Poster Session, Thursday, June 17Theme F686 - N1123Gradient Model<strong>in</strong>g of Strengthen<strong>in</strong>g and Soften<strong>in</strong>g <strong>in</strong> Inelastic Nanocrytall<strong>in</strong>e Materials withReference to the Triple Junction and Gra<strong>in</strong> BoundariesBabur Deliktas 1 * and George Z. Voyiadjis 21 Department of Civil Eng<strong>in</strong>eer<strong>in</strong>g, Mustafa Kemal University, Hatay, Iskenderun 31200, Turkey1 Department of Civil and Environmental Eng<strong>in</strong>eer<strong>in</strong>g, Louisiana State University, Baton Rouge, LA 70803, USAAbstract-The work presented here provides a generalized structure for model<strong>in</strong>g poly<strong>crystals</strong> from micro to nano size range. The poly<strong>crystals</strong>tructure is def<strong>in</strong>ed <strong>in</strong> terms of the gra<strong>in</strong> core, the gra<strong>in</strong> boundary and the triple junction regions with their correspond<strong>in</strong>g volume fractions.Depend<strong>in</strong>g on the size of the crystal from micro to nano different types of analyses are used for the respective different regions of the polycrystal.The analyses encompass local and nonlocal cont<strong>in</strong>uum or crystal plasticity. Depend<strong>in</strong>g on the physics of the region dislocation based <strong>in</strong>elasticdeformation and/or slip/separation is used to characterize the behavior of the material. The analyses <strong>in</strong>corporate <strong>in</strong>terfacial energy with gra<strong>in</strong>boundary slid<strong>in</strong>g and gra<strong>in</strong> boundary separation. Certa<strong>in</strong> state variables are appropriately decomposed to energetic and dissipative components toaccurately describe the size effects. Additional entropy production is <strong>in</strong>troduced due to the <strong>in</strong>ternal subsurface and contact<strong>in</strong>g surface.This new formulation does not only provide the <strong>in</strong>ternal <strong>in</strong>terface energies but also <strong>in</strong>troduces two additional <strong>in</strong>ternal state variables forthe <strong>in</strong>ternal surfaces (contact surfaces). One of these new state variables measures tangential slid<strong>in</strong>g between the gra<strong>in</strong> boundaries and the othermeasures the respective separation. A multilevel Mori-Tanaka averag<strong>in</strong>g scheme is <strong>in</strong>troduced <strong>in</strong> order to obta<strong>in</strong> the effective properties of theheterogeneous crystall<strong>in</strong>e structure and to predict the <strong>in</strong>elastic response of a nanocrystall<strong>in</strong>e material. The <strong>in</strong>verse Hall-Petch effect is alsodemonstrated. The formulation presented here is more general and it is not limited to either polycrystall<strong>in</strong>e or nanocrystall<strong>in</strong>e structured materialsHowever, for more elaborate solution of problems a f<strong>in</strong>ite element approach needs to be developed.The material model<strong>in</strong>g of nanocrystall<strong>in</strong>es has beenemphasized recently by Gleiter (2000). He po<strong>in</strong>ted out theoutstand<strong>in</strong>g possibilities of the so called, microcrystall<strong>in</strong>ematerials that are usually def<strong>in</strong>ed as the s<strong>in</strong>gle or multi phasepolycrystall<strong>in</strong>e metallic materials with gra<strong>in</strong> sizes typicallyless than 100nm. It has been well recognized thatnanaocrystall<strong>in</strong>e materials may exhibit <strong>in</strong>creased strength andharden<strong>in</strong>g, improved toughness, reduced elastic modulus andductility, enhanced diffusivity, higher specific heat, enhancedthermal expansion coefficient, and superior soft magneticproperties <strong>in</strong> comparison with conventional polycrystall<strong>in</strong>ematerials (Ashby, 1970; Hall, 1951; Petch, 1953).The plastic deformation mechanisms of nanocrystall<strong>in</strong>estructure are much more complicated than those of thepolycrystall<strong>in</strong>e material. Few of the controversial issues of theplastic behavior of the nano/polycrystall<strong>in</strong>e materials are <strong>in</strong>regard to the work harden<strong>in</strong>g and strengthen<strong>in</strong>g <strong>in</strong> suchmaterials. For example, experimental studies reported by Q<strong>in</strong>gand X<strong>in</strong>gm<strong>in</strong>g (2006) showed that when the gra<strong>in</strong> size ofnanocrystall<strong>in</strong>e is greater than a critical value, the Hall-Petch(H-P) relation is satisfied for a wide range of nanocrystall<strong>in</strong>ematerials. However, as