Evaluating high temperature elastic modulus of ceramic coatings by relative method

Transcription

1 Journal of Advanced Ceramic 7, 6(4): 88 ISSN CN -54/TQ Reearch Article valuating high temperature elatic modulu of ceramic coating by relative method Guanglin NI, Yiwang BAO *, Detian WAN, Yuan TIAN State Key Laboratory of Green Building Material, China Building Material Academy, Beijing 4, China Received: June 6, 7; Revied: Augut 7, 7; Accepted: Augut 9, 7 The Author() 7. Thi article i publihed with open acce at Springerlink.com Abtract: The accurate evaluation of the elatic modulu of ceramic coating at high temperature (HT) i of high ignificance for indutrial application, yet it i not eay to get the practical modulu at HT due to the difficulty of the deformation meaurement and coating eparation from the compoite ample. Thi work preented a imple approach in which relative method wa ued twice to olve thi problem indirectly. Given a ingle-face or double-face coated beam ample, the relative method wa firtly ued to determine the real mid-pan deflection of the three-point bending piece at HT, and econdly to derive the analytical relation among the HT moduli of the coating, the coated and uncoated ample. Thu the HT modulu of the coating on beam ample i determined uniquely via the meaured HT moduli of the ample with and without coating. For a ring ample (from tube with outer-ide, inner-ide, and double-ide coating), the relative method wa ued firtly to determine the real compreion deformation of a plit ring ample at HT, econdly to derive the relationhip among the lope of load-deformation curve of the coated ring, the HT modulu of the coating and ubtrate. Thu, the HT modulu of ceramic coating can be evaluated by the ubtrate modulu and the load-deformation data of coated ring. Mathematic expreion of thoe calculation were derived for the beam and ring ample. CVD-SiC coating on graphite ubtrate were elected a the teting ample, of which the meaured modulu ranging from room temperature to demontrated the validity and convenience of the relative method. Keyword: elatic modulu; ceramic coating; high temperature (HT); relative method; SiC Introduction Ceramic coating have attracted coniderable attention of material cientit and mechanical engineer due to their wide application in aeropace, aviation, energy, petrochemical, and chemical indutry field to withtand high temperature (HT) [ ]. The HT ceramic coating are ued for three main function, viz. ) to protect the ubtrate againt corroion or * Correponding author. -mail: ywbao@ctc.ac.cn oxidation; ) to minimize the wear; ) to reduce the heating damage of ubtrate [4 8]. The HT elatic modulu of coating i one of the important parameter for the ecurity and reliability of coating/ubtrate compoite component. For example, the level of reidual tre i influenced by the mimatch of elatic modulu between coating and ubtrate material [9], and the trength of the bonded ytem i alo governed by the elatic mimatch []. However, there exit great challenge in evaluating the modulu of ceramic coating, epecially at high and ultrahigh temperature. Previou tudie on the HT elatic modulu of the

2 J Adv Ceram 7, 6(4): ceramic coating mainly involve three apect. ) It i to tudy the effect of HT treatment on the coating modulu. The coating were cooled to ambient temperature after thermal expoure at HT, and the modulu wa determined by ultraonic or nanoindentation method at room temperature [,]. ) It i to meaure the HT modulu of the free-tanding coating by common tet method ued for bulk material after tripping the coating from the ubtrate [ 5]. Yet it i difficult for thin ceramic coating becaue mot of them are tightly bonded on ubtrate and hardly eparated from the ubtrate. ) It i to utilize the indentation method directly to evaluate HT modulu of coating at temperature below [6 8]. However, the drawback tem from the oxidation, eroion, and tiffne degradation of the indenter at HT that affect deeply the meaurement [9,]. Additionally, the indention method only meaure the local modulu that i different from the practical modulu, epecially when the coating tructure i inhomogeneou []. Therefore, it i urgent and ignificant to develop feaible approache to evaluate the practical elatic modulu of ceramic coating at high or ultrahigh temperature. Uually, the product form of HT component with coating are plate or tube. For example, the blade of the ga turbine engine, with urface thermal barrier ceramic coating, are plate-like tructure []. And part of the wing leading edge on re-entry vehicle with protective coating are platy in tructure []. In addition, the coated tubular component are often ued at HT and the coating are required to be on the inide or outide urface of the tube. For intance, the thermal prayed coating are on the out wall of boiler tube [4,5], and ome HT coating are on the inner urface of the nozzle wall, gun barrel, and engine cylinder liner [6 ]. Alo the enamel coating are applied on both inide and outide urface of the combutor liner []. For the coating on the tubular or circular part, they are hardly machined into the beam or plate ample. It i of great ignificance to tet the elatic modulu of the tubular coating without changing the hape of the component. Therefore, it i in great need to develop method to meaure the elatic modulu of coating on beam and tube ample. Since conventional method i difficult to meaure the modulu of ceramic coating at HT, the relative method i conidered a an effective olution. The relative method i a kind of technical conideration of an indirect tet, in which the le meaurable parameter can be determined from the directly tetable parameter [ 4]. The bending method and plit ring method are uually ued to meaure the modulu of monolithic beam and ceramic tube at room temperature, repectively [5 8]. In thi work, the bending method and relative method were combined together to etimate the HT elatic modulu of coating on beam ample, and the HT modulu of coating on ring ample wa determined by uing the plit ring method and relative method in combination. By comparing the difference between the cro-beam diplacement of tet ample and rigid reference piece under the identical load [9], the relative method wa utilized for the firt time to obtain the accurate deflection or deformation of the bending piece or plit ring ample at HT. Thu, the HT modulu of coated and uncoated ample can be meaured. And the relative method wa ued for the econd time to deduce analytical formula of the coating modulu from the comparion between the mechanical repone of coated and uncoated ample. The approach need to ue relative method twice in the preent reearch and it i convenient and reliable for determining HT elatic modulu of ceramic coating. The main meauring tep of thi method are: ) determining the real HT deformation of tet ample by the relative method via three-point bending tet or plit ring compreing experiment, ) evaluating elatic modulu of the monolithic beam or plit ring ample through the load and accurate deformation, and ) evaluating elatic modulu of coating via the deduced analytical relation. Baic principle. Determining HT elatic modulu of coating on beam ample For a beam ample, the three-point bending tet i widely ued to evaluate the elatic modulu through the ratio of load-increment P to deflection increment f []: L P () 4Hb f where L i the pan in mm, H and b are the thickne and width of the ample in mm repectively. When the unit of P i N and the unit of f i mm, the unit of the calculated modulu i MPa.

