Fatigue Crack Paths 2003

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Figure 2. Descritption of local crack growth direction by two angles

Thecalculation of the angles is based on the 61’-criterion by Schollmannet al. [3]. In

this criterion both angles dependon the stress intensity factors K1, K H and K mfor all

three crack opening modes. Theyare given by:

—6KItan E —KH 6-12tan2 E + 4KI—12KH tan E ~ 2 2 2

~ —6K1tan E -K,, 6-12tan2 E —32Kfntan E ~

2

2

2

(1)

(P0

8 KIn cos

1 t]! 0 = — arctan

(2)

KI 3cos&+cos3(p0 —KIl 3sin&+3sin3(p0

2

2

2

2

It is noticeable that Equation 1 is an implicit fitnction of (00, which has to be solved

numerically.

Determination ofthe local crack growth increment

Reasonably the magnitude of the local loading at any point of the crack front can be

described by calculating a comparative stress intensity factor Kv. B y application of the

(Sf-criterion, for instance, this K v is givenby

2

~

(3)

+ \/|:KI cos2[%)—3 K “sin((pO

+ 4K?II