PSI - Issue 13

Alexey Smolin et al. / Procedia Structural Integrity 13 (2018) 680–685 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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Herein we present a multiscale model which is based on MCA method and used for 3D simulating zirconia-based ceramic composite with small pores and large soft cylindrical inclusions. Small pores (their size corresponded to the automaton size and was equal to 1 μm ) were explicitly considered at the first scale of the model as proposed by Smolin (2017). The response function of automata corresponded to the loading curve for nanocrystalline ceramics ZrO2(Y2O3) with a total porosity of 2% (Smolin, 2014). Inter-automaton bond rupture criterion used in the calculations was formulated as a threshold value for equivalent shear stress. Simulations at this scale resulted in effective elastic and strength properties of porous ceramics which was used as a matrix material for the final composite containing soft cylindrical inclusions (their properties corresponded to human bone) differently oriented in space. At the second scale, we explicitly considered two types of structure for cylindrical inclusions. The inclusions diameter was equal to 100 μm, the height 300 μm. The automaton size at the second scale of the model was equal to 50 μm, the specimen size 3 mm. The specimens of the first type contained the inclusions inclined at 45° with respect to the compression direction, as shown in Fig. 1, i.e. here all inclusions had the same orientation. For the specimens of this type, the total volume fraction of cylindrical inclusions varied from 5 % up to 20 %. The second type of inclusions structure was obtained by random rotation of the initial inclusions shown in Fig. 1 about axis Z . To avoid merging of the inclusions we varied fraction of this type of inclusions from 5 % to 11 %, because it is difficult to manage close packing of randomly oriented cylinders.

a b Fig. 1. Schematic of (a) unidirectional and (b) randomly oriented cylindrical inclusions placed in a model cubic specimen. For each value of volume fraction of the inclusions, there were considered five representative specimens with inclusions of the same size and orientation but with the unique position in space. We simulate uniaxial compression of these specimens along axis Z . Using the loading curve obtained from the simulation, the elastic modulus in compression (the slope of the linear part of the curve) and the compression strength (its maximum value) were determined for each specimen. The Poisson’s ratios along axis X and Y were determined by the displacement of four gauge automata positioned at outside planes of the specimen along the corresponding axis. All these values are random variables due to random inclusion arrangement. As shown, for example, by Rinne (2009) the failure process is governed by Weibull distribution model, which assumes the following cumulative distribution function       t F t    ( ) 1 exp (1)