By combining MatScape and S-Life Plastics, this approach becomes an efficient and practical method for conducting a complete fatigue strength assessment. The approach and practical benefits are presented here.
The Challenge of Cyclic Strength in Plastics - Why the Experimental Route Is Often Impractical
Assessing the fatigue strength of plastics is one of the more demanding tasks in FEA of vibration-loaded components. A key issue: reliable fatigue data is often unavailable. The reason is clear - obtaining such data is extremely labor-intensive.
To generate meaningful S-N curves, numerous tests must be conducted across different stress levels, from which the corresponding number of cycles to failure can be determined. For instance, if you ask ChatGPT about the cost of generating an S-N curve, you’ll get the breakdown shown in Figure 1. Typical costs are quoted between $15,000 and $50,000 USD, with turnaround times of 2 to 6 weeks - for a single S-N curve. In our experience, these are realistic figures. But that’s rarely the end of it: temperature, humidity, mean stress, and - especially for fiber-reinforced plastics - fiber orientation and other factors significantly affect fatigue behavior (Figure 2). These influences further expand the test matrix. The total cost for a semi-useful experimental characterization of a single commercial plastic grade under relevant application conditions can easily exceed $100,000 USD. This has been confirmed to us by customers in the automotive industry.
Another problem: test duration. For plastics, increasing frequency is limited due to self-heating, which must be avoided. As a result, executing the full test matrix can take several months. The time and financial effort involved in experimentally determining fatigue properties is significant - and often unacceptable, especially in early development stages. For small and mid-sized companies, this is typically beyond feasible scope.
That’s why alternative, pragmatic methods to estimate cyclic fatigue data are of high interest. One such approach - already proven in practice - relies on using available static material data. This method allows a first estimation of fatigue strength without the massive effort of full-scale testing. It is implemented in our software tools MatScape and S-Life Plastics.
Efficient Estimation of Fatigue Strength - A Proven Practical Approach
The method implemented in our software for estimating cyclic strength is based on a simplified, yet sound concept originally proposed by Oberbach [1]. It was subsequently refined and significantly extended by Stommel, Stojek, and Korte [2] - with the goal of providing a practical and reliable alternative to labor-intensive fatigue testing.
The basic idea is easy to understand (Figure 3): Starting from the known static strength obtained from a short-term tensile test, a material-specific factor is applied to estimate the reversed fatigue strength at 107 load cycles - a proxy for the endurance limit, referred to here as "quasi-endurance strength". If a different number of load cycles or a mean stress is to be considered, correction factors are applied automatically. These are computed by the software without requiring additional input data.
We’re not reinventing the wheel here - we’re building on well-established methods from the field of metallic materials. Formally, this approach is based on the concept of synthetic S-N curves or standard S-N curves, as applied in the FKM Guideline [3] for metallic components. While this approach is standard in the metals sector, our implementation makes it accessible to plastics by adapting it to their specific material behavior. Below, we outline how this method is implemented in our material modeling software MatScape.
From the Stress-Strain Curve to a Complete Fatigue Strength Assessment
To use this method, short-term stress-strain curves at the relevant temperature must be available. From these, S-N curves are derived for each temperature and mean stress condition - see Figure 4 for examples at R = -1 (fully reversed) and R = 0 (fully pulsating). Unlike the original method, which used a constant slope exponent, we determine the slope as temperature-dependent, since plastics exhibit significantly stronger temperature sensitivity than metals in typical application ranges.
In the upcoming release of MatScape, a graphical representation of mean stress sensitivity using a Haigh diagram will be available (Figure 5). These diagrams can be generated for different temperatures and load cycles. Even the effect of weld lines - which can significantly reduce fatigue life under cyclic loading - can be considered. Weld line reduction factors can be calculated per material using the integrated “Weld Line Calculator” in MatScape. Mean stress sensitivity is modeled using a simple Goodman approximation [4], providing a conservative estimation.
A complete fatigue strength assessment for an FEA-simulated plastic part can then be performed in conjunction with S-Life Plastics. The software directly accesses the cyclic material data calculated in MatScape. This applies to both pre-included commercial material grades and custom-added grades.