the gra<strong>in</strong> size of metals decreasebeyond the critical value, the H-P slope becomes negative.The so called <strong>in</strong>verse soften<strong>in</strong>g effect of the H-P relation isobserved for some nanocrystall<strong>in</strong>e materials (Nieh and Wang,2005; Tjong and Chen, 2004; Zhao, et al., 2003). This <strong>in</strong>verseHall–Petch phenomenon was first expla<strong>in</strong>ed <strong>in</strong> terms ofporosity <strong>in</strong> nanocrystall<strong>in</strong>e materials. This explanation wasproved <strong>in</strong>correct when high quality NC materials wereproduced and, they still exhibited a negative Hall–Petch slope(Khan, et al., 2000). To understand the <strong>in</strong>verse Hall–Petchphenomenon, numerous studies were conducted. Many modelsare based on the rule of mixtures and on the competition oftwo or more mechanisms (Carsley, et al., 1995). Meyers et al.(2006) and Qiang and X<strong>in</strong>gm<strong>in</strong>g (2006) presented veryapproximate models based on the rule of mixtures as <strong>in</strong>composite materials <strong>in</strong> order to show the <strong>in</strong>verse soften<strong>in</strong>geffect of the H-P relation.The computational methods available for simulat<strong>in</strong>gnanocrystall<strong>in</strong>e materials are clearly imperfect but they maybe capable of provid<strong>in</strong>g important <strong>in</strong>sights <strong>in</strong>to the behaviorof nanoscale materials. Therefore, <strong>in</strong> this paper, thetheoretical bases for model<strong>in</strong>g the <strong>in</strong>elastic behavior of thematerial is based on the thermodynamic framework andconstitutive laws given <strong>in</strong> the works of Voyiadjis andDeliktas (Voyiadjis and Deliktas, 2009a; b) where thetheoretical concepts have been elaborated <strong>in</strong> detail. Thepresent treatment is different than that previously proposedby Voyiadjis and Deliktas (Voyiadjis and Deliktas, 2009a; b)<strong>in</strong> that this new formulation does not only provide the<strong>in</strong>ternal <strong>in</strong>terface energies but also <strong>in</strong>troduces two additional<strong>in</strong>ternal state variables for the <strong>in</strong>ternal surfaces (contactsurfaces). By us<strong>in</strong>g these <strong>in</strong>ternal state variables togetherwith displacement and temperature, the constitutive model isformulated as usual by state laws utiliz<strong>in</strong>g free energies andcomplimentary laws based on the dissipation potentials. Oneof these new state variables measures tangential slid<strong>in</strong>gbetween the gra<strong>in</strong> boundaries and the other measures therespective separation. A homogenization technique isdeveloped to describe the local stress and stra<strong>in</strong> <strong>in</strong> thematerial. The material is characterized as a composite withthree phases: the gra<strong>in</strong> core, the gra<strong>in</strong> boundaries and triplejunctions. The model presented for a general case is thenapplied to pure copper under uniaxial tensile load. The resultsare compared with the experimental data.The geometrical representation of the RVE proposed bydifferent authors (Meck<strong>in</strong>g and Kocks, 1981; Pipard, et al.,2009) can be conceptually described by three regions such asthe gra<strong>in</strong> core, the gra<strong>in</strong> boundary, and triple junctions withtheir correspond<strong>in</strong>g <strong>in</strong>ternal <strong>in</strong>terfaces, respectively. In thiswork the simplified nanocrystall<strong>in</strong>e structure shown <strong>in</strong> Figure1b is represented as a 2D triangle representative volumeelement (RVE) of a composite material with three phases;gra<strong>in</strong> core, gra<strong>in</strong>-boundary, and triple junction (see Figure 1).6th Nanoscience and Nanotechnology Conference, zmir, 2010 713
PPPPPPPoster Session, Thursday, June 17Theme F686 - N1123Evaluation of Permeability of Masterbatch-Based PA6/nanoclay Composite Films11UMohammad FasihiUP0F P*and Mohammad Reza Abolghasemi0TPTechnology of Polymer Research Group, Iranian Academic Center for Education, Culture and Research (ACECR), Branch of AmirkabirUniversity of Technology, Tehran, Iran,Abstract-This study focuses on the effect of the nanoclay masterbatch on the extent of exfoliation and barrier properties of PA6/organoclaynanocomposite films. Gas permeability through nanocomposite films decreased significantly just by load<strong>in</strong>g a small amount of nanoclay.Theoretical models fit the experimental data appropriately.Over the last decades, a great deal of researches have beendevoted to the different fields of polymer-layered