Fatigue Strength

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Fatigue strength or continuous fatigue strength

Determination of fatigue strength

The aim of a vibration test or fatigue test is to determine the vibration strength, or fatigue strength σ_D for short. σ_D characterises the maximum stress amplitude σ_a that a test specimen can withstand an infinite number of times without unacceptable deformation. At all stress amplitudes above σ_D, the test specimen breaks. Since this destruction of the plastic test specimen occurs in the linear-elastic or linear-viscoelastic deformation range, the term fatigue is used in this context. The fractures that occur are referred to as fatigue fractures.

Indexing is done with capital letters in order to distinguish between the stress parameters to be set and characteristic values of the fatigue strength. The type of stress is indicated by ‘z’ for tension, ‘d’ for compression and ‘b’ for bending.

Example: σ_zD... Fatigue strength in the alternating tension range

Frequently used special cases of fatigue strength are:

• Alternating strength σ_W = σ_a = σ_o = |σ_u| for σ_m = 0.
• Threshold strength σ_Sch = 2 σ_a for σ_m = σ_a.
• The time-dependent fatigue strength σ_(N) characterises the stress amplitudes above σ_D at which fatigue fracture of the test specimen occurs.
• σ_z(6) means time-dependent strength in the alternating tensile range of 10⁶ load cycles.

N is always the number of cycles or load cycles and N_C is the limit number of cycles that is reached without fracture of the test specimen.

Performing WÖHLER tests

Fatigue strength is determined using the WÖHLER test. This consists of a series of single-stage vibration tests, i.e. with stress cycles of constant amplitude σ_a at a constant mean stress σ_m or constant stress ratio R.

The stress should be selected so that at least one test specimen breaks at a low number of cycles and another test specimen runs through to the limit number of cycles N_C. The selected stress amplitudes σ_a are plotted on a double logarithmic scale as a function of the number of cycles N endured until fracture. Connecting the individual measurement points results in the Wöhler curve (Fig. 1), which is referred to as the S–N curve.

Fig. 1:

Schematic WÖHLER curve (S–N curve) for plastics compared to metallic materials

As expected, the S-N line shows an increase in the number of cycles N with decreasing stress amplitude. In metallic materials, especially structural steels, the WÖHLER line approaches a horizontal line above a certain number of cycles N_D. This stress limit, at which no fracture occurs even after an infinite number of cycles, is the fatigue vibration strength, often referred to simply as fatigue strength σ_D. To determine this value in practice, the WÖHLER test must be carried out until a limit number of cycles N_G is reached. Values for N_G derived from experience are 2•106 for steels and 10 to 50•106 for light metals. For non-metallic materials and metallic materials under corrosive stress, the WÖHLER line (S–N line) continues to decline even at very high fatigue cycles. For plastics, a fatigue strength based on 7•107 fatigue cycles is determined. However, fatigue fractures are to be expected here even at higher fatigue cycles.

Test equipment for fatigue testing

Servo-hydraulic universal testing machines (Fig. 2) can be used to perform dynamic tests at medium frequencies, while pulsators (electrodynamic principle) or cyclic bending machines can be used at high frequencies. These machines must always have closed control loops for force and deformation (see also: tensile test control). When measuring temperature dependence, a temperature control chamber must also be connected.

Fig. 2:

Servo-hydraulic testing machine MTS 319.25 from MTS Systems GmbH, Berlin, for performing WÖHLER tests

See also

• Vibration test
• Fatigue
• Test specimen for fatigue tests
• Vibration fracture
• Vibration-induced creep fracture

Reference

• 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