The Paris-Erdogan equation is derived from empirical considerations, and has no real
theoretical basis. The equation models the relationship between the velocity of crack
propagation and an abstract quantity called the range of stress intensity, which
describes the magnitude of the stress at the crack tip. This range is denoted 
and is usually defined as 
, where the
constant Q reflects the crack geometry, 
is the stress range, and a
is the length of the crack.
The form of the Paris-Erdogan equation is
where C and m are regarded as material constants that depend
upon factors such as frequency, temperature and stress ratio. The
stress ratio, which is defined to be 
has
an important effect on crack growth, according to
[2], but does not explicitly appear in
Paris-Erdogan.
The Paris-Erdogan equation gives good results for long cracks when the material constants are known, but a large effort is required to determine them, since they are functions of many variables. R is an observable and where it appears in the model explicitly, the effort in determining the remaining material constants is much reduced. An empirical equation which incorporates the stress ratio, R, is the Forman equation.