The crack tip geometry and averaged stresses over individual
elementary material blocks
Figure 1.
A crack and the discrete elementary material blocks
Figure 2.
The idealized crack tip geometry and the discrete structure of a material1.
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/Di) 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 growth1:
Figure 7.
Where,
Kmax,tot
Total maximum stress intensity factor
ΔKtot
Total stress intensity range
ΔKth
Threshold stress range
Piece-wise linear crack growth equation where total driving force Δκ=(Kmax,tot)p(ΔKtot)1−p.
