Temperature-dependent materials for Durability calculations

Material behavior

The physical behavior of materials depends on the temperature. The following properties, which influence the fatigue behavior, can be defined as temperature-dependent.

• Stress-strain behaviorElastic: Young's modulus, shear modulusElasto-plastic: stress-strain curveVisco-plastic: creep behavior

• Fatigue and strength behaviorTensile (compressive, shear) strengthSN curve dataStrain-life data

Tests (for which the temperature is known and preferably constant) usually provide the values for parameters. The Specialist Durability tools support material data for multiple temperatures. As it is impossible to test at all temperatures that occur during the real load cycle of components, the Specialist Durability tools infer the parameters from the fields defined in the material definition by interpolating data between temperatures for which data is available. The formulas are given in the individual sections below.

The Material data set

The Simcenter 3D Isotropic material can contain a temperature-dependent Durability material definition.

To create a temperature-dependent Durability material, you must define at least one of the properties in the Durability tab of the Isotropic Material dialog box as temperature dependent. You can think of a temperature-dependent Durability material definition as a collection of material nodes in which each node contains the full definition of all material properties for a given temperature.

Durability properties

You can define the Durability properties in the following groups as temperature-dependent:

• Fatigue Strength

• Fatigue Ductility

• Cyclic Parameters

• Test Condition Parameters

• Endurance Limit

You can mix temperature-dependent properties with constant properties. If you define multiple Durability properties as temperature-dependent, the same temperatures must be used in all the temperature-dependent fields.

Note:

For a temperature-dependent material, the software does not dynamically calculate the grayed-out properties of the Endurance Limit group inside the dialog box. The Durability solver calculates the needed values based on the given material definition.

Other properties

Other properties in the isotropic material can have a temperature-dependent definition. These properties are not limited to using the same temperatures as the Durability properties. The software will determine the value of these properties at the temperatures of the Durability material nodes.

Depending on the type of Durability analysis, the Durability solver uses one or more of the following properties:

• Max stress tension

• Max stress compression

• Max shear stress

• Young's modulus

• Shear modulus

• Poisson's ratio

Interpolation methods for temperature-dependent material inside the solver

To get the material properties, the software interpolates the material properties from the material node with a temperature below the current temperature and the material node with a temperature higher than the current temperature.

When the current temperature is outside of the range of the material nodes defined by the Durability properties, the material properties for the closest temperature are used.

Stress life material interpolation

The endurance limit cycle count and stress level are linearly interpolated in log scale. The slope k is linearly interpolated. If the two material nodes have different ranges for the slopes, the cycle counts for slope changes from both nodes are used and the resulting slope is calculated in each of the new ranges.

Tensile strength and compressive strength are linearly interpolated in log scale.

The following example shows stress life interpolation.

Stress life material data

	Specified Data 273.15 K	Interpolated Data 293.15 K	Specified Data 313.15 K	Interpolated Data 328.15 K	Specified Data 333.15 K
SMax	700 MPa	648.07 MPa	600 MPa	523.32 MPa	500 MPa
N**e	2e6	1.732e6	1.5e6	1.107e6	1e6
S**e	80 MPa	80 MPa	80 MPa	72.06 MPa	70 MPa
k0	5	5	5	5.75	6
S1		100 MPa	100 MPa	100 MPa	110 MPa
k1		5.25	5.5	5.875	6.5
S2				110 MPa
k2				6.25

SN Curves

Strain life material interpolation

The strain life material is determined by two formulas.

1. Ramberg-Osgood:

2. Manson-Coffin-Morrow:

The basic idea behind the consistency of the parameters is that the sums in Ramberg-Osgood and Manson-Coffin-Morrow represent the elastic and the plastic portion of the strain. The elastic and the plastic portion each lead to the same mapping from the strain ε to the number of fatigue cycle Nf, i.e.

with

as well as

Interpolation of Ramberg-Osgood

You can interpret the Ramberg-Osgood formula as the summation of two lines defined in the log-log diagram.

• Elastic line:

• Plastic line:

For a better interpolation, especially between high and low, the formulas are written as functions of ε. Low n might occur for high temperatures where there is a high plasticity starting from a given stress.

• Elastic line:

• Plastic line:

The first formula suggests a log interpolation of E. However, the difference between log and linear interpolation in E is probably marginal as long as the material does not melt (i.e. the relative variation of E is probably small). A linear interpolation of E is selected here as it is more common in literature.

The second formula suggests a log interpolation of K' and a linear interpolation of n'.

Note:

Although there is a slight symmetry in the formulas between E and K', the interpolation of K' is not switched to linear, as it is done for E, because the variation in K' might be larger than in E and then the difference between a linear and logarithmic interpolation is larger as well.

Interpolation of Manson-Coffin-Morrow

The main idea is a log-log interpolation in ε and Nf.

The elastic strain defines a line in the log-log diagram

The two interpolate parameters σ'f and b are specified by the definition that log(2Nf) should interpolate linear as a function of εe.

This results in a harmonic interpolation of b and a log interpolation of

The plastic strain defines a line in the log-log diagram

The two interpolation parameters ε'f and c are specified by the definition that log(2Nf) should interpolate linear as a function of εp.

This results in a harmonic interpolation of c and a log interpolation of

Interpolation of other properties

The endurance limit is interpolated in log-scale in the number of cycles N**E.

The static limit S**Max for tension and S**Min for compression can be transformed by the Ramberg-Osgood relation and the Manson-Coffin-Morrow relation to a strain ε or to a number of cycles N. The interpolation will be performed in the strain values, i.e. εMax and εMin. The temperature-dependent values are log interpolated. For the static limit values, which need to be given as stresses, the corresponding stress values are calculated by the Ramberg-Osgood relation after the interpolation.

The Young’s modulus E and the shear modulus G are linearly interpolated. The definition of the shear modulus is where ν is the Poisson Ratio; this can also be written as . As G and E are interpolated linearly, νG also has to be interpolated linearly. The interpolation of ν is therefore a two-step interpolation. In a first step G is linearly interpolated and in a second step νG is linearly interpolated to receive ν.

Interpolation in Torsion

If the material data is provided in torsion the interpolation is conducted in torsion.

The following example shows strain life material interpolation.

Strain life material data

	Specified Data 296.15 K	Interpolated Data 473.15 K	Specified Data 573.15 K	Interpolated Data 673.15 K	Specified Data 773.15 K
SMax	1100.016 MPa	1037.09 MPa	1000 MPa	659.655 MPa	400 MPa
N**e	1953670	1959780	1963240	2024970	2088650
σ'f	1100 MPa	1026.66 MPa	987 MPa	588.144 MPa	365 MPa
b	-0.099	-0.098	-0.097	-0092	-0.087
ε'f	0.619	0.939	1.27	1.936	3.197
c	-0.546	-0.635	-0.699	-0.759	-0.831
K'	1118 MPa	1006.84 MPa	949 MPa	551.932 MPa	321 MPa
n'	0.218	0.202	0.193	0.148	0.103
E	210000 MPa	201693 MPa	197000 MPa	183500 MPa	170000 MPa
ν	0.29	0.29	0.29	0.29	0.29

Ramberg-Osgood curves

Manson-Coffin-Morrow Curves

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Temperature-dependent materials for Durability calculations, Simcenter 3D 2021.1 Series

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