The development of contact and noncontact technique to study the heat dissipation in metals under loading

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1 Te development of contact and noncontact tecnique to study te eat dissipation in metals under loading More info about tis article: ttp:// Abstract * ICMM UB RAS, Ac. Koroleva Str., 63 Perm, Russia, fedorova@icmm.ru by A. Iziumova*, A. Vsivkov* and O. Plekov* Tis work is devoted to te development of experimental tecnique allowing te analysis of energy balance in metal specimens during mecanical test and construction of eat sources field. Te use of infrared termograpy (IRT) is connected primarily wit problem of definition of te time constant related to te eat losses. Te goal of tis work is to develop te tecnique wic allows avoiding te additional experiments consisting in cooling test to find eat losses constant. Proposed tecnique is a combination of contact (eat flux sensor) and noncontact (IR camera) equipment wic could be used during mecanical test.. Introduction Nowadays infrared termograpy (IRT) is widely used in different areas of life suc as medicine [], defectoscopy [], warfare, security control etc. Also IRT as an important application in scientific researces as a relatively simple noncontact metod of temperature measurement of object surface. Tere are a lot of works devoted to study of material state under deformation on te basis of so-called energy approac, were IRT is used to determine te mecanical [3, ] and termal caracteristics [5, 6, 7] and to evaluate te damage degree of material by construction of eat source field of material surface. According to te last task determination of time constant related to eat losses plays an important role in accuracy of suc calculations and in assessment of energy balance of materials under loading conditions. Usually te additional cooling test is performed to define tis constant. In present work te eat flux sensor is proposed to avoid additional experiment and to find te required time constant during mecanical test directly. Tis sensor consists of two Peltier elements. One of tem plays a role of eat stabilizer. Anoter one is used for measurement of potential drop U (in Volts) wic appears because of te temperature difference between plates of Peltier element (Peltier Seebeck effect). Te main goal of tis work was to compare standard metod of determination of time constant related to eat losses and proposed tecnique based on eat flux sensor in real conditions of mecanical test.. Materials and experimental conditions In tis work titanium alloy specimens (Ti-.8Al-.8Mn) were tested under quasistatic tensile conditions. Smoot dog-bone-saped specimens (figure ) were used. Fig. : Geometry of specimen for tensile testing Specimens surface on te one side were specially prepared for infrared record before testing. Preparation consisted of two stages. In te first step specimen s surface was polised by abrasive paper wit different grain sizes. Te second step was to coating te polised surface by a tin layer of amorpous carbon to decrease te emissivity of surface. Anoter side of specimens was used for installation of te eat flux sensor. To provide a good termal contact te specimen surface under eat flux sensor was coated by termal paste. Figure sows te sceme of te experimental setup consisting of electric mecanical testing macine Simadzu AG-X Plus (3 kn), IR camera FLIR SC5, eat flux sensor and video extensometer Simadzu TRViewXS. Te caracteristics of te IR camera are te followings: a spectral range of 3 5 μm, a maximum frame size of 3 56 pixels, a spatial resolution of m and a temperature sensitivity of 5 mk at 3 K. Te calibration of te IR camera was made on te basis of te standard calibration table. To exclude an influence of internal sources on te experimental conditions, experimental setup was covered by black screen. IR camera and eat flux sensor record data continuously during mecanical test. Figure 3 illustrates a true stress-strain curve obtained experimentally. Te strain rate was 5 - sec -. 33

2 True stress, МПа 6 Fig. : Sceme of experimental setup ( specimen, eat flux sensor, 3 video extensometer, infrared camera, 5 grips of te testing macine, 6 reference points for video extensometer) 5 5 True strain, % Fig. 3: True stress-strain curve for titanium alloy Ti-.8Al-.8Mn Te developed eat flux sensor is described in details in [8]. Tis sensor consists of two Peltier elements. One of tem plays a role of eat stabilizer. Anoter one is used for measurement of potential drop U (in Volts) wic appears because of te temperature difference between plates of Peltier element. Calibration function () sows te dependence between eat flux in Watts and potential drop in Volts. W, 6U,. () Heat flux sensor allows us measuring te eat flux on te specimen surface during mecanical test in combination wit IR camera. As a result of experiment te stress-strain curve of titanium alloy Ti-.8Al-.8Mn, evolution of temperature field of specimen surface and eat flux were obtained by video extensometer, IR camera and eat flux sensor, respectively. 3. Determination of time constant From mecanical point of view in suc experiments te main goal of infrared data processing is to calculate a eat source field during quasistatic test and to evaluate te energy balance in materials under deformation before damage. As a result tis information is used in energy based approac to propose a criterion of damage. Usually to calculate a eat source field caused by plastic deformation, eat conductivity equation () is applied to infrared termograpy data. T(x, y,z, t) T(x, y,z, t) T(x, y,z, t) T(x, y,z, t) c Q(x, y,z, t) k, t x y z () were T(x,y,z,t) temperature field, ρ material density (75 kg/m3), c eat capacity (569 J/(kg K)), k eat conductivity ( W/(m K)), Q(x,y,z,t) eat sources field, x,y,z coordinates, t time. Termal constants of investigated titanium alloy were specified by autors on te base of tecnique described in details in [9]. In general tis tecnique is modification of standard flas metod []. Te main feature of it is possibility to define te eat conductivity and eat diffusivity simultaneously during te same experiment. Infrared camera allows one to register te temperature field on te specimen surface witout control of temperature distribution in tickness of specimen. Tis is te reason of using enoug tin specimens in experimental investigations. It makes possible to assume tat te temperature distribution in tickness is omogeneous. Heat conductivity equation in suc case as to be averaged on z-coordinate (tickness). Te standard operation of averaging [] was used. Difference θ (x,y,t) between average temperature and temperature of environment was written as follows: / (3) / '( x, y, t) ( T(x, y,z, t) T ) dz (x, y, t) T, were T initial temperature of environment in termal equilibrium, specimen tickness. Boundary conditions expressed as: 333

