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Steel Designers' Manual - 6th Edition (2003)
268 Fracture and fatigue
where E is Young’s modulus and s¢ f, e¢ f, b and c are considered to be material properties.
It is worth noting that the first term of the right hand side is an elastic stress
term which dominates at low loads and long lifetimes. The second term is a plastic
strain term which dominates at high loads and short lifetimes.
The strain–life approach is preferred over the S–N method since it is almost identical
to the S–N approach at long lives and elastic stresses, and is more general for
problems of short lives, high strains, high temperatures or localized plasticity at
notches.
The technique is:
(1) determine the strains in the structure, often by finite element analysis;
(2) identify the maximum local strain range, the ‘hot spot’ strain;
(3) read, from the strain–life curve, the lifetime to first appearance of a crack at
that strain at that position.
Variable-amplitude loads are dealt with in the same way as in the S–N method, with
the local hot spot strains and their associated lifetimes being determined for each
block of loading.
The strain–life, or local strain, method has wider use in fatigue assessments in the
engineering industry than the S–N method and is available in commercial computer
software.
7.6.7 Fracture mechanics analysis
Fatigue life assessment using fracture mechanics is based on the observed relationship
between the change in the stress intensity factor, DK, and the rate of growth of
fatigue cracks, da/dN. If experimental data for crack growth rates are plotted against
DK on a logarithmic scale, an approximate sigmoidal curve results, as shown in Fig.
7.13. Below a threshold stress intensity factor range, DK th, no growth occurs. For
intermediate values of DK, the growth rate is idealized by a straight line. This
approach was first formulated by Paris and Erdogan, 16 who proposed a power law
relation of the form:
da
dN
m
= A( DK)
(7.11)
where da/dN is the crack extension per cycle, A, m are crack growth constants, and
DK = Kmax - Kmin where K max and K min are the maximum and minimum stress intensities respectively
in each cycle. Since the crack growth rate is related to DK raised to an exponent,
it is important that DK should be known accurately if meaningful crack growth
predictions are to be made.