New Approach to Predict the Micromechanical. Behavior of a Multiphase Composite Material

Transcription

1 Advanced Studies in Theoetical Physics Vol. 8, 2014, no. 20, HIKARI Ltd, New Appoach to Pedict the Micoechanical Behavio of a Multiphase oposite Mateial EL Guesse, M.O. Bensalah, A. Ettouhai* and O. Fassi Fehi LMM Univesity Mohaed V -Agdal, * LS Univesity Mohaed V -Agdal Faculty of Science, BP 1014 Rabat, Moocco opyight 2014 EL Guesse, M.O. Bensalah, A. Ettouhai and O. Fassi Fehi. This is an open access aticle distibuted unde the eative oons Attibution License, which peits unesticted use, distibution, and epoduction in any ediu, povided the oiginal wok is popely cited. Abstact The pesent wok focuses on the study of the behavio of coposite ultiphasic. In this wok, the behavio of coposite ultiphasic has been studied in tes of pediction, in ode to contibute to pesent a icoechanical appoach behavios using the hoogenization ethods. The fist step is to know the behavio of the coposite ateial, and the second step to conside consite injected fibes in the fist atix behavio consideed, ie two-stage hoogenization fo the equivalent behavio. The Moi Tanaka Model has been used to pedict the echanical behavio. The use of this odel is based on its copatibility with the coposites at high fibe volue content. The esults obtained in the siulation using a pogaing language ae copaed with those fo analytical odeling of the echanical behavio of coposite hoogenized. Keywod: oposite, coposite ultiphasic, Behavio, Hoogenization. 1. Intoduction Multiphase ateials ost often the esult of the assebly of two ateials. The cobination of diffeent ateials usually also gives the coposite new popeties that each coponent can povide alone.

2 870 EL Guesse, M.O. Bensalah, A. Ettouhai and O. Fassi Fehi In this wok the insulato atice Silica (SiO2) has been studied. The Baiu Titanate (BaTiO3) has been selected as intinsic piezoelectic ateial used as filles[4]. The Methods of hoogenization used to estiate the acoscopic popeties of a heteogeneous ateial fo the popeties of the constituent phases and soe paaetes chaacteizing thei spatial distibutions. The objective of this wok is to develop a odel to pedict the icoechanic behavio of a atix coposite einfoced by paticles. This odel is based on the desciption of the pocessing acoss the gain and scale tansition technique of Moi-Tanaka, the filles oientation is also used in this odel. 2. Matheatical foulation The coposite is exained assued a copound atix, denoted by the index and inclusions denoted by the index ''. These inclusions can be aligned o andoly oiented in the atix.[1] 2.1 The self-consistent odel All einfoceents ae assued ebedded in a hoogeneous ediu called equivalent, having the ective popeties.[5] n 1 1 I S ( ) 1 f ( ) 2.2 The appoxiation of Moi Tanaka: This odel assues that the einfoceent is ebedded in an infinite ediu having the popeties of the atix: [ I ( n 1 Q ) I n 1 f ( S 1 I) Q whee: Q ( ) S ( ) 2.3 The influence of the oientation of the inclusions on the behavio 2.4 By intoducing the tansition atix (3 Eule angles) [ I ( n 1 t f P Q P ) I n 1 f P ( S 1 1 I) Q P Whee: P : oientation atix whee tansition atix.[5] In this pat of atheatical odeling, a ethod of hoogenization of piezoelectic coposite (Moi Tanaka) was developed in ou pevious wok. We ecall the ain equation obtained by the ethod of Moi Tanaka in the cas of coposite with an elastic inclusion. t 1 1

