sensors Article

Application of CCG Sensors to a High-Temperature Structure Subjected to Thermo-Mechanical Load Weihua Xie 1 , Songhe Meng 1, *, Hua Jin 1, *, Chong Du 2 , Libin Wang 1 , Tao Peng 1 , Fabrizio Scarpa 3 and Chenghai Xu 1 1

2 3

*

Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China; [email protected] (W.X.); [email protected] (L.W.); [email protected] (T.P.); [email protected] (C.X.) Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China; [email protected] Advanced Composites Centre for Innovation and Science (ACCIS), University of Bristol, Bristol BS8 1TR, UK; [email protected] Correspondence: [email protected] (S.M.); [email protected] (H.J.); Tel.: +86-451-8641-7560 (S.M.); Tel.: +86-451-8640-2343 (H.J.)

Academic Editors: Teen-Hang Meen, Shoou-Jinn Chang, Stephen D. Prior and Artde Donald Kin-Tak Lam Received: 31 July 2016; Accepted: 19 September 2016; Published: 13 October 2016

Abstract: This paper presents a simple methodology to perform a high temperature coupled thermo-mechanical test using ultra-high temperature ceramic material specimens (UHTCs), which are equipped with chemical composition gratings sensors (CCGs). The methodology also considers the presence of coupled loading within the response provided by the CCG sensors. The theoretical strain of the UHTCs specimens calculated with this technique shows a maximum relative error of 2.15% between the analytical and experimental data. To further verify the validity of the results from the tests, a Finite Element (FE) model has been developed to simulate the temperature, stress and strain fields within the UHTC structure equipped with the CCG. The results show that the compressive stress exceeds the material strength at the bonding area, and this originates a failure by fracture of the supporting structure in the hot environment. The results related to the strain fields show that the relative error with the experimental data decrease with an increase of temperature. The relative error is less than 15% when the temperature is higher than 200 ◦ C, and only 6.71% at 695 ◦ C. Keywords: fibre optic sensors; strain and temperature; chemical composition gratings (CCGs); high temperature application; hot structure; thermo-mechanical

1. Introduction Over the past two decades many fibre Bragg grating (FBG)-based sensors have been developed for applications in high-temperature environments due to their unique features [1–4]. Some examples of the interesting characteristics that characterise FBGs are their low weight, compact size, electromagnetic and radiofrequency compliance, durability, long-distance transmission capabilities and good heat resistance [5,6]. FBG sensors are regrouped into classes that include type I, type II and long-period gratings, photonic crystal fibres, sapphire gratings and chemical composition gratings (CCGs), the latter also commonly called regenerated FBGs (RFBGs). RFBGs have been used in environments up to 1295 ◦ C [7] and are typically produced from hydrogen-loaded optical fibres by applying an annealing treatment at temperatures between 800 ◦ C and 1000 ◦ C [8]. The original grating is completely erased and a new grating refractive index modulation is generated following the annealing process. The main advantages of RFBGs are their ultrahigh temperature stability, good grating qualities and their potential for measuring reflected light.

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To produce stable thermal sensors for high temperature environments Fokine [9–14], Zhang [15,16], Barrera [20–22], [23–25] and others [26–30] have devoted significant To Canning produce [7,17–19], stable thermal sensors Guan for high temperature environments Fokine [9–14], efforts to the study of the design, production and related technologies of RFBGs. Recently, number Zhang [15,16], Canning [7,17–19], Barrera [20–22], Guan [23–25] and others [26–30] have adevoted of research groups begun to production focus theirand efforts ontechnologies the application of RFBGs in significant efforts to thehave studyalso of the design, related of RFBGs. Recently, high-temperature environments. Issues related the utilisation of RFBGs in these challenging a number of research groups have also begun to focus their efforts on the application of RFBGs environmental conditions are related to the safe the packaging andofinstallation of thechallenging sensors in in high-temperature environments. Issues related utilisation RFBGs in these structures, because silica-based RFBGs to arethe extremely brittle and fragile after theof annealing process environmental conditions are related safe packaging and installation the sensors in [1]. Méndez et al. [31,32], Selfridge et al. [33], Sai Prasad and co-workers [34] have used metal structures, because silica-based RFBGs are extremely brittle and fragile after the annealing process [1]. substrates to [31,32], provideSelfridge the connection between the optical fibre sensors theused structure. Mamidi et Méndez et al. et al. [33], Sai Prasad and co-workers [34]and have metal substrates al.provide [35], Reddy et al. [36], Barrera et al. and Azhari et al.and [39]the have also usedMamidi a metal et or al. ceramic to the connection between the[37,38] optical fibre sensors structure. [35], tube to encapsulate the RFBGs to perform measurements in high temperature environments. Reddy et al. [36], Barrera et al. [37,38] and Azhari et al. [39] have also used a metal or ceramic tube to In a previous workto[40] we have described a in simple to apply CCG sensors on ultra-high encapsulate the RFBGs perform measurements high method temperature environments. temperature ceramic materials (UHTCs) in order to measure strains in thermal environments up to In a previous work [40] we have described a simple method to apply CCG sensors on ultra-high 1000 °C. This background work has shown the promise of using CCGs for applications in high temperature ceramic materials (UHTCs) in order to measure strains in thermal environments up to temperature environments. Aerospace hot structures and thermal protection systems (TPS) are ◦ 1000 C. This background work has shown the promise of using CCGs for applications in high examples ofenvironments. some of the most likely hot applications sensors, whichsystems are subjected to temperature Aerospace structures for andCCG thermal protection (TPS) are simultaneous thermal and mechanical load [41]. The thermo-mechanical coupling makes the examples of some of the most likely applications for CCG sensors, which are subjected to simultaneous measurement of high temperature however extremelycoupling difficult makes and expensive. In this paper thermal and mechanical load [41]. strains The thermo-mechanical the measurement of we present an experimental method that can identify the presence of a simultaneous high temperature strains however extremely difficult and expensive. In this paper wethermal present and an mechanical load on athat structure subjected to high of temperatures by thermal using CCGs. We carry out experimental method can identify the presence a simultaneous and mechanical loada thermo-mechanical experiment related to the application of CCGs on an ultra-high temperature on a structure subjected to high temperatures by using CCGs. We carry out a thermo-mechanical ceramic material structure. The results the experiments and from theoretical experiment related(UHTC) to the application of CCGs on from an ultra-high temperature ceramic material formulas (UHTC) are compared and analysed. also develop a FE theoretical model to simulate and explain structure. The results from the We experiments and from formulasthe areexperiments compared and analysed. the failure mechanism based on the stress distribution and strain field variation. The relative errors We also develop a FE model to simulate the experiments and explain the failure mechanism based on between the CCG sensor and FE method related to the strain measurements are also compared and the stress distribution and strain field variation. The relative errors between the CCG sensor and FE discussed. method related to the strain measurements are also compared and discussed. 2.2. Experimental Experimental Design Design