3 9 J Adv Ceram 7, 6(4): 88 f can be obtained by the accurate inductance micrometer or other diplacement meter at ambient temperature. However, f i hardly meaured by the device in harh thermal environment directly. In order to acquire the accurate mid-pan deflection at HT, a imple relative method i introduced. Baed on the relative method, a bending tet ample with two upport bar and a reference ample without upport bar hould be the ame ize and loaded under the identical teting condition, a hown in Fig.. Two diplacement of the cro-beam, f and f, will be obtained for the tet ample (Fig. (a)) and the reference ample (Fig. (b)) under the ame P. Since the bending deformation of the reference ample can be ignored, f can jut repreent the ytematic error of loading Fig. Tet chematic illutration of the real high temperature deflection: (a) normal three-point bending tet, (b) error corrected tet. ytem generated by the teting ytem flexibility and the contact diplacement of pecimen and fixture. Thu, the difference of cro-beam diplacement between the tet ample and reference ample, denoted a f f, i equal to the real deflection of the bending pecimen under the given load-increment. The HT elatic modulu of beam ample can be determined via the following equation: L P H 4H b f f () here, H i the HT elatic modulu of the beam piece in MPa. In thi work, two common coating pattern on beam were dicued: ) ingle-face coating (Fig. (a)) and ) double-face coating (Fig. (b)). To get the accurate deformation of the coated beam ample at HT, the reference pecimen with the ame ize a the coated tet piece are needed. In the preent reearch, the elatic moduli of the uncoated and coated ample were defined a and, repectively. q and q can be meaured by q. () at HT. Let the modulu of coating be. f The ratio of modulu wa defined by /. f.. Determining HT modulu of ingle-face coating on beam ample For the ingle-face coated piece a hown in Fig. (a), it HT elatic modulu ( q ) can be obtained by uing the relative method and q. (): Fig. Schematic illutration of cro-ection of beam pecimen with different coating configuration: (a) ingle-face coating, (b) double-face coating. Fig. Schematic of the cro-ection tranformation of a ingle-face coated ample: (a) heterogeneou cro-ection, (b) homogeneou ection.

4 J Adv Ceram 7, 6(4): 88 9 L P 4 H h b f f q q q () Here, b i the width of the coated piece, H and h the thickne of the ubtrate and coating repectively. fq and fq are the deflection increment of the tet coated piece and reference ample under the ame load increment ( P ), repectively. Baed on the material mechanic, the heterogeneou cro-ection (Fig. (a)) can be converted into the homogeneou one (Fig. (b)) conited only of the ubtrate material by the principle of equivalent tiffne [4]. vidently, the bending tiffne of the heterogeneou cro-ection beam ample i the ame a that of the homogeneou ection beam pecimen. Naturally, the mid-pan deflection of the two beam ample will be equivalent under the ame load. PL PL f 48 I 48 I (4) q Here, I i the inertia moment of the heterogeneou beam ample with coating, I the inertia moment of the equivalent homogeneou ample, and f the mid-pan deflection. quation (4) can be implified to q I I (5) Baed on the theory of material mechanic [4], I and I have the form: I bh h H h I bh bh bhh 4 H h (6) Combining q. (5) and q. (6), a implified relation i derived by (7) 4 where h, qh H h hh Hh HhH h, 4 and qh H h H. A q and can be obtained by q. () at HT, i determined by the following equation: 4 (8) Hence, the modulu of the coating i calculated by f 4 4 (9).. Determining HT modulu of double-face coating on beam ample For the double-face coated ample a hown in Fig. (b), the elatic modulu of the compoite ytem ( q ) can be meaured by the relative method and q. (): L P q () 4 H h h b f f Here, h and h are the thickne of the upper and lower coating, repectively. According to the equivalent tiffne concept [4], the heterogeneou cro-ection (Fig. 4(a)) can be converted into the homogeneou one (Fig. 4(b)) for which the width of coating i multiplied by time and the modulu of the homogeneou piece ha the ame value a the ubtrate. The ditance from the lower coating urface (tenile urface) to the neutral axi, y c, ha the form: H h hh h h H h yc () h h H Baed on the theory of material mechanic [4], the inertia moment of the heterogeneou and homogeneou ection, I and I, have the form: I bh h h q q Fig. 4 Schematic of the equivalent cro-ection tranformation of a double-face coated ample: (a) heterogeneou cro-ection, (b) homogeneou ection.

