Response of FBG Sensors Embedded in SRM Interface of combustor When Subjected to Tri-Axial Normal Loadings

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1 This article has bee accepted ad published o J-STAGE i advace of copyeditig. Cotet is fial as preseted. IEICE Electroics Epress, Vol.* No.*,*-* Respose of FBG Sesors Embedded i SRM Iterface of combustor Whe Subjected to Tri-Aial Normal Loadigs ZHANG Lei, CHANG Xilog, ZHANG Youhog ad LIU Walei Xi a Hi-Tech Istitute, Xi a 715, Chia; a) lwy_l@163.com Abstract: I this paper, polymer packaged fiber Bragg gratig (FBG) sesors are istalled iside of the combustor wall to moitor the health of solid rocket motor. The resposes of sesor embedded i adhesive specime composed of propellat, isulatio ad case whe subjected to aial ad uaial tesile stress are ivestigated. The strai distributio ad spectrum of FBG were simulated whe the specime suffered from differet ormal loadigs by fiite elemet method ad computer simulatio techology. The result is validated by ais ad uais tesile test. It is show that the proposed type of sesig system ca measure the bod stress(the radial stress) i SRMs. Keywords: Solid rocket motor, FBG, optical sesors, Iterface Classificatio: Optical systems Refereces IEICE 17 DOI: /ele Received Jue 8, 17 Accepted July 14, 17 Publicied July 31, 17 [1] Ruderma, G. A. (5). Health maagemet ad strategy for air force missiles. Rep. AFRL-PR-ED-TP-5-7, U.S. Air Force Research Laboratory, Edwards Air Force Base, CA. [] Iqbal, M. M., ad Liag,W. (6). Modelig the moisture effects of solid igrediets o composite propellat properties. Aerosp. Sci. Techol., 1(8), [3] Little, R. R., Cheler, H., ad Buswell, H. J. (6). Developmet, testig, ad applicatio of embedded sesors for solid rocket motor health moitorig. Proc., 37th Aual Cof. of Frauhofer Istitute for Chemical Techology (ICT), Frauhofer Istitute for Chemical Techology, Pfital, Germay. [4] Craig M. Lopati : U.S. Patet US B1 (1). [5] Ahduog Q. Le, A.M.ASCE1, L. Z. Su, Ph.D., M.ASCE; ad Timothy C. Miller, Ph.D. Health Moitorig ad Diagosis of Solid Rocket Motors with Bore 1

2 IEICE Electroics Epress, Vol.* No.*,*-* Cracks Joural of Aerospace Egieerig, ASCE, 16, 9(3): [6] Le, A. Q., Su, L. Z., ad Miller, T. C. (13). Detectability of delamiatios i solid rocket motors with embedded stress sesors. J. Propul. Power, 9(), [7] Riiotis, C., Eieder, L., Bacallari, L., ad Tussiwad, G. (13). Fiber optic architectures for strai moitorig of solid rocket motors propellat. Ses. Lett., 11(8), [8] Udd, E., ad Beterou, J. (1). Improvemets to high-speed moitorig of evets i etreme eviromets usig fiber Bragg gratig sesors. Proc., SPIE: Fiber Optic Applicatios ad Sesors IX, SPIE, Belligham, WA, Vol. 837, 837L-1-837L-13. [9] Lopati, C., ad Gristei, D. (15). Active sesig for moitorig the properties of solid rocket motor propellat grais. Propellats, Eplos., Pyrotech., 4(), [1] B.K.A. Ngoi, J. Paul, L.P. Zhao b, Z.P. Fag.(4).Ehaced lateral pressure tuig of fiber Bragg gratigs by polymer packagig. Optics Commuicatios 4 (4) [11] Botsis J, Humbert L, Colpof F, et al. Embedded fiber Bragg gratig sesor for iteral strai measuremets i polymeric materials[j]. Optics ad Lasers i Egieerig, 5,43 (3-5): Itroductio Rocket motors are oe of the largest items that dictate missile system service life. Thus, structure health moitorig is of sigificat iterest for the safety ad reliability of solid rocket motors (SRMs) [1]. The ability to detect damage i SRMs will help eable timely, accurate, ad reliable assessmet of structural itegrity, ad thus will yield great cost savigs ad prevet catastrophic structural failures. Because SRMs are cooled from the cure temperature to a ambiet temperature, radial stresses persist i the grai throughout its life. Ad SRMs ca develop critical flaws that ca cause catastrophic failure at igitio. There are three primary failure mechaisms: propellat agig, bore crackig, ad delamiatio (debod) at the iterfaces betwee the propellat, isulatio, ad case []. As the Fig1 show, i regios of the grai where a highly triaial stress state eists. Classical approaches used to predict ad detect material degradatio have bee to develop agig models for predictig the state of a material, give a assumed or measured evirometal history, ad the use of o-destructive testig methods such as ultrasoud ad X-rays. Both approaches, as curretly practiced, are iadequate to meet the eeds of a real-time, self-sesig health moitorig system. Thus, i recet years efforts have bee devoted to ivestigate a etirely ew approach to meet the goal of self-sesig ordace the use of embedded sesors [3]. Several types of embedded sesors are beig ivestigated i the solid rocket motor commuity [4]. Bod lie sesors are small pressure sesors used to measure the stress betwee the propellat ad case. The sesors are used to detect the perturbatio i the stress field due to the presece of damage. Amog the several types of sesors that could be cosidered, electrical strai-gage-based bod stress sesors, which measure the ormal stress betwee the grai ad lier, have

