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278 Mechanical Engineering Design
• Fatigue strength exponent b is the slope of the elastic-strain line, and is the power to
which the life 2N must be raised to be proportional to the true-stress amplitude.
Now, from Fig. 6–12, we see that the total strain is the sum of the elastic and plastic
components. Therefore the total strain amplitude is half the total strain range
ε ε e ε p
= + (a)
2 2 2
The equation of the plastic-strain line in Fig. 6–13 is

ε p c
= ε (2N) (6–1)

F
2
The equation of the elastic strain line is
ε e σ F b
= (2N) (6–2)
2 E
Therefore, from Eq. (a), we have for the total-strain amplitude

ε σ F b c

= (2N) + ε (2N) (6–3)
F
2 E
5
which is the Manson-Coffin relationship between fatigue life and total strain. Some
values of the coefficients and exponents are listed in Table A–23. Many more are
included in the SAE J1099 report. 6
Though Eq. (6–3) is a perfectly legitimate equation for obtaining the fatigue life of
a part when the strain and other cyclic characteristics are given, it appears to be of lit-
tle use to the designer. The question of how to determine the total strain at the bottom
of a notch or discontinuity has not been answered. There are no tables or charts of strain-
concentration factors in the literature. It is possible that strain-concentration factors will
become available in research literature very soon because of the increase in the use of
finite-element analysis. Moreover, finite element analysis can of itself approximate the
strains that will occur at all points in the subject structure. 7

6–6 The Linear-Elastic Fracture Mechanics Method

The first phase of fatigue cracking is designated as stage I fatigue. Crystal slip that
extends through several contiguous grains, inclusions, and surface imperfections is pre-
sumed to play a role. Since most of this is invisible to the observer, we just say that stage
I involves several grains. The second phase, that of crack extension, is called stage II
fatigue. The advance of the crack (that is, new crack area is created) does produce evi-
dence that can be observed on micrographs from an electron microscope. The growth of

5 J. F. Tavernelli and L. F. Coffin, Jr., “Experimental Support for Generalized Equation Predicting Low Cycle
Fatigue,’’ and S. S. Manson, discussion, Trans. ASME, J. Basic Eng., vol. 84, no. 4, pp. 533–537.
6 See also, Landgraf, Ibid.
7 For further discussion of the strain-life method see N. E. Dowling, Mechanical Behavior of Materials,
2nd ed., Prentice-Hall, Englewood Cliffs, N.J., 1999, Chap. 14.