5 9 J Adv Ceram 7, 6(4): 88 h H c c I bh bh y bh bh h y h bh bh H h yc () The coated beam with ection Fig. 4(a) and Fig. 4(b) ha the ame tiffne. A implified relation i derived by ubtituting q. () into q. (5). () 4 where 4 are the coefficient of the cubic equation of one unknown and can be calculated by b bhh h h H h h h h h h bhh H H h h bh h hh h bh h h H h h b q H h h H h h Hbh h H h h h h H bh q H h h H h h bh q 4 H h h H (4) Thu, the value of can be obtained by olving q. () via the calculator of univariate cubic equation or MATLAB oftware, noting that i a real number and >. Then the HT modulu of coating can be evaluated by f. Obviouly, the HT elatic modulu of coating on beam piece can be evaluated by the coated ample geometrical dimenion and the HT modulu of the coated and uncoated ample. Notably, the relative method i ued twice, i.e., firt to meaure the HT modulu of the coated and uncoated ample via q. (), and then to evaluate the HT elatic modulu of coating via q. (9) or q. (). The three-point bending experiment for determining the HT modulu of coating by thi novel relative method are performed in the following tep: ) remove the coating and prepare the ubtrate ample by grinding or cutting, ) manufacture the reference ample which have the ame ize a the ubtrate and coated ample, ) record the cro-beam diplacement of the tet piece and reference ample under identical load-increment at the ame etting temperature, 4) calculate the HT modulu of ubtrate and coated ample by q. (), and 5) finally calculate the value of f by q. (9) for ingle-face coating or q. () for double-face coating.. Determining HT elatic modulu of coating on ring ample The accurate evaluation of the modulu of the tet piece i very crucial to the determination of the coating modulu. According to the reearch reult of Ref. [], the ratio of q to ( q / ) ha a ignificant influence on the value of. For intance, the value of calculated by the meaured q / of.4 i.9% higher than that computed by the meaured q / of., with h/ H value of.5. That i, only 9.9% increae of the meaured q / lead to.9% rie of the calculated value of for the compoite with a thin coating. So the accurate meaurement of the modulu of uncoated and coated piece ha a ignificant impact on the etimation of the modulu of coating. The more accurate tet reult of elatic modulu of the tube or ring material will be obtained by the plit ring compreing tet with the conideration of the effect of axial and hear tre. That i, the plit ring pecimen i uffered with bending moment, axial and hear tre under the compreive load. According to the force analyi of plit ring ample a hown in Fig. 5, the internal force of any ection of the ample have the form: N Pin, Q P co, M PR in (5) where N i the axial force, Q the hear force, M the bending moment, P the applied load, the angle between the cro-ection and the vertical line, and R the curvature radiu of geometrical centroidal axi of the cro-ection. Take the derivative of the above internal force by the Fig. 5 Schematic diagram of force analyi of the plit ring pecimen.

6 J Adv Ceram 7, 6(4): 88 9 applied load: N Q M in, co, R in (6) P P P The deformation energy of the plit ring ample in the compreion proce can be determined by the following equation: π M MN N kq U R d SR AR A GA (7) here, i the elatic modulu, S the tatic moment of the entire cro-ection to the neutral axi, G the hear modulu, k a geometric contant dependent on the hape of cro-ection. Baed on the material mechanic [4], k =. for a rectangular ection. Baed on Catigliano theorem [4], the vertical diplacement of the force acting point during elatic deformation range i derived by U π M M M N M M P SR P AR P AR P N N kq Q R A P GA P d (8) Combining q. (6) and q. (8), and noting that G /, a general expreion for can be obtained: πr P R.4.4 A e (9) where P / i the lope of load-diplacement curve during the elatic deformation range, e the ditance between the geometrical centroidal axi and neutral layer, A the area of the cro-ection, Poion ratio of material. Poion ratio of. i ued for mot brittle material, uch a ceramic and gla. And the parameter in q. (9) can be determined via the geometrical dimenion of the ample: R r R r R r R, A br r, e () R ln r where R i the outer radiu, r the inner radiu, and b the width (axial length) of plit ring pecimen. Thu to obtain the accurate HT deformation of the ample, i een a the critical iue for evaluating the HT elatic moduli. Baed on the relative method [9], a rigid dik which ha the ame outer diameter and width a the plit ring tet piece i conidered a the reference ample. At HT, the real deformation of a tet piece can be obtained through comparing the meaured cro-beam diplacement between the tet piece and a reference pecimen under the ame load, a hown in Fig. 6. Two cro-beam diplacement, and, will be obtained for the plit ring and rigid dik under a fixed load-increment, P, repectively. The tiffne of the rigid dik i much higher than that of the plit ring piece, o the deformation of the rigid dik under P can be ignored and it cro-beam diplacement ( ) can repreent the ytematic error of loading ytem which are induced by the loading frame, fixture, loading device, and contact deformation. Thu, the difference of the diplacement between the plit ring and the rigid dik i equal to the real deformation of the plit ring tet piece at HT. () By ubtituting q. () into q. (9), the HT modulu of the tet piece can be obtained: πr P R H.4.4 () A e where H i the elatic modulu of tet pecimen at HT. In thi work, three common coating pattern on tube were dicued: outer-ide coating (Fig. 7(a)), inner-ide coating (Fig. 7(b)), and double-ide coating (Fig. 7(c)). To get the accurate deformation of the coated plit ring ample at HT, the rigid reference dik with the ame outer radiu and width a the coated piece are needed... Determining HT modulu of outer-ide coating on ring ample For a plit pecimen with outer-ide coating a hown in Fig. 7(a), a relationhip between the modulu of the ubtrate, P /, and geometrical dimenion of coated ample can be obtained by rearranging q. (9) baed on the concept of equivalent tiffne. Fig. 6 Schematic diagram of (a) the plit ring and (b) the rigid reference dik.

