Issue 25

H. Askes et alii, Frattura ed Integrità Strutturale, 25 (2013) 87-93; DOI: 10.3221/IGF-ESIS.25.13

 UTS [MPa]

K Ic

L

Material

Ref.

[MPa·m 1/2 ]

[mm] 0.011 0.015 0.076 0.008 0.014 0.077 0.012 0.010 0.010 0.016 0.016 0.031 0.069 0.006 0.010 0.010 0.026 0.026

SiC

[21] [21] [21] [21] [22] [22] [23] [24] [27] [28] [29] [26] [25] [25] [30] [30] [31] [28]

620 650 200 920 290 920 915 880 700 700 510 340 790 610 610 390 390 210

3.7 4.5 3.1 4.6 7.8 4.5 5.6 5.0 5.0 5.0 5.0 5.0 5.0 3.5 3.5 3.5 3.5 3.5 3.5

N 4 O 3 N 4 O 3 N 4 N 4 N 4 N 4 N 4 N 4 N 4 O 3 O 3 O 3 O 3 O 3 O 3

Si 3 Al 2 Si 3 Al 2 Si 3

Sialon

1160

Si 3 Si 3 Si 3 Si 3 Si 3 Si 3

[25, 26]

Al 2 Al 2 Al 2 Al 2 Al 2 Al 2

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.

Inherent Strength

UTS

 / 

th

SiC Si3N4 Al2O3 Sialon

0.5

LEFM

GM

L=2√2 l

0.05

F 2 · a/L

0.01

0.1

1

10

100

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.

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