Fatigue Crack Paths 2003

y

’

σ

1

σ

ϕ

τ

ϕz

τ

rϕ

τ

rϕ

τ

τ

σ

σ

rz

rz

r

z

x

τ

ϕ

z

ϕz

r

P

crack

ψ

z

Figure 5. Cylindrical coordinate system and stress components at a 3Dcrack front.

P L A N EM I X E MD O D CER A CPKR O B L E M S

Plane Mixed Mode problems are characterised by the superposition of the fracture

modes I and II. Within the scope of the linear elastic fracture mechanics (i.e. the

dimensions of the plastic zone around the crack is small in comparison to the crack

length and the other dimensions of the structure) the stress field at the crack tip is

determined by the intensity factors KI and KII. Crack growth can take place in stable as

well as unstable manner.

Fracture Criteria for Unstable Crack Growth

In the context of unstable crack growth especially the following questions are of

interest:

• Whendoes the crack growth become unstable?

• To which direction does the unstable crack grow?

• At what loading level or at what crack length does a structure fail?

• Whatis the magnitude of safety vs. unstable crack growth/fracture in a

structure?

Those questions can be answered by so-called fracture criteria for plane Mixed Mode

problems. The most important concepts will be explained in the following.

For pure ModeI-loading unstable crack growth occurs, if the ModeI stress intensity

KI reaches the fracture toughness KIc:

Ic I K≤ K

(2)

The application of this criterion to a Mixed Mode situation would result in a non

conservative estimation for the risk of fracture. For a plane Mixed Modeloading of a

crack besides the stress intensity factor KI also the stress intensity factor KII has an

influence on the beginning of unstable crack growth and thus on the fracture of

components and structures.