Materials for engineering, 3rd Edition - (Malestrom)

∆ε e /2 = ∆σ/2E = σ a /E
where E is Young’s modulus.
Thus, using equation [2.23] we obtain:
Determination of mechanical properties 59
∆ε /2 = σ′ / E(2 N )
b [2.28]
e f f
and combining equations [2.23] and [2.27] we can write the total strain
amplitude:
b c
∆ε/2 = σ′ / E(2 N ) + ε′
(2 N )
[2.29]
f f f f
Equation [2.29] forms the basis for the strain-life approach to fatigue design,
and Table 2.1 gives some strain-life data for some common engineering
alloys.
Fatigue crack growth – the use of fracture mechanics
The total fatigue life discussed so far is composed of both the crack nucleation
and crack propagation stages. Defect-tolerant design, however, is based on
the premise that engineering structures contain flaws and that the life of the
component is the number of cycles required to propagate the dominant flaw
– taken to be the largest undetectable crack size appropriate to the particular
method of non-destructive testing employed.
Fracture mechanics may be employed to express the influence of stress,
crack length and geometrical conditions upon the rate of fatigue crack
propagation. Thus, by employing equation (2.17), a stress range ∆σ applied
across a surface crack of length a, will exert a stress intensity range, ∆K,
given by:
∆K = Y∆σ πa) 1 2
[2.30]
where Y is the geometrical factor.
Pre-cracked test-pieces may thus be tested under fluctuating stress and the
growth of the crack continuously monitored, for example by recording the
change in resistivity of the specimen. After calibration, the resistivity changes
may be interpreted in terms of changes in crack length and the data may be
plotted in the form of crack growth per cycle (da/dN) versus ∆K curves.
Figure 2.17 illustrates schematically the form of crack growth curve obtained
in the case of ductile solids.
For most engineering alloys, the curve is seen to be essentially sigmoidal
in form. Over the central, linear, portion (regime B in Fig. 2.17) the fatigue
crack growth rate (FCGR) is observed to obey the Paris power law relationship:
da/dN = C(∆K) m [2.31]
where C and m are constants.