The experimental experimental setup work (Figure 1) was designed to simulate a realistic service The setupused usedininthis this work (Figure 1) was designed to simulate a realistic condition represented by a thermal protection shield (TPS) on a hot external structure, like in service condition represented by a thermal protection shield (TPS) on a hot external structure, like hypersonic vehicles [42,43]. The The UHTC specimen [40] was vertically from the bottom in hypersonic vehicles [42,43]. UHTC specimen [40]heated was heated vertically from the through bottom the hole on the workbench. The diameter of the heating spot was 20 mm and the distance from the through the hole on the workbench. The diameter of the heating spot was 20 mm and the distance laser the heating-lens mounted mounted at the bottom of bottom the gantry to the specimen 200 mm. The200 vertical from laser heating-lens at the of the gantry to thewas specimen was mm. displacement of the UHTC specimen was fixed by a horizontal vice along the two borders. The The vertical displacement of the UHTC specimen was fixed by a horizontal vice along the two borders. minimum force was adjusted to produce a friction force to balance the weight of the specimen. The minimum force was adjusted to produce a friction force to balance the weight of the specimen.

Figure Figure1.1.Scheme Schemeillustrating illustratingthermal-mechanical thermal-mechanicalexperimental experimentalapparatus. apparatus.

Corundumceramic ceramic plates plates were wereplaced placedon onthe thecontact contactarea areabetween betweenthe theUHTC UHTCspecimen specimenand and Corundum the horizontal vice to reduce heat transfer. In this situation, the thermal expansion of the UHTC inaa the horizontal vice to reduce heat transfer. In this situation, the thermal expansion of the UHTC in verticaldirection directionwas wasrestricted restrictedupon uponheating heatingand andaacompression compressionstress stresswas wasthen theninduced inducedalong alongthis this vertical

