° to 540°C showed a good result. Tempering done above this temperature resulted in a bad hardening effect.
(4) When the steel was annealed at 720°C, the result was least favorable.

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