3 IEICE Electroics Epress, Vol.* No.*,*-* received the most attetio, ad it has bee show that they ca have sigificat value i their ability to validate grai stress predictios [5,6]. However, the eed for electrical leads eterig the motor presets safety cocers that may preclude this method ecept for laboratory applicatios. Optical fiber strai sesors [7-9], particularly Fiber Bragg gratig (FBG) strai sesors, have also received some attetio, optical sesors are cosidered as the preferable solutio i such eviromets, due to their electromagetic iterferece immuity ad their iheret electrical ad eplosio safe characteristics. Furthermore, FBG are ideal for multiple sesor applicatios as may of these gratigs ca be employed either i series or i parallel. There are, however, several issues with fiber optics that eed to be addressed ad overcome before this techology ca be used i geeral i SRMS. Fibers are typically made from brittle material such as glass. This results i beig fragile ad difficult to hadle. This paper proposes a ew method usig fiber Bragg gratigs by polymer packagig sesors for measurig the bod stress betwee the propellat ad isulatio. There are three advatages for usig polymer packagig the FBG. Firstly, the FBG is so very brittle that the survival rate is difficult to guaratee i the embeddig process. It eeds special protectio to prevet breakig. Secodly, the bubbles or impurities may be formed aroud the FBG i embeddig process. They will geerate stress cocetratio causig the spectrum peak splittig or chirp which provides a uambiguous idicatio of the strai, ad it is difficult to iterpret the results. Lastly, the bod stress is perpedicular the bod iterface embedded FBG sesor. The lateral pressure tuig of FBGs suffers from the drawback of low lateral pressure sesitivity, arrow tuig rage ad stress iduced birefrigece. This ca be achieved by coatig or packagig the FBG with a material havig low elastic modulus ad very high Poisso s ratio, which ca effectively trasfer the stress applied i oe directio to the mutually perpedicular directios. I this paper, the FBGs coated by a wafers package of HTPB/TDI elastic mass,the structure diagram of sesor as the Fig.1 show. Case Lier Y O Py P P P FBG Z Ploymer Metal plate X Fig.1. Propellat Stresses at grai-lier-case, Structure diagram of sesor The spectral respose of coated FBGs embedded i adhesive specime subjected to aial ad uaial tesile stress are studied ad preseted. HTPB(hydroyl-termiated polybutadiee) resi is a good bider i solid rocket propellat. It is characteried by low glass trasitio temperature, proper mechaical property after curig, age resistace, havig very low stiffess ad very high Poisso s ratio value. It is thermally stable ad retais room temperature 3

