Crack Paths 2012

G E A RSTEEL —area = 220 P m

'KIII/'KIth,LC =

0.96

1.50

a: coplanar crack depth

1.25

'KIII/'KIth,LC = 0.75

N: numberof cycles a = 480P m N 7.5x105 cycles

'KIII/'K

= 0.62

Ith,LC

'K III /'K Ith,LC

= 0.49

'KIII/'KIth,LC = 0.40

1.00

a = 80 P m N 1.2x105 cycles

0.75

a = 50 P m

N = 2.5x105 cycles

0.50

Proposed conservative

Original DangVan

a = 117 P m

0.25 1.

locus

N = 106 cycles aN = 02xP10m6 cycles

locus

Vh/Vw

-1.5

-1.0

-0.5

0.0

0.5

1.0

(a)

'KIII/'KIth,LC = 1.57

2.05

a = 1 2 5 0 P m N . x105 cycles G E A RSTEEL —area = 630 P m a: coplanar crack depth N:numberof cycles

'KIII/'KIth,LC = 1.20

'KIII/'KIth,LC = 1.00

'KIII/'KIth,LC = 0.85

'KIII/'KIth,LC = 0.70

'K II /'K

= 0.55

Ith,LC

a = 1072Pm, N = 1.3x105 cycles

a = 359 Pm,N = 1.2x105 cycles

1.0

a = 400 Pm, N = 1.2x105 cycles a = 110Pm, N = 5x105cycles

a = 0 Pm, N =106cycles

0.5

Original DangVan

locus

Proposed conservative

locus

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Vh/Vw

(b)

Figure 8. Application of Dang Van’s Criterion. Gear steel – Load Path 3. a) Defect size

¥area = 220 Pm, b) Defect size ¥area = 630 Pm.

The SIF’s onto a prospective propagation plane identified by the propagation angle T,

see Fig. 9.a, are expressed by:

c o s 2 1

sin2

K

K

­

2

k

1 2

2 K Q

Q

I

II

I

I

I

III

III

T

T

° ° ®

(2)

2 s i n 2 1 2 K cos2 T Q T

2 k K

°

°¯

where KI, KIII are the SIF’s applied to the crack. By applying these formulas to the

max could be calculated by maximizing kI and kIII at

different load cycles, kI,max and kIII,

each point of the load cycle. The results shown in Fig. 8.a could be re-plotted as shown

in Fig. 9.b.

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