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direction. of the the UHTC UHTC along alongthe thehorizontal horizontaldirection directiontoto direction.The TheCCG CCGsensor sensor was was attached attached to the surface of measure its thermo-mechanical response. measure its thermo-mechanical response. The using Ge-doped Ge-doped silica silicafibres fibresat atthe theInstitute Instituteofof TheCCG CCGsensor sensorused usedin in this this study study was fabricated using Photonics (Jinan University, Guangzhou, China). A high-purity aluminaalumina adhesiveadhesive (Rebond PhotonicsTechnology Technology (Jinan University, Guangzhou, China). A high-purity 989FS, Cotronics Corp., New York, NY, USA) was used to connect the CCG to the specimen. size (Rebond 989FS, Cotronics Corp., New York, NY, USA) was used to connect the CCG The to the ofspecimen. the specimen was of 40 the mmspecimen × 45 mmwas × 540 mm. UHTC in this study was fabricated The size mmThe × 45 mm ×sample 5 mm.used The UHTC sample used in this from ZrB2 from (Northwest Institute Non-ferrous Metalfor Research, Xi’an,Metal China) and SiC studycommercial was fabricated commercial ZrB2for (Northwest Institute Non-ferrous Research, powders (Weifang Micro-powder Ltd., Weifang, China). powder mixtures of ZrB Xi’an, China) and Kaihua SiC powders (WeifangCo. Kaihua Micro-powder Co.The Ltd., Weifang, China). The2 powder of ZrB 2 with 15%in v/v SiC were ball-milled ethanol formilling eight hours with a hard with 15% mixtures v/v SiC were ball-milled ethanol for eight hours in with a hard tool and dried in a milling evaporator. tool and dried in a powder rotatingwas evaporator. Milled powder wasin then hot-pressed uniaxially in a rotating Milled then hot-pressed uniaxially a boron nitride coated graphite ◦ C for boron nitride coated graphite at 1950and °C for 60 min a vacuum and 30 MPa it ofgood pressure was die at 1950 60 min under die a vacuum 30 MPa of under pressure was applied, giving oxidative ◦ C [44]. applied,up giving it good oxidative stability up to 2000 °C [44]. stability to 2000 high-power fibre-coupled fibre-coupled laser laser (DILAS Diodenlaser AAhigh-power Diodenlaser GmbH, GmbH, Mainz-Hechtsheim, Mainz-Hechtsheim,Germany. Germany. ◦ C)was Laser class: Compact-980.10-1500C, output power: 1500W, wavelength: 980 nm ± 10 nm@25 Laser class: Compact-980.10-1500C, output power: 1500W, wavelength: ± 10 nm@25°C) was usedtotoheat heat specimen in this study. The temperature of the specimen was controlled by used thethe specimen in this study. The temperature of the specimen was controlled by adjusting adjusting the laser heater output power according to the temperature response data. An optical the laser heater output power according to the temperature response data. An optical fibre-grating fibre-grating (si425 demodulator (si425 Optical Sensing Interrogator, Micron Optics, Atlanta, GA,to demodulator Optical Sensing Interrogator, Micron Optics, Inc., Atlanta, GA,Inc., USA) was used USA) reflected was used to record signals. reflectedA wavelength signals. A thermocouple was mounted on the record wavelength thermocouple was mounted on the adhesive layer to measure adhesive layer to measure the temperature of the specimen and a multi-channel temperature signal the temperature of the specimen and a multi-channel temperature signal acquisition instrument acquisition instrument (LR8402-21, HIOKI, Nagano, Japan) was used to record temperature (LR8402-21, HIOKI, Nagano, Japan) was used to record temperature responses. The thermocouple responses. The thermocouple signal was mainly used for is temperature compensation, which is signal was mainly used for temperature compensation, which generally adopted to decouple CCGs generally adopted to decouple CCGs signals [45]. signals [45]. Experimental Results 3.3. Experimental Results and and Analysis Analysis 3.1.Experimental ExperimentalResults Results 3.1. Thedesigned designedexperimental experimental rig rig is is shown shown in Figure Figure 2. The thermo-mechanical The thermo-mechanicalexperimental experimentaltest test was performed using a CCG sensor with centre wavelengths of 1550.521 nm. During the test, the was performed using a CCG sensor with centre wavelengths 1550.521 nm. During the test, the specimenwas wasslowly slowlyheated heatedbybyadjusting adjustingthe theoutput outputpower power the laser heater, and response of specimen ofof the laser heater, and thethe response of the the CCG sensor and thermocouples was recorded the instruments. Thestopped test stopped the CCG sensor and thermocouples was recorded by theby instruments. The test when when the UHTC UHTC specimen fractured at 695 °C. specimen fractured at 695 ◦ C.

Figure for the the thermo-mechanical thermo-mechanical test. test. Figure 2. 2. Experimental Experimental rig rig for

Thefracture fracturewas waslocated located at at the the centre centre of of the the specimen specimen in The in an an area area parallel parallelto tothe thedirection directionofofthe the CCG sensor (Figure 3). During the test the specimen’s compression stress along the vertical CCG sensor (Figure 3). During the test the specimen’s compression stress along the verticaldirection direction increasedalongside alongsidethe the temperature, temperature, because because its increased its expansion expansion at at that that direction directionwas wasconstrained constrainedby bythe the horizontal vice. Cracks were generated when local stress exceeded the UHTCs strength at that horizontal vice. Cracks were generated when local stress exceeded the UHTCs strength at that specific specific temperature, and theoccurred fracture with occurred with propagating to theoffragility of the temperature, and the fracture propagating cracks duecracks to thedue fragility the UHTCs. UHTCs.

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Figure 3. 3. Photo Photo of of UHTC UHTC specimen specimen with with aa fracture fracture after test. Figure after aaa test. test. Figure 3. Photo of UHTC specimen with a fracture after

curve of the measured response signals from the CCGs versus the temperature is shown shown in The curve curve of ofthe themeasured measuredresponse responsesignals signalsfrom fromthe theCCGs CCGs versus the temperature is shown The versus the temperature is in Figure 4a. As can clearly be observed from that plot, the response of the wavelength presents in Figure clearly observed fromthat thatplot, plot,the theresponse responseof ofthe the wavelength wavelength presents presents aa Figure 4a.4a. AsAs cancan clearly bebe observed from nonlinear increase increaseversus versusthe the temperature. Nonlinearity is affected affected by many many factors, such as the the nonlinear temperature. Nonlinearity is affected by many factors, such as the as highly increase versus the temperature. Nonlinearity is by factors, such highly temperature-dependent nature of the thermo-optical coefficient and the thermal expansion temperature-dependent nature of the thermo-optical coefficient and the thermal expansion coefficient highly temperature-dependent nature of the thermo-optical coefficient and the thermal expansion coefficient offibres the silica silica fibres [46], the theinvariation variation in of thethe period of fibre the optical optical fibre sensor and the the of the silicaof [46], fibres the variation the period optical sensor fibre and the elastic-optic coefficient the [46], in the period of the sensor and elastic-optic coefficient [47]. Figure 4b shows the results of the relative variation in wavelength coefficient [47]. Figure 4b shows the results of the relative variation in wavelength versus temperature, elastic-optic coefficient [47]. Figure 4b shows the results of the relative variation in wavelength versus temperature, as well well as as the the quadratic quadratic curve-fitting of the the experimental data.fitting Tableparameters lists the the as well temperature, as the quadratic curve-fitting of the experimental data. Table 1 lists the curve versus as curve-fitting of experimental data. Table 11 lists curveafitting fitting parametersinterval. with aa 95% 95% confidence interval. Similar quadratic thermal responses have with 95% confidence Similar quadratic thermal responses havethermal been recorded in other curve parameters with confidence interval. Similar quadratic responses have been recorded in other studies [40,48–50]. studies [40,48–50]. been recorded in other studies [40,48–50].

