A BEHAVIOR OF ELASTIC AND PLASTIC STRAIN FOR (α+γ) DUAL PHASE STAINLESS STEELS IN ROTATING BENDING TEST

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1 Copyright JCDS - Interntionl Centre for Diffrction Dt 24, Advnces in X-ry Anlysis, Volume ISSN A BEHAVIOR OF ELASTIC AND LASTIC STRAIN FOR (+) DUAL HASE STAINLESS STEELS IN ROTATING BENDING TEST 1 Hjime Hirose, 2 Mshide Gotoh, 2 Tomonori Yno nd 3 Toshihiko Sski 1 Reserch center, Kinjo University, Mtto, Jpn 2 Grdute school, Knzw University, Knzw, Jpn 3 Deprtment of Mterils Science nd Engineering, Knzw University, Knzw, Jpn ABSTRACT JIS-SUS329 is duplex steel tht consists of two-phse (+)-Fe mterils. It hs good resistnce to corrosion nd oxidtion. Therefore, this mteril should be use for the shft of cr, the screws holding ship together, nd so on. In this study, the effect of residul stress nd plstic deformtion on ftigue strength of SUS329 ws exmined. Residul stress mesurement ws pplied to new X-ry stress mesurement method, which contins the prmeters of residul stress x nd misfit of plstic strin by micromechnics. As result, interesting behviors of elstic strin nd plstic strin in rotting bending ftigue test were recorded. INTRODUCTION A new method for determining plstic strin in composite mterils using X-ry diffrction ws developed by the uthors in recent yers[1]. The present method ws derived by using both Eshelby s pproch[2] nd the Mori-Tnk theory[3] to express the stress stte in composite mterils. JIS-SUS329 is dul phse stinless steel tht consists of ferrite Fe nd ustenite Fe. Becuse dul phse stinless steel is greter thn other single phse stinless steels in mechnicl strength, it is expected to be used for structures such s the chemicl plnts, het exchngers, nd so on. However, the structures mentioned bove re generlly loded repetedly in the long run. And it is reported tht frctures in the structures re lmost cused by ftigue filure in metls. Therefore, it is importnt tht mechnicl strength nd physicl property of the mteril is evluted in ftigue stte. In ftigue process, crystlline structures in mteril re cused not only elstic strin but lso by plstic deformtion relted to disloction mechnism. In this study, the effect of residul stress nd plstic deformtion on ftigue strength of SUS329 ws exmined using X-ry diffrction methodology.

2 ISSN This document ws presented t the Denver X-ry Conference (DXC) on Applictions of X-ry Anlysis. Sponsored by the Interntionl Centre for Diffrction Dt (ICDD). This document is provided by ICDD in coopertion with the uthors nd presenters of the DXC for the express purpose of educting the scientific community. All copyrights for the document re retined by ICDD. Usge is restricted for the purposes of eduction nd scientific reserch. DXC Website ICDD Website -

3 Copyright JCDS - Interntionl Centre for Diffrction Dt 24, Advnces in X-ry Anlysis, Volume ISSN THE RELATIONSHI BETWEEN ELASTIC STRAIN/STRESSES MEASURED BY X-RAYS AND THE LASTIC STRAIN DISTRIBUTION Outline of the misfit of plstic strin mesurement hs been described by Sski et l.[1]. In X-ry stress mesurement, the stress in ech phse of composite mteril cn be mesured seprtely. The stress in ech phse is clled phse stress, it cn be mesure by the X-ry diffrction profile from ech phse. Mcro stress cn lso be mesured using following eqution; ( M M I I ) = (1 f )( ) + f ( ), (1) M I where is the mcro residul stress, is the residul stress of mtrix, is the residul stress of inclusion nd f is the volume frction of inclusion. In this study, the Fe phse is determined s mtrix nd Fe phse is determined s inclusion. Otherwise, phse stress is described by micromechnics, which is contined Eshelby s pproch nd the Mori-Tnk theory. = 3U ( ) 3B f ( M M 1 I I = 3U ( ) 3B1 (1 f )( ), (2) ), (3) where = is determined s the misfit of plstic strin by. (4) I M By the eqution (2) nd (3), hs following form; U I I U M M = ( ) ( ), (5) Q Q where U, U nd Q re determined by U µ β ( µ µ ) =, 3B µ U =, Q = B1{3U (1 f ) + 3U f }, 3B B 1 2( β 1) µµ =, 3B µ = E, 2(1 + ν ) µ = E, B = µ { β f ( β 1)}( µ µ ), 2(1 + ν ) 2(4 5ν ) β =, (6) 15(1 ν )

