Section 2.4.5. Damage Integration Models
Rewriting Equation 2.4.1 such that the integration is conducted
between the initial crack length (ao)
and any intermediate crack length (aK)
between ao and the
critical crack length results in
where t(N) is the elapsed time (number of load
cycles) corresponding to growing the crack ao
to the intermediate crack length aK. The next cycle of the applied stress (the N + 1 cycle) induces a crack length
growth increment DaN+1. The damage integration model provides the
analysis capability to determine this crack length growth increment. The growth increment DaN+1
is equated to the constant amplitude crack growth rate, which in turn is
determined from a function of stress intensity factor range (DK)
and stress ratio (R), i.e.,
The stress intensity factor range and stress ratio in Equation
2.4.4 are determined by using the maximum and minimum stresses in the N+1 cycle of the given stress history
and evaluating the stress intensity factor coefficients associated with the
given structural geometry at the crack length aK. Subsequent
to the direct calculation of the two crack tip parameters DK
and R, and prior to their insertion
in Equation 2.4.4, DK
and R are modified to account for the
effect of prior load history using retardation models. Retardation models account for high-to-low
load interaction effects, i.e., the phenomena whereby the growth of a crack is
slowed by application of a high load in the spectrum. Failure to account for high-to-low load interaction via a
retardation model leads to conservative (~2 to 5 times shorter) life.
There are numerous functional forms of Equation 2.4.4 and
numerous models describing retardation.
The following list describe the general scheme of the crack growth
Step 1 - Knowing crack length aK, determines the stress
intensity factor coefficient, K/s.
Step 2 - For the given stress cycle, Ds,
and the coefficient K/s, determine the stress intensity factor cycle, DK, and stress ratio R.
Step 3 - Utilizing the retardation
model, modify the stress-intensity cycle DK
and R to account for previous load
Step 4 - Determine the growth rate for
the stress-intensity factor cycle to establish the crack growth increment.
Section 5 provides a current state-of-the-art summary of the
procedures and techniques that are used in damage integration models.