2.1. Fatigue driving stress theory
It is well known that the S-N curve of a material can be expressed using a power function as follows:
whereis the fatigue strength constant, is the fatigue strength index, is the applied cyclic stress, andis the fatigue life.
In the new approach to nonlinear damage accumulation developed by Kwofie and Rahbar8,9, it is argued that although the applied loading is constant, the transient driving loading, which varies continuously with fatigue loading, is the primary causative factor for damage accumulation and is defined as the fatigue driving stress.
For a given stress loading, the fatigue driving stress function can be expressed as:
Where is the life-fraction of load and is an increasing function with respect to , as the number of loading cycles increase from zero to , increases from to Thus, at we have
Thus it is expected that while the applied cyclic load may be constant, the fatigue driving stress will increase with cycling until the fatigue strength constant is reached, at which point fracture of the specimen is expected to occur9.
2.2. Existing models based on fatigue driving stress theory
2.2.1.K-R model
By equivalence of fatigue driving stress, models based on fatigue driving stress theory have been developed. Taking a two-stage cyclic loading as an example, the fatigue lives corresponding to different stresses loading and are and respectively, and the growth law of fatigue driving stress is presented in Figure 1.