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Local Stress-Strain Fatigue Method ( ε-N )

Beam Stress and Deflection Analysis
Strength and Mechanics of Materials

Local Stress-Strain Fatigue Method ( ε-N )
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Although most engineering structures and machine components are designed such that the nominal stress remains elastic (Sn < σys) stress concentrations often cause plastic strains to develop in the vicinity of notches where the stress is elevated due to the stress concentration effect. Due to the constraint imposed by the elastically stresses material surrounding the notch-tip plastic zone deformation at the notch root is considered strain controlled.

The basic assumption of the strain-life fatigue analysis approach is that the fatigue damage accumulation and the fatigue life to crack initiation at the notch tip are the same as in a smooth material specimen (see the Figure) if the stress-strain states in the notch and in the specimen are the same. In other words:

The local strain approach relates deformation occurring in the immediate vicinity of a stress concentration to the remote or local pseudo-elastic stresses and strains using the constitutive response determined from fatigue tests on simple laboratory specimens (i.e. the cyclic stress-strain curve and the strain-life curve.

From knowledge of the geometry and imposed loads on notched components, the local stress-strain histories at the tip of the notch must be determined (Neuber or ESED method).

Fatigue damage must be calculated for each cycle of the local stress-strain history (hysteresis loops, linear damage summation)