(a) (a)

(b) (b)

Figure 4. 4. (a) Variation Variation and (b) (b) relative variation variation of wavelength wavelength alongside temperature. temperature. Figure Figure 4. (a) (a) Variation and and (b) relative relative variation of of wavelength alongside alongside temperature. Table 1. 1. Fitting Fitting parameters parameters of of experimental experimental data data (R (R222 == 0.986). 0.986). Table Table 1. Fitting parameters of experimental data (R = 0.986). Parameter Value Standard Error Error Parameter Value Standard −5 −8 Coefficient of the first-order term K T1 1.18 × 10 9.98 × 10 −5 Parameter Value Error Coefficient of the first-order term KT1 1.18 × 10 9.98Standard × 10−8 −9 −10 Coefficient of the second-order term K T2 −1.39 × 10 1.52 × 10 −9 −10 − 5 Coefficient of the second-order term K T2 −1.39 × 10 1.52 × 10 Coefficient of the first-order term KT1 1.18 × 10 −4 9.98−5× 10−8 Universal constant constant C C −2.20 ×× 10 10 1.28 ×× 10 10−5 −4 − 9 Universal −2.20 1.28 Coefficient of the second-order term KT2 −1.39 × 10 1.52 × 10−10 Universal constant C −2.20 × 10−4 1.28 × 10−5

3.2. Analysis Analysis of of the the Results Results 3.2.

3.2. Analysis of the Results We have have used Equation (1) (1) [50] [50] to to denote denote the the quadratic quadratic relationship relationship between between the the relative relative We used Equation   /  variation of the measured total wavelength response and the temperature: BB / relationship BB and the temperature: variation of the measured total response We have used Equation (1) wavelength [50] to denote the quadratic between the relative variation of the measured total wavelength response ∆λ /λ and the temperature:   BB = KB TB  K T 22  C (1) (1)  = KTT11T  KTT 22T  C ∆λ B BB 2 = K ∆T + KT2 ∆T + C (1) λ B of the T1 where K KT1 T1 represents represents the the coefficient coefficient first-order term, term, K KT2 T2 represents represents the the coefficient coefficient of of the the where of the first-order second-order term, term, and and C C is is aa universal universal constant. constant. The The first-order first-order term term coefficient coefficient K KT1 T1 can can also also be be second-order written in the following form [40]: written in the following form [40]:

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where KT1 represents the coefficient of the first-order term, KT2 represents the coefficient of the second-order term, and C is a universal constant. The first-order term coefficient KT1 can also be written in the following form [40]: KT1 = (α + ζ ) + Kε β (αs − α)

(2)

where α, ζ and Kε denote the thermal expansion coefficient, thermo-optical coefficient and strain sensitivity coefficient of the CCGs, respectively. The term αs denotes the thermal expansion coefficient of the UHTC and β is the strain transfer coefficient used to characterise the strain difference between the structural and the actual sensed strains induced by the adhesive layer. The sensed5 strain can be Sensors 2016, 16, 1686 of 12 represented by the actual structural strain multiplied by factor β [50]: KT 1       K  s   

ε C = β(αs − α)∆T

(2)

(3)

where α, ζ and Kε denote the thermal expansion coefficient, thermo-optical coefficient and strain sensitivitythe coefficient of the CCGs, The term αdirection s denotes the thermal expansion where εC denotes CCGs-sensed strainrespectively. along the horizontal for this test. coefficient of the UHTC and β is the strain transfer coefficient used to characterise the strain From Equations (2) and (3) it is possible to derive the following relation: difference between the structural and the actual sensed strains induced by the adhesive layer. The sensed strain can be represented by the actual structural strain multiplied by factor β [50]:

K − (α + ζ ) ∆T ε C = CT1   ( Ks   )T ε

(3)

(4)

where εC denotes the CCGs-sensed strain along the horizontal direction for this test.

