Fatigue Crack Paths 2003

1− = − i i ε ε

n

ε

(1)

2

where n ε is the average incremental strain, n is the increment number with i = n-1.

The incremental damage parameter is calculated using the simulated strain gradient

divided by the total strain gradient:

ε − ε

i

1−i

=

D

(2)

n

εΔ

Cr

where

C r ε Δ is the total strain gradient at a typical critical distance.

The relative distance from the surface of each strain increment is introduced through

a function that modifies the damage values with regard to surface distance, for example:

1 ) ) ( 1 ( n *

*

∑ − −

= D D n n

D

n

(3)

1

where

*nD is the modified damage parameter.

After calculating the modified incremental damage, the total life to failure is summed

as, Fig. 3b:

) D N (

∑− = 11

N

fD*

n * n f n

(4)

where *fD N are the modified cycles to failure for a particular surface strain range and

fn N is the number of cycles to failure at a certain depth along the critical path,

n ε at that depth.

corresponding to the average incremental strain

A eq u i v a l e n t S t r a i n

(a)

(b)

ε

ε

1

ε

1 ε

1

2

d0 3 ε 4 ε 2 ε 2 3ε

d1 d2 d3 Depth from the surface

3 ε 4 ε

v e r a g e

ε

4 ε

Nf1 Nf2 Nf3

Nf4

Cycles to Failure Nf

Figure 3. (a) The subsurface average strain and strain increments; (b) The predicted

life to failure using the calculated average strain.