7 94 J Adv Ceram 7, 6(4): 88 Fig. 7 Schematic illutration of plit ring pecimen with (a) outer-ide coating, (b) inner-ide coating, and (c) double-ide coating. Here, R R.4.4 π P A e i the modulu of the ubtrate, () the real compreion deformation of the ubtrate/coating compoite ytem, R the curvature radiu of geometrical centroidal axi of the homogeneou equivalent cro-ection of the coated ample, e the ditance between centroidal axi and neutral layer of the equivalent compoite cro-ection, and A the area of the equivalent compoite cro-ection. Auming the cro-beam diplacement of coated ample i under the fixed load-increment P at HT, the real HT deformation of the coated piece i, and q. () can be rewritten a H R R.4.4 π P A e (4) where H i the HT modulu of the ubtrate. A hown in Fig. 7(a), r i the inner radiu of the ubtrate, R i the outer radiu of the ubtrate, R c i the outer radiu of the outer-ide coating, and b i the width of compoite pecimen. Through the geometrical analyi of the compoite ection, the calculation formula of R, e, and A are acquired via a method of equivalent tiffne. hh.5h.5h R r H h hh.5h.5h h H e r H h R R h ln ln r R A bh bh (5) Here, H i the thickne of the ubtrate and H R r, h i the thickne of outer-ide coating and h Rc R. Combining q. (5) and q. (4), a relationhip among, P /, and i given by H (6) where 5 are contant determined by B B7 B4 B8 h HhB B7 B B B H B B h HhB h B B8 BB BB B4 B8 H 5 B5 B9 H BB HhB5 B9 BB B 4 B (7) Hb R where B, B ln, B π P r R h ln, B Hh h, B 4 H, B5 BB4 R rh.4.4 r, B6 BB Brh, B7 Bh, B B Hh.4. B hr, B B H. B 8 4.4B Hr, B.4.4B B B4 rbh rhb B Hr B 4 B rB h,, B. 4 B4 8 4, B B6, B4 BB 6 B B 5, B5 B B5. Thu, the value of can be obtained by olving q. (6) via the calculator of quartic equation or MATLAB oftware, noting that i a real number and >. Then the HT modulu of coating can be evaluated by (8) f H.. Determining HT modulu of inner-ide coating on ring ample For a plit ring piece with inner-ide coating a hown in Fig. 7(b), auming it cro-beam diplacement i 4 under the fixed load-increment P at HT, the real HT deformation of the coated piece i 4. Thu, q. () can be rewritten a

8 J Adv Ceram 7, 6(4): H 4 R R.4.4 π P A e (9) A hown in Fig. 7(b), r c i the inner radiu of the inner-ide coating. The geometrical analyi of the compoite cro-ection i conducted and R and e have the form:.5 h.5h hh R rc H h.5h.5h hh hh e rc () H h R r ln ln r rc here, H i the thickne of the ubtrate and H R r, h i the thickne of the inner-ide coating and h r r c. Combining q. (9) and (), a implified relation among H, P /, and i derived by 4 () 4 5 where 5 are the coefficient of the quartic equation and can be calculated by C C7 C4 C8 h HhC C7 C4 C C H C C h HhC h C C8 CC CC 4 4 C8 H C HhC 5 C9 CC C4 C5 C9 H C 4 C () 5 C where C C H Hb 4, π P R Hh, C ln r, 4 C h, C.4.4 C C C C rh r, 5 c c C6 CC Crh c, 7 Ch C, C C Hh C rh, 8 c C C H C rh, 9 c C C rch, c c c ln r, rc C CC rc H rc h, C C rc H, c C C4C6, C4 CC6 C4C5, C5 CC5. Thu, can be obtained by olving q. () and the HT modulu of inner-ide coating i determined by. f H.. Determining HT modulu of double-ide coating on ring ample For a plit ring piece with double-ide coating a hown in Fig. 7(c), auming it cro-beam diplacement i 5 under the fixed load-increment P at HT, the real HT deformation of the coated piece i 5. Thu, q. () can be rewritten a H 5 R R.4.4 π P A e () A hown in Fig. 7(c), r c i the inner radiu of the inner-ide coating and R c i the outer radii of the outer-ide coating. H i the thickne of the ubtrate and H R r. h ( h R c R ) and h ( h r r c ) are the thickne of the outer-ide and inner-ide coating, repectively. The geometrical analyi of the compoite cro-ection i conducted and, A, R, and e have the form: A bh b h h R H h h H hh h h H.5h h.5h H h H h.5h rc.5h h.5hh h H h.5h e rc (4) Rc r R ln ln ln R rc r Combining q. () and (4), a implified relation among, P /, and i derived by H (5) where 5 are the coefficient of the quartic equation and can be calculated by D D 6 D7 DD DD4 D6 D D5 D D D D D D D D D D D D D D D 5 4 6D D7 D D4 DD4 5 D8 D D4 D6D5 D8 D D5D5 D6 4 4 D (6) Hb 5 where D, D h π P h h H h, H D Hh, D h h,

