Fatigue–Strength Surface: basis for structural analysis under dynamic loads

Abstract

The relation between fatigue strength and number of load cycles to failure is usually represented by Wohler curves. The four-parametric Weibull function shows a good relation between the static and dynamic strength in the low- and high-cycle fatigue range for a constant stress ratio R (minimum stress/maximum stress) (see Jarosch and Stepan in Fatigue properties and test procedures of glass reinforced plastic rotorblades. American Helicopter Society, 25th Annual National Forum, Paper No. 370, 1969; Och in Fatigue strength, AGARDograph No. 292, helicopter fatigue design guide, 1983; Bansemir and Emmerling in Fatigue substantiation and damage tolerance evaluation of fiber composite helicopter components, applied vehicle technology panel: applications of damage tolerance principles for improved airworthiness of rotorcraft, Corfu, Greece, 1999). However, in addition to the number of load cycles to the failure, fatigue strength also depends on the stress ratio R as well. In predicting the lifetime of a component, a more proper way for the presentation of fatigue life test data is the Goodman approach. This often used method affords the user to predict lifetime at any stress ratio, but does not represent the real material behaviour fully. The Goodman diagram does not take into account the combined effect of low-cycle fatigue and high-cycle fatigue. One better way to build an accurate relation between the fatigue strength, number of load cycles to failure and the stress ratio is to add the third dimension. The result is a three-dimensional view of the fatigue strength as a function of number of load cycles to failure and stress ratio R. Hence, the mathematical description of the fatigue strength as a kind of a surface function depending on the number of load cycles to the failure and the stress ratio is of high interest and indeed the focus of this study. The surface function represents the real material behaviour in low-cycle fatigue range as well as in high-cycle fatigue range more accurate compared to basic Goodman approach. For the determination of the Fatigue–Strength Surface, a so-called F–S Surface, test points with different stress ratios are necessary. The surface function can be adapted to the test points using a nonlinear regression analysis based on least square method. Therefore, it is advisable to use either the three-dimensional Weibull function or a surface function which consists of Tschebyscheff Polynomials. To enhance the regular two-dimensional Weibull function to a three-dimensional model, the four Weibull parameters are described as functions of the stress ratio. This method can be used to analyse the material behaviour based on the results of coupon or component tests. In case of coupon tests, this method is applied and validated as described in the paper. Furthermore, the use of material F–S Surface is compared with Goodman approach. For this purpose, mean surfaces of coupon test specimens with a survival probability of 50% are used. Especially in high-cycle fatigue range and for the stress ratios greater than zero, Goodman approach shows a slight deviation from the actual fatigue strength. In order to consider such effects, lifetime calculations are performed in Eurocopter Deutschland GmbH by using the reduced, so-called working S–N curves which are based on component test results. It has been found that the F–S Surface tends to describe the real fatigue strength in a more accurate way. This may lead to a longer lifetime of components and the possibility to extend the margins of components. This paper is developed from the Diploma thesis “Prediction of the dynamic strength behaviour of structural elements based on S–N–R surfaces created by nonlinear regression analysis of experimental data” (see Weinert in Prediction of the dynamic strength behaviour of structural elements based on S–N–R-surfaces created by nonlinear regression analysis of experimental data Technische Universitat Dresden 2011).