INFLUENCE OF ANISOTROPY OF PYROLYTIC CARBON ON EFFECTIVE PROPERTIES OF CARBON/CARBON COMPOSITES

Size: px

Start display at page:

Download "INFLUENCE OF ANISOTROPY OF PYROLYTIC CARBON ON EFFECTIVE PROPERTIES OF CARBON/CARBON COMPOSITES"

Amelia Malone
6 years ago
Views:

INFUENE OF NISOTOY OF YOYTI ON ON EFFETIVE OETIES OF ON/ON OMOSITES I. Tsuov. Dach ad T.S. Goss Depatmet of Mechacal Egeeg Uvesty of New Hampshe Duham NH 0384 US go.tsuov@uh.

1 INFUENE OF NISOTOY OF YOYTI ON ON EFFETIVE OETIES OF ON/ON OMOSITES I. Tsuov. Dach ad T.S. Goss Depatmet of Mechacal Egeeg Uvesty of New Hampshe Duham NH 0384 US SUMMY Effectve elastc popetes of cabo/cabo compostes fabcated by chemcal vapo fltato ae pedcted tag to accout the cyldcal othotopy of pyolytc cabo layes. Mcoscopc obsevatos ae used to chaactee mcostuctue of the composte. The effects of asotopy o the oveall mateal espose ae dscussed. Keywods: cabo/cabo compostes mcomechacs asotopy effectve popetes. INTODUTION Ths pape deals wth the mcomechacal modelg of cabo/cabo compostes (/) fabcated by chemcal vapo fltato (VI) of cabo fbe pe-fom. The techology of VI volves sythess of pyolytc cabo (yo) patcles fom hydocabo gas ad the deposto o cabo fbes. The pocess esults fomato of a poous pyolytc cabo matx fllg space betwee the fbes. Ths matx s ogaed the cyldcally othotopc layes cocetcally located aoud fbes as show Fg. a. These layes coespod to dffeet degees of pefeed oetato (o textue) of basal plaes yo that ca be chaacteed by the degee of optcal asotopy polaed lght mcoscopy see [] ad efeeces thee. The umbe of layes the wdth ode ad stuctue ae stogly flueced by the paametes of fltato such as tempeatue pessue esdece tme etc. Fgue. Example of a fbe suouded by seveal layes of yo havg dffeet levels of textue: fom mcogaph to model. ased o data fom [].

2 evous effots to pedct the effectve elastc popetes of / compostes mostly assumed the equvalet sotopc behavo of yo []. Ths assumpto s useful the evaluato of cotbuto of poosty ad mophology of the efocemet to the oveall espose of the mateal. Howeve to aalye the fluece of fabcato paametes ad to udestad local stess cocetatos the composte the asotopy ad homogeety of the matx mateal ca ot be eglected. Ou appoach to pedctg the effectve elastc popetes of / composte s based o the soluto of the elastcty poblem fo oe fbe suouded by a umbe of layes of dffeetly textued cyldcally-othotopc yo see Fg.. y cosdeg mechacal espose of ths obect to seveal basc load cases (axal teso tasvese hydostatc teso axal shea ad tasvese shea) all compoets of the oveall mateal stffess teso fo ths cyldcal cluso ca be detemed. Ths esult ca be used combato wth oe of the well developed mcomechacal models ethe composte cylde assemblage by Hash ad ose [3 4] o geealed selfcosstet scheme by hstese ad o [5] to pedct the oveall composte popetes. Geeal soluto of the basc poblems s chose the fom poposed by Hash [4]. The tegato costats the geeal soluto ae detemed to satsfy the exteal bouday codtos ad the cotuty of dsplacemets ad tactos at the tefaces betwee layes. Such a appoach povdes ot oly the oveall mechacal popetes of the composte but also the dstbuto of stas ad stesses aoud fbes fo basc loadg cases. Ths fomato offes a valuable sght o the fluece of the yo coatg mcostuctue o stess cocetatos ad possble modes of falue / composte. I ths pape we demostate ou appoach by cosdeg the axsymmetc poblem fo a multlayeed cylde subected to the -plae tasvese hydostatc loadg (teso o compesso) ad the pescbed axal elogato. We poduce explct aalytcal fomulae fo dsplacemets ad stesses all layes. The soluto of the elastcty poblem s used to deteme the effectve logtudal Youg s modulus osso s ato ad tasvese (omal to fbe) bul modulus of the oveall composte mateal. ESTI FIEDS IN MUTIYEED OMOSITE YINDE We cosde a mateal system cosstg of a cyldcally-othotopc o tasvesely sotopc cylde of adus suouded by (-) cocetc layes (... ) whee ae the coodates the cyldcal coodate system as show Fg.. The layes ae assumed to be pefectly boded so the dsplacemets ad adal compoets of tacto ae cotuous though the teface betwee ay two adacet layes. Each -th laye s cyldcally othotopc ad chaacteed by stffesses. The heght of the cylde s h h / h /. The coe cylde ( ) s teated as the fst laye.

