Fatigue Crack Paths 2003

K

II

Fracture curve for

K

IIC

combined ModeI

3D Fracture surface

and ModeII loading

Range of stable

crack growth for

combined ModeI

and ModeII loading

K

KI

IC

Threshold surface

K

IIIC

KIII

Figure 14. KI-KII-KIII-diagram for Mixed Modeloading with

the fracture limit and the Threshold surface.

This condition can be written downby the formula

c,I th,I K K ΔK < Δ < Δ (26) v

Hereby ΔKv is the cyclic comparative stress intensity factor, which can be derived from

Eq. 25:

2I

( K 4 K 4 K 21 K 2K Δ α + Δ α + Δ = ΔΔ (27) ) ()2III2 2 I I 1 I v

As before, α1=1.155 and α2=1.0.

For 3D- Mixed Modeproblems crack growth simulations can be performed also by

the means of the Finite Element method. I.a. the program system A D A P C R A C Ki3s aD

valuable tools for such kind of simulations [18, 19].

C O N C L U S I O N

For theoretical determination of crack paths and the examination of crack and crack

growth problems in real structures several hypotheses and concepts are available. Under

consideration of experimental experiences with the brittle fracture behaviour of cracks

can be pointed out, that for plane Mixed Modeproblems the criteria by Erdogan/Sih and

Richard and for 3D-Mixed Mode Problems the criteria by Schöllmann et al. and

Richard are well suited for the description of crack growth. For the purpose of analysing

crack paths and crack propagation processes under fatigue loading in real structures

those concepts have to be implemented in Finite-Element programs. Special cases, like