9 96 J Adv Ceram 7, 6(4): 88 D H R r R D ln ln, D ln r c 4, 5 R rc 6, D7 DD DDr c, D8 DD DDr 4 c, D9 D8.4.4r c, D DD, D DDD 4.4.4D Dr c, D D D4.4.4 D Dr 4 c, D.4.4 D DDr c, D D D D D r DD r, D.4.4 D DDr 4 c D, D c 4 c 5, 6 D5D7 7 D5D9 D6D7, D8 D6D9. Thu, can be obtained by olving q. (5) and the HT modulu of inner-ide coating i determined by f H. Obviouly, the key for evaluating the HT modulu of the coating on tube i to obtain the accurate deformation of coated and uncoated ample, and the analytical relation among H, P /, and. Relative method can be ued to determine the HT modulu of the ubtrate via q. () for the firt time, and then to meaure the HT elatic modulu of coating via q. (6) (8) for the outer coated piece, q. () and () for the inner coated ample, and q. (5) and (6) for the double coated pecimen. The plit ring compreing tet for determining the HT modulu of coating by the relative method are performed in the following tep: ) prepare the ubtrate, compoite piece, and rigid dik which have the ame geometrical dimenion a the ubtrate and coated ample, ) heat the ubtrate and rigid dik to the etting temperature and compre the ample in the elatic deformation range, ) record the cro-beam diplacement of the ubtrate and reference piece and calculate the HT modulu of the ubtrate via q. (), 4) compre the coated ample and rigid dik at HT and record each cro-diplacement, 5) ubtitute the meaured data and the geometrical dimenion of the coated piece into q. (6) (8), () and (), and (5) and (6), 6) olve the q. (6), (), and (5). Thu, the HT moduli of coating can be got by. Material and experimental proce f To check the reliability of the relative method, ilicon carbide (SiC) coating prepared by uing chemical H vapor depoition (CVD) method on graphite ubtrate were ued a the teting ample. Graphite i an attractive material for HT application and ha been widely ued a tructural material due to the excellent HT mechanical propertie [4,4]. And SiC i being conidered a a protective coating to protect the graphite from oxidation [44,45] due to it excellent and uperior propertie of melting point, thermal hock reitance, and chemical inertne [46]. The mechanical propertie of SiC coating are the eential prerequiite for achieving it functionality. Among them the HT elatic modulu of uch coating material i of high importance, becaue it will determine the value of thermal reidual tre which appear upon heating or cooling [47], define the lifetime of the material, and play a major role in the reliability of the component a a whole. Wherea the in itu, accurate, and reliable elatic modulu of SiC coating at high and ultrahigh temperature have not been dicued o far. The homogeneou graphite wa prepared by iotatic preing method, while the CVD-SiC coating were fabricated by pyrolyi of methyltrichloroilane (MTS) in hydrogen (H ) at and 5 Pa for h with the coating thickne of about 6 μm for the beam ample and 4 μm for the ring piece. During the preparation of SiC coating, the MTS flow rate wa.75 L/min and the volume ratio of H to MTS wa controlled at : by a flowmeter. The prepared CVD-SiC coating are polycrytalline tructure a hown in Ref. [48], and the main phae i β-sic. In order to obtain the reliable data, the ratio of the coating thickne to the ubtrate thickne hould be larger than /, and the thickne of the coating hall be larger than μm. The ample dimenion were meaured by a vernier caliper, and the average ize of beam and ring ample i about 6 mm (length) mm (width) mm (thickne) and mm (inner radiu) 5 mm (outer radiu) 7. mm (width), repectively. Furthermore, all the ring pecimen were cut with the plit of 6 mm. At leat three ample hould be teted to obtain an average value. The rigid dik with the ame outer radiu and width a the plit ring ample wa made of graphite. The thickne of the SiC coating wa meaured by the digital microcope (VHX-6, KYNC, Japan). Microtructure were examined uing a canning electron microcope (S-48, Hitachi, Japan). The phae analyi and crytalline tructure of the SiC coating were invetigated uing an X-ray diffractometer (D8 ADVANC, Brucker Corporation).

