The SN curve eastimate the service life of materials above 10^{3} (often >10^{4}) cycles. The corresponding stress level is usually below 2/3 of yielding stress. The "lowcycle fatigue" model, on the other hand, is made for 10^{4} cycles and below. The stress level usually steps into plastic range.  
StrainLife Equation  
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:

Bridge between High and Low Cycles  
The CoffineManson formula describes the relationship between plastic strain and fatigue life in the lowcycle highstrain fatigue regime. Basquin's equation, on the other hand, describe highcycle low strain behavior

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