4 IEICE Electroics Epress, Vol.* No.*,*-* characteristics across a wide temperature ragig from -4 to 7. As Fig. show, schematic diagram of a solid rocket motor ad a array of four FBG sesors at the midplae of the motor.optical sesors evely distributed alog the circumferece of the motor at the propellat/isulatio iterface. A Grai Perforatio Debod Case Isulatio Lier 1 Sesors Propallat 4 3 A Fig.. Schematic diagram of a solid rocket motor ad a array of four FBG sesors at the midplae of the motor Priciple Whe the fiber is straied aially, the fiber elogates or compresses, chagig the fiber gratig spectral period ad the output spectrum goes to loger or shorter wavelegths, respectively. The coditio of high reflectio or Bragg coditio, relates the reflected wavelegth or Bragg wavelegth, λ B, to the gratig period, Λ, ad the mea effective ide of refractio,. The most geeral relatioship betwee strai ad iduced chage i the reflected wavelegth i a FBG (with the fiber ais parallel to the directio) ca be epressed by B (1) However, a three dimesioal state of strai prevails aroud a FBG embedded i the propellat/isulatio iterface. Various eperimetal studies have show that the trasverse load respose of FBGs is etirely differet from aial loadig. Whe a FBG is subjected to o-egligible trasversal strais, its optical respose is geerally affected. Thus, trasversal strais essetially iduce birefrigece i the fiber core, which may lead to the separatio of the iitial Bragg peak ito two distict oes alog two polariatio aes. Cosequetly, Eq. (1) splits ito the followig relatios alog the two itrisic polariatio aes of the fiber, () By (3) By y Where λ B, λ By,, y are the reflected wavelegth ad effective idees of refractio for the ad y polariatio aes, respectively (with the fiber ais parallel to the directio).the chage reflective ide ca be epressed: [ ( )] (4) P 11 P 1 y 4

5 IEICE Electroics Epress, Vol.* No.*,*-* [ ( )] (5) y P 11 y P 1 Where ɛ, ɛ y,ɛ are the priciple strai compoets of the fiber core at ay poit P(, y, ) i the X,Y ad Z directio, is the effective refractive ide of the ustressed. Δ,Δ y are the effective refractive ide X,Y polariatio aes. The most geeral relatioship betwee strai ad iduced chage i the reflected wavelegth i a FBG ca be epressed by B (6) B By y (7) B Equatio ca be obtaied by relatio (4)(5) [ P P ( )] (8) B 11 1 y B [ P P ( )] (9) By B 11 y 1 Where P 11,P 1 are photoelastic coefficiet. B By B ( P 1 P 11)( y) (1) oe otices that the peak separatio Δλ -Δλ y oly depeds liearly o the trasversal strais differece ɛ -ɛ y. Whe the iduced birefrigece is egligible (i.e. ɛ ad ɛ y are equal), a simplified equatio ca be obtaied by averagig relatios (8)(9), B 1 P 1 P 11 P 1 y B [ ( )( )] (11) Assumig further that ɛ,y =- νɛ,where ν is the Poisso s ratio of the fiber, ad Eq. (11) simplifies to B P 1 ( v P P 11 1) P e B (1 ( )) (1- ) (1) where the ew strai optic costat P e ca be easily determied eperimetally. This relatio poits out that the shift i wavelegth of the Bragg peak is proportioal to the applied aial strai. Whe it is uiform, shifts occur without modificatio of the iitial spectrum shape ad ɛ is easily obtaied from (1). However,it has bee show that a o-uiform strai distorts the shape of the reflectio spectrum. 5

6 IEICE Electroics Epress, Vol.* No.*,*-* 3 Fiite elemet simulatio I order to simulate the loadig coditio of shell/isulatio/lier/ propellat bodig system. A adhesive specime is desiged for rectagular adhesive specime embedded optical sesor accordig to Chiese aerospace idustry stadard of P.RC, QJ The adhesive specime is composed of steel shell, two pieces of isulatio, lier, block of HTPB propellat.the propellat cast ad cured betwee two layers of lier boded to NBR (itrile-butadiee rubber) isulatio, which had bee boded previously to steel plates ad the optical sesor lie betwee isulatio ad propellat (Fig.3). Costat load eperimet with differet load magitude ad agles were performed,ad the chagig characteristics of FBG sesors were obtaied. Fiite elemet simulatio of the tesile test process was carried out to scrutiie the strai distributio o the FBG ad thereby to compute the wavelegth respose characteristics. The simulatio was carried out usig commercial software ANSYS. The schematic of the model ad the coordiate system used is show i Fig.3. The cetral ais of the fiber is desigated as Z ais ad the directio of perpedicular to the specime shell plate is desigated as the Y ais. The applied boudary coditios are as follows: For the upper shell plate, the degree of freedom is arrested as a fied support, allowig the bottom shell plate to move i the loadig directio. I order to simplify the calculatio, the viscoelastic material oly cosiders equilibrium modulus. The material properties used for the simulatio is show i Table I. To aalye the respose of FBG subjected to stress i differet directio, the followig 3 case have bee studied. Property Elasticity modulus, E (MPa) TableI Material prosperities Possio s ratio,ν Sie(mm) Fiber gratig Φ.15 Case propellat Isulatio Adhesive layer 5.3.5~.5 Polymer coatig Metal plate Photoelastic coefficiet P 11 =.113 P 1 =.5 Λ(m) Δ Fied support Case Isulatio Propellat FBG sesor Y X P Z 6