10 J Adv Ceram 7, 6(4): The upport pan for the three-point bending tet wa 5 mm. The lower and upper limit of the load were 5 N and 4 N for the bending tet and plit ring compreing experiment, repectively. The loading rate wa controlled at. mm/min by the cro-beam diplacement for the both experiment. It i emphaized that, before the HT loading tet, the accuracy of cro-beam diplacement hould be calibrated by uing an accurate inductance micrometer (MT, Qinghai Meauring & Cutting Tool Group Company, China) in order to enure the reliability of meaured reult. An empirical deviation within.5% would be acceptable in thi work. The elevated temperature teting wa performed in graphite heater furnace capable of reaching temperature of under high vacuum (lower than Pa). The temperature below were meaured by thermocouple inerted from the ide of the furnace and the temperature exceeding were meaured by an optical pyrometer. The furnace hall be capable of heating the tet fixture, puhing rod and tet piece a well a maintaining a uniform and contant temperature during the tet. The heating rate for all elevated temperature tet wa /min followed by a min iothermal hold at the deired temperature. The HT loading experiment were performed by the mechanical teting intrument (DSZ-III, China Building Material Tet & Certification Center, China). In order to verify the validity of the relative method, the teted reult of the coating modulu meaured by an inductance micrometer were compared with that evaluated by the difference of cro-beam diplacement at room temperature. The room temperature loading tet were carried out by the univeral mechanical teting machine (MTS Criterion C45, MTS Sytem Corporation, America) with the cro-head peed of. mm/min. The mid-pan deflection and the vertical diplacement of the loading location were teted by an inductance micrometer at ambient temperature. Fig. 8 Cro-ection micrograph of the SiC coated graphite. happen to change gently at the interface and the above mathematical derivation can be ued effectively to evaluate the modulu of SiC coating. In order to verify the validity of the relative method combined with the three-point bending tet at room temperature, the mid-pan deflection of the beam ample were determined directly by an inductance micrometer and teted indirectly via the difference of the cro-beam diplacement between the bending ample and reference piece. Both the elatic modulu of graphite ubtrate and SiC/graphite compoite ytem were calculated by q. () via uing the micrometer and q. () via the cro-beam diplacement, with the teted reult hown in Fig. 9. Both of the teted modulu of graphite ubtrate and SiC/graphite compoite are baically the ame. Plugging the teted data and the dimenion of compoite into q. (9), the modulu of SiC coating could be obtained. The mean value of 4 Reult and dicuion 4. Validity of the relative method The graphite beam and ring ample coated with SiC coating were ued in thi work. Figure 8 how the cro-ection micrograph of the coated piece. The boundary between the coating and ubtrate can be een obviouly and well connected with each other, with the dene SiC coating on the left ide, which mean that the coating i tightly integrated with the ubtrate and no lip occurred at the interface. Thu, the train would Fig. 9 latic modulu of graphite ubtrate and SiC/graphite compoite at room temperature meaured by three-point bending tet.

11 98 J Adv Ceram 7, 6(4): 88 elatic modulu of SiC coating wa etimated a 7.7±8. GPa via the micrometer (the relative method wa ued only once) and 9.±.76 GPa via the cro-beam diplacement (the relative method wa ued twice). The teted modulu of SiC coating how a tiny deviation of 4.8% at room temperature. It ha revealed that the approach which need to ue the relative method econdly i valid and reliable to determine the elatic modulu of coating by the three-point bending tet. To verify the validity of the relative method combined with the plit ring compreing tet at room temperature, the vertical diplacement of the loading location wa determined by the micrometer and the cro-beam diplacement difference, repectively. The elatic modulu of the graphite ubtrate wa obtained by q. (9) via uing micrometer and q. () via the cro-beam diplacement difference. The outer-ide coating modulu wa obtained by ubtituting the teted ubtrate modulu, vertical diplacement, and geometrical dimenion of the SiC/graphite compoite plit ring piece into q. (6) (8). And the inner-ide coating modulu wa calculated by q. () and (). The teted and calculated data of the SiC/graphite compoite are diplayed in Table. The mean value of the elatic modulu of the outer-ide SiC coating were etimated a 8.69 GPa teted and 87. GPa by the micrometer and cro-beam diplacement difference, repectively. Both of the two teted reult are cloe and within the acceptable error range. The elatic modulu of the inner-ide SiC coating meaured by the micrometer wa GPa which i very imilar to that meaured uing the cro-beam diplacement difference (8.78 GPa). Table Meaure data of SiC coated on graphite ubtrate Outer-ide b H h f (GPa) f coating (mm) (mm) (mm) (mm) (mm) (GPa) Average 8.69± ±8.8 Inner-ide coating (mm) 4 b H (mm) (mm) (mm) h (mm) f f (GPa) (GPa) Average 78.76± ±5.56 ΔP = 6 N, R c = 5. mm, r c =.95 mm, ν =.. = 9.5±.5 GPa, = 9.6±.6 GPa; the ubcript and refer to the data determined by the micrometer and the difference of cro-beam diplacement, repectively. It can be een that the ytematic error of loading ytem can be repreented by the cro-beam diplacement of the reference ample. The tet reult demontrated that the relative method i valid and reliable to determine the elatic modulu of ceramic coating by comparing to the teted reult via micrometer, alo it can be applied to evaluate the coating modulu at high and ultrahigh temperature. 4. HT elatic modulu of SiC coating evaluated by the relative method The ingle-face coated beam ample and plit ring piece with outer-ide coating were ued to determine the elatic modulu of coating at HT. The temperature dependence of elatic modulu of SiC coating meaured by the relative method i diplayed in Fig.. The modulu of SiC coating meaured by relative three-point bending tet are accordant baically with that teted by relative plit ring compreing experiment from ambient temperature to. The meaured modulu of SiC coating wa 69.8±7.6 GPa and 74.6±6.55 GPa, repectively, by relative three-point bending and plit ring tet at room temperature. And the meaured reult are imilar to the previou data reported by Bellan and Dher (54± GPa) [49], Liu and Xiang ( GPa) [5], and Leien et al. (47 66 GPa) [5] for CVD-SiC. For the relative three-point bending tet reult, the coating elatic modulu increaed nearly linearly to 44.6 GPa at 5, and teadily reduced to 8.5 GPa at 5. Above 5, the coating modulu decreaed quite rapidly to GPa at which declined nearly by 47.% compared with the room temperature modulu. For the relative plit ring compreing meaurement, the imilar temperature dependency of the SiC coating modulu wa alo dicovered a hown in Fig.. The modulu of SiC coating increaed to 48.4 GPa at 5, and then decreaed lightly to 8.88 GPa at 5. Above 5, the coating modulu reduced dramatically to 4.99 GPa at. Alo the comparion among the meaured temperaturemodulu profile and the other meaurement [5 54] i howed in Fig.. The everal other tet have been performed between room temperature and 5, and the ued method (micro-tenile tet, -point/4-point bending tet, and

