Steels_ Metallurgy and Applications, Third Edition

Low-carbon strip steels 111

0.1

|

.~ 0.Ol

c

m 0.001

0.0001

Strain-life curves I

l

9 RQC-IO0

= Man-Ten

I 10 10 2 10 3 10 4 10 5 I0 e 10 7

Reversals to fallure, 2Nf

Figure 1.110 Strain-life curves for two structural steels (After Landgraf 62)

In this way the total fatigue damage and hence fatigue life Ni to crack initiation
may be calculated. The simplest method to use is the linear damage rule put
forward by Palmgren 163 and Miner. 164 According to this rule, if the proportions
of the various strains m in the strain history are Pl, P2, P3... Pro, etc., and the
numbers of cycles to crack initiation for these strains taken from the strain-life
curve are N l, N2, N3... Nm, etc., then the cumulative damage is given by:

Damage = plNi/Nl + p2Ni/N2 + p3Ni/N3..., etc.

and failure is expected to occur when E pmNi/Nm -- 1.
A difficulty with this method (or any other method) is that the calculation of
the proportion of each active strain from a highly irregular and random sequence
of cyclic strains is not straightforward. Several methods have been proposed of
which the rainflow method is probably the most accurate one. Further details of
these methods are given in a complete conference proceedings. 165
An alternative way of carrying out a fatigue test is to use a series of constant
cyclic stresses to develop a stress-life curve. It is said 162 that this approach is
more suited to long-life fatigue problems but less suited to low-cycle problems
involving relatively large plastic strains. With this method, a stress may be iden-
tified below which the number of cycles to crack initiation is never reached. This
stress is regarded as the fatigue strength of the steel. The relationship between
the fatigue strength and the monotonic tensile strength depends on the yield to
tensile strength ratio of the steel t66 since the yield or proof stress is the parameter
which influences the onset of plastic deformation.

Fatigue crack growth

Fatigue crack growth rates may be measured using a standard testing method t67
and a type of specimen, as illustrated in Figure 1.111. Before testing, a crack is
formed at the notch tip using a suitable load cycle and a stress intensity factor
at the crack tip is defined which depends on the crack length, the specimen