Fatigue Crack Paths 2003

where the two unknownsa* and [2* (semi-axes of the new crack front) can be deduced

through the condition that the coordinates of the new points A* and C*, obtained from

those of the old points A and C by employing the Paris-Erdogan law, must satisfy

Eq.(3). Details of this procedure can be found elsewhere [7]. In the following

examples, the material constants Q and m of the fatigue law (da/d NI Q (AK1 )m , with

da/d N in m mcycle'1 and the SIF range A K1 in N mm‘3/2) are assumed to be equal to

1.64 X 10'10 and 2, respectively. The axial force (F) and the bending moment( MX )

are madeto vary from zero to a m a x i m u mvalue in each fatigue loading cycle, so that

A O ' FI A O ' MIX

The curves of crack aspect ratio against relative crack depth are shown in Fig. 5 for

tension (Fig 5a-b) and bending (Fig. 5c-d), in the case of notched (pd I 0 1 )and

unnotched ( pd I <><>) bars. It can be noted that, for notched bars, the crack front tends to

becomestraight as the crack depth increases. O n the other hand, for unnotchedbars,

the a — if curves approach an inclined asymptote with increasing 6 . Results from some

1.2

5

pa =O0.1

Ref. [14] (K,= 2.29s)

pd=oo

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1 °5=0 3 cr,=0.5

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Ref. [4] 00150.83

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Ref-[5]- rxu=0.53 A0c,,=0.6

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1.0 I 3

D 01,5050

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4

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. (d)

1

0.0 0.2 0.4 0.6 0.8

1.0

0.0 0.2

0.4 0.6 0.8 1.0

RELATIVEC R A CDKEPTH,I';= a/ D

RELATIVEC R A CDKEPTH,E,= a/ d

Figure 5. Crack aspect ratio vs relative crack depth curves for notched ( pd I 0.1) and

unnotched( p d I O0 ) bars :

(a) to (b) tension; (0) to (d) bending.