12 J Adv Ceram 7, 6(4): Fig. Meaured elatic modulu of SiC coating from room temperature to HT from thi work and other previou related meaurement. nanoindentation) can hardly be applied to determine the modulu at the ultrahigh temperature (over 5 ) due to the invalidity of the previou method. The elatic modulu temperature profile teted by thi work and other previou reearche are different a hown in Fig., i.e., the elatic modulu meaured by thi work increaed at firt and then decreaed, wherea the modulu teted by Ref. [5 5] jut decreaed with the rie of temperature. Thi difference i mot probably caued by the different ample condition, i.e., the HT modulu are meaured in itu in thi work, but the free-tanding SiC ample were required to be ued in Ref. [5 5]. The in itu meaurement of the HT modulu of the SiC coating are influenced by the thermal tre generated by the mimatch of the thermal expanion coefficient between the coating and ubtrate material during the coure of heating. Although the in itu meaurement of the coating modulu can be realized by the nanoindentation, the meaurement reult of the nanoindentation [54] how a large catter becaue it allow only the invetigation of the local modulu that are often different from the practical modulu. So the modulu meaured by nanoindentation and relative method are not comparable. Alo, the nanoindentation cannot work at higher temperature due to the oxidation and tiffne degradation of the indenter. The oberved increae and decreae in modulu mut be a reult of change in the microtructure and the tre tate of material. The increae in modulu of SiC coating from room temperature to 5 wa correlated to the thermal compreive tre of the coating during the heating proce. The microtructure and urface morphology of the SiC coating before and after the HT tet wa characterized uing SM. A hown in Fig. (a), the microcrack were oberved on the coating urface. According to the reearch reult of Wei et al. [4], the thermal expanion coefficient of SiC coating wa greater than that of graphite ubtrate. So the coating wa under compreive tre caued by the thermal mimatch during the heating proce and the cloure of microcrack may occur. The improvement in coating modulu wa enabled by the reduction of the micro-defect. When the tet temperature exceeding 5, the coating modulu decreaed gradually due to the progreive weakening of the interatomic bond with the rie of temperature. The trong modulu degradation occurred at temperature higher than 5, a hown in Fig.. Thi behavior wa attributed primarily to grain-boundary liding, thermal oftening, and diffuional creep [55,56]. Simultaneouly, the decreae in coating modulu i accelerated by the relaxation of reidual compreive tre [57] in the SiC coating at HT. From Fig., a ignificant change in urface morphology before and after the HT tet can be een. The grain edge of the coating can be detected clearly (a) (b) Fig. SM image of the SiC coating urface: (a) before the HT tet, (b) after the HT tet.

13 J Adv Ceram 7, 6(4): 88 before the HT tet. However, the urface of the SiC coating i mooth after the HT tet and the material mut generate oftening under the HT environment. The decreae in modulu i enhanced by the oftening of the material. The XRD meaurement before and after the HT experiment are hown in Fig.. The β-sic, tacking fault (SF), and graphite can be detected in the SiC coating before the HT tet, and the α-sic i found in the SiC coating after HT tet, i.e., β-sic wa tranformed to α-sic at elevated temperature during the HT tet. And the planar defect (tacking fault) concentration reduced after the HT tet. The reduction in defect can improve the mechanical propertie of material. However, the progreive weakening of the interatomic bond, thermal oftening, and HT creep can decreae the elatic modulu, and the thermal degradation of the modulu i more obviou than the improvement of the modulu reulted by the defect reduction. Therefore, the HT elatic modulu decreaed with the rie of temperature. A hown in Fig., the meaured reult of HT elatic modulu of SiC coating by relative three-point bending tet were cloe to the teted reult by relative plit ring experiment. The both reult could verify each other and howed the effectivene and correctne of the relative method. 5 Concluion The HT elatic modulu of ceramic coating wa evaluated by uing relative method via the three-point bending tet or plit ring compreing experiment. The relative method wa ued twice: once to determine the real deformation of the tet piece at HT and again to derive the equation for calculating elatic modulu of the ceramic coating via the propertie of the ubtrate and compoite. By thi way, elatic modulu of ceramic coating at high temperature hall be conveniently determined. Baed on the mechanic of material, the analytical equation were derived for two type of coated ytem: ) ingle-face and double-face coating on the beam ubtrate and ) outer-ide, inner-ide, and double-ide coating on the ring ubtrate. At ambient temperature, the deformation of the beam and ring ample, f and, were determined by an inductance micrometer and the cro-beam diplacement difference between the tet ample and rigid reference piece, repectively. Then the modulu of SiC coating on bulk graphite wa calculated by ubtituting the meaured P and f into q. (), (), and (9). And the modulu of outer-ide and inner-ide SiC coating on graphite tube wa calculated by ubtituting the teted P and into q. (6) (8) and () and (), repectively. Both the experimental reult meaured by the micrometer and relative method at room temperature were very cloe with light relative deviation only, and how the validity of the relative method for evaluating the elatic modulu of ceramic coating. It turn out that the ytematic error of the tet machine can be repreented Fig. XRD pectra of the SiC coating before and after HT experiment.