3 New appoach to pedict icoechanical behavio Application and intepetation of esults In this section, we ipleented the equations in the MATLAB softwae pogaing, nad we have taken as an application, the piezoelectic coposite: Silicon Dioxide/Baiu Titanate (SiO2/BaTiO3).[3] Table 1 suaized the echanical popeties of the atice and the fille. Young s Modulus (GPa) Poisson s atio Silica (SiO2) Baiu Titanate (BaTiO3) Table1: Mechanical popeties of SiO2 and BaTiO3. In the fist step, the self-consistent odel is used to obtain the actual popeties of the coposite Silica and baiu titanate.[4] The 1 equivalent behavio thus obtained is then consideed in the second stage, as a new atix to which ae added the piezoelectic fibes. The elastic behavio equivalent hoogeneous 2 (coposite ti-phasic) is then obtained using the ethod of Tanaka, Moi. To validate ou odel, we siulated ou poga with the ethod of teinal odels entioned above "Voigt and Reuss", while etaining the data peviously used in the case of an insulato (silica) Eodèle EV ER + - Et 0 0 0,1 0,2 0,3 0,4 Figue2: Result of siulation with the ethod of teinal odel Voigt, Reuss, Hashin and Sticka infeio, Hashin and Stickan supeio Thee-phase piezoelectic coposite gives significant esults copaed with a biphasic coposite. Is theefoe obseved that ou odel is alost between the lowe teinal of Reuss and Voigt supeio teinal, which has been pedicted theoetically, it can only confi the icacy of ou odel.[3]

4 872 EL Guesse, M.O. Bensalah, A. Ettouhai and O. Fassi Fehi 4. onclusion Hee we intoduced the following hoogenization ethods, siulation elastic behavio of coposites consist of at least thee phases: step 1: get lespopiétés actual 1 of the coposite Silica and baiu titanate, 2 The equivalent behavio thus obtained is then consideed in the second stage, as a new atix which ae added piezoelectic fibes. The ect of fibe on the elastic behavio is ipotant. In this wok we pesented a study of piezoelectic fibe coposites, based on the hoogenization odel Moi Tanaka, it was developed in the case of a ateial that contains a high quantity of inclusions. The esults offe infoation on the behavio of piezoelectic coposites. It appeas clealy, that a elatively lage incease of the volue faction of inclusions and the oientation of the inclusions has an ect on ateial coposite. So we can conclude that: - The igidity of the ateial inceases and depends on the volue faction (oe volue faction inceases o defoation also inceases). - thee-phase piezoelectic coposite gives significant esults copaed with a biphasic coposite. The ethod odels teinal lowe bound of voigt and uppe bound of Reuss allowed us to test and validate ou odel. Refeences [1] A. Eliouni, Application de Quelques Modèles d hoogénéisations à la pédiction du odule d young ectif des atéiaux coposites à fibes végétales. Méoie de pojet de fin d études : Maste Enegie et Technologie des atéiaux. Univesité Mohaed V-Agdal, Faculté des Sciences Rabat, (2012). [2]. ollad, T. Benzineb, E. Patoo, and M.O. Bensalah, Micoechanical analysis of pecipitate ects on shape eoy alloys behaviou, Mateials Science and Engineeing A, (2008), [3] I. Elguesse, M.O. Bensalah and O. Fassi Fehi, ontibution To Pedict The Micoechanics Behavio Of A Metal Matix oposite Reinfoced By Paticles Of Shape Meoy Alloy (SMA) : ase Al / uznal. Advanced Studies Theoetical Physics, Edited by Hikai, (2014). [4] I. Elguesse, M.O. Bensalah and Z. Sadoune, The Micoechanics Modeling Piezoelectic oposite Mateials by Method of Hoogenization Moi Tanaka: Study of Piezo-coposite SiO2/BaTiO3. Advanced Studies Theoetical Physics, Edited by Hikai, 7 (2013),

5 New appoach to pedict icoechanical behavio 873 [5] I. Elguesse, Z. Sadoune, M.O. Bensalah, and O. Fassi-Fehi, ontibution to study of coposite Mateials Based Piezoelectic Fibes: Use Moi-Tanaka Hoogenization Model. Advanced Studies Theoetical Physics, Edited by Hikai, 7 (2013), Received: June 5, 2014