Modeling and Study of the Effect of Weakening Factor on Elastic Property of Particulate Metal Matrix Composites

Transcription

1 Indian Soiety fo Non-Destutive Testing Hydeabad Chapte Po. National Semina on Non-Destutive Evaluation De. 7-9, 2006, Hydeabad Modeling and Study of the Effet of Weakening Fato on Elasti Popety of Patiulate Metal Matix Composites S. Adalaasu Vikam Saabhai Spae Cente, Tivandum Abstat Metal matix omposites mateials have emeged as potential andidate fo a vaiety of stutual appliations in the aeonautial / aeospae, tanspotation, defene and spots industies beause they ae onsideably heape and easie to poess. A MMC is nomally fabiated using a dutile metal (e.g., Al, Ti o Ni) as the matix mateial and a eami mateial (e.g., alumina, SiC o gaphite) as dispesoids. Combining the metalli popeties suh as good dutility and toughness of the matix with eami popeties suh as high stength, hadness and elasti modulus of the dispesoids, the omposites exhibit high toughness; speifi stength, stiffness and good wea esistane. Patiulate metal matix omposites (PMMCs) ae a lass of omposites that have evoked keen inteest, lagely due to the pomise of impoved popeties ove onventional metals and alloys. Among the many eami einfoements SiC has been found to have exellent ompatibility with the Almatix. Conventional liquid metallugy and powde metallugy ae the two ommonly employed methods by whih these omposites ae poessed. The test speimens used in these expeiments ae poessed though liquid metallugy. Hene these omposites exhibit the onventional asting defets as well as the omposite defets. The pesene of fine poosity in MMC auses a edution in mehanial popety of metal matix omposites poduts. These poosities ae bound to ome, as it is a ast podut. A theoetial model to pedit the elasti popety of metal matix omposites is deived in this pape. A fato that epesents the weakening aused by the pesene of poosity is also inluded in the model. The elasti modulus of the podut based on theoetial models ae also alulated and ompaed with the expeimental values. Fo the expeimental elasti popety estimation ultasoni veloity measuements ae made use of. Results indiated that ultasoni testing is moe appopiate tehnique to evaluate the quality of omposite as the elasti popeties deived by ultasoni veloity values of defetive speimens ae deviating with pedited values.. In this pape an attempt has been tied to standadize an ultasoni method fo evaluating the quality of the omposite speimens. Pimaily ultasoni tehniques ae seleted, as the veloity of ultasoni is muh influened by the onstituent elements and its omposition in the medium though whih it tavels. Keywods: Metal matix omposites, Elasti modulus, and Ultasoni veloity 1. Intodution Metal matix omposites mateials have emeged as potential andidate fo a vaiety of stutual appliations in the aeonautial / aeospae, tanspotation, defene and spots industies beause they ae onsideably heape and easie to poess

2 S. Adalaasu [1-3]. A MMC is nomally onsists of a dutile metal as the matix mateial and a eami mateial as dispesoid. Hene the MMC will exhibit a ombination of metalli popeties and eami popeties. Resulting in high toughness; speifi stength, stiffness and good wea esistane. Among the many eami einfoements SiC has been found to have exellent ompatibility with the Al-matix. Conventional liquid metallugy and powde metallugy ae the two ommonly employed methods by whih these omposites ae poessed [4,5]. The test speimens used in these expeiments ae poessed though liquid metallugy. 2. Theoetial Model fo Pedition of Young's Modulus In ode to estimate the elasti popety of the MMC initially a theoetial model is to be deived Ou ealie woks on MMC fo finding out Young s modulus of omposites esulted in deiving a model (R6) E = E m (1- V ) + X E V (1) Whee E, E m and E ae Young s modulus of omposite, matix and einfoement espetively, V the volume fation of the dispesoid, V is effetive volume fation of dispesoid and it given by V = V. e (b. V ) Whee 'b' is a haateisti onstant and a funtion of l/d atio and given by b = {23.04-[5-0.2(l/d) 2 ]} 1/2 fo 1 l/d 25 b = 1 fo l/d > 25 and X is the weakening fato and is given by X = a. e (b. V ) Whee 'a' is a fato indiating the effetiveness esulted by the oientation of dispesoid and it is fo disontinuously dispesoids used in poessing these speimens. Though the above-explained model ould faily onu with the expeimental values, voids ae not taken into aount in deiving this model, as they ae not desiable in the final podut. But in atual patie it an be seen that voids ould not be eliminated totally. Hene it is impeative to onside the effet of voids on mehanial popeties. This neessitates modifying equation (1) taking into aount the effet of poosity on elasti popeties of the matix mateial. Aodingly the fato E m equies a oetion. Fo adding a oetion to E m it is assumed that the einfoement patiles of volume fation V ae unifomly distibuted in poous matix mateial. Thus, the effetive elasti modulus of the matix, E eff, ontaining poosity of volume fation f an be detemined by using Eshelby model [17]. In this model the effetive bulk modulus K eff, and shea modulus µ eff, ae alulated fo an isotopi mateial with bulk modulus K and shea modulus µ ontaining a volume fation of andomly distibuted, non-inteating, spheial voids. K eff = K / 1+Af whee A = onstant and is given by A = 1+ 3K/4 µ and µ eff = µ / 1+Bf whee B = onstant and is given by B = 5(3K + 4 µ) / (9K + 8 µ) The effetive Young's Modulus of matix is then deived as E eff = 9 K eff / 1+(3 K eff / µ eff ) (2) 154

