A universal functional for the physical description of fatigue crack growth in high-cycle and low-cycle fatigue conditions and in various specimen geometries

Abstract A simple universal functional is shown here to correlate fatigue crack growth data of a wide variety of materials (metals, polymers), test conditions (high-cycle and low-cycle fatigue), and specimen configurations (tension and bending). The proposed functional is a power law that relates the normalized remaining ligament size to the normalized remaining fatigue life in a cyclically loaded specimen. The functional evolved from the idea that at any stage during fatigue, the remaining fraction of cycles required to fracture the specimen, completely, depends on the remaining fraction of section to be broken by the fatigue crack before that final fracture. More importantly, the surrogate form of the functional is shown to provide excellent descriptions of the raw crack-length-versus-cycles data in fatigue crack growth. The functional provides a new physical basis to characterize fatigue crack growth in materials and is promising for extensions in to more complicated fatigue loading conditions.