7 Strai Refelctivity(dB) Strai(με) IEICE Electroics Epress, Vol.* No.*,*-* Fig.3. Adhesive specime embedded FBG sesor, The schematic of the model ad the coordiate system Case1: The loadig directio is alog Y-ais (ais tesile stress) Whe the loadig directio is alog Y-ais (see Fig.4), the loadig compoet directio are alog Z-ais P ad X-ais P, P= P=. Fig.4 shows the distributio of the strai at the three ais of the FBG with respect to the applied load. It could be see that strai i the Z-directio ɛ is compressive i ature ad its magitude is very high compared to the compressive radial strais ɛ ad ɛ y. At a load of.1mpa, the magitude of aial strai is whereas the radial strais i the X- ad Y-directios are oly ad , respectively. This is crucial i coectio to the requiremet of superior aial strai for the ceter wavelegth of the FBG to have improved sesitivity to the applied lateral load. Sice the plae of the gratigs is perpedicular to the ais of the fiber oly the aial strai ɛ ca produce maimum gradiet i the period of the gratig durig strai tuig. The shift i the ceter wavelegth is calculated with respect to a ceter wavelegth of 155 m. As the Fig.4(c) show,it ca be see that ɛ ad ɛ y are superimposed ad shifts almost at the same rate with respect to the applied load. The differece betwee the two is so little, which is too egligible. Accordig to the formula(1),it caot cause apparet peak splittig. The FBG s reflectio spectra ca be simulated by the software Optigratig. Fig.4(d) shows strai correspodig optical spectral wavelegth uder differet agles. y - ε -4 ε y ε -6 P Legth(μm) ε ε y ε Iitial Load(MPa) Wavelegth(m) (c) (d) Fig.4. The loadig directio is alog Y-ais, Distributio of the strai at the three ais of the FBG with respect to the applied load,(c) Strai at the ceter of the FBG due to lateral loadig, (d)wavelegth shiftig of FBG uder differet magitude stress Case : The loadig compoet directio is alog X-ais ad Y-ais. 7

8 Strai(με) Reflectivity(dB) Strai(με) IEICE Electroics Epress, Vol.* No.*,*-* As show i Fig.5, the specime is subjected to a uais loadig which has the compoets i X-ais ad Y-ais directio, the Z-ais compoet is. The agle betwee the loadig directio ad Y-ais directio is α. Fig.5 shows the strai distributio at the ais of FBG whe the specime is subjected to the loadig whose X-ais compoet ad Y-ais compoet two values are both.1 MPa. I this case, the degree of α is 45. We ca see that the distributio of strai o three ais directio is the same as the case1 (as Fig 4 show), amely the loadig compoet alog X-ais directio has little ifluece o the distributio of strai o FBG. The respose of FBG sesor is simulated at costat weight loadig whe α is 15,3,45,6 ad 75. Fig. 5 (c) shows the variatio of the strai at the ais of the FBG with respect to the differet agles applied load. It is observed that ɛ ad ɛ y are superimposed ad shifts almost at the same rate with respect to the applied load. The differece betwee the two is so little,it still caot cause apparet peak splittig. The shapes of the reflectio spectrum have little chage compared with the iitial. There is o reflectio spectrum badwidth broade ad peak spitted. Fig.5(d) shows strai correspodig optical spectral wavelegth uder differet agles. It ca be see that the absolute value of three aes strai ɛ,ɛ y ad ɛ are all decreasig with the icrease of α.as a result, the wavelegth drifts toward the icreasig as the α icreases. y - ε ε -4-6 ε y Py P α P Legth(μm) - -4 ε Iitial ε y - -8 ε (deg) (c) Wavelegth(m) (d) Fig.5. The loadig compoet directio is alog X-ais ad Y-ais, Distributio of the strai at the three aes of the FBG with respect to the applied load,(c) Strai at the ceter of the FBG due to lateral loadig,(d) Wavelegth shiftig of FBG uder differet agle stress Case 3 The loadig compoet i three directio all eist. 8