3 Elasti Popety of Patiulate Metal Matix Composites Replaing E m by E eff in equation (1) gives, E = E eff (1- V ) + X E V (3) In ode to veify the validity of the above said equation, the esults obtained ae ompaed with Halpin-Tsai [18] equations, modified equation of Hemans [19] and Hill's [20] wok. The modified equation of Hemans and Hill s to suit patiulate omposites is as given below, P / P m = 1+ ξηv p / 1 - ηv p (4) Whee P and Pm epesent moduli of omposite and matix espetively, η and ξ ae empiial fatos and η is given by η =[(P / P m ) - 1] / [(P / P m ) + 1] Fo pediting the bulk modulus K, substitute ξ as ξ = 2 (1-2V m ) / (1+ V m ) Fo pediting the shea modulus µ, substitute ξ as ξ = (7-5 V m ) / (8-10 V m ) Fom the values of K and µ the young's modulus an be alulated using equation (2) 3. Expeimental Poedue 3.1 Mateial The hot olled 2124 aluminum alloy (Al- 4.4 Cu-1.5 Mg-0.6) matix omposite plates ontaining 10 wt % (7.8 vol %) of silion abide patiles (SiC p ) with an aveage size of 23 µm wee seleted fo this expeimental tial. The sizes of the speimen, shown in Fig. 1, wee 175 X 125 X 6-8mm. Eight suh piees wee seleted and identified asa1, A2, B1, B2, C1, C2, D1 and D2. These speimens wee subjeted to ultasoni and x-ay evaluation. Fig. 1: Hot olled omposite plate 3.2 Poessing The synthesis of MMC was aied out using onventional sti asting tehnique. The leaned metal ingots wee melted in a pit funae. The einfoing patiulate silion abide was peoxidised and then intodued into the liquid matix alloy at a onstant ate. Afte that the melt was heated and ast into a metal mold to obtain omposite ingots of (250 x 225 x 40) mm. Afte homogenizing the ingots wee foged in two steps using 0.5 and 1.0 ton foging hamme to edue the thikness to mm. Late, the foged blanks wee ut into two halves and olled in a high stip olling mill to obtain sheets of thikness 6-8 mm. Afte seonday poessing, the plates wee solutionised, quenhed and aged. 3.3 Poosity Measuement Aveage volume peentage of poosity of eah speimen is alulated by Ahimedean piniple. 3.4 Ultasoni Veloity Measuement The test piees wee divided into 35 zones and subjeted to ultasoni testing wheein the ultasoni veloity in eah zone is measued using a delay pobe and a Kautkame make thikness gauge. The measued veloities of the piees ae epesented in Figs. (2,3,4,5). 3.5 X-Ray Radiogaphy The test speimens of the expeimental tials ae subjeted to X-Ray adiogaphy using single wall single image tehniques. 155

4 The exposue paametes ae seleted in suh away as to obtain a density of 2.5 appoximately in the egion of inteest. Among the piees tested, D1 and D2 wee found to be defetive. S. Adalaasu 6500 VELOCITY IN PLATE-D VELOCITY IN PLATE A VELOCITY (mt /se) VELOCITY( mt / se ) LOCATIONS PLATE-1 PLATE-2 Linea (PLATE-2) Linea (PLATE-1) Figue LOCATION PLATE- A1 PLATE-A2 Linea (PLATE-A2) Linea (PLATE- A1) Figue 2 VELOCITY IN PLATE B Table 2: Aveage values of poosity ontent in speimens afte olling Speimen Identifiation Avg. vol % of poosity A1, A B1, B C1,C D1,D VELOCITY(mt /se) LOCATIONS PLATE-1 PLATE-2 Poly. (PLATE-2) Poly. (PLATE-1) Figue 3 4. Results and Disussion The aveage value of poosity ontent in the olled speimen is given in Table 2. The possible poosity ontent in the speimen may be due to the ai entapment though votex at the time of poessing and sine the melt beomes less fluid due to futhe addition of SiC, it will be diffiult fo aleady entapped ai bubbles to esape fom the melt duing solidifiation. VELOCITY (mt/se) VELOCITY IN PLATE-C LOCATIONS PLATE-1 PLATE-2 Linea (PLATE-1) Linea (PLATE-2) Figue 4 Fom figues 2 to 4, it is seen that the deviation in veloity fom mean shows a unifomity thoughout the plate. It indiates unifom distibution of patiles and absene of objetionable defets. In Fig. 5 the low values of veloity obseved in speimen is due to the effet of voids. Like wise patile agglomeation is found to be the eason fo high veloity obseved in some loations as waves an tavel at a high veloity in SiC patiles. Futhe the Young s moduli of the speimens ae 156

