Characterization of ALON optical ceramic

Mesoscale modeling of nonlinear elasticity and fracture in ceramic polycrystals under dynamic shear and compression

“…10(a) and (b), predicted Weibull moduli for AlON microstructures are significantly lower that those for SiC. Table 8 compares Weibull parameters from the present work with those obtained from other modeling (Foulk and Vogler, 2010) and experimental (Klein and Miller, 2001;Warner et al, 2005;Patel et al, 2006;Ray et al, 2007;Furnish et al, 2007;Wereszczak et al, 2010) studies. For the present modeling results, nominal strength r 0 is substantially greater in SiC (0.52 GPa) than in AlON (0.35 GPa), as would be expected from the prescribed interfacial strengths in Table 2: t c SiC =t c AlON % 1:9 > 0:52=0:35 % 1:5.…”

“…The shear stress at failure (i.e., the shear strength) s for a given simulation is defined as the peak stress at which @ s=@c ¼ 0. For simulation results analyzed here, the probability f of failure at or below a given shear stress s is found by ordering the results of many simulations from lowest to highest shear strength and assigning the jth result in a series of n simulations a failure probability f j ¼ 1 n ðj À 1 2 Þ (Warner et al, 2005;Furnish et al, 2007). A plot of lnfln½1=ð1 À f Þg versus ln s exhibits slope m (the Weibull modulus).…”

“…Weibull distributions are often used to characterize failure behavior of brittle solids, including polycrystalline ceramics (Warner et al, 2005;Brannon et al, 2007;Foulk and Vogler, 2010;Graham-Brady, 2010;Leavy et al, 2010). Let s P 0 denote an independent variable.…”

“…A plot of lnfln½1=ð1 À f Þg versus ln s exhibits slope m (the Weibull modulus). A ''nominal strength'' (Warner et al, 2005) for a series of simulations is calculated as r 0 ¼ expðÀb=mÞ, where b is the vertical intercept of the linear fit to this plot, noting that f ðr 0 Þ ¼ 1 À expðÀ1Þ % 0:632. Recall that the higher the value of Weibull modulus m, the lower the variability or scatter in variable s.…”

Dynamic compressibility, shear strength, and fracture behavior of ceramic microstructures predicted from mesoscale models

“…Standard deviation is larger in AlON than SiC, possibly a result of greater anisotropy and smaller fracture strength and energy that render AlON more sensitive to cracking at grain boundaries or triple junctions favorably oriented for fracture. Table 6 lists Weibull statistics for values of τ predicted from simulations; shown for comparison are statistics from static flexure experiments on much larger specimens [5,34]. A cumulative Weibull distribution predicts probability f of failure at or below a given shear stress τ as…”