9 Strai(με) Reflectivity(dB) Strai(με) IEICE Electroics Epress, Vol.* No.*,*-* Aalysis by Case ca be see, the loadig compoet alog X-ais directio has little ifluece o the distributio of strai o FBG. Whe the specime is subjected to a loadig whose compoet i three directios all eist, this ca be simplified that the specime is subjected to a uais loadig which has oly the compoets i Y-ais ad Z-ais directio, the X-ais compoet is (see Fig.6 ). The agle betwee the loadig directio ad Y-ais directio is α. Fig.6 shows the strai distributio at the ais of FBG whe the specime is subjected to the loadig whose Z-ais compoet ad Y-ais compoet two values are both.1 MPa. I this case, the degree of α is 45. It could be see that the distributio strai i the Z-directio ɛ o the FBG approimates liear fuctio. At the cetre of FBG, the magitude of aial strai is whereas the radial strais i the X- ad Y-directios are oly ad , respectively. The respose of FBG sesor is simulated at costat weight loadig whe α is 15,3,45,6 ad 75. Fig.6 (c) shows the variatio of the strai at the ais of the FBG with respect to the differet agles applied load. It ca be see that ɛ ad ɛ y are superimposed ad shifts almost at the same rate with respect to the applied load. The differece betwee the two is still so little, it caot cause apparet peak splittig. Fig.6(d) shows strai correspodig optical spectral wavelegth uder differet agles. The shapes of the reflectio spectrum all broade with the icrease of the agle α. The badwidths value at - db as the table Ⅱ show. Table Ⅱ The badwidths value at - db i differet agle α Origial Badwidth at - db (m) y ε -8 ε y - -4 Py α P P Legth(μm) ε Iitial (c) α,deg ε ε y ε Wavelegth(m) (d) 9

10 F(N) IEICE Electroics Epress, Vol.* No.*,*-* Fig.6. The loadig compoet directio is alog X-ais ad Y-ais, Distributio of the strai at the three ais of the FBG with respect to the applied load, (c) Strai at the ceter of the FBG due to lateral loadig, (d) Wavelegth shiftig of FBG uder differet agle stress Accordig to aalysis for the respose of the sesor i above three cases, it ca be cocluded that the stress perpedicular to the bodig iterface (the force i the Y-ais directio) affects the drift of the ceter wavelegth of the sesor, the two are iversely proportioal to the liear relatioship. The sesor is ot sesitive to stress respose i the X-ais directio ad which ca be egligible i the testig. Ad the stress i the aial directio of the fiber (the Z-ais directio stress) may causes a large stress gradiet to appear o the gratig because the strai distributes ouiformly o the FBG. It results i the wideig of the reflected wave of the FBG sesor. Take advatage of the FBG sesor respose, we ca locate the debodig i the SRM iterface i Fig.. Whe debodig occurs betwee the sesors 1 ad positios, the iterfacial adhesio stress chages with the chage of temperature aroud the SRM. The amout of chage i the bod stress at the 1 ad positios differet from the amout of chage i the adhesive stress at the 3 ad 4 positios. Whe the defect is relatively large, the positio ear debodig of the sesor will form a large strai gradiet caused by stress i the directio of the gratig, the the sesor reflectio wave shape will appear wideig pheomeo. 4 Eperimets The FBG sesig system used i this eperimet is show i Fig.7. Stepwise stress tesile tests were made to validate the respose of the sesors embedded. As the Fig.7 show, the cycle loadig ad uloadig eperimet were doe with three cycles, maimum loadig is 35N ad the magitude of stepwise loadig is 7N. A set of graphs of stress-peak wavelegth of FBG sesor uder aial ad uaial cyclig loadigs for the double plate test specime were obtaied load Circulator 5 15 ASE Light Source 1 5 Fig.7. test Moitorig system of chages i the reflectio, Method of cycle loadig Times As the Fig.8 show, peak shift with respect to applied load i ais tesile test. The curves appear dowward tedecy after every cycle result for the character of viscoelastic for HTPB solid propellat. This suggests that the specime i the process of loadig ad uloadig eperimet the iterface bod stress chage take place which ca be measured by the ceter wavelegth of FBG. It is very 1

