Prediction of scatter in fatigue properties using discrete damage mechanics

Generic microstructures are represented via a two-dimensional discrete lattice of linear-elastic springs with a Normal distribution of static strengths. These springs represent grain boundaries and damage is constrained to intergranular cracking. The fatigue behavior is described with a Basquin law (the same in all springs), whereas damage accumulates via a Palmgren-Miner law. Lattices were 'cycled' under fully reversed strain and replicas with different local geometries were used to obtain statistics. Results show that geometrical disorder and load redistribution alone result in a lognormal distribution of cycles to failure at a fixed strain. Macroscopic Coffin-Manson behavior was observed, where the exponent was the same as in the Basquin law of individual springs. This indicates that lattice models can replicate experimentally observed behavior, while making it possible to study effects of microstructural and geometric variability separately. Discussion on size effects and how to extend the model to actual materials is offered.