A procedure to measure thermal conductivities of anisotropic laminates by infrared thermography. by BERARDI P.G." and CUCCURULLO G.

Transcription

1 A prcedure t measure thermal cnductivities f anistrpic laminates by infrared thermgraphy by BERARD P.G." and CUCCURULLO G.* stilut di ngegneria 'Meccanica, Via Pnte Dn Melill 84084, Fiscian (SA), taly Abstrcu:t n this paper an experimental prcedure t determine the thermal cnductivities f CFRP thermplastics laminates sheets is presented. The methd is based n Laser heating and. nfrared Scanning Radimeter System. The thermal cnductivities are estimated by matching the experimental data with the analytical slutin, previusly derived fr the temperature field f heated specimens '. ntrclductin Thermal measuring methds are ften used as a suitable technique t evaluate a wide range f verall cmpsites characteristics as: thermal prperties, prsity, delaminatin, adhesi0n quality, density, reinfrcement cefficient [1-4]. These last influence mainly the mechanical prperties f cmpsites, but als sme aspects as the thermal stress evaluatin in the laminates [5], which affect the machining accuracy f the wrkpiece [6]; therefre thermal analysis and evaluatin f the thermal characteristics f structural cmpsites [7-11] are needed. n this wrk thermal cnductivities f unidirectinal Carbn Fibre Reinfrced Plastic slabs tjre evaluated by means f an autmatic prcedure emplying integrated Laser heating and nfrared Scanning Radimeter system., The analytical slutin btained fr the temperature field in an anistrpic slab subjected t a cnfined heating and cled by frced cnvectin is used t accmplish the data reductin f experimental tests in rder t btain the unknwn cnductivities. First experimental results cnfirm the feasibility f the prpsed methd as a fast and cnmical nn-destructive testing. 2, Basic equatins and analytical slutin. y h,ta ) Ow L kx +- S ----f X Fig, 1 The slab subjected t a strip heating and cled by radiative-cnvective heat transfer t an!fnbient at unifrm temperature is cnsidered, figure 1; in particular the strip heating presents. QRT 94 - Eurtherrn Series 42 - EET ed., Paris 1995

2 a gaussian spatial distributin, O=Ow ma x exp(_y2/l2), characterized by tw parameters: Ow ma x, the m aximum heat flux incident'n the wall and.e, the strip heating width. The slab is thermally anistrpic and is mdeled as an rthtrpic hmgeneus slid, characterized by the three principal thermal cnductivities which, fr the present heating cnfiguratins, tum ut t be nly tw, Le. kx and ky The energy balance and the bundar y cnditir:'ls fr - gaussian strip heating can be written in dimensinless frm as: txx+ty y =O lx(o,y)/bi =-t(o,y)+ exp(-y2/a2) t x (1,Y)=O ty(x,o)=o t(x,)=o (1) (2) (3) (4) (5) where: x=xls; y=y/(s (kylk x ) 1 2); t=(t-ta) /(a.ow, ma x lh); a. is the slab absrbitivity; h is the heat transfer cefficient; Bi=h s!kx is the Bit number; a=.e/(s (kylk x )12) is the dimensinless strip heating width. t has t be nted that the thermal anistrpy f the slab appears as a stretching effect n the reference length nrmal t the heat flux. 3. Temperature field The prblem being linear, the slutin fr gaussian strip heating can be sught by summing up the system respnse t a single unit step input: 00 t(x,y)= L<Pn CO{An (1-x)] <>n(y, a) (6) n=l <>n(y, a)1 [ a.[; 14 exp(a n 2 a 2 /4)] = 2A n csho" n y)erfc(yla +A n a2) + + A n exp(-a n y)[erfc(a n a2+ yla)-erfc(a n a2- yla)] (7) where An' the eigenvalues related t the Bit number, and the cnstants <Pn are given by [7]: n rder t reduce the number f parameters t be measured and recalling that infrared detectin allws t measure surface temperatures, it is cnvenient t redefine a nrmalized temperature with respect t the maximum ne (Le. the maximum temperature attained n the expsed surface): t+=t(x,y)/t(o,y)= t(x,y)/tw(y)=(t(x,y)-ta)/(tw(o)-ta)= (x, y, Bi, a) The abve dimensinless temperature distributin results t be independent f the heat flux absrbed at wall, Le. f the slab absrbitivity and the maximum heat flux incident n the wall. 4. Experimental apparatus. The experimental apparatus cnsists essentially f CFRP/APC2 sheets (400mm x 400mm expsed surface and 1-2-3mm thickness) made up f epxy resin matrix in which unidirectinal carbn_ fibres HTS (graphitizatin temperature 1500 C) are embedded; the fibre vlume fractin is abut 45%. The test sheets, adiabatic n the bttm, are heated with a CO2 laser surce and cled by a frced air flw at ambient temperature. the-related heat transfer (8) (9) 82