silicatenanocomposites which have shown promis<strong>in</strong>g improvements[1-3]<strong>in</strong> properties, at low filler volume fraction.POne of the great attractive applications of polymer-layeredsilicate nanocomposites is the field of packag<strong>in</strong>g. Thereduction of oxygen permeability is of crucial importances<strong>in</strong>ce oxygen as an atmospheric component which promotesthe spoilage mechanism of food. Incorporat<strong>in</strong>g layered silicate<strong>in</strong>to the polymeric matrix, ord<strong>in</strong>arily, improves gas barrierproperties of the polymer by reduc<strong>in</strong>g the volume available forgas transport as well as mak<strong>in</strong>g a more tortuous path for[4-6]penetrant molecules. PThe current study exam<strong>in</strong>ed the effect of nanoclaydispersion by us<strong>in</strong>g particulate nanoclay and nanoclaymasterbatch, on morphology and oxygen permeability ofpolyamide-6 /layered silicate nanocomposite films bear<strong>in</strong>gdifferent concentrations of nanoclay, as a potential candidatefor good packag<strong>in</strong>g applications. Furthermore, thepermeability data has also been compared to the theoreticalmodels.XRD results showed flat diffraction profile and the absenceof any basal reflections <strong>in</strong>dicated that the ordered layers ofnanoclays <strong>in</strong> the nanocomposites have been disrupted.With regards to the crystall<strong>in</strong>e structure, all films exhibited aostrong reflection at 21.5P dist<strong>in</strong>guished t crystal form which showed that the load<strong>in</strong>g of nanoclay didnot alter crystal structures <strong>in</strong> th<strong>in</strong> films.Although XRD scan results suggested only a low degree of<strong>in</strong>tercalation, the morphology observed with TEM <strong>in</strong>dicatedthe presence of both <strong>in</strong>tercalated and exfoliated structures. Thegeneral impression obta<strong>in</strong>ed from TEM was that the use ofmasterbatch builds up a higher degree of exfoliation thatconfirms the better properties of masterbatch-basednanocomposites. The maximum aspect ratio of the layers asdeduced from the TEM micrographs was about 210 <strong>in</strong> allsamples.Oxygen permeability was reduced by a factor of 4 over thepure polyamide by <strong>in</strong>corporation of 3 wt% nanoclay. As thenanoclay load<strong>in</strong>g was <strong>in</strong>creased to 7 wt%, only a slightimprovement <strong>in</strong> permeation resistance was observed.Several studies on model<strong>in</strong>g the barrier properties ofpolymer nanocomposite have been performed based on the[7],tortuous pathway concept by Cussler.P Fredrickson and[8,9]Gusev et al.P Bharadwaj improved Nielsen’s model by[6]simply <strong>in</strong>troduc<strong>in</strong>g a new order parameter. P Another model[10]called NG model was developed by Ghasemi et al.PPThetheoretical models fit the experimental data properly.In summery, we showed improvements <strong>in</strong> oxygen barrierand mechanical properties by <strong>in</strong>creas<strong>in</strong>g the silicate content. Inparticular, nanocomposite films based on masterbatchexhibited the best performances. XRD scans and TEMmicrographs collectively demonstrated the good dispersionand orientation of silicate platelets <strong>in</strong>side the matrix, as well asthe possible presence of polymer-clay <strong>in</strong>teractions. Thetheoretical model fitted the experimental data very well.Figure 1. TEM images of specimens (a) particulate nanoclay-basedfilms (b), (c) masterbatched-based films*Correspond<strong>in</strong>g author:mohammadreza.abolghasemi@gmail.com[1] Ke, Y., Long, C., Qi, Z, J. Appl. Polym. Sci. 1999, 71, 1139-1146.[2] Becker, O., Cheng, Y., Varley, J. R., Simon, G. P,Macromolecules 2003, 36, 1616-1625.[3] Alexandre, M., Dubois, P. Mater. Sci. Eng. 2000, 28, 1-63.[4] H. Yamamoto, Y. Mi, S.A. Stern, J. Polym. Sci., Part B:Polym. Phys. 1990, 28, 2291-2304.[5] Fornes, T. D., Paul, D. R., Polymer 2003, 44, 4993-5013.[6] Liu, L., Qi, Z., Zhu, X. J. Appl. Polym. Sci. 1999, 71, 1133-1138.[7] Yang, W.H. Smyrl, E.L. Cussler, J. Membr. Sci. 2004, 231,1-12.[8] G. H. Fredrickson, J. Bicerano, J. Chem. Phys. 1999, 110,2181-2188.[9] A.Gusev, H.R. Lusti, Adv. Mat., 2001, 13, 1641-1643.[10] E. Ghasemi, A. H. Navarchian, “Model<strong>in</strong>g the Effects ofSilicate Layer Orientation on Barrier Properties of Polymer/ClayNanocomposites”, proceed<strong>in</strong>g of 9th International Sem<strong>in</strong>ar onPolymer Science and Technology (3TISPST3T 2009), Tehran, Iran.6th Nanoscience and Nanotechnology Conference, zmir, 2010 714
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