The strain values εC sensed can be calculated using relation: Equation (4) from the experimental From Equations (2) andby (3) CCGs it is possible to derive the following data. Then, the practical structural strain can be calculated by the following equation, while the values KT 1      T (4) C  of β at different temperatures can be found from [40]: K 

The strain values εC sensed by CCGs can ε Sbe=calculated ε C /β using Equation (4) from the experimental data. Then, the practical structural strain can be calculated by the following equation, while the values of β at different temperatures can be found from [40]:

(5)

The theoretical strain of the specimen can be solved by considering the thermal deformation (5) S = C  specimen along the horizontal direction relations. If we denote εTh as the theoretical strainof the (CCGs’ direction), its The finaltheoretical value contains effects ofcan thebestrain horizontal and vertical directions: strain of the the specimen solvedin byboth considering the thermal deformation relations. If we denote εTh as the theoretical strain of the specimen along the horizontal direction (CCGs’ direction), its final value contains effects strain in both horizontal and vertical ε Th = α) ∆T + υof(the αs − α) ∆T (αs −the directions:

(6)

where υ is the Poisson’s ratio of the UHTC material. Figure 5 shows a comparison between the (6) Th   s    T  υ  s    T experimental and theoretical strain. One can observe the existence of good agreement between the two where υ is the Poisson’s ratio of the UHTC material. Figure 5 shows a comparison between the data sets. experimental The nonlinear strain in Figure was calculated byagreement using Equation and experimental theoretical strain. One can observe5the existence of good between (4), the in which the parameter KT1sets. hasThe been obtained from the response of the CCGs. The theoretical two data nonlinear experimental strain in Figuresignals 5 was calculated by using Equation (4), in strain in which the parameter T1 has Equation been obtained response signals of the CCGs. The theoretical Figure 5 was calculated by Kusing (5).from Thethe maximum relative error is 2.15%, indicating that strain in Figure 5 was calculated by using Equation (5). The maximum relative error is 2.15%, the CCGs sensor can provide a good strain measurement under thermo-mechanical loading for the indicating that the CCGs sensor can provide a good strain measurement under thermo-mechanical external hot structure to which it is applied. loading for the external hot structure to which it is applied.

Figure 5. Comparison of theoretical and experimental strains.

Figure 5. Comparison of theoretical and experimental strains.

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4. FiniteElement ElementAnalysis Analysisand andDiscussions Discussions 4. Finite 4.1. Finite Element Model A finite element element method method (FEM) (FEM) was was used used to to simulate simulate the the thermo-mechanical thermo-mechanical test test process. process. It is worth thethe use use of a robust FE model represent the phenomenon could be instrumental worth mentioning mentioningthat that of a robust FE tomodel to represent the phenomenon could be to reduce the time available for the experimental tests, and especially the financial costs associated instrumental to reduce the time available for the experimental tests, and especially the financial costs to full-scaletoexperimental trials. A full-size model of the model UHTC specimen and associated full-scale experimental trials.three-dimensional A full-size three-dimensional of the UHTC the adhesive was builtlayer usingwas thebuilt finiteusing element analysis (FEA)analysis software (ANSYS, Version 16.1), specimen andlayer the adhesive the finite element (FEA) software (ANSYS, as shown16.1), in Figure 6a. TheinFEFigure model6a. wasThe assumed to be was a combination of two a Version as shown FE model assumed to be aquarter-spheres combination ofand two half-cylinder, approximately. The detailed dimensions The of the adhesive layer and UHTC specimen layer used quarter-spheres and a half-cylinder, approximately. detailed dimensions of the adhesive in this studyspecimen are shown in Table The CCG sensor in was ignored inCCG the FE model due to its small and UHTC used in this2.study are shown Table 2. The sensor was ignored in thesize. FE The material of the UHTC and properties adhesive are in Tables 3–5. The are properties listed model due toproperties its small size. The material of shown the UHTC and adhesive shown not in Tables in theThe tables at other temperatures estimated by linear interpolation. Heat transferby analyses 3–5. properties not listed in can the be tables at other temperatures can be estimated linear were carried out withtransfer three dimensional twenty-node DC3D20 elements. Thermal-mechanical analyses interpolation. Heat analyses were carried out with three dimensional twenty-node DC3D20 were carried out with three dimensional elements. mesh convergence study elements. Thermal-mechanical analyses twenty-node were carriedC3D20 out with three Adimensional twenty-node had been performed, and showed that the mesh was sufficient and for the stress that within critical C3D20 elements. A mesh convergence study hadsize been performed, showed thethe mesh size region to converge. was sufficient for the stress within the critical region to converge.

(a)

(c)

(b)

Figure 6. 6. (a) Finite element model; (b) mechanical and (c) thermal boundary conditions of finite element analysis. Table 2. Dimensions of the adhesive adhesive layer layer and and UHTC UHTC specimen. specimen. Table 2. Parameter Parameter Value (mm)

Length Length 20

Value (mm)

Density (kg/m3) 4960 Density (kg/m3 ) 4960

Adhesive Layer Adhesive Layer Width Height (Sagitta) Width Height 6 2.5(Sagitta)

UHTC Specimen UHTC Specimen Length Width Thickness Length Width Thickness 45 40 5

20 6 2.5 45 40 Table 3. Mechanical properties of the UHTC material [51,52].

