Crack Paths 2012

2 1 1 2 1 2 2 22 1 1 2 0 A H A H A θ H θ θ ⎛ ⎞ ⎛ ⎞ ∂ ∂ ∂ ⎜ ⎟ + ⎜ ⎟ = +

(1)

,

⎜ ⎝

∂

∂

∂

⎟ ⎠

⎝ ⎠

θ

m

where H1, H 2 are generalized stress intensity factors [MPa.mp] and A 11 , A12, A 22 are

known functions (see e.g. [20] for details). In comparison to classical L E F Mquantities

H1, H 2 don’t belong explicitly to crack loading modes, but contain contributions of both

depend on radial distance r from the

(normal and shear) modes. Functions A11, A12, A 22

stress concentrator (crack) tip. Distance for determination of crack propagation direction

depends on material properties of material where the crack propagates to what is

disadvantage of this criterion.

Table 1. Observed angles of initial crack orientation relative t the

Table 2. Material characteristics of individual

components of the laminate [6,17]

interface and direction of futher

crack propagation (average

experimental values)

Al2O 3

ZrO 2

component

material characteristics

ZrO2

Al2O3

φ1 [deg] φ2[deg] φ1[deg] φ2[deg]

Young modulus [MPa] 3.8.105

2,1.105

52.5

60.4

58.0

43.9

0.26

73.0 82 5

77.5 8 0

0.31

64.5 78

53.4 72 0

Poisson’s ratio [-]

CTE[K-1]

8.5x10-6

10.3x10-6

E X P E R I M E N TDA LT A

As a base for determination of crack

propagation in layered ceramics the

experimental results published in [8,17]

were used. The experimental samples

were of size 2 x 2.5 x 25 m m(width x

height x length)

prepared by

deposition.

Samples

electrophoretic

contained 59 layers of alumina (Al2O3 a

mean particle size ~ 400nm) and zirconia

(ZrO2 a mean particle size ~ 150nm)

with thickness of 42 μm. The change of

direction at interfaces of propagating cra k induced by Vickers indent ion was bserv (Fig. 2). Select d data Figure 3. Scheme of numerical model:

layered ceramics with initial internal crack

with tips at material interfaces

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