Page 445 - Biaxial Multiaxial Fatigue and Fracture

A Damage Model for Estimating Low Cycle Fatigue Lives Under Nonproportional Multiaxial Loading 429

Fig.5. Explanation of cycle counting of strain waves under nonproportional straining.

it to be inapplicable to the life prediction under more complex nonproportional strain histories.
Therefore, some modifications of the strain range are required. This section will show the
concept of a simple damage model for the life prediction by combining the equivalent strain
parameter, AENP, with Miner’s law.

Cyclic Strain Counting

In the nonproportional LCF tests, the strain amplitude is changed in a complex manner due to the
direction change of principal stress and strain directions. Using a hollow cylinder specimen,
amplitudes of axial strain (E) and shear strain (y) are changed depending on the strain history, so
that the strain wave becomes a kind of cyclically random straining. For the evaluation of the
nonproportional LCF life under such a random straining, appropriate cyclic counting methods
and damage models for nonproportional LCF are needed. However, there is no appropriate
cyclic counting method for nonproportional straining in the equivalent strain parameter of Eq.(4).
Therefore, this study proposes a new cyclic counting method for nonproportional straining.
Figure 5 shows the strain waves that are the projections of the strain path in Fig.3 on the I and
11-planes. The I-plane is the El,,,-plane and the 11-plane the plane inclined at an angle of 45
degrees to I-plane in specimen. This picture suggests that nonproportional strain paths are