Page 449 - Biaxial Multiaxial Fatigue and Fracture

A Damage Model for Estimating Low Cycle Fatigue Liwes Under Nonproportional Multiaxial Loading 433

but it is not easy to get a conclusive equation of the total damage, since dl and dl1 are not always
independent of each other. However, the appropriate formula must be determined, so for the
present, we define the total damage in this model by

Table 3 lists the accumulated damage values of d1 and dr1 of each case for the I and 11-planes,
when the total damage D becomes unity, ie., reaches the fatigue life.
In the following, the procedure for the determination of D is exemplified for some cases.

Table 3. Value of dl and d11 at fatigue life (D=l).
- ~ ~~
Case 0,5 6,7 - 9, 11 1,2, 12 - 14 3,4, 10

Proportional loading. In proportional straining tests where the principal strain direction is
always fixed, the nonproportional intensity factor fNp takes the value zero and then the strain
amplitude on 11-plane remains then also equal to zero. In this case, the total damage can be
expressed by

This formula corresponds to Miner's equation under uniaxial loading. Thus, in the uniaxial
tensiodcompression test of Case 0 and the combined tensiodcompression and reversed torsion
tests in which the strain waves of E and y are in-phase such as in Case 5, the total damage is
simply expressed by

Nl
D=d -- (for Case 0 and 5) (9)
I-
Nlf

Cruciform loading. For cruciform shaped straining as in Case 1-4, the total damage is
determined by the sum of damages, dr and d11. If the strain path crosses at right angles in the
El(t)-&t) diagram as in Case 1 and 2, d1 and dll can be equated as in Eq.( 10).