Axial versus torsion tests

You can use either axial tests or torsional tests to determine the strain-life material properties (see the figure below). The strain-life equations in torsion are

where G is the shear modulus, Kʹγ and n' are the cyclic strength coefficient and hardening exponent in shear, τʹf and γʹf are the fatigue strength and ductility exponents in shear, respectively. These material properties are related to the number of reversals to crack initiation, 2Nf, in the same manner as for axial data.

Note:

The torsional formulas are given in γ, which is twice the shear component of the strain tensor.

Axial and torsional tests

The basic concept behind the tension-torsion conversion is that the two formulas should be equivalent in the resulting formulas for the von Mises stress and strain for pure tension stress and pure torsional strain.

This results in the following relation between tension and torsion parameters:

Relation of axial to torsional parameters
G
Kʹf
τʹf
γʹf

n', b and c and are the same for tension and torsion.

For the endurance limit, NE is kept unchanged, and the stress and strain values are converted according to the stress and strain relations as described in the table above.

The tensile strength is converted according to the stress relation. In torsion calculations, the compressive strength is not used. If a torsion material definition is used in a tension calculation, the compressive strength is three times the tensile strength.

Specialist Durability lets you define either axial or torsional strain-life fatigue coefficients. When you define the strain-life for a material using the Durability page of the Isotropic Material dialog box, you can enter the strength and ductility coefficients and exponents, and the cyclic parameters. In the Test Condition Parameter group, the Test Type list indicates whether these material properties are from tension or torsion tests. If you select Tension, the software assumes that the values for the material properties are from axial tests. If you select Torsion, the software assumes that the values are from torsional tests.

Note:

The properties in the material dialog box are the same in the tensional and the torsional case, but the software treats them as tensional material properties or as torsional material properties depending on the setting of Test Type.

Note:

The Test Type of Bending is not yet supported.

For an analysis, you select either axial or torsional damage parameters. If the material data sheet contains matching properties, then the software uses these properties directly. If the material data sheet indicates that the input parameters do not match the current damage parameter, the software converts the material parameters from tension to torsion or vice versa by the relations given below.

Derivation of the relations

The relations listed in the tables above are derived by the following formulas.

The von Mises stress and strain are defined as follows:

This results in the following values for pure tension:

And the following values for pure torsion:

Furthermore, the general relation between Young’s Modulus and Shear Modulus holds, i.e.

This results in the following transformation:

Inserting the relations of the von Mises values into the Ramberg-Osgood equation, one gets the following relation

This results in the relation

Inserting the relations of the von Mises values into the Manson-Coffin-Morrow equation, one gets the following relation

This results in the two relations

Learn more

Local stress-strain behavior

Constant amplitude life curves

Endurance limit and static failure

Determining material properties

Mean stress and damage parameters

Notch analysis

The strain-life analysis in Specialist Durability

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Axial versus torsion tests, Simcenter 3D 2021.1 Series

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