Table 3. Mechanical properties of the UHTC [51,52]. Elastic Modulus (GPa)material Compressive Strength (MPa) Poisson’s Ratio 20 ºC 1400 ºC 20 ºC 800 ºC Elastic Modulus (GPa) Compressive Strength (MPa) 0.165 463.0 158.7 1106.4 1009.2 Poisson’s Ratio 20 ◦ C 1400 ◦ C 20 ◦ C 800 ◦ C

Table properties of the UHTC material [40,53]. 0.1654. Thermal463.0 158.7 1106.4

T (ºC) 20 303 594 891 1196 Table º 4. properties of the88.86 UHTC material Thermal conductivity (W/m· C)Thermal 112.00 110.63 67.70 [40,53]. 61.67 Specific heat (J/kg·ºC) 700.00 777.61 828.19 869.36 1013.46 T (−6◦ C) 20 303 594 891 1196 CTE (10 ºC−1) 3.31 5.45 6.67 7.20 7.62 112.00 110.63 88.86 67.70 61.67 Thermal conductivity (W/m·◦ C) Specific heat (J/kg·◦ C)Table 5. Properties 700.00 777.61 828.19 869.36 1013.46 of the adhesive material [54]. CTE (10−6 ◦ C−1 ) 3.31 5.45 6.67 7.20 7.62

Density (kg/m3) 3700

CTE (10−6 ºC−1) 8.1E-6

5

Thermal Conductivity (W/m·ºC) 85.18

Specific Heat (J/kg·ºC) 1004.16

1009.2

1499 64.04 1016.08 1499 8.03 64.04 1016.08 8.03

Elastic Modulus (GPa) 370

1806 50.77 1083.27 1806 8.43 50.77 1083.27 8.43

Poisson’s Ratio 0.2

The mechanical and thermal boundary conditions are illustrated in Figure 6b,c. The displacements of two side faces of the specimen along the vertical direction were fixed to the

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Table 5. Properties of the adhesive material [54]. Density (kg/m3 )

CTE (10−6 ◦ C−1 )

Thermal Conductivity (W/m·◦ C)

Specific Heat (J/kg·◦ C)

Elastic Modulus (GPa)

Poisson’s Ratio

3700

8.1E-6

85.18

1004.16

370

0.2

The mechanical and thermal boundary conditions are illustrated in Figure 6b,c. The displacements Sensors 2016, 16, 1686 7 of 12 of two side2016, faces of the specimen along the vertical direction were fixed to the constraints representing Sensors 16, 1686 7 of 12 theconstraints horizontalrepresenting vice. The temperature history curve measured during the experimental test (Figure the horizontal vice. The temperature history curve measured during the 7) constraints representing the horizontal vice. Theastemperature historyboundary curve measured during was applied to the bottom of the specimen thesurface temperature condition. The the total experimental test (Figuresurface 7) was applied to the bottom of the specimen as the temperature experimental test (Figure 7) was applied to the bottom surface of the specimen as the temperature heating timecondition. was 2570 The s. Heating area was 25 mm circular area, which is the same as that boundary total heating timeawas 2570diameter s. Heating area was a 25 mm diameter circular boundary condition. The totalareas heating timebottom was 2570 s. Heating area were was aspecified 25 mm diameter circular of area, the laser heater oflaser the and top surface as top the surface radiation which is thespot. sameOther as that of the heater spot. Other areas of the bottom and area, which is the same as that of the laser heater spot. Other areas of the bottom and top surface boundary condition withradiation a surfaceboundary emissivity of 0.85. with Natural convection was of not0.85. considered were specified as the condition a surface emissivity Natural in were specified as the radiation boundary condition with a surface emissivity of 0.85. Natural convection wasthe notUHTC considered in this study. theassumed UHTC and were and assumed be this study. Both and adhesive layerBoth were be adhesive isotropic layer materials remained convection was not considered in this study. Both the UHTC and adhesive layer were assumed be and remained in the linear they were always in isotropic the linearmaterials elastic range during analysis, andelastic they range were during alwaysanalysis, perfectlyand bonded to each other. isotropic materials and remained in the linear elastic range during analysis, and they were always perfectly bondedsimulation to each other. The experimental simulation carried out basedthermo-mechanical on the sequential The experimental was carried out based on the was sequential perfectly bonded to each other. The experimental simulation was carriedcoupled out based on the sequential coupled thermo-mechanical analysis with a Newton-Raphson method. analysis with a Newton-Raphson method. coupled thermo-mechanical analysis with a Newton-Raphson method.

Figure7.7.Temperature Temperature history history curve curve of the experimental test. Figure test. Figure 7. Temperature history curveof ofthe theexperimental experimental test.

and Discussion 4.2.4.2. Results and Discussion 4.2.Results Results and Discussion The temperature distributions atatthe analysis are given in 8.8.ItItcan The temperature distributionsat theend endofof ofthe the thermal analysis are given inFigure Figure canItbe be The temperature distributions the end thethermal thermal analysis are given in Figure 8. can seen that the maximum temperature of the specimen at the centre reached the value of 695 °C while◦ seenthat that the maximum of of thethe specimen at the reached the value 695 °C be seen maximumtemperature temperature specimen at centre the centre reached the of value of while 695 C the minimum temperature was 681.2 °C localised atatthe corners ofof the specimen. The large ◦C thethe minimum temperature was 681.2 °Cand and localised thethe corners while minimum temperature was 681.2 and localised at corners ofthe thespecimen. specimen.The Thelarge large thermal conductivity value ofofthe material made the temperature difference thermal conductivity value theUHTCs UHTCs material the maximum maximum temperature difference thermal conductivity value of the UHTCs material mademade the maximum temperature difference lower lower◦than 14 °C. thanlower 14 C.than 14 °C.

