Then, in order to quantitatively asses the effects of stochasticity of real microstructures on the fracturedamage behavior, the curves resulting from the 50 different computations have been averaged and standard deviations have been calculated. Figure 6 reports the average damage-vs-strain curve and the same curve +/- the standard deviation. The average curve (solid line) would coincide with the damage curve obtained with the continuously graded model. The two dashed curves (mean +/- standard deviation) plot how much the damage response can vary in real (and thus stochastic) microstructures. In other words, this micro-mechanic model is able to illustrate the influence of discreteness and randomness of the microstructure on the damage accumulation. As observed also in previous studies [6], the need to consider microstructural features for modeling FGM is evident and therefore a complete micro-mechanical model should take into account the main microstructural details. Figure 5: damage parameter for a graded microstructure and a homogeneous material Figure 6: effects of stochasticity on the damage accumulation Then, a new set of computations was performed on the same microstructures, but varying the Weibull moduli (m=25 for both phases, σ0=0.34GPa and 0.06GPa for alumina and glass respectively). This choice of parameters corresponds to a realistic one for those materials, since the Weibull parameter σ0 is a characteristic strength, related the mean fracture stress of the materials [9]. The fracture behavior in this case is different from the first set of experiments, resulting in less failures in the alumina phase where the
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