Necessary and sufficient condition for additivity in the sense of the Palmgren–Miner rule

Formal conditions are established regarding the compatibility of the Palmgren–Miner rule with laws describing the damage development during fatigue. The Palmgren–Miner rule can be used for fatigue life predictions, if and only if, the damage development rate can be presented as a product of the functions of stress (strain) amplitude and current amount of damage. Important properties of the additive damage development laws are derived and methods are proposed for checking whether a particular damage development law is consistent with the Palmgren–Miner rule. Some of the reasons for inaccurate fatigue life predictions based on the Palmgren–Miner rule are rationalised using the derived condition for additivity.