# Strain-Life (E-N) Approach

Strain-life analysis is based on the fact that many critical locations such as notch roots have stress concentration, which will have obvious plastic deformation during the cyclic loading before fatigue failure. Thus, the elastic-plastic strain results are essential for performing strain-life analysis.

## Neuber Correction

Neuber correction is the most popular practice to correct elastic analysis results into elastic-plastic results.

Where, ${\sigma}_{e}$ , ${\epsilon}_{e}$ is locally elastic stress and locally elastic strain obtained from elastic analysis, $\sigma $ , $\text{\epsilon}$ the stress and strain at the presence of plastic strain. Both $\sigma $ and $\text{\epsilon}$ can be calculated from Equation 5 together with the equations for the cyclic stress-strain curve and hysteresis loop.

## Monotonic Stress-Strain Behavior

Where, $A$ is the current cross-section area, $l$ is the current objects length, ${l}_{0}$ is the initial objects length, and $\sigma $ and $\text{\epsilon}$ are the true stress and strain, respectively, Figure 1 shows the monotonic stress-strain curve in true stress-strain space. In the whole process, the stress continues increasing to a large value until the object fails at C.

## Cyclic Stress-Strain Curve

- Stable state
- Cyclically hardening
- Cyclically softening
- Softening or hardening depending on strain range

- ${K}^{\text{'}}$
- Cyclic strength coefficient
- ${n}^{\text{'}}$
- Strain cyclic hardening exponent

## Hysteresis Loop Shape

## Mean Stress Correction

The fatigue experiments carried out in the laboratory are always fully reversed, whereas in practice, the mean stress is inevitable, thus the fatigue law established by the fully reversed experiments must be corrected before applied to engineering problems.

Morrow's equation is consistent with the observation that mean stress effects are significant at low value of plastic strain and of little effect at high plastic strain.

Improves the MORROW method by ignoring the effect of negative mean stress.

The SWT method will predict that no damage will occur when the maximum stress is zero or negative, which is not consistent with the reality.

When comparing the two methods, the SWT method predicted conservative life for loads predominantly tensile, whereas, the Morrow approach provides more realistic results when the load is predominantly compressive.

## Damage Accumulation Model

In the E-N approach, use the same damage accumulation model as the S-N approach, which is Palmgren-Miner's linear damage summation rule.