Damage Initiation for Ductile Materials in Low-Cycle Fatigue

The damage initiation criterion is a phenomenological model for predicting the onset of damage due to stress reversals and the accumulation of inelastic strain in a low-cycle fatigue analysis. It is characterized by the accumulated inelastic hysteresis energy density per cycle, $\mathrm{\Delta }w$ , in a material point for a stabilized cycle. The cycle number in which damage is initiated is given by

where $c_1$ and $c_2$ are material constants, and ${\mathrm{\Delta }w}_0$ is a reference value of the accumulated inelastic hysteresis energy density per cycle.

The use of the reference energy density, ${\mathrm{\Delta }w}_0$ , makes the above form of the damage initiation law different from the more standard Coffin-Manson type relations. It is recommended that for ${\mathrm{\Delta }w}_0$ (which has units of energy density), you choose a value of 1.0 in the unit system in which the initiation law is calibrated to the available test data. If a different unit system is then used, you must convert the material constant $c_1$ based on its dimension of cycle. In this case, you must also convert ${\mathrm{\Delta }w}_0$ appropriately to the new system to ensure that the physical results are invariant to the choice of the unit system.

The initiation criterion can be used in conjunction with any ductile material.