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.