4 Copyright JCDS - Interntionl Centre for Diffrction Dt 24, Advnces in X-ry Anlysis, Volume ISSN where E, E is Young s modulus of mtrix nd inclusion, respectively. And ν, oisson s rtio of mtrix nd inclusion, respectively. The misfit of plstic strin clculted using the eqution (5) with the phse stress mesurement of ech phse. ν is lso cn be EXERIMENTAL Tble 1. Chemicl composition. (wt.%) C Si Mn S Ni Cr Mo N φ12 R4 φ15 Figure 1. A shpe of specimen. (unit:mm) Tble 2. Mechnicl properties of SUS329. Yield strength, M 553 Tensile strength, M 777 Elongtion, % 4 Reduction re, % 71 Specimen Figure 1 shows the shpe of specimen. Dimeter of prt of giving highest lod is 12mm. Chemicl composition of the specimen re shown in Tble 1. In ddition, Tble 2 shows mechnicl properties of SUS329. Figure 2 shows the microgrph of specimen. Volume frction of ech phse ws mesured with the point count method using pictures of grins. As result, f f.54 :.46 ws obtined, nd the flt Fe : Fe = dispersion of inclusions Fe were in mtrix Fe. Figure 2. Microgrph of specimen. Rotting bending test nd X-ry stress mesurement A schemtic illustrtion of experiment is shown in Figure 3. The mchine of rotting bending test ws simply supported by bem type clled Ono-shiki, with rottion speed of 18 r.p.m., stress rtio of 1 = R. Figure 4 shows S-N curves mesured in this test. Ftigue limit ws obtined s 35M. Therefore, the stress mplitude ws set for =325, φ= ψ x ψ Bending moment 22 Irdited re Figure 3. Schemtic illustrtion of experiment.

5 Copyright JCDS - Interntionl Centre for Diffrction Dt 24, Advnces in X-ry Anlysis, Volume ISSN nd 4M becuse of investigtion of stress behvior in X-ry stress mesurement. Stress mesurements were executed t the eight cycles, which is indicted s experimenttion point in Figure3. X-ry tube voltge ws 3kV, nd tube current ws 1mA. Cr-K rdition ws used for Fe phse, nd lso Cr-Kβ ws used for Fe phse. Mesured plne ws Fe2 nd Fe3 for ech phse. Bending stress is generted on the surfce perpendiculr to xil direction of specimen by the weight. Bending stress on the surfce of specimen is different from internl stress t the center. In other words, the stress grdient is generted to rdius direction of specimen. Therefore, bending stress on the surfce of specimen become mximl tensile nd miniml compress on reverse side. The 475 men stress in irrdited re of X-ry : Non Frcture 45 : Frcture cn be mesured with X-ry stress : Experimenttion 425 point mesurement. Informtion obtined by Limit =35M 4 the X-ry residul stress mesurement 375 is lmost from the surfce of 35 specimen, becuse the penetrtion 325 depth of X-ry is bout few micrometers. Figure 4. S-N curves nd experimenttion point. RESULTS AND DISCUSSION Stress mplitude, M The behvior of residul stress for cycle number is shown in Figure 5. Figure 5 () shows the behvior under ftigue limit, nd (b) shows over ftigue limit Limit = 35 M. Under ftigue limit, residul stress before ftigue test ws compressive bout 3M in Fe phse, nd ws tensile bout 15M in Fe phse. As the cycle number incresed, vlue of residul stress pproched bout M up to N=1 3 cycles, nd remined nerly constnt over N=1 3 cycles in ech phse. In ddition, the behvior of stress on mplitude =325M ws similr to the behvior of stress on mplitude =35M. On the other hnd, the behvior of stress over Limit = 35 M ws different from the cse under ftigue limit. About Fe phse, the tendency of stress vrition ws similr to the cse under ftigue limit. However, only the tendency of Fe phse over ftigue limit ws different when it is compred to tht of others. As cycle number incresed, vlue of residul stress pproched bout -1M up to N=1 3 cycles, nd ws rough round M over N=1 3 cycles in Fe phse. Figure 6 shows the behvior of the misfit of plstic strin for cycle number. As cycle number incresed, vlue of the misfit of plstic strin pproched bout up to N=1 3 cycles in ll mplitude. They indicted similr tendency over N=1 3 cycles except for =4M. In other words, the misfit of plstic strin converged constnt vlue under ftigue limit, nd it ws unstble over ftigue limit. Here, the stte of plstic