3 T( x, y,z, t) T( x, y,z, t) z z z z / T( x, y,z, t) k ( T(x, y,z, t) T ) dz, z z / () were β eat excange coefficient in perpendicular direction to specimen surface. Considering expressions (3) and boundary conditions (), integration of equation () allows one to obtain relation (5) for determination of eat source field caused by plastic deformation during specimen testing. ( x, y, t) T Q x y t c x y t k x y t int (,, ) (,, ) (,, ), (5) were θ(x,y,t) is temperature field on specimen surface, Δθ(x,y,t) is Laplace operator of temperature field, Q int(x,y,t) is eat source field (W/m 3 ), τ is time constant wic is related to te eat losses [, ]. As a result numerical finite difference sceme of equation (5) applying to te IR data could allow us to calculate te eat source field using infrared data. Figure illustrates te area of interest for calculation of eat source field to compare infrared camera data and data of eat flux sensor wit a goal of time constant τ assessment. Suc coice of area is due to te size of eat flux sensor. During deformation te specimen is extended. Heat flux sensor is fixed on a special rigid support and just put to te specimen. It means as if te specimen slides under te sensor. Despite of tat a good termal contact provided by termal paste between te specimen and sensor allows registering te eat flux at all stages of deformation. Initial stage of mecanical test Final stage of mecanical test Place of calculation of eat source field = Place of mount of eat flux sensor on te oter side of specimen Fig. : Place of eat sources field calculation to assess time constant τ In tis work te time constant τ was evaluated by two ways. Te first one was te standard metod of cooling test after local point eating of specimen surface [3]. Te second way was using te data of eat flux sensor and infrared camera. 3.. Standard procedure of time constant determination (cooling test) Before beginning of mecanical test, temperature measurements of te specimen surface after point eating were performed. In tis work te eterogeneous eating was provided by momentary contact wit te soldering-iron. To evaluate time constant τ te eat conductivity equation (5) wit zero eat source value was used: ( x, y, t) T ( x, y, t) ( x, y, t), (6) 33

4 were α is termal diffusuvity. To obtain correct results, te experimental temperature data was filtered bot in time and in space using standard Gaussian kernel. Results of filtering procedure are presented in figure 5 and 6. Figure 5 illustrates field of temperature cange after momentary local eating. Cuts and marked in figure 5 are sown in figure 6A and B. Figure 6C presents original data (solid line) and time filtered data (dased line) in te point wit maximum temperature marked in figure 5 by symbol O. Data processed by filter demonstrate satisfactory correlation wit original data. Fig. 5: Temperature field after momentary local eating Temperature, o C x, pxls 9 Temperature, o C y, pxls Temperature, o C Time, s Original data Filtered data A B C Fig. 6: Illustration of data filtering: A and B original data (solid line) and space filtered data (dased line) along te section and, respectively, C original data (solid line) and space filtered data (dased line) in te point wit maximum temperature Te time derivation and te Laplace operator of temperature field in equation (6) were calculated separately by using te metod of forward finite difference sceme realized in Matlab. Ten eac term in equation (6) was integrated over te square area A limiting te ot spot marked in figure 5. To define time constant τ te criteria (7) was used. () t A A( t) ( t), A (7) were subscript A means integration over te area A. Figure 7A and B sow te time dependence of eac term in expression (6) and teir sum wit te optimal value of te time constant τ according to te criteria (7). 6 x -6 tau= sec 6 x -6 tau= sec d A /dt, -a* A, A /, o C/sec - - d A /dt -a* A A / d A /dt + A / - a* A, o C/sec Source Time, sec Time, sec A B Fig. 7: A time dependence of terms of te expression (6), B sum of terms in equation (6) versus time wit τ determined by criteria (7)

