Crack Growth Mechanism

The idealized crack tip geometry and the discrete structure of a material^¹.

The following assumptions were applied in this method:

The material is assumed to be composed of identical elementary material blocks of a finite dimension $ρ *$ in Figure 1 and Figure 2
The fatigue crack can be analyzed as a sharp notch with a finite tip radius of dimension $ρ *$
The material cyclic and fatigue properties used in the crack growth model are obtained from the Ramberg-Osgood cyclic stress strain curve
Figure 3.

and the strain-life(eN) fatigue curve
Figure 4.
The number of cycles $N$ to failure of the first elementary material block at the crack tip can be determined from the strain-life fatigue curve (Figure 4) by accounting for the stress-strain history at the crack tip and by using the Smith-Watson-Topper (SWT) fatigue damage parameter and Miner rule. Once accumulated damage reaches 1, $N$ is a summation of life ( $1 / D i$ ) of found cycles.
Figure 5.
The fatigue crack growth rate can be determined as the average fatigue crack propagation rate over the elementary material block of the size $ρ *$ .
Figure 6.

With the above assumptions and average linear stress over the elementary block with the size

ρ *

, the following crack growth equations can be derived to calculate crack growth^¹:

Where,