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Created page with "{{Language_sel|LANG=ger|ARTIKEL=Ermüdung}} {{PSM_Infobox}} Fatigue __FORCETOC__ ==Fundamentals== In practical use, components are often exposed to oscillating loads in addition to static stresses. These are often referred to as dynamic stresses, but must be distinguished from impact loads (see: impact loading plastics). Even if these oscillating stresses are within the linear..."

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{{Language_sel|LANG=ger|ARTIKEL=Ermüdung}}
{{PSM_Infobox}}
Fatigue
__FORCETOC__

==Fundamentals==

In practical use, components are often exposed to oscillating loads in addition to static [[Stress|stresses]]. These are often referred to as dynamic stresses, but must be distinguished from impact loads (see: [[Impact Loading Plastics|impact loading plastics]]). Even if these oscillating stresses are within the linear-elastic or linear-viscoelastic range, they can lead to [[Component Failure|failure of the component]] at significantly lower stresses and strains than in the case of static loading.

If the strain amplitude exceeds the limit of [[Linear-viscoelastic Behaviour|linear viscoelasticity]], damage occurs, e.g. in the form of [[Crack|microcracks]]. Static [[Strength|strength]] and [[Deformation|deformation]] characteristics must therefore not be used for the dimensioning (see: [[Plastic Component|plastic component]], dimensioning) of structural parts subjected to oscillating stresses.

==Stress and strain controlled fatigue test==

Vibrating stress refers to periodically alternating stress, and the test procedure for determining [[Material & Werkstoff|characteristic values]] under this [[Stress|type of stress]] is referred to as a vibration test. There are two different variants:

* Stress-controlled vibration test in which a constant stress is superimposed with a constant stress amplitude (elimination of stress [[Relaxation Plastics|relaxation]] required)
* Strain-controlled fatigue test in which a constant strain is superimposed on a constant strain amplitude (elimination of [[Creep Plastics|creep]] under load required)

This superimposition of the stress or strain generated at the beginning of the test with a periodic stress or strain amplitude is shown graphically in '''Fig. 1''' below.

[[File:Fatigue_Fig-1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Stress–time and strain–time diagram for oscillating stress
{|
| width="50px" |<math>\sigma</math>o
| width="250px" |upper stress
| width="50px" |<math>\epsilon</math>o
| width="100px" |upper strain
|-
|<math>\sigma</math>u
|lower stress
|<math>\epsilon</math>u
|upper strain
|-
|<math>\sigma</math>m
|average stress
|<math>\epsilon</math>m
|average strain
|-
|<math>\sigma</math>a
|stress amplitude
|<math>\epsilon</math>a
|strain amplitude
|}
|}

A complete stress cycle is referred to as a load cycle or oscillation cycle. The mean stress (mean strain) <math>\sigma</math>m (<math>\epsilon</math>m) is the pre-stress (pre-strain) mentioned above, <math>\sigma</math>a (<math>\epsilon</math>a) characterises the amplitude of the superimposed stress (strain), <math>\sigma</math>o (<math>\epsilon</math>o) and <math>\sigma</math>u (<math>\epsilon</math>u) characterise the largest and smallest stress (strain) values occurring in a vibration cycle.

==Types of vibration==

In testing practice, the following types of oscillations can be realised (see '''Fig. 2'''):

* Triangular oscillation (triangle)
* Half-triangular oscillation (half-triangle)
* Sine oscillation
* Half-sine oscillation
* Square or trapezoidal oscillation
* Half-square oscillation
* Triangle ramp
* Random oscillation

[[File:schwingungen.jpg|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Types of oscillations in [[Continuous Vibration Test|vibration test]]
|}

==Stress cases for a sinusoidal vibration==

In testing practice, sinusoidal oscillation is usually preferred because it offers the highest control loop stability.

Depending on the stress values, this so-called single-stage continuous vibration test can be carried out in three stress ranges with a total of seven stress cases ('''Fig. 3''').

[[File:Fatigue_Fig-3.jpg|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px"|Stress cases and areas in vibration testing
|}

Depending on how the test is conducted, either the mean stress and stress amplitude or the upper and lower stresses are specified as stress values. In the stress-controlled continuous vibration test, the stress ratio ''R'' = <math>\sigma</math>u / <math>\sigma</math>o is specified as a [[Material Parameter|material parameter]]. A distinction must be made between:

* '''Tensile threshold range''' <math>\sigma</math>o</math> and <math>\sigma</math>u are positive; <math>\sigma</math>m ≥ <math>\sigma</math>a; 0 ≤ ''R'' < +1,
* '''Alternating range''' <math>\sigma</math>o and <math>\sigma</math>u have opposite signs; <math>\sigma</math>m < <math>\sigma</math>a ; 0 ≤ ''R'' < -1 and
* '''Compression threshold range''' <math>\sigma</math>o and <math>\sigma</math>u are negative; <math>\sigma</math>m ≥ <math>\sigma</math>a; 0 ≤ ''R'' < +1.

==Determination of fatigue strength==

Assuming a constant mean stress, the aim of the test is to determine the fatigue vibration strength or [[Fatigue Strength|fatigue strength]] <math>\sigma</math>D. The [[Fatigue Strength|fatigue strength]] <math>\sigma</math>D characterises the maximum stress amplitude <math>\sigma</math>a that a test specimen can withstand an infinite number of times without unacceptable deformation. At all stress amplitudes above <math>\sigma</math>D, the test [[Specimen|specimen]] will [[Fracture|fracture]]. For the practical determination of <math>\sigma</math>D, the WÖHLER test can be performed to determine S–N curves, which reflect the relationship between the level of stress and the determined fatigue life. The WÖHLER test is performed on [[Plastics|plastics]] up to a number of vibration cycles of ''N'' ≥ 107.

Information on the test specimen shapes used for the experimental determination of fatigue behaviour can be found under [[Test Specimen for Fatigue Tests|test specimens for fatigue tests]].

==See also==

* [[Vibration Test|Vibration test]]
* [[Test Specimen for Fatigue Tests|Test specimen for fatigue tests]]
* [[Fatigue Strength|Fatigue strength]]
* [[Vibration-induced Creep Fracture|Vibration-induced creep fracture]]
* [[Vibration Fracture|Vibration fracture]]

==References==

* DIN 50100 (2022-12): Load Controlled Fatigue Testing – Execution and Evaluation of Cyclic Tests at Constant Load Amplitudes on Metallic Specimens and Components
* DIN 53442 (1990-09): Flexural Fatigue Testing of Plastics using Flat Specimens
* ISO 3385 (2014-07): Flexible Cellular Polymeric Materials – Determination of Fatigue by Constant-load Pounding
* [[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 156–166 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see [[AMK-Library]] under A 22)
* [[Bierögel,_Christian|Bierögel, C.]], Grellmann, W.: Fatigue Loading. In: Grellmann, W., [[Seidler,_Sabine|Seidler, S.]]: Mechanical and Thermomechanical Properties of Polymers. Landolt-Börnstein. Volume VIII/6A3, Springer, Berlin (2014) pp. 241–285 (ISBN 978-3-642-55165-9; see [[AMK-Library]] under A 16)
* [https://researchgate.net/profile/Ralf-Lach Lach, R.], [http://192.168.81.5/wiki/index.php/Grellmann,_Wolfgang Grellmann, W.]: Mechanical Properties Characterization. In: Comprehensive Polymer Science. 2nd Edition, Elsevier (2026), https://doi.org/10.1016/B978-0-323-95486-0.00173-3

[[Category:Fatigue]]

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