Peridynamic model for fatigue cracking.

The peridynamic theory is an extension of traditional solid mechanics in which the field equations can be applied on discontinuities, such as growing cracks. This paper proposes a bond damage model within peridynamics to treat the nucleation and growth of cracks due to cyclic loading. Bond damage occurs according to the evolution of a variable called the "remaining life" of each bond that changes over time according to the cyclic strain in the bond. It is shown that the model reproduces the main features of S-N data for typical materials and also reproduces the Paris law for fatigue crack growth. Extensions of the model account for the effects of loading spectrum, fatigue limit, and variable load ratio. A three-dimensional example illustrates the nucleation and growth of a helical fatigue crack in the torsion of an aluminum alloy rod.