Fatigue

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Fatigue

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-elastic or linear-viscoelastic range, they can lead to 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 viscoelasticity, damage occurs, e.g. in the form of microcracks. Static strength and deformation characteristics must therefore not be used for the dimensioning (see: 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 characteristic values under this 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 required)
Strain-controlled fatigue test in which a constant strain is superimposed on a constant strain amplitude (elimination of 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.

Fig. 1:

Stress–time and strain–time diagram for oscillating stress

$\sigma$ _o	upper stress	$\epsilon$ _o	upper strain
$\sigma$ _u	lower stress	$\epsilon$ _u	upper strain
$\sigma$ _m	average stress	$\epsilon$ _m	average strain
$\sigma$ _a	stress amplitude	$\epsilon$ _a	strain amplitude

A complete stress cycle is referred to as a load cycle or oscillation cycle. The mean stress (mean strain) $\sigma$ _m ( $\epsilon$ _m) is the pre-stress (pre-strain) mentioned above, $\sigma$ _a ( $\epsilon$ _a) characterises the amplitude of the superimposed stress (strain), $\sigma$ _o ( $\epsilon$ _o) and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _u (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon} _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

Fig. 2:

Types of oscillations in 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).

Fig. 3:

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 = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _u / Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _o is specified as a material parameter. A distinction must be made between:

Tensile threshold range Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _o</math> and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _u are positive; Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _m ≥ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _a; 0 ≤ R < +1,
Alternating range Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _o and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _u have opposite signs; Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _m < Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _a ; 0 ≤ R < -1 and
Compression threshold range Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _o and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _u are negative; $\sigma$ _m ≥ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _D. The fatigue strength Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _D characterises the maximum stress amplitude Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _a that a test specimen can withstand an infinite number of times without unacceptable deformation. At all stress amplitudes above Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _D, the test specimen will fracture. For the practical determination of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} _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 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 specimens for fatigue tests.

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, W., 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, C., Grellmann, W.: Fatigue Loading. In: Grellmann, W., 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)
Lach, R., 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