3 Fg.. omposte cylde stuctue The cylde s subected to the -plae tasvese hydostatc loadg T ad the pescbed axal sta. The esultg defomato wll be axsymmetc: thee wll be o agula dsplacemet ad the adal dsplacemet wll deped upo the adal coodate oly.e. u u. Equlbum equato yelds the followg dffeetal u : equato fo adal dsplacemet u u u 0 () whee / ad mateal costats assume the coespodg values fo each laye. The geeal soluto of ths oday dffeetal equato s gve by Hash [4]: u b () b whee ad ad ae the tegato costats. Ths soluto esults the followg expessos fo omal stess compoets:

4 . (3) The tegato costats ad assume dffeet values fo each laye:.... These values ca be foud fom the cotuty codtos:. u u (4) Followg the fluece matx appoach smla to that used by Hevé ad Zaou [6] fo sotopc costtuets we ca epeset equatos (4) the matx fom: V V... (5) whee T ; V s the vecto of tegato costats of a -th laye (... ) ad vecto T ; depeds o the mateal popetes ad exteal adus of -th laye. Matx s gve by:. epesetato (5) allows us to costuct a ecuet pocedue to fd all tegato costats ad thus obta the complete dsplacemet ad stess felds as gve by equatos () ad (3). The pocedue s descbed the text to follow. et us solve matx equato (5) fo the set of tegato costats of the th laye: M V N V (6)

5 whee N ad. M Fomula (6) ca be utled to expess the tegato costats ay th laye tems of tegato costats of the st laye (e coe cylde): V V (7) whee N T ad the compoets of ae as follows: ] [ ] [ N. ] [ ] [ N Expadg fomula (7) ad assgg 0 fo the coe cylde to avod sgulaty at the cete 0 we poduce the followg epesetato fo the vecto of tegato costats:. 0 M M Thus tegato costats of ay laye ca be expessed tems of the tegato costat. I patcula fo the oute -th laye:

6 . lteatvely all tegato costats ca be expessed tems of. Fst we expess as. The fo each -th laye:... (8) Usg these expessos fo the tegato costats dsplacemets ad stesses each laye ca be foud fom fomulae () ad (3) tems of paametes ad whch ae detemed fom the bouday codtos of the coespodg poblem as show below. ogtudal Defomato of the ylde I the case of logtudal elogato o cotacto of the cylde wth o lateal costats the bouday codtos ae u. 0 (9) Substtutg the expesso fo the adal compoet of stess (3) the followg equato s obtaed: 0. Ths equato cotas two tegato costats of the -th laye: ad. Expessg tems of ad by meas of the secod equato (8) we deve the expesso fo the tegato costat :

7 . (0) Tasvese hydostatc loadg Fo ufom tasvese lateal compesso o teso of the cylde the bouday codtos ae u h 0. () / T The fst codto of () defes the plae sta mode of defomato so that 0. The secod codto ca be utled to poduce the equato fo the tegato costats ad. Substtutg the expaded expesso fom () fo we obta:. T Expessg tems of tegato costat : usg (8) we poduce the desed fomula fo the T. () HTEIZTION OF MIOSTUTUE Whe obseved by polaed lght mcoscopy at the mcomete scale the pyolytc cabo matx aoud fbes appeas the fom of cyldcal layes wth dffeet wdths ad optcal asotopy. ceased optcal asotopy coelates wth a ceased degee of pefeed oetato (textue) of basal plaes pyolytc cabo. Depedg o the optcal asotopy the followg classes of textue ca be dstgushed: sotopc low medum ad hgh textued [7]. The textue ca be chaacteed o the sub-mco legth scale by selected aea electo dffacto (SED) a tasmsso electo mcoscope by measug oetato agles (Os) [8]. O ages.4 O 0.88 O.4 ad O 0.88 coespod to low medum ad hgh textued cabo espectvely.

8 et us cosde / specme maufactued at the Uvesty of Kalsuhe by chemcal vapo fltato of cabo fbe felts at methae pessue of 5 a (see e et al. [8] whee ths patcula composte s desgated as Mat_). To obta O as fucto of the dstace to fbe suface the SED vestgatos wee pefomed wth the selected aea apetue allowg the aalyss of a specme aea of about 550 m damete see Fg. b. The measued values of O wee utled to deteme the asotopc mechacal popetes of the matx mateal aoud fbe. ased o the value of O the sets of the elastc modul wee calculated by applyg the aalytcal modelg pocedue developed [9]. The basc dea of ths pocedue s to epeset the mateal at the aolevel as a system of coheet domas of cabo basal plaes. The oetato of these domas s descbed by the expemetally obseved O value whch coespods to the wdth at half maxmum of the oetato o the dstbuto cuve. The mechacal popetes of the domas ae assumed to be those of hghly odeed pyolytc gaphte (Veg et al. [0]). The oveall popetes of dffeetly textued pyolytc cabo ae obtaed by applyg the homogeato pocedue fo aggegates of domas. moe detaled pesetato of ths pocedue ca be foud at et al. [9]. The esultg dstbuto of the layes havg dffeet (othotopc) mateal popetes s show Fg.c ad the stffess compoets Ga ae povded Table ([]). The popetes of the T300 cabo fbe ae tae fom []. Table.Mechacal popetes of costtuets / composte. aye t t Fbe MIOMEHNI MODEING OF / OMOSITES The effectve popetes of a budle of udectoal VI-desfed cabo fbes ca be detemed f the soluto of the elastcty poblem fo multlayeed cylde s ow. These popetes ca the be used as a basc buldg bloc mcomechacal modelg of / compostes havg vaous popetes ad fbe oetato pattes. To obta the effectve popetes of the udectoal fltated cabo fbes we use the composte cylde assemblage model toduced by Hash ad ose [3 4]. The effectve modul ae detemed by assgg ceta choces of homogeeous bouday codtos dsplacemets (o tactos). If these codtos esult a state of stess wth homogeeous tactos (o dsplacemets) o the coespodg boudaes the

