Unique mechanical propertiesof nanocrystalline metals have attracted considerable interest over the pasttwo decades. A vast majority of nanocrystalline metals exhibit ultra-highstrengths or hardness, but lower tensile elongation and fracture toughness,which severely limit their application in many fields. The strength of themetals is related to the microstructure as described by the well-knownHall–Petch relationship. Generally, itis observed that the rate of strength increases by decreasing the mean grainsize below 100 nm and the strength decreases by decreasing the grain size belowabout 20–10 nm mean grain size; such a behavior has been commonly indicated asinverse Hall-Petch breakdown, implying a transition in the deformation modes ofmetals by decreasing the grain size from nanocrystalline range down to very lowlevels.
Observation of nanocrystalline materials SEM/TEM images from severalpublications revealed that nanocrystalline materials consist of randomlypolyhedral shaped grains. In order to represent the realisticmicrostructure of nanocrystalline materials into Representative Volume Element (RVE),the micro-structure geometry has been developed using Voronoi tessellationalgorithm. In each RVE, detailed three-dimensional modelling of the grain andgrain boundaries as randomly-shaped sub-volumes is performed (Figure 1), ?he previously statedtechnique has been utilizedin arrange to produce the microstructure of nanocrystallinematerials.The Voronoi algorithm has been utilized forthe creation of random grain volume fractions by generating periodic geometriesbased on the technique of Christoffersen 1. The procedure for the generationof periodic discretization of the granulates (grains) for application with thefinite element method is described in detail. The developed procedure is appliedto pure nanocrystalline copper at volume fractions of 80% and 90% taking alsointo consideration the parameter grain size.
The RVE geometricalmodel is meshed using tetrahedral finite elements (Figure 2), proper material laws at each sub-volume are assignedand the RVE is loaded under representative loading conditions. Thus, the basicmechanical properties of the material ( for instance Young’s Modulus of Elasticity) can benumerically predicted without the need to perform an extensive mechanical testcampaign. For validation purposes, a limited number of experiments isnecessary. The developed methodology will provide the means to design theessential nanocrystalline material microstructure based on the requiredmaterial properties.
The results of finite-element modelling of Young’sModulus of nanocrystalline metals, taking intoconsideration the volume fraction of grains and their grain boundaries, arereported. The aforementionedcomputational results have been compared with the most commonly used analyticalexpressions of Mori-Tanaka and Rule of Mixtures for the evaluation of mechanical behaviour ofcomposite materials. The above comparison gave a clear evidence that thecomputational results are in compliance with the analytical expressions withoutany notable divergence.