5 As it is sown in Figure 7B te sum of terms in expression (6) wic is equal to eat source value, is close to zero. Tis result was obtained wit optimal value of time constant of s. 3.. Applying of eat flux sensor to time constant definition Heat flux sensor directly registers eat flux under self-surface in time during mecanical test. To compare tis data wit eat calculated by IR data, eat source field obtained by equation (5) was integrated in lengt and widt of interest area (figure ): ab Q ( t) e Q ( x, y, t) dxdy, IR (8) were a and b corresponding lengt and widt of interest area, e tikness of specimen. Te time constant τ was picked out so as to provide a good correlation between eat sources values obtained by contact sensor and on te basis of IRT data. Te eat flux versus time obtained by contact sensor and on te basis of infrared termograpy data wit τ= s is presented in figure 8. int Heat flux, Watt 8 6 = sec Data of IRT Data of contact sensor 5 5 time, s Fig. 8. Illustration of time constant determination by data of eat flux sensor and IRT data Data in figure 8 demonstrate a good agreement from to seconds. Significant differences in data after sec could be explained by starting of large plastic deformation and canging of material density and eat capacity. Tat is wy in te last stage of deformation (after 5 %) te calculation of eat flux by eat conductivity equation (5) is not correct. Figure 9 illustrates eat flux versus deformation before 5% of strain. Data obtained by IRT and using contact sensor are in a good agreement from to 5% of strain wen eat flux was canged gradually. In figure red color sow limit of applicability of proposed tecnique on stress-strain curve. Poor correlation of data at te beginning part of experiment could be explained by termal inertia of eat flux sensor to te fast canges of eat sources. Heat flux, Watt 3 = sec Data of IRT Data of contact sensor 5 5, % Fig. 9: Heat flux obtained by IR data (τ = s) and contact sensor versus strain True stress, МPа True strain, % Fig. : stress-strain curve of titanium alloy Ti-.8Al-.8Mn; limits of applicability of proposed tecnique on stress-strain curve 336

6 Te time constant related to te eat losses wic is calculated on area coating of sensor (area of interest in figure ), is valid for full specimen in current conditions. Tat is wy wen we ave defined time constant, eat source field could be determined on any part of specimen surface, and energy balance could be constructed for full specimen.. Conclusions As a result te time constant τ was determined by standard procedure of cooling test after point eating of te specimen surface and using developed tecnique based on applying of eat flux sensor. In te first case value of time constant was seconds, in te second case tis constant was seconds. Proposed tecnique requires some improvements to increase te accuracy of time constant determination and to overcome te inertia effect of contact sensor. Despite of tat preliminary results allow us to conclude tat proposed tecnique of measurement te time constant could be used in experimental works. Data of time constant related to te eat losses wic were obtained by two ways demonstrated satisfactory agreement. Developed tecnique allows to avoid additional experiments of cooling after point eating and to find te required time constant during mecanical test directly. So tat, proposed tecnique reduces time of experiment and provides enoug precise result of time constant τ. ACKNOWLEDGMENTS Te reported study was funded by RFBR according to te researc project No о_a and No.- -. REFERENCES [] Lairi B.B., et al., Medical applications of infrared termograpy: A review, Composites Science and Tecnology. Vol. 69, pp. 3, 9. [] Vavilov V.P., Świderski W., Derusova D., Ultrasonic and optical stimulation in IR termograpic NDT of impact damage in carbon composites, Quantitative InfraRed Termograpy Journal. Vol., Is., pp. 6-7, 5. [3] La Rosa G., Risitano A., Termograpic metodology for rapid determination of te fatigue limit of materials and mecanical components, International Journal of Fatigue. Vol., pp ,. [] Punnosen S., Mukopadyay A., et al., Determination of critical strain for rapid crack growt during tensile deformation in aluminide coated near-α titanium alloy using infrared termograpy, Materials Science & Engineering. Vol. A 576, pp. 7-, 3. [5] Dong H., Zeng B., Cen F., Infrared sequence transformation tecnique for in situ measurement of termal diffusivity and monitoring of termal diffusion, Infrared Pysics & Tecnology. Vol. 73, pp. 3-, 5. [6] Martínez K., et al., Termal diffusivity measurements in solids by pototermal infrared radiometry: Influence of convectioneradiation eat losses, International Journal of Termal Sciences. Vol. 98, pp. -7, 5. [7] Massard H., Fudym O., Orlande H.R.B., Batsale J.C., Nodal predictive error model and Bayesian approac for termal diffusivity and eat source mapping, C. R. Mecanique. Vol. 338, pp. 3 9,. [8] Vsivkov A., Iziumova A., Plekov O., Bär J., Experimental study of eat dissipation at te crack tip during fatigue crack propagation, Fracture and Structural Integrity. Vol. 35, pp. 3-37, 6. [9] Zelnin M., Iziumova A. and Plekov O., Te determining termal constant of metals by infrared termograpy, AIP Conference Proceedings (In press). [] Tseng-Wen Lian et all., Rapid termal conductivity measurement of porius termal insulation material by laser flas metod, Advanced Powder Tecnology. Vol., pp. -, 6. [] Boulanger T., Crysocoos A., Mabru C., Galtier A., Calorimetric analysis of dissipative and termoplastic effects associated wit te fatigue beavior of steel., International journal of fatigue. Vol.6, pp. -9, [] Crysocoos A., Louce H., An infrared image processing to analyse te calorific effects accompanying strain localization, International journal of engineering science. Vol. 38, pp ,. [3] Crysocoos, A., Balandraud, X. and Wattrisse, B., Identification procedure using full-field measurements applications in mecanics and structures, Proc. of CNRS summer scool, Montpellier, -5,