9 effectve modul ae gve by the elatos betwee the volume aveage stas ad stesses. The axsymmetc aalyss pocedue peseted the Elastc Felds secto eables us to deteme thee mateal paametes of the equvalet tasvesely sotopc mateal: logtudal Youg s modulus ad osso s ato ad tasvese bul modulus. elatg aveage stesses ad stas a composte cylde subected to bouday codtos (9) povdes values fo axal paametes: E u (3) whee s the axal stess aveaged ove the cylde coss secto. Tasvese bul modulus K T s foud usg bouday codtos (): K T T. (4) u et us evaluate how asotopy of yo layes flueces pedctos fo these mateal paametes. We cosde the cabo fbe/yo matx system descbed the pevous secto. Substtutg values fom the Table to (3) we obta that E Ga If the yo s assumed to be sotopc the equvalet Youg s modulus ad osso s ato of the matx mateal ca the be foud fom the ule of mxtue as E m Ga m These values esult the pedcto fo the tasvese bul modulus K T Ga. Howeve explct calculato usg equato (3) that taes to accout asotopc popetes of yo layes poduces otceably lowe estmate of the tasvese bul modulus amely K T 7. 96Ga. Thus eglectg the othotopc layeed atue of yo / compostes may cause sgfcat oveestmates (up to seveal tmes as ths example) of the effectve tasvese mateal modul the fltated cabo budles. ONUSIONS closed-fom aalytcal soluto of the axsymmetc elastcty poblem fo fbes suouded by multple cyldcally othotopc layes was poposed. Ths soluto was utled to pedct the effectve elastc popetes of udectoal budles of cabo fbes suouded by yo matx of vayg textue. It was show that eglectg the asotopc atue of yo mateal may esult sgfcat accuaces pedcted values of ceta mateal paametes.

10 KNOWEDGEMENTS The authos gatefully acowledge the facal suppot of the Natoal Scece Foudato though the Dvso of Mateals eseach gat DM Mateals Wold Netwo: Mult-Scale Study of hemcal Vapo Ifltated abo/abo ompostes. efeeces.. at I. Tsuov T. oehle N. oel T. Shvasa. e D. Gethse Numecal studes of the fluece of textual gadets o the local stess cocetatos aoud fbes cabo/cabo compostes ommu. Nume. Meth. Egg I. Tsuov. at. Nova E. Schac Mcomechacal Modelg of oous abo/abo ompostes Mech. dv. Mate. Stuct Z. Hash. W. ose The Elastc Modul of Fbe efoced Mateals. ppl. Mech Z. Hash Themoelastc popetes ad coductvty of cabo/cabo fbe compostes Mech. Mate M. hstese K. H. o Solutos fo effectve shea popetes thee phase sphee ad cylde models. Mech. hys. Solds E. Hevé. Zaou Elastc ehavo of Multply oated Fbe efoced ompostes It.. Egg. Sc e K.. Hüttge O the Temology fo yolytc abo abo e D. Gethse W. Zhag K.. Hüttge Textue hages the Matx of a Ifltated abo Fbe Felt Studed by olaed ght Mcoscopy d Selected ea Electo Dffacto abo at. e E. Schac D. Gethse Modelg the Effect of Mcostuctue o the Elastc opetes of yolytc abo abo Veg.-M. Gebet. Wae upublshed Isttut fü Westoffude I Uvestät Kalsuhe (TH) at pesoal commucatos G. Wagoe. aco Elastc ostats ad Themal Expaso oeffcets of Vaous abo Fbes Exteded bstacts of 9 th eal abo ofeece

GREEN S FUNCTION FOR HEAT CONDUCTION PROBLEMS IN A MULTI-LAYERED HOLLOW CYLINDER

GREEN S FUNCTION FOR HEAT CONDUCTION PROBLEMS IN A MULTI-LAYERED HOLLOW CYLINDER Joual of ppled Mathematcs ad Computatoal Mechacs 4, 3(3), 5- GREE S FUCTIO FOR HET CODUCTIO PROBLEMS I MULTI-LYERED HOLLOW CYLIDER Stasław Kukla, Uszula Sedlecka Isttute of Mathematcs, Czestochowa Uvesty