numero25

H. Askes et alii, Frattura ed Integrità Strutturale, 25 (2013) 87-93; DOI: 10.3221/IGF-ESIS.25.13 91 Material Ref.  UTS K Ic L [MPa] [MPa·m 1/2 ] [mm] SiC [21] 620 3.7 0.011 Si 3 N 4 [21] 650 4.5 0.015 Al 2 O 3 [21] 200 3.1 0.076 Sialon [21] 920 4.6 0.008 Si 3 N 4 [22] 1160 7.8 0.014 Al 2 O 3 [22] 290 4.5 0.077 Si 3 N 4 [23] 920 5.6 0.012 Si 3 N 4 [24] 915 5.0 0.010 Si 3 N 4 [25, 26] 880 5.0 0.010 Si 3 N 4 [27] 700 5.0 0.016 Si 3 N 4 [28] 700 5.0 0.016 Si 3 N 4 [29] 510 5.0 0.031 Si 3 N 4 [26] 340 5.0 0.069 Al 2 O 3 [25] 790 3.5 0.006 Al 2 O 3 [25] 610 3.5 0.010 Al 2 O 3 [30] 610 3.5 0.010 Al 2 O 3 [30] 390 3.5 0.026 Al 2 O 3 [31] 390 3.5 0.026 Al 2 O 3 [28] 210 3.5 0.088 Table 1 : Mechanical properties of the investigated engineering ceramics. The curve plotted in the chart of Fig. 2 summarises the predictions made through the gradient enriched crack tip stresses calculated according to GM, the l vs. L relationship being the one given by Eq. (14). Such estimates were obtained by solving GM FE models simulating a bi-dimensional rectangular plate with a central through-thickness crack and subjected to tensile loading. The considered gross widths ranged in the interval 0.25mm-64mm. The ratio between the semi-crack length, a, and the gross width was set constant and equal to 0.05. This resulted for the modelled cracked samples in a shape factor, F, invariably equal to unity. Finally, the boundary conditions of the gradient-enrichment step were taken as zero Neumann conditions throughout. 0.05 0.5 0.01 0.1 1 10 100  th /  UTS F 2 · a/L SiC Si3N4 Al2O3 Sialon Inherent Strength LEFM L=2√2 l GM Figure 2 : Accuracy of gradient enriched tip stresses in estimating the transition from the short- to the long-crack regime under Mode I static loading, the mechanical properties of the considered engineering ceramics being summarised in Tab 1. The chart of Fig. 2 clearly suggests that, as far as engineering ceramics are concerned, gradient-enriched crack tip stresses are successful in modelling the transition from the short- to the long-crack regime. In particular, the above diagram makes it evident that GM is capable of matching the inherent material strength in the very short-crack region by correctly modelling, at the same time, the long-crack behaviour as well.