The evaluation of the fatigue strength of plastics is difficult. Among other things, this is due to the fact that fatigue strength properties are often not available. This in turn is due to the fact that the determination of such data is very time-consuming. S/N curves (Woehler curves) have to be generated from individual measurements for different stress levels with the corresponding failure load cycles. In addition, dependencies of the S/N curve on temperature and, if necessary, moisture content, and in the case of fiber-reinforced materials also on the fiber orientation (Fig. 1), as well as on the mean stress have to be taken into account. The consideration of these influences, leads to a comprehensive test matrix. A time acceleration of the test procedure is limited for plastics with regard to a maximum allowable test frequency, since self-heating should be avoided. The time and financial effort involved is considerable. Alternative procedures for determining fatigue strength properties are therefore desirable. In the following, an approach is presented that makes it possible to perform an initial estimation of fatigue strength limits based on often existing static properties. The approach is implemented in the material editor of our software Converse and S-Life Plastics.

**Simplified Approach**

The simplified approach proposed here is originally based on the proposal by Oberbach [2] and has been modified and comprehensively extended by Stommel, Stojek, Korte [3]. The concept is briefly outlined here (Fig. 2). Starting from a known static strength limit from a short-term tensile test, the fatigue strength is determined by means of a factor for a load cycle number of 10^{7} ("quasi-endurance fatigue strength", purely alternating). Depending on the actual stress situation, i.e. to what extent a mean stress is present and whether the assessment is to be carried out for load cycles lower than 10^{7}, appropriate correction factors may have to be determined. The implemented approach determines these factors automatically, no additional strength properties are required. Further details are given in [3].

The concept is formally comparable to the approach for metallic materials as presented in the FKM guideline [4]. In the metallic field, the concept of "synthetic Woehler lines" is established by deriving fatigue strength properties from static properties.

**Validation on the Basis of Experimental Data**

An exemplary validation of the plausibility of the fatigue strength properties estimated by computation using the method described above was carried out using measured fatigue strengths of a PA66 reinforced with 50 wt.% short glass fibers taken from the literature [5]. The basis of the computational estimation from static properties were short-term stress-strain curves from publicly available sources (e.g. Campus) or corresponding data available in Converse and S-Life Plastics (Fig. 3).

__Study Design__

Short-term stress-strain curves of an Ultramid A3WG10 in wet condition with principal fiber orientation in test direction were taken as a basis for the computational estimation. Although the reference does not explicitly state the moisture condition of the specimens, static properties (ultimate stress, Young's modulus) are presented, which suggest in terms of magnitude that the material is an air-moist material. Validation was performed for unnotched specimens (K_{t} = 1) at test temperatures of 23°C (RT) and 130°C (experimental). Since no static short-term curve at 130°C was available as a basis for the estimation, the curve at 120°C was used for simplified calculation; no interpolation was performed. Purely pulsating (R=0) and purely alternating (R=-1) cyclic loading was considered. For the alternating load of unnotched test specimens, however, no entire S/N curve is given in the reference, but only a single-point value at N=10^{6}, which is then considered as an indication for the stress ratio R=-1.

__Study Results__

The procedure implemented in Converse and S-Life Plastics, automatically provides, in terms of a push-button solution, per temperature and for stress ratios R=0 and R=-1, S/N curves in the High Cycle Fatigue regime (HCF) between 10^{4} and 10^{7} load cycles. This is done for all plastic grades available in the material database delivered with the software. The experimental S/N curves in Fig. 4 are plotted in terms of nominal stress amplitudes at a probability of survival of PÜ=50 %. In contrast to the reference, the slope exponent of the experimental curves was recalculated in the load cycle range between 10^{4} and 10^{7} to ensure comparability with the computational estimate.

The comparison between measured and estimated S/N curves shows that both the absolute location of the S/N curves, the slope exponent and the differentiation by temperature and stress ratio can be represented with surprisingly small deviations from the measurement (Fig. 5). Assuming usual scattering measures for fatigue strengths limits, the curves determined with the method can be converted from 50% probability of survival to, for example, 90% probability of survival, in order to have a more reliable basis for the assessment of the component.

**Conclusion**

The results presented here are exemplary and do not allow a generalization of the correlations or predictive accuracies for other materials as well. Nevertheless, the results as well as further practical experience at PART Engineering prove that the method provides plausible estimates of fatigue strength properties. The method currently does not take into account the notch sensitivity factor due to local stress gradients. This can lead to a considerably less conservative assessment than on the basis of pure nominal S/N curves.

The method is thus well suited for estimating the fatigue strength of components with comparatively little effort and under the assumption that only static strength properties are known. For example, in the context of optimization or concept studies (Fig. 6), initial assessments can be made on the basis of simple FEM analyses with a linear-elastic isotropic material model. In later development phases or when serious damage consequences are assumed, more elaborate procedures can be added as required, such as [1], which also consider anisotropic strengths.

Taking into account, the comparatively large scatter in the experimental determination of fatigues strength limits, the estimated fatigue strength properties provide a solid working basis for conducting a fatigue strength assessment of plastics.

The procedure is fully implemented in S-Life Plastics, providing an easy-to-use approach to fatigue strength assessment of plastics that can be mastered by occasional users and non-materials experts. This is in line with our claim to offer practice-oriented software that delivers fast, robust and reliable results in daily work.

*[1] A. Jain, J. M. Veas, S. Straesser, W. V. Paepegem, I. Verpoest, und S. V. Lomov, „The Master SN curve approach – A hybrid multi-scale fatigue simulation of short fiber reinforced composites“, Composites Part A: Applied Science and Manufacturing, Bd. 91, S. 510–518, 2016, doi: doi.org/10.1016/j.compositesa.2015.11.038.*

*[2] Karl Oberbach, „Calculation of Plastic Components, Calculation Methods and Allowable Strength Limits“, in Tagungsband Konstruieren mit Kunststoffen, 11. Konstruktions-Symposium der DECHEMA, Frankfurt/Main, 1981, Bd. 91, S. 181–196.
An annotated reprint in English language in pdf format is* available here free of charge

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*[3] M. Stommel, M. Stojek, und W. Korte, FEM zur Berechnung von Kunststoff- und Elastomerbauteilen, 2. Aufl. München: Carl Hanser Verlag, 2018.
Available only in German language* here

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*[4] FKM-Guideline: Analytical Strength Assessment of Components in Mechanical Engineering, 7th Edition. Frankfurt a. M.: VDMA Verlag, 2020.*

*[5] E. Moosbrugger, J. Hartmann, und M. Weber, „Entwicklung von hochfesten und zyklisch kriechbeständigen verstärkten Thermoplasten für eine betriebsfeste Auslegung von Sicherheitskomponenten im Kraftfahrzeug“ BMBF-Rahmenprogramm: WING Werkstoffinnovation für Industrie und Gesellschaft, Förderkennzeichen: 03X3010, Robert Bosch GmbH, Waiblingen, 2010.*

**Author**

Dr. Wolfgang Korte is Managing Director at PART Engineering GmbH, Bergisch Gladbach, Germany.