11 IEICE Electroics Epress, Vol.* No.*,*-* useful to determie the quality of bodig iterface i the log term health moitorig of SRMs. Fig.8 shows the relatioship betwee the ceter wavelegth of FBG ad tesile stress whe tesile stress directio has a agle betwee the Y-ais. I this eperimet the agle is 39. It is the same as case3 which loadig compoet directio is alog -ais ad y-ais. I the eperimet, the compoet of loadig i Z directio is so little that we caot observe the shapes of the reflectio spectrum broade. However, with the icrease of tesile stress, the spectrum will evetually appear broadeig pheomeo. I order to fid out the relatioship betwee the aial tesile data ad the o-aial tesile data, the mea values of the FBG ceter wavelegths uder the same stress are obtaied for the two eperimetal data. The relatioship of average ceter wavelegth betwee tesile stress ad compariso with aalytical value ca be show as the Fig.8(c). The wavelegth-stress curve ca be show by i four oblique lies. It ca be see that the absolute value of the lie gradiet of aalytical are larger that of the test. The mai reaso for this is that the materials such as propellat, polymer coatig, Isulatio ad adhesive layer are high-molecular polymer which have the properties of viscoelastic materials. The viscoelasticity of material whose elasticity modulus decrease with time whe the stress is costat. The relatio betwee elasticity modulus ad time ca be epressed by proy format: t E( t ) = E + Eiep( - ) (13) t E i=1 i Where Et () is the relaatio modulus, E is the equilibrium modulus, t E i relaatio times for each Proy compoet, Ei is relaatio kerel elastic moduli. The viscoelastic material s elasticity modulus for simulatio is the equilibrium modulus E which is less tha real modulus i the tesile test. Accordig to the sesor strai trasfer model, whe the elastic modulus of each layer decreases, the strai of the gratig icreases, which leads to the absolute value of the lie gradiet of aalytical are larger tha that of the test. As the table Ⅲ show, the liear fittig (y =a+b) of relatioship of average ceter wavelegth betwee tesile stress has bee carried out. It ca be see that the liearity is up to.99, which shows there is a good liear relatioship betwee the average ceter wavelegth of FBG ad tesile stress. Where b value represets the ceter wavelegth variatio with load icremet, the ratio of two is.777 which just equal to the cos39. A coclusio ca be draw that the variatio of ceter wavelegth is oly related to the loadig s compoet of Y ais whe the shape of spectrum does t apparet sigificat broadeig. 11

12 Wavelegth(m) Wavelegth(m) Wavelegth(m) IEICE Electroics Epress, Vol.* No.*,*-* First cycle(load) First cycle(uload) Secod cycle(load) Secod cycle(uload) Third cycle(load) Third cycle(uload) First cycle(load) First cycle(uload) Secod cycle(load) Secod cycle(uload) Third cycle(load) Third cycle(uload) Load(MPa) Load(MPa) Liear fit of aial test Aalytical value of aial test Liear fit of uaial test Aalytical value of uaial test Load(MPa) (c) Fig.8. Peak shift with respect to applied load i ais tesile test, Peak shift with respect to applied load i uais tesile test, (c) Relatioship of average ceter wavelegth betwee tesile stress ad compariso with aalytical value Table Ⅲ Fittig parameters ad liearity Test Parameter A Parameter B Liearity Aial Uaial Coclusio I this paper, the strai distributio of the adhesive specime uder differet directio forces are simulated by fiite elemet method, ad the respose of FBG spectrum are simulated. The results show that the desig of the FBG sesor ceter wavelegth ca effectively reflect the chage of the iterface bodig stress (the compoet i the Y-ais directio). The sesor is ot sesitive to the stress i the X-ais directio. However, the FBG spectrum will broade whe a large stress gradiet is i Z-ais directio. Accordig to the arragemet of sesors i Fig FBG sesors evely distributed alog the circumferece of the motor at the propellat/isulatio iterface, we ca determie the approimate positio of the defect by the chage of FBG ceter wavelegth which chage with the variatio of bod stress. Whe there is a large stress gradiet i circumferetial directio, it ca be reflected from the reflectio spectrum. Ackowledgmets The paper is fiacially supported by the Natioal Scietific Support program of Chia (Grat No ). 1