Using a notch factor for modeling the local plastic behavior

The durability solver performs fatigue evaluations on a finite element (FE) model which allow you to include the notched areas using finer FE meshes. Using nonlinear FE solutions, you can calculate the plastic strains in the notched areas for fatigue evaluations. However, if the yielding is localized in the notched areas, you may want to do the following:

• Exclude the notches from the FE model.

• Use linear FE solutions to calculate stresses and strains.

• Use notch factors to account for local yielding in the fatigue evaluation.

The notch factor is a ratio of the fatigue strength of the specimen with no stress concentration to the fatigue strength of a similar specimen with a notch.

Depending on the selected fatigue life criterion, the durability solver uses either Neuber's rule or Fuch's method to account for the local plastic behavior.

Neuber's rule

The durability solver applies Neuber's rule to determine local cyclic stresses and strains from a given notch factor for all fatigue life criteria except stress life. The equation of Neuber's rule is defined as follows:

where

• is the local stress amplitude.

• is the local strain amplitude.

• is the nominal stress amplitude.

• is the nominal strain amplitude.

• Kt is the fatigue notch factor.

With the cyclic stress-strain relation, the local stress and strain amplitudes in the equation can be calculated by Newton-Raphson iterations.

Fuchs method

The solver uses the Fuchs method to include the notch factor when the stress life criterion is used. Using this method, the notch factor is treated as a stress concentration factor NOTE. The S-N curves shown in the following figure are calculated in the following order:

1. The notched stress amplitude at 106 reversals, is calculated by dividing the stress amplitude at 106 reversals by the stress concentration factor, Kt:where is the notched stress amplitude at 106 reversals. is the un-notched stress amplitude at 106 reversals.

2. The notched stress life curve is approximated by a line drawn between the point representing the notched stress amplitude at 106 reversals (A) and the un-notched stress amplitude at 103 reversals (B).

	The X-axis represents the number of reversals to failure.The Y-axis represents the stress amplitude.The notched stress life curve is shown in blue.The un-notched stress life curve is shown in red.

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Transient events

Durability damage evaluation

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Introduction to durability analysis

Understanding the strength evaluation

Strength calculations for orthotropic failure criteria

Fatigue evaluation on element free faces

Fatigue life criteria

Biaxial fatigue evaluation on element free faces

Understanding cyclic stress-strain behavior

Understanding the fatigue safety evaluation

Cumulative damage

Random fatigue methods

Strain and stress calculations from strain gage leg data

Strain gage transverse corrections for rosette legs

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Using a notch factor for modeling the local plastic behavior, Simcenter 3D 2021.1 Series

© 2020 Siemens

H.O. Fuchs, R.I. Stephens, “Metal Fatigue in Engineering”, Wiley, 1980.

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