Figure 2.1.1 presents a schematic of
typical growth behavior for a crack being observed in a structural element as
it moves from an initial damage size to a damage size that causes structural failure
(loss of structural safety). Note that
the x-axis measures either the elapsed time (t) during which loading is applied or the number of loading events
(N) applied, and the y-axis measures
the corresponding length of crack observed in the structure. Typically, the elapsed time is given in
operational flight hours and the number of loading events is counted (grossly)
by the number of the aircraft’s flights.
Figure 2.1.1. Schematic of Observed Crack Growth Behavior
for a Typical Structural Cracking Problem
The crack grows in response to the cyclic loading applied to
the structure. Any crack will grow a
given increment (Da) in a given number
of loading events (DN), the rate being measured by Da/DN. When the crack length reaches a critical
the growth becomes unstable, thereby inducing failure.
When the crack (a)
reaches the critical length, the measure of loading (t or N) reaches the
structural life limit (tf
or Nf). The structural life limit is a measure of
the maximum allowable service time (or number of accumulated service events)
associated with driving the crack from its initial length (ao) to the critical length (acr). It is the
objective of the Damage Tolerant Requirements to ensure that cracks do not
reach levels that could impair the safety of the aircraft during the expected
lifetime (ts or Ns) of the aircraft, i.e., tf (Nf) must be greater than ts (Ns).
As can be noted from Figure 2.1.1,
when the crack is small, it grows very slowly.
As the crack gets longer, the rate of growth increases until the crack
reaches the critical size acr,
whereupon fracture of the structural element ensues. While the subcritical crack growth process occurring for a < acr may take twenty to thirty years of service, the
fracture process is almost instantaneous.
Studies of the failure process indicate a very close relationship
between the length of crack at failure and the load or stress that induces the
onset of rapid fracture.
Typically, this relationship between crack length and failure
strength level is as shown in Figure 2.1.2. The cracked element strength is referred to
as the residual strength (sres) since this represents the remaining
strength of a damaged structure. By
considering the basic elements of Figures 2.1.1 and 2.1.2 collectively, a residual strength diagram can be
developed as a function of elapsed time (or loading events).
Figure 2.1.2. Schematic of Relationship Between Failure
Strength and Crack Length for a Typical Single Element Type Structure
A residual strength diagram is presented in Figure 2.1.3; this diagram shows that while the
structure is young (t<< tf) the residual strength
capacity is basically unimpaired because the crack is both small and doesn’t
grow much with time. As the structure
starts to age, the residual strength capacity is shown to decrease and just
prior to failure, the rate of decrease in residual strength capacity is
accelerating because now the crack is rapidly becoming very large. When the residual strength capacity equals
the level of the maximum stress in the operational history, failure occurs.
Figure 2.1.3. Residual Strength Diagram Relationship
Between Residual Strength Capacity and Elapsed Time
As implied by the residual strength diagram, a ten to twenty
percent change in the maximum applied stress in the operational history would
not normally affect the allowable structural life significantly, assuming that
the subcritical crack growth process (Figure 2.1.1)
was unaffected. Normally, when the
loads in the operational history change, the subcritical crack growth process
changes its pattern of growth and this in turn affects the residual strength
diagram and the allowable structural life.