(a) (a)

(b) (b)

Figure Figure8.8.Temperature Temperaturecontour contourofof(a) (a)top topview viewand and(b) (b)bottom bottomview viewatat2570 2570s.s. Figure 8. Temperature contour of (a) top view and (b) bottom view at 2570 s.

The Thetemperature temperaturefield fielddistribution distributionhas hasbeen beenused usedasasaathermal thermal load load to to predict predict the the internal internal stresses in the structure. The transient stress analysis results showed that the primary stress stresses in the structure. The transient stress analysis results showed that the primary stresson onthe the specimen specimenwas wasa acompressive compressiveone one(vertical (verticaltotothe theCCG), CCG),and andwas wascaused causedby bythe theconstraints constraintsprovided provided bybythe thehorizontal horizontalvice. vice.By Bycomparing comparingthe thethermal thermalstress stresscontours contoursatatdifferent differenttimes, times,ititisispossible possibleto to draw drawthe thesame sameconclusion conclusionabout aboutthe thespecimen’s specimen’sstress stressalong alongthe they-direction: y-direction: stresses stresses are are always always

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The temperature field distribution has been used as a thermal load to predict the internal stresses in the structure. The transient stress analysis results showed that the primary stress on the specimen was a compressive one (vertical to the CCG), and was caused by the constraints provided by the horizontal vice. By comparing the thermal stress contours at different times, it is possible to draw the same conclusion about the specimen’s stress along the y-direction: stresses are always negative (i.e., compressive), and the minimum compressive stress in absolute value is located at the bonding region between the UHTC and the adhesive layer, while the maximum compressive stress (magnitude) Sensors 2016, 16, 1686 8 of 12 is located in the area around the boundary of the bonding area. The compressive stress distributions along the y-direction an adhesive layer at 1900layer s and distributions along thewithout y-direction without an adhesive at 2000 1900 s are and shown 2000 s in areFigure shown9a,b. in The compressive stress at the four borders reached 1053 MPa at 1900 s (Figure 9a) and exceeded Figure 9a,b. The compressive stress at the four borders reached 1053 MPa at 1900 s (Figure 9a) and the UHTCs’ tensile strength that specific temperature (446 ◦ C). (446 °C). exceeded thecompressive UHTCs’ compressive tensileatstrength at that specific temperature

(a)

(b)

(c) Figure 9. 9. Comparison Comparison of of failure failure positions Figure positions between between FEA FEA and andtest testat at(a) (a)1900 1900s;s;(b) (b)2000 2000s;s;(c) (c)2570 2570s.s.

According to the FE analysis, the temperature of the border after 2000 s was around 484 °C, and According to the FE analysis, the temperature of theTwo border after 2000areas s wasnear around 484 ◦ C, and the corresponding compressive strength was 1048 MPa. strip-shaped the connection the corresponding compressive strength was (Figure 1048 MPa. near the connection region exceeded their compressive strength 9b).Two If westrip-shaped compare theareas locations of the failure region exceeded their compressive strength (Figure 9b). If we compare the locations of failure with the fracture point shown in Figure 9c, it is apparent that the fracture occurred in thethe location with the fracture shown incompressive Figure 9c, itstress. is apparent that the fracture location corresponding topoint the maximum The FEA results provideoccurred evidenceintothe justify the corresponding to the maximum compressive stress. The FEA results provide evidence to justify the observed experimental results. The micro-cracks present in the structure may have been generated observed experimental results.thermal The micro-cracks in s, thefollowed structure have been generated as a result of the constrained expansion present after 2000 bymay crack propagation until as a result of the constrained thermal expansion after 2000 s, followed by crack propagation until fracture occurred. fracture occurred. The strain on the specimen can also be obtained from the FEA analysis. We selected all the The strain online the where specimen also bebonded obtainedatfrom the FEA adhesive analysis. surface, We selected the nodes nodes along the the can CCG was the UHTCs’ thenallcalculated along the line where the CCG was bonded at the UHTCs’ adhesive surface, then calculated the the average value of the nodal mechanical strains along the x-direction and obtained the average strain value the nodal mechanical curves. strains along x-direction andwere obtained the strain versus time and versusoftime and temperature These the numerical values then compared with the strain temperature curves. numerical values 10a). were By then comparedthe with theelement strain values measured by values measured by These the CCG sensor (Figure comparing finite simulation results the CCG (Figure 10a). element results the experimental with thesensor experimental data By we comparing found thatthe thefinite results of thesimulation two methods arewith in good agreement. data we6 found thatthe therelative results error of theof two are inwhich good decreased agreement.for Table 6 provides the relative Table provides themethods two results, increasing temperatures. error of the two results, which decreased temperatures. error The relative error was however larger infor theincreasing low temperature regimeThe (lessrelative than 100 °C),was duehowever to the strain value being itself very small. Above 200 °C the relative error was less than 15%, and the relative error between the two methods at the final temperature of 695 °C was only 6.71%. Within the elastic range we can use the strain to calculate the corresponding stresses, according to Hooke's law. As shown in Figure 10b, the structural compressive stress curves were calculated over time by using the strain of the FEA and the CCG sensor. At the same time, the compressive strength of the UHTC at the corresponding temperature was also obtained (see Figure 10b). Both

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and the temperature range of the corresponding times were roughly 446 °C–483 °C, respectively. This was in agreement with the experimental results. between simulations and experimental results were mainly derived from9 the Sensors The 2016,discrepancies 16, 1686 of 12 representation of the boundary conditions and assumptions like the use of adiabatic boundary conditions. In the actual experiment, it was difficult to completely insulate the specimen from the larger in the low temperature regime (less 100 ◦displacement C), due to theconstraints strain value being itself very small. surrounding environment and to keep thethan applied constants. Nonetheless, ◦ Above 200 C the relative was less 15%, the relative error between the two methods the results show that theerror FE model is than capable toand represent the physics and provide some robustat ◦ the final temperature 695 C was only 6.71%. predictions about theof thermo-mechanical coupling occurring inside the structure.