3 cefficient is measured by preliminary tests with strip heating n istrpic slabs whse cnductivity is knwn [8]. A cmputer assisted ptical system can realize strip heating by driving the laser spt alng a line at 10Hz. The surce presents a gaussian spatial distributin, Q=Qwmax exp(-'f2/e2); the maximum heat flux and the strip heating width are cntrlled via sftware: The maximum heat flux and the related slab absrbitivity are nt measured because the experimental surface temperatures are nrmalized with respect t their maximum value; while the characteristic length, E, is measured by strip heating t, recalling that fr Bi the nrmalized temperature prfile recvers the nrmalized heat flux distributin, [9]. r _ --._._-----_.-! L... Test sheet Fig. 2 Surface temperatures are detected by using an nfrared Thermgraphy System (Agema Thermvisin 870mC 8000), with thermal sensitivity f abut 0.1 C and spatial reslutin f abut 1 mm2 per pixel. '4 5. Experimental prcedure The CFRP/APC2 are mdeled as rthtrpic hmgeneus slids, characterized by the three principal cnductivities,, kl1 and ks. n particular kl1 is the slab cnductivity alng the fibres (lngitudinal cnductivity); and ks are the cnductivities nrmal t the fibres which, due t the expected unifrm fibre distributin, can be assumed t be the same, =ks (transverse cnductivity). T measure the tw unknwn thermal cnductivities tw different heating cnfiguratins are used: the first strip heating is parallel t the fibres directin, figure 3a, while the secnd is nrmal t the fibres, figure 3b. This chice allws t decuple the lngitudinal and transverse cnductivity effects: in fact the parallel strip heating gives directly the transverse slab cnductivity (the slab respnse is istrpic), while the thermal respnse t the nrmal strip heating is related t lngitudinal and transverse cnductivities. Therefre the experimental prcedure prvides the fllwing steps: fr each experiment, tw different strip heating are perfrmed: the first ne is nrmal t the fibres directin, the secnd ne is parallel t the fibres the surface-ambient temperature difference, detected by means f nfrared Thermgraphy, is nrmalized with respect t its maximum value 83

4 the surface temperature integral, 1= J (T w(y) Ta)/(T w(o)-t a) d(y/s)=f [ Bi, 01 is calculated; nce h and are knwn, the surface integral results t depend nly n the tw unknwn thermal cnductivities f CFRP slab: =f[k x ' k y /kxl y,r, 4' strip h ting Y,'ll 1. strip h 8ting )... h, Ta ::::: Q W efig)-.- :We.: Figs. 3a and 3b the integral values related t the tw strip heating are used t determine the tw slab cnductivities by cmparing them with the analytical slutin; in particular, being 1(11 heating)=f[k;" 1], the transverse cnductivity, kl l ' is directly btained; frm 1(.1 heating)=f[k;" k r /k;,l ne has the cnductivity rati, kl l /k l;,. " Tests are perfrmed n CFRP/APC2 laminae with different thickness, namely s=1-2-3mm, different maximum heat flux incident n the wall and different ambient temperatures. n figure 4a, b the surface temperature plts fr nrmal and parallel strip heating are reprted and cmpared with the analytical slutins. Tw(y)- Ta Tw(O)- Ta 1\\ ' 4 analy ical s lutio!, \ s mll Y/s 80 t- '\ l,,- Y/s 80 Fig. 4a: nrmal strip heating Fig. 4b: parallel strip heating n the previus fig. the infrared plts related t the same slab thickness result t be quite cincident thus shwing that the nrmalized surface temperature is independent f the maximum heat flux absrbed at wall and the ambient temperature, as expected. 84

