Fatigue Crack Paths 2003

After substituting the near-field solutions of Eq. 1 into Eq. 19, considering oz=0 and

differentiating partially by (p0 the following formulation can be found for (00:

—6Kltan (p_° —Kn 6—12tan2 & + 4KI—12KHtan (P_° - 2 2 2

(P

(P

(P

.[_ 6K1 tan[?°J _ 1({6 _ 12tan2

_ 32x1, tan[?°)

(20)

2

2

2 ‘1/2

-[1+tan2£(P?0D

}-{4K1—12KHtan[(p2—°H

+64K%HLI+tanZL(P—ZOD}

: 0

The second deflection angle \[10 (Figure 10) is defined by the direction of 61’ and can be

calculated according to the calculation of the maximumprincipal stress angle using Eq.

21:

1 \[10 I 5arctan[

(F,((PO)—(YZ((PO)

21.4%) J

(21)

During the investigation of fatigue cracks under superimposed normal and shear loading

the determination of a comparative stress intensity factor Kv is necessary for the

calculation of the portion of crack propagation. For plane loading conditions Kv is only

depending on K1 and KH. Dealing with three-dimensional crack fronts K m has to be

taken into consideration as well. F r o mEq. 18 a formulation for Kv can be derived as

follows:

KV : %cos[(p2—°){Kl cos2

— 3K1, sin((p0)

(22)

2

3 + ‘ / [ K I c o s 2 [ % ) — E K n s i n ( ( p O ) ] +4KI2II I K I c

where Klc is the fracture toughness for pure ModeI-loading.

Criterion by Richard

In order to simplify the prediction of crack growth under multiaxial loading

approximation functions have been developed [7]. Furthermore, the formulas are helpful

for practical application.

The function Eq. 8 can easily be extended for Mixed-ModeI+II+III loading conditions

by replacing the denominator (K1 +|KH|) by (K1 +|K11|+|K1H|).

This leads to the new

approximation function for the crack deflection angle (00 as defined in Figure 10:

(00 I T A IKIII

+B[ IKIII

)2

(23)

K 1 + | K 1 1 I + | K 1 1 1 I K 1 +IKIII+IKIIII

where(p0<0° for K H > 0and (p0>0°for K H < 0and K1 0.