E-N Curves

e-n curves graph infographic

E-N Curves

When conducting a strain based fatigue analysis (https://fea-solutions.co.uk/strain-based-fatigue-analysis/), the E-N curves of the materials used are required, where E stands for ε (epsilon), the symbol for strain, and N for the number of loading cycles with the graph showing the mean stress over the number of cycles required for the component to fail.

The E-N graph shows three types of strain – elastic, plastic and total strain. The lines for elastic and plastic strain against load cycles to failure show a linear relationship with the total strain against cycles to failure being an addition of the two components.

If the E-N curve is not available for any of the materials that are being analysed, it can be approximated using the following equation:
Equation - FEA-Solutions (UK) Ltd - Finite Element Analysis For Your Product Design
This relationship is called the Coffin Manson Curve and uses the following inputs:
– Δε/2 = total strain amplitude
– σf = fatigue strength coefficient
– E = Modulus of elasticity
– Nf = Number of cycles to failure
– 2Nf = Number of reversals to failure
– b = fatigue strength exponent
– c = fatigue ductility exponent

Exponents b and c are material specific and again need to be approximated if not available. For steels, b = -0.087, and c = -0.58. This approach is called Seeger/Beste approximation and is commonly used in FEA software.

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