Uncertainty on Fatigue Damage Accumulation for Composite Materials Authors:

1. Uncertainty on Fatigue Damage Accumulation for Composite Materials Authors: Henrik Stensgaard Toft, Aalborg University, Denmark John Dalsgaard Sørensen, Aalborg University / Risø-DTU, Denmark

2. Contents • Introduction • Composite Material used for Testing • Constant Amplitude Fatigue Tests • Variable Amplitude Fatigue Tests • Conclusion and Future Work www.dong.dk www.vestas.com

3. Introduction Fatigue design of composite material is normally performed using a deterministic design approach. The uncertainties related to fatigue design are in general large which allows for adopting a probabilistic design approach where the uncertainties can be treated in a rational manner. The objective of the present work is establish probabilistic models for: • Uncertainty on the SN-curve • Uncertainty on damage accumulation Primary focus on composite materials used in wind turbine blades.

4. Introduction Deterministic fatigue design is normally based on a: • Linear SN-curve (log-log scale) • Miner Rule for linear damage accumulation Other types of SN-curves and damage accumulation models have been proposed, see e.g. [1,2]. [1] V.A. Passipoularidis, Fatigue Evaluation Algorithms: Review, Materials Research Division, Risø-DTU, 2009. [2] N.L. Post, S.W. Case, J.J. Lesko, Modelling the variable amplitude fatigue of composite materials: A review and evaluation of the state of the art for spectrum loading, Int. J. Fatigue, 30 (2008), pp. 2064-2086.

5. Introduction Uncertainties can in general be divided into three groups: • Physical uncertainty (Aleatory uncertainty) • Model uncertainty (Epistemic uncertainty) • Statistical uncertainty (Epistemic uncertainty) www.lmglasfiber.com

6. Composite Material used for Testing Material Database: • OptiDAT database (www.kc-wmc.nl) Composite material: • Epoxy Glass Fiber Reinforced Plastic (GFRP) Geometry: • Geometry R04 MD • Lay-up: [[45, 0]4; 45] • Size: 25 x 150mm www.kc-wmc.nl

7. Constant Amplitude Fatigue Tests For composite materials the fatigue strength is dependent on the mean stress. Therefore several SN-curves are collected in a Constant Life Diagram using: • Constant amplitude data for 7 different R-ratios.

8. Constant Amplitude Fatigue Tests SN-curves are fitted using the Maximum-Likelihood Method in order to model the physical and statistical uncertainties. The Likelihood function is given by: The statistical uncertainty is calculated using the Hessian Matrix:

9. Constant Amplitude Fatigue Tests Parameters in SN-curves: Static tension and compression strength:

10. Constant Amplitude Fatigue Tests

11. Constant Amplitude Fatigue Tests

12. Variable Amplitude Fatigue Tests The model uncertainty related to Miners rule for damage accumulation is determined based on variable amplitude fatigue tests. Load spectra's • Wisper spectrum • WisperX spectrum

13. Variable Amplitude Fatigue Tests Mean and standard deviation for accumulated damage at failure. • High uncertainties compared e.g. welded steel details. • Significant model uncertainty related to Miners rule for composite materials. • Lognormal distribution (negative damage avoided)

14. Conclusion & Future Work Fatigue design contains the following uncertainties: • Physical uncertainty: SN-curves • Statistical uncertainty: Parameters in the SN-curves • Model uncertainty: Miners rule Model uncertainty on Miners rule can be modelled by a Lognormal distribution with mean and standard deviation equal to approx. 0,50. Partial safety factors for fatigue design of wind turbine blades can be calibrated using the stochastic models given in the present paper. www.vestas.com

15. Uncertainty on Fatigue Damage Accumulation for Composite Materials Authors: Henrik Stensgaard Toft, Aalborg University, Denmark John Dalsgaard Sørensen, Aalborg University / Risø-DTU, Denmark