When plastic strain occurs, the service life of material decreases, often no more than 10^{4}, a.k.a., in lowcycle fatigue range. The research of lowcycle fatigue was traditioanlly done for pressure vessels, power machinery that are exposed to a heat source/sink which induces thermal expension (thermal stress) to the structure. The lowcycle fatigue is usually presented as the plastic strain in log scale against cycles to failure N also in log scale.
To add Fig 1213, lowcycle fatigue
The result of lowcycle fatigue is near a straight line for common metal meterials such as steel and is often referred as CoffinManson relation:
where 
is the amplitude of plastic strain.

is fatigue dutility coefficient defined by the strain intercept at 2N = 1. For common metal materials, .

N is the number of strain cycles to failure and 2N is the number of strain reversals to failure.

c if called fatigue ductility exponent. For common metal materials, 0.7 < c < 0.5. A smaller c value results in a longer fatigue life.

