Page 289 - Aircraft Stuctures for Engineering Student

270 Airworthiness and airframe loads

care must be taken to ensure that the formula used and the way in which the nominal
stress is defined are compatible with those used in the derivation of a.
There are a number of methods available for determining the value of K and a. In
one method the solution for a component subjected to more than one type of loading
is obtained from available standard solutions using superposition or, if the geometry
is not covered, two or more standard solutions may be compounded7. Alternatively, a
finite element analysis may be used.
In certain circumstances it may be necessary to account for the effect of plastic flow
in the vicinity of the crack tip. This may be allowed for by estimating the size of the
plastic zone and adding this to the actual crack length to form an effective crack
length 2al. Thus, if rp is the radius of the plastic zone, al = a + rp and Eq. (8.63)
becomes

(8.68)
in which Kp is the stress intensity factor corrected for plasticity and a1 corresponds to
al. Thus for rp/t > 0.5, i.e. a condition of plane stress
2
r -- or rp =; (I> a2 (Ref. 9) (8.69)

in which fy is the yield proof stress of the material. For rp/t < 0.02, a condition of
plane strain

(8.70)

For intermediate conditions the correction should be such as to produce a
conservative solution.
Having obtained values of the stress intensity factor and the coefficient a, fatigue
crack propagation rates may be estimated. From these, the life of a structure
containing cracks or crack-like defects may be determined; alternatively, the loading
condition may be modified or inspection periods arranged so that the crack will be
detected before failure.
Under constant amplitude loading the rate of crack propagation may be repre-
sented graphically by curves described in general terms by the law
da
- =f(R, AK) (Ref. 10) (8.71)
dN
in which AK is the stress intensity factor range and R = Smin/Smax. Eq. (8.63) is
If
used
AK = (Smax - Smi,)(ra)'a (8.72)
Equation (8.72) may be corrected for plasticity under cyclic loading and becomes

AK~ = (Smax - Smin)(ral)fal (8.73)
in which u1 = a + rp, where, for plane stress

(Ref. 11)