Crack Paths 2012

fixed at the clamping region of one end of the specimen. At the other end the normal

force F and torsional momentMT were introduced via a reference point. The degrees of

freedom of the reference point are coupled with the degrees of freedom of the

neighbouring clamping region in such a way that for the clamping region only rigid

body translations along and rotations around the specimen axis are allowed. The middle

portion of the model is considered as the crack growth region with refined mesh as

shown in Fig 4 (a). Along the notch root, there are four potential crack initiation sites

numbered 1, 2, 3 and 4 clockwise, shown in Fig 4 (b).

crack initiation analysis

1 i end a E Na D

no

crack growth

specimen notch geometry

yes

one full cycle loading

1i i a a a

boundary conditions

crack initiation position

determined (

) ,maxθσ

F(tmax)

MT(tmax)

SIFs analysis

crack propagation

F: KI KII

Keq calculate

step

MT: KI KII

F F t

K K

θ θ

superposition

one full cycle

Keq,max

max

I I I ,

*

loading

M t

M

θ

eq K K

max

combinedKI KII

tmax

T

T

*

Figure 3. Simulation algorithm procedure

Figure 4. (a) Finite element model, (b) Crack initiation sites

One full load cycle was analysed for the uncracked specimen. Solutions for unit load

cases F=1and MT=1are provided,

F σ and

M σ . The tangential stress σ along the notch

root, location s , at each time t is

t F s t M s t s F T M σ σ σ , . (1)

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