5 The measured surface temperature integrals, 1(11 heating)=14.2 and 1(.1.. heating)=25, lead t =0.6±6% W/mK and k r / =7.5±4%; these values, related t a CFRP with a fibre vlume rati f 45%, are quite similar t thse fund in literature [10]. 6. Sme remarks and cnclusins. The abve measured values f thermal cnductivitie fr CFRP/APC2 sheets seem t be realistic when cmpared with values fund by [11]: =O.72W/mK and k l] / =10. t hrs t be nted that in literature different values f thermal cnductivities are fund: this can be explained by cnsidering that even if the istrpic cnductivities f the materials which are cmpsing the CFRP slabs were knwn, the principal cnductivities cannt be directly related t them because they depend n the gemetrical dispsitin f the fibres and n cupling effects at the fibre-matrix interface; furthermre structural imperfectin and fibre-packing uncertainties limit the applicability f theretical mdels. Experimental tests carried ut using the abve prcedure enabled the authrs t evidence its feasibility; in particular: the analytical mdel seems quite satisfactry t describe the experimental results; the experimental prtcl tgether with the analytical mdel allws a fast-nn destructive measurement, an autmatic cntrl and lw cst set up; Next develpments we are wrking at are intended tward: imprvement f present prcedure, by cnsidering the time histry f surface temperature different heating methds, such as mving surces with respect t the slab REFERENCES [1] MATSSE (G.) - Nn-destructive testing - Prc. nt. Cnf. Advancing with Cmpsites, 1988, Milan,, pp [2] HARRS (B.), Phillips (M.G.) - Nn-Destructive Evaluatin f the Quality and ntegrity f Reinfrced Plastics - Develpment in GRP Technlgy, Applied Science Publishers, [3] COMPOSTE DESGN ENCYCLOPEDA, Test Methds -v.6, University f Delaware, [4] LAMNE (A.S.), DEGOVANN (A.S.), MALLET (D.) Detectin f subsurface defects by a thermal methd - Prc. nt. Cnf. Advancing with Cmpsites,1988, Milan,, pp: [5] 01 ilio (A.), TAGLiAFr=RR (V.) - Thermai damage in iaser cutting f (O/90j2s Aramide/Epxy laminates - Cmpsites, 1989, pp [6] TAGLAFERR (V.) 01 LO (A.) CRVELL VSCONT. (1.)- Laser cuffing f fibre reinfrced plyester - Cmpsites, 1985, pp [7] BERARD (P.G.), CUCCURULLO (G.) - Thermal respnse evaluatin f an anistrpic slab subjected t a cnfined heating - Prc. X Cngr. U..T., 1993, Milan. [8] BERARD (P.G.), CUCCURULLO (G.) - nfrared measurements. f.thermal cnductivities fr anistrpic slab CFRP thermplastic laminates - Wrkshp nfrared Technlgy and Applicatins, 1993, Capri. [9] BERARD (P.G.), TAGLAFERR.(V.), CUCCURULLO (G.) - Thermal Cnductivities in Unidirectinal CFRP - Advancing with Cmpsites, 1994, Milan. [10] PLLNG (M. w.) - Thermal Cnductivity f CFR Cmpsites - Jur. f Material Science, 14: [11] MALDAGUE (X. P.V.) - Nn destructive evaluatin f materials by infrared thermgraphy- 1993, Springer-Verlag 85