X-ray Stress Measurement on the Confined Portion of Steel Structure by the Procedure of its Diffraction by Kin-ichi Nagai, Mitsumasa Iwata, Kydzo Kiku

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1 X-ray Stress Measurement on the Confined Portion of Steel Structure by the Procedure of its Diffraction by Kin-ichi Nagai, Mitsumasa Iwata, Kydzo Kikuchi, Yuji Okumoto and Hiroe Kobayashi In this report of a basic study for the residual stress measurement of a practical welded structure through X-ray, the authors derive the ƒó-sin2ƒõ method, named tentatively, in which the direction of incident X-ray can be selected arbitrarily, and then investigate to apply the present method to such the portion of a structure as where the direction of incident X-ray is confined by the shapes and arrangements of other members of a structure. Results are summarized as follows; (1) The present method involves the multiple regression analysis of the linear statistical model, in which diffraction angles for incident X-ray on an arbitrary direction is treated as a random variable, and from the solutions of the analysis, the expectations and confidence intervals of stresses are estimated on all directions at a measured portion. (2) The present method, where the direction of incident X-ray is not confined theoretically, can also be applied on such the geometrically confined portion in direction as above-mentioned, and then makes it possible to estimate the stress on any direction at a measured point with accuracy enough for practical usage. ( 3) For obtaining a more accurate stress at such the confined portion by the present method, it is necessary to increase degrees of freedom through increasing a number of informations of diffraction angle of X-ray, and also, to obtain the informations over the range of the incident angle of X-ray as wide as possible. (4) The apparent diffraction angle of strain-free crystals is treated as one of the partial regression coefficients and estimated through multiple regression analysis.

2 Fig. 1 Stress and strain system in X-ray stress measurement Fig. 2 X-ray diffraction by crystals under loading condition and strain-free condition Fig.3 ƒãƒ³ƒõ-ƒ³-sin2ƒõ surface 60

5 溶接学会誌 3.実第45巻(1976)第12号1041 験的確認 60キロ級調質高張力鋼の単軸引張試験における応力測定にφ-sin2ψ 法とsin2ψ 法を適用し,その結果を比較することによって本法の妥当性を実験的に確認した, さらに,その測定結果をもとに本法の狭隘箇所への適用を検討した. 3.1実験方法板厚12.7mmの60キロ級調質高張力鋼板を625 1時間の応力除去焼鈍を行ない,Fig.4にで示す形状の試験片を採取した.試験片表面は,機械加工の後電解研摩により表面加工層の厚さを表裏それぞれ約0.3mm 除去して仕上げた.応 Photo.1に力除去焼鈍後の顕微鏡組織は, 示すように結晶粒径が5 15μ の回折線写真は,Photo.2にである.そ Photo. 1 Microstructure of used steel (HT60) after stress relief annealing Photo. (211) Debye-Scherrer of used steel 示すごとく完全に連続しており,十分精度の高い測定が可能な結晶粒度であることを示している. X線応力測定は,理学電機製のStrainflex MSF型装置を用い,平行ビームによるカウンタ法で行なっており,その測定条件をTable 1に示す.同装置は,従来のsin2ψ 法による応力測定に用いられているもので, Fig.1に示した入射X線の方向(Φ,ψo)のうち,ψ0は精度よく設定できるようになっている.しかし,Φ を変化させる回転機構が設けられていないので,本実験では試験片を回転台に載せた引張り治具に取付け.試験片の X線照射位置すなわちFig.1の原点を回転台の中心軸上に一致させて,任意の φ に設定できるようにした. 2 φ は回転台の角度目盛りによって測定できるようにしてある.Φ を0 から180 の範囲で18 おきに10方向に変化させ,各 φ においてψoをに0,15,30,45 らの入射X線標準的なsin2ψ 法 Table 1 Conditions of X-ray ring by crystals diffraction technique と同様の4方向に変えて,合計40方向かの回折角 Φψ を測定した.なお,試験片表面に任意に設けたX軸とゴニオメータの走査方向との相対位置を明らかにしておく必要があるので,Fig.1 のOQとX軸を一致させ,その方向を Φ=0とした. 本実験ではこのX軸を便宜的に荷重軸にほぼ一致させている.また,本法の結果と比較するために,各 φ における θ Φψ からsin2ψ 重は無負荷を含めて6段法により σφ を求めた.引階に変化させ,Fig.4に張荷示す位置に465付したひずみゲージによって機械的応力 σm 測定した. 材料定数としては,日委員会の共同研究結果本材料学会,X線によるX線 / E= mm2/kgお kgか Fig. 4 Details of tensile test mm2を specimen 63 ら計算したv=0.27お用いた. 材料強度部門的弾性定数(1+v) よびv/E ,5mm2 よびE= kg

6 Fig. 5 Stress a on the direction 0 to loading obtained with X-ray stress measurements Fig. 7 Sampling of measurements for direction of incident X-ray to be confined by the procedure of its diffraction; Symbol indicates direction of incident X-ray Table 2 Expectations and 95% confidence intervals of stress ax on loading direction in each sample Fig. 6 (a) Correlation of X-ray stress ag and mechanical stress am on loading direction and (b) Sampling of measurement for direction of incident X-ray to be selected, arbitrarily; Symbol indicates direction of incident X-ray 64

7 Table 4 Expectations and 95 % confidence intervals of the apparent diffraction angle ƒ o by strain-free crystals in each sample Table 5 Results by numerical iteration of leastsquare method Fig. 8 95% confidence intervals of stress co in each sample Table 3 Expectations of direction ƒá of principal stress in each sample

8 7) A. M. Mood, F. A. Graybill, D.C. Boes; Introduction to the Theory of Statistics, McGrawhill-Kogakusha, (1974), 181

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