6 Copyright JCDS - Interntionl Centre for Diffrction Dt 24, Advnces in X-ry Anlysis, Volume ISSN Residul stress x, M Residul stress x, M 1-1 Are1-2 Are2-3 35M 325M (i) Fe phse. 1 Are2-1 Are M Residul stress x, M () Under ftigue limit. Residul stress x, M M Are1 325M 1-1 Are (ii) Fe phse M 1 Are1 Are (iii) Fe phse. (iv) Fe phse. (b) Over ftigue limit. Figure 5. Reltion between phse residul stress nd cycles. Misfit of plstic strin x M M 325M Figure 6. Reltion between misfit of plstic strin nd cycles. Force Crystl Initil Slip Compress Go bck Figure 8. An ide of stress reduction. Initil (b) Are2 () Are1 (c) Are3 Figure 7. Behvior of elstic nd pltic strin. Force Fe e.s. increse p.s. stedy e.s. increse p.s. stedy e.s.= elstic strin p.s.= plsric strin Fe e.s. increse p.s. stdy Micro crck e.s. increse p.s. reduction nd stedy Figure 9. Instbility of residul stress in Fe. Be unstble

7 Copyright JCDS - Interntionl Centre for Diffrction Dt 24, Advnces in X-ry Anlysis, Volume ISSN strin for ech phse is considered. Figure 7 shows the concept figure of the movement between residul stress nd plstic strin. The verticl xis nd the horizontl xis re determined s the residul stress nd the plstic strin, respectively. In the initil stte, the reltionship is drwn like Figure 7() by Figure 5 nd Figure 6. In re1 3μm indicted in Figure 5, the residul stress of Fe nd Fe pproched bout M, nd the plstic strin will Figure 1. SEM observtion of micro crck. become like Figure 7(b). Stress reduction mechnism is explined using Figure 8. The forces given to crystls will induce the slip immeditely fter ftigue test begins. If the crystls re given compressive stress, generted stress by compression might be reduced by the slip. In re2, the work hrdening should pply to the restrint of slips in cse of excessive disloction. Otherwise, the movement in re3 is indicted in Figure7(c). In re3, the misfit of plstic strin ws unstble due to instbility of the residul stress in Fe phse. This mechnism cn be explined using Figure 9. If the crck is ppered in Fe grins, the elstic strin should be unstble by stress relese due to crck opening. Figure 1 shows micro crck of frcture surfce by SEM. Judging from size of micro crck, there my be crcks in grin. CONCLUSIONS Min results in this study re summrized s following: (1) In cse up to N=1 3 cycles, vlue of residul stress pproched bout M s cycle number incresed except for =4M regrdless of ftigue limit 35 M. Slip mechnism Limit = could explin cuse of residul stress reduction. (2) In cse over N=1 3 cycles, the residul stress of Fe phse over ftigue limit ws unstble t between nd 1M. It is thought tht micro crcks cuse these phenomen. (3) In cse over N=1 3 cycles, the misfit of plstic strin over ftigue limit ws lso unstble. Therefore, it is possible to forecst the life of dul-phse stinless steels SUS329 by X-ry methodology. REFERRENCES [1]T, Sski;Z, Lin;Y, Hirose, Trnsction of JSME (Series A), 1997, 66, [2]J, D, Eshelby, roc. R. Soc. London, 1957, A241, 376. [3]T, Mori;K, Tnk, Act. Met., 1973, 21, 571.