(a)

(b)

Figure 10. The curves of (a) strain and (b) stress over time. Figure 10. The curves of (a) strain and (b) stress over time. Table 6. Relative errors of mechanical strain between FEA and experimental results. Table 6. Relative errors of mechanical strain between FEA and experimental results. ◦ Temperature Temperature (°C ) ( C) 100 100 18.96% RelativeRelative Errors Errors 18.96%

200 200 14.92% 14.92%

300 400 400 500 500 600 300 600695 13.79% 8.10% 8.10% 6.71% 13.79% 13.19% 13.19%9.91% 9.91%

695 6.71%

5. Conclusions Within the elastic range we can use the strain to calculate the corresponding stresses, according to

Hooke’s law.work, As shown in Figure 10b, the structural stress curves was wereevaluated calculated over In this the application of a CCG fibre opticcompressive sensor on a hot structure and a time by using the strain of the FEA and the CCG sensor. At the same time, the compressive strength simple method to perform a combined thermal and mechanical load test has been presented. A highof the UHTC at the also obtained (see Figure 10b). Both compressive temperature testcorresponding was performedtemperature on a UHTCwas specimen that was subjected to thermo-mechanical stresses were greater than the material compressive strength in the 1900 s–2000 s range, and the loads. The response characteristics of the bonded CCG were highlighted by a signal decoupling ◦ C–483 ◦ C, respectively. This was in temperature range of the corresponding times were roughly 446 technique on the basis of a temperature compensation method. The results showed that the relative agreement withthe thetest experimental error between results andresults. the theoretical strain value was less than 2.15%. The finite element The discrepancies between simulations and experimental were field, mainly derived method was used to simulate the experimental process, and the results temperature stress field from and the representation of the boundary conditions and assumptions like the use of adiabatic boundary strain field were calculated and analysed. The finite element analysis showed that the compressive conditions. the actualregion experiment, it was difficultvalue to completely insulate thethermo-mechanical specimen from the stress of theIn connecting exceeded the strength of the material in the surrounding environmentwhich and toexplains keep thethe applied displacement coupling environment, failure of the hot constraints supportingconstants. structure.Nonetheless, Numerical the results show that the FE model is location capableand to represent the physics and provide someasrobust simulations can accurately predict the time of the failure of thermal structures, well predictions about the thermo-mechanical coupling occurring inside the as the corresponding stress failure values. The numerical analysis can structure. also reasonably explain the failure mechanism observed during the test. Furthermore, the numeric simulation results showed 5.that Conclusions the relative error of the strain decreased alongside an increase in temperature. The relative error wasIn lower the temperature was higher than 200 andstructure only 6.71% 695 °C. and a this than work,15% thewhen application of a CCG fibre optic sensor on °C a hot wasatevaluated simple method to perform a combined thermal and mechanical load test has been presented. A high Acknowledgements: This research was supported by the Project of National Natural Science Foundation of temperature test was performed on a UHTC specimen that was subjected to thermo-mechanical loads. China (11272107, 11472092 and 11502058) and the National Basic Research Program of China (2015CB655200). The response characteristics of the bonded CCG were highlighted by a signal decoupling technique on The authors thank the Institute of Photonics Technology (Jinan University, Guangzhou, China) for providing the basis of a temperature compensation method. The results showed that the relative error between CCG sensors. the test results and the theoretical strain value was less than 2.15%. The finite element method was used to simulate the experimental process, and the temperature field, stress field and strain field were calculated and analysed. The finite element analysis showed that the compressive stress of the connecting region exceeded the strength value of the material in the thermo-mechanical coupling environment, which explains the failure of the hot supporting structure. Numerical simulations can accurately predict the location and time of the failure of thermal structures, as well as the corresponding stress failure values. The numerical analysis can also reasonably explain the failure mechanism

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observed during the test. Furthermore, the numeric simulation results showed that the relative error of the strain decreased alongside an increase in temperature. The relative error was lower than 15% when the temperature was higher than 200 ◦ C and only 6.71% at 695 ◦ C. Acknowledgments: This research was supported by the Project of National Natural Science Foundation of China (11272107, 11472092 and 11502058) and the National Basic Research Program of China (2015CB655200). The authors thank the Institute of Photonics Technology (Jinan University, Guangzhou, China) for providing CCG sensors. Author Contributions: W.X. and S.M. conceived and designed the experiments; L.W. and T.P. performed the experiments; H.J. and F.S. analyzed the experimental data; C.D. and C.X. contributed to the specimen manufacturing and FE analysis; W.X. and F.S. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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