14 J Adv Ceram 7, 6(4): 88 by the rigid reference ample, thu the accurate deformation of the tet pecimen can be obtained by the cro-beam diplacement difference. The imple method can alo be applied to the evaluation of coating elatic modulu at high and ultrahigh temperature. The deformation of the beam and ring ample at HT were determined by comparing the cro-beam diplacement of the tet machine between the tet piece and rigid reference ample under identical load condition. The elatic modulu of SiC coating on graphite beam and outide urface of graphite ring were evaluated by the relative method from room temperature to. The temperature dependency of coating modulu meaured by three-point bending tet accorded well with that teted by plit ring compreing experiment. The reult diplayed that the coating modulu increaed about 5.9% at 5 compared to the ambient temperature modulu, and then reduced with the increae of temperature. At temperature over 5, the coating modulu decreaed rapidly and reached only 5.7% of the room temperature modulu at. It i demontrated that the relative method i a convenient and accurate approach to evaluate the HT elatic modulu of ceramic coating. Acknowledgement Thi work wa upported by the National Natural Science Foundation of China (No. 5477), and National High-tech R&D Program of China (86 Program, No. 5AA44). Reference [] Özel A, Ucar V, Mimaroglu A, et al. Comparion of the thermal tree developed in diamond and advanced ceramic coating ytem under thermal loading. Mater Deign, : [] Lima CRC, Cinca N, Guilemany JM. Study of the high temperature oxidation performance of Thermal Barrier Coating with HVOF prayed bond coat and incorporating a PVD ceramic interlayer. Ceram Int, 8: [] Zhang Y-L, Li H-J, Yao X-Y, et al. Oxidation reitant Si Mo Al coating for C/SiC coated carbon/carbon compoite at high temperature. Surface ng, 8: [4] Yao D-J, Li H-J, Wu H, et al. Ablation reitance of ZrC/SiC gradient coating for SiC-coated carbon/carbon compoite prepared by uperonic plama praying. J ur Ceram Soc 6, 6: [5] Li H-J, Xue H, Wang Y-J, et al. A MoSi SiC Si oxidation protective coating for carbon/carbon compoite. Surf Coat Tech 7, : [6] Yang Q, Senda T, Hiroe A. Sliding wear behavior of WC % Co coating at elevated temperature. Surf Coat Tech 6, : [7] Scrivani A, Rizzi G, Bardi U, et al. Thermal fatigue behavior of thick and porou thermal barrier coating ytem. J Therm Spray Tech 7, 6: [8] Kehavarz M, Idri MH, Ahmad N. Mechanical propertie of tabilized zirconia nanocrytalline B-PVD coating evaluated by micro and nano indentation. J Adv Ceram, : 4. [9] Teixeira V. Numerical analyi of the influence of coating poroity and ubtrate elatic propertie on the reidual tree in high temperature graded coating. Surf Coat Tech, 46 47: [] Lee KS. Damage tolerance in hardly coated layer tructure with modet elatic modulu mimatch. KSM Int J, 7: [] Wei Q, Zhu J, Chen W. Aniotropic mechanical propertie of plama-prayed thermal barrier coating at high temperature determined by ultraonic method. J Therm Spray Tech 6, 5: [] Rajendran V, Karthik A, Srither SR, et al. ffect of high temperature on the urface morphology and mechanical propertie of nanotructured Al O ZrO /SiO thermal barrier coating. Surf Coat Tech 5, 6: [] Girolamo GD, Marra F, Schioppa M, et al. volution of microtructural and mechanical propertie of lanthanum zirconate thermal barrier coating at high temperature. Surf Coat Tech 5, 68: 98. [4] Girolamo GD, Marra F, Blai C, et al. High-temperature mechanical behavior of plama prayed lanthanum zirconate coating. Ceram Int 4, 4: [5] Pulci G, Tului M, Tirillò J, et al. High temperature mechanical behavior of UHTC coating for thermal protection of re-entry vehicle. J Therm Spray Tech, : [6] Shang FL, Zhang X, Guo XC, et al. Determination of high temperature mechanical propertie of thermal barrier coating by nanoindentation. Surface ng 4, : [7] kner M, Sandtröm R. Mechanical propertie and temperature dependence of an air plama-prayed NiCoCrAlY bondcoat. Surf Coat Tech 6, : [8] Wheeler JM, Armtrong DJ, Heinz W, et al. High temperature nanoindentation: The tate of the art and future challenge. Curr Opin Solid St M 5, 9: [9] Wheeler JM, Michler J. Invited article: Indenter material for high temperature nanoindentation. Rev Sci Intrum, 84:. [] Wheeler JM, Oliver RA, Clyne TW. AFM obervation of diamond indenter after oxidation at elevated temperature. Diam Relat Mater, 9: [] Tillmann W, Selvadurai U, Luo W. Meaurement of the Young modulu of thermal pray coating by mean of everal method. J Therm Spray Tech, : 9 98.

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