When plastic strain occurs, the service life of material decreases, often no more than 10⁴, a.k.a., in low-cycle fatigue range. The research of low-cycle 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 low-cycle fatigue is usually presented as the plastic strain in log scale against cycles to failure N also in log scale.

The result of low-cycle fatigue is near a straight line for common metal meterials such as steel and is often referred as Coffin-Manson 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.

The Coffine-Manson formula describes the relationship between plastic strain and fatigue life in the low-cycle high-strain fatigue regime. Basquin's equation, on the other hand, describe high-cycle low strain behavior

where	is the amplitude of alterning stress
	is the amplitude of elastic strain
	E is Young's modulus
	is fatigue strength coefficient and is approximately equal to the monotonic true fracture stress .
	N is the number of strain cycles to failure and 2N is the number of strain reversals to failure.
	b if called fatigue strength exponent. For common metal materials, -0.12 < b < -0.05. A smaller c value results in a longer fatigue life.

Manson proposed a simplified formula known as the mothod of universal slopes

where	is the amplitude of alterning stress.
	is the true strain at fracture intension.
	E is Young's modulus.
	N is the number of strain cycles to failure.