Fatigue Crack Paths 2003

and confidence interval

Table 1 includes the average values of experimental angles expˆα

min exp,ˆα , max exp,ˆα calculated on assumption of normal distribution of angle αexp with

probability equal to 0.99.

Table 1. Average values of experimental angles

expˆα

No Numberof

max max σ τ λ σ = expˆα

σr -

minexp,ˆα

maxexp,ˆα

specimens

deg

deg

deg

-

1

10

-

0

1.5

0.4

2.6

2

5

-

∞

43.6

39.2

47.9

3

8

1.00

0.50

20.5

15.8

25.2

4

5

1.00

1.00

31.4

27.5

37.3

5

5

0.50

0.54

16.2

12.3

20.0

6

5

0.50

0.97

28.2

24.2

32.3

7

6

0.01

0.56

4.8

0.8

8.7

8

5

0.01

0.97

31.2

26.3

36.2

Magnification: 60 times

Figure 2. Experimental slope αexp of fatigue crack line

A V E R A G IPN RG O C E D UARNE DW E I G HFTU N C T I O N S

Averaging procedure of the Euler angles should take into account factors influencing

the fatigue fracture behavior. The positions of principal axes which have great influence

on fatigue fracture should be emphasized. Hence, in averaging procedure the different

weight functions based on different postulates are taken into account. The mean

directions of the principal stress axes may be described by the weighted mean Euler

angles:

∑ = ψ ψ θ θ ϕ ϕ ∑ = ∑ = t t t t t t

(1)

,

N N t t k k t t k k k t t k 1 1 1 ) ( W ) ( W 1 ˆ ) ( W ) ( W 1 ˆ ) ( W ) ( W 1 ˆ N