PSI - Issue 2_A

Stefan Kolitsch et al. / Procedia Structural Integrity 2 (2016) 3026–3039 Stefan Kolitsch/ Structural Integrity Procedia 00 (2016) 000–000

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2.2. Experimental crack initiation line

The experimental results are shown in Fig. 2. The crack initiation line is given by the points where a crack length of 20 µm was detected by the DCPD equipment (green crosses), the failure line by the points of failure (red crosses). It can be observed that the slopes of the crack initiation and failure curves are different and depend also on the notch geometry. Also the number of cycles between crack initiation and failure is higher for the sharp notch than for the mild notch. A detailed statistical assessment can be performed by means of linear regression. For distinguishing between mild and sharp notches, the categorical variable isMild is introduced; isMild takes the values -1 for sharp and 1 for mild notches. The following linear models for the initiation and failure S/N curves (subscripts “i" and “f”, respectively)

⋅ isMild N A C isMild N A C = + ( = + ⋅ ( i i i

⋅ isMild B D isMild B D ⋅ i i

log log

) (

⋅ ) log

+ +

∆

σ

(1a,b)

) (

⋅ ) log

+ +

∆

σ

f

f

f

f

f

account for the ordinate intercept and the slope disregarding the influence of the notch geometry by means of the parameters A and B , respectively; the influence of the notch geometry on the ordinate intercept and the slope is introduced by the parameters C and D . An analogous model for the logarithm of the initiation lifetime fraction N i / N f reads

N

f i

⋅ isMild A C p p

⋅ isMild B D p p

log

= + (

) (

⋅ ) log

+ +

∆

σ

.

(2)

N

Inserting Eq. (1a,b), one obtains A p = A i – A f , B p = B i – B f , C p = C i – C f , D p = D i – D f . Of course, owing to the statistical scatter, these relations between the parameters of the different regressions hold only approximately. However, the regression coefficient D p is determined only at a level of significance of p ≈ 0.15, i.e., it has to be regarded as statistically insignificant. The model of choice for the initiation lifetime fraction is therefore

N

f i

⋅ isMild A C p p

B

log

= + (

)

log

+

⋅

∆

σ

.

(3)

p

N

The regression parameters are given in Table 1.

Table 1. Regression parameters for Eqns 1-3.

Model

Parameter

Value 28.86 -7.63 6.97 -2.21 27.88 -7.25 5.69 -1.84 1.53 -0.57 0.17

A i B i C i D i A f B f C f D f A p B p C p

Crack initiation S/N curve, Eq. 1a

Fracture S/N curve, Eq. 1b

Initiation lifetime factor, Eq. 3