5 Elasti Popety of Patiulate Metal Matix Composites alulated using the mean longitudinal veloity (V L ) value obtained. E ρ = ( 1+ σ )( 1 2σ ) ( 1 σ ) V 2 L studied futhe. Also deviated a veloity value obtained in speimens (D1 and D2) lealy indiates the pesene of defets in it and it is visualised by X-ay inspetion. whee υ and ρ ae the Poisson s atio and density of the omposite espetively. The effetive Poisson s atio and density of the omposite mateial ontaining a poous matix of volume fation of poosity, v p and einfoement patile of volume fation v is given by the ule of mixtues law as σ m ( 1 v )( v ) = σ v + v 1 p and m ( 1 v )( v ) ρ = ρ v + ρ 1. Table 3: Compaison of Elasti Modulus Method Value Obtained (in GPa) Using Pesent Equation By Halpin and Tsai Equation By Expeiment Table 3 shows a ompaison of expeimental data with pedited values of elasti modulus of % SiCp omposite. It is lea that pedition aoding to the pesent equation is well in ageement with the expeimental value and the standad Halpin and Tsai Equation. Also an ultasoni veloity measuement on omposite poduts an be used as a nondestutive method fo quality evaluation of the podut. The equation (3) an be used fo the pedition of elasti modulus. Howeve its effetiveness with espet to highe peentage of dispesoids ae to be p Figue 6 Table 4: Vaiation of Elasti Modulus with Vol% of Poosities Speimen Identifiation Table 4 and Fig. 6 indiates the effet of poosity on the elasti popeties of patiulate metal matix omposites. The poosities and the debond ae the main auses fo the weakening of metal matix omposites. In this pape it is assumed that the debond will esult in poosities and so the estimation of volume % of poosities inludes debonding also. 5. Conlusion Avg. vol % of poosity A1, A B1, B C1,C Young s Modulus in GPa D1,D A theoetial model has been poposed fo pediting the Young's modulus of 10 % SiC einfoed Al matix omposite poduts. An ultasoni veloity method fo defet detetion and evaluating the elasti popety of omposites is also poposed. The deived data fom the poposed model and expeimental ae well in ageement with those deived fom established models. 157

6 S. Adalaasu Moe expeiments ae planned to study the effetiveness of the poposed model fo highe peentage of dispesoids. 6. Aknowledgement The autho is thankful to Geneal Manage, IFF, MEE, VSSC and D. R. M. Pillai, S. Dy. Dieto, RRL (T) fo thei suggestions and guidane while pusuing this expeiment and Deputy Dieto, VSSC (MEE), Deputy Geneal Manage, QCI, MEE, VSSC fo thei enouagement and pemission to ondut this expeiments. Also the authos ae thankful to Dieto, VSSC, fo his appoval to publish this pape. 7. Refeenes 1. K.G.Satyanaayana, R.M.Pillai and B.C.Pai, (ed) Tends in Metal matix omposites - The Indian Expeiene, Pub. RRL, Tivandum. 2. M.K.Soappa, J.Po. Teh. 1997, 63, p A.Ibahim, F.A.Mohammad and F.J. Lavenia, J.Mat.Si., 1991, 26. P P.K.Rohatgi, Cast Metal matix omposites, Metals Handbook, 9 th edition, 15, p G.S.Upadhyaya, Key.Eng. Mat., , 1993, p P.N.Bindhumadfhavan, Heng Keng Wah and O.Pabhaka, J.Non.Des.Eva., 21(1), p C.Delebae, I.Baquet, C.Buneel, J.M.Rouvaen and Z.Deouihe, NDT&E Int., 25,1992, p C.K.Fang, R.L.Fang, W.P.Weng and T.H. Chuang, Mat.Cha., 43, 1999, p D.J.Roth, D.B.Stang, S.M.Swikad, M.R.DeGuie and L.E.Dolhet, Mat.Eva., July 1991, p P.K.Liaw, R.E.Shannon, and D.K.Hsu, Mat.Che. and Phy., 39, 1995, p E.G.Nesvijski, Comp.St., 48, 2000, p J.Kim and P.K.Liaw, JOM, 50(11), 1998, p G.C.Das, V.K.Sama and Guhaan Singh, 10 th Asia- Paifi Confeene on NDT 14. R.Pakash, Composites, 11(4), 1980, p Y.D.Huang, J.Non.Des.Eva., 20(3), 2001, p K.G.Satyanaayana, S. Adalaasu, A.G. Gopalakishnan Nai, S.G.K.pillaiV.K.Vaidyan,and S.Mahadevan, J.Non Des. Eva J.D.Ehelby, Po. Roy. So. London, 1957, A 241, p J.C.Halpin and S.W.Tsai, Env. In Comp. Mat. Des., 1967, AFML, TR J.J.heman, Po. Kon. Ned. Akad, v Wetensh B65, 1967, p R.Hill, J.Meh. Phy. Solids, 12, 1964, p