Crack Paths 2009

) d a (

e 1 = β − β β + π σ Δ Δ = β− 2 1 K 1 g I

1 a 6 ⎜⎝⎛ −ρ β = + ρ

⎟⎠⎞

d 2 W

× +

2141

ψ ×−

(2)

123773 10 β = × ψ × − × ψ × 133130 10 2 2 3 2 2

15185 10

2

766

W d2a+ = ψ and m m 1 0 a m m 1 ≤ ≤ .

where

Finally, the SIFs for the single edge notched specimens have been evaluated

according to the following expressions [9]:

2 1 α α + π σ Δ = ) d a ( g

(3)

Δ

K

I

where

β−

= α −

1a75.7 ⎜⎝⎛ ρ− + ρ = β ⎟⎠⎞

e 1

1

d W

2

2

2

3

9 8 5 1 0 5 5 3 6 5 1 0 1 6 9 6 9 1 0 8 3 5 3 2 − ψ × × + ψ × × − ψ × × + ψ × × − = α (4) 10447157 2

d a +and m m 2 0 a m m 3 5 . 0 ≤ ≤ .

In this last expression, ψ =

W

Figure 6 shows all the available crack propagation rates as a function of the range of

the modeI SIF ΔKI,

as well as the fitted long crack Paris’ law (of which the constant m

and C are also reported). As a comparison, the long crack Paris’ law previously derived

by the authors for the same material is plotted too [4]. The figure highlights the well

knownand anomalous crack growth behaviour of short cracks, of which the propagation

rate is higher than that predicted by the long crack law for the same applied SIF range.

Differently, when cracks grow up to a certain distance far from the notch tip, their

propagation behaviour collapse onto the long crack behaviour. It should be noted that

data for single edge notched specimens refer to crack length lower than 10 mm.Above

such a length, the loading condition applied by the testing system differs too muchfrom

that simulated in the numerical model, which in turn is realistic for crack lengths shorter

than about 10 mm.

DISCUSSION

Short crack behaviour is widely addressed in the technical literature, since the

pioneering work due to El Haddad-Smith-Topper [2]. Explanations of their higher than

expected propagation rates or, at threshold conditions, lower threshold values than

expected from L E F Mare usually based on crack closure development considerations,

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