Validation Using Experimental Data - How Reliable Is the Estimation?
How well does this estimation method for cyclic strength actually work in practice? To answer that question, we validated the method using published experimental fatigue data from a PA66 reinforced with 50 wt% short glass fibers [5].
For the numerical estimation, we used short-term stress-strain curves - publicly available via databases such as CAMPUS, or directly accessible within MatScape (Figure 4). In this example, the reference material was Ultramid A3WG10 in a moist condition, with fiber orientation aligned with the loading direction. While the source did not specify the moisture condition explicitly, the reported static properties (e.g., tensile strength, Young’s modulus) suggest a conditioned, humid-state material.
Validation was performed on unnotched specimens (stress concentration factor Kt = 1) at two temperatures: 23 °C (room temperature) and 130 °C (elevated temperature). Two loading conditions were considered: R = 0 (fully pulsating tension) R = −1 (fully reversed tension-compression). For the R = −1 case, no full S-N curve was available in the literature - only a single-point value at N = 106 cycles, which was used for comparison.
The experimental S-N curves (Figure 6) were presented as nominal stress amplitudes at a 50% survival probability. To ensure comparability with the computed curves, the slope exponent of the experimental data was re-evaluated over the range of 104 to 107 cycles.
The Result Convinces
The comparison shows excellent agreement in terms of: the overall position of the S-N curves, the slope exponent, and the influence of temperature and load ratio (see Figures 6 and 7). Taking into account the typical scatter of fatigue data, the computed curves for 50% probability of survival can also be conservatively adjusted to higher survival probabilities, e.g., 97.5%, which is crucial for robust design validation.
Conclusion and Outlook - Faster, More Reliable Results with Significantly Less Effort
The benefits of the presented method are obvious: Instead of costly and time-consuming fatigue testing, only a few static material parameters are needed - these are often already available or can be obtained at minimal effort. A simple short-term tensile test is usually sufficient. Figure 1 (right column) shows an example cost breakdown for such tests: Typical costs range from $100 to $2,000 USD, with turnaround times of one to two weeks - just a fraction of what fatigue testing would require.
To be clear: This does not mean experimental S-N data is obsolete. In critical applications - especially in safety-relevant designs - experimental validation is still necessary and appropriate.
However, in many cases, especially during early development or when test data is unavailable, a numerical estimation is the only economically viable path. It’s also important to remember that experimental data itself is subject to scatter: Figure 8 illustrates the typical variation in measured S-N curves. Even small differences in stress amplitude can lead to significant differences in fatigue life, as fatigue life is logarithmically dependent on the stress amplitude.
This highlights the importance of accuracy in numerical analysis - including proper meshing, material modeling, and boundary conditions. After all, the most accurate S-N curve is of little use if the stress amplitudes in the part are not simulated precisely. In practice, the accuracy of computed fatigue life tends to fall within a factor of 2 - 3 of experimental component test results. And that’s already a success.
A fitting quote from German mathematician Carl Friedrich Gauss applies here:
“Nothing shows a lack of mathematical education more than overly precise calculations.”
In other words: the Pareto principle holds here as well - 80% of the benefit with 20% of the effort (Figure 9). As a nice coincidence, Gauss was once featured on the old German 10-DM banknote - bringing us full circle back to the topic of cost.
Final Note
With MatScape and S-Life Plastics, a worldwide unique solution is now available that enables engineers to perform a complete fatigue strength assessment for plastic components- quickly and cost-effectively, based on a minimal set of static material parameters. MatScape is fully integrated into S-Life Plastics, and available to all its users - bringing greater efficiency to both development and simulation.
[1] 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.
[2] M. Stommel, M. Stojek, und W. Korte, FEM zur Berechnung von Kunststoff- und Elastomerbauteilen, 3. Aufl. München: Carl Hanser Verlag, 2025. Available only in German language here. An edition in English language is in preparation.
[3] FKM-Guideline: Analytical Strength Assessment of Components in Mechanical Engineering, 7th Edition. Frankfurt a. M.: VDMA Verlag, 2020.
[4] Goodman relation, Wikipedia, https://en.wikipedia.org/wiki/Goodman_relation
[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
