13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A Model Allowing for the Influence of Geometry and Stress in the Assessment of Fatigue Data Constanze Przybilla1,2,*, Roland Koller2, Alfonso Fernández-Canteli1, Enrique Castillo3 1 Department of Construction and Manufacturing Engineering, University of Oviedo, 33203 Gijón, Spain 2 Laboratory for Mechanical Systems Engineering, EMPA, 8600 Dübendorf, Switzerland 3 Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Santander, Spain * Corresponding author: przybillaconstanze@uniovi.es Abstract Usually, the Wöhler field of a material is obtained from fatigue lifetime data resulting from testing specimens of reduced size in the laboratory. This basic information finds subsequent application in lifetime prediction of larger structural and mechanical components. Thus, an important question arises: how can the S-N field be transformed into an ideal one referred to a characteristic size (length, area or volume) subjected to a constant stress distribution in order to achieve a safe structural integrity design? In this work, the influence of specimen geometry and variable stress state on the fatigue lifetime distribution for constant amplitude fatigue tests is investigated. An experimental program has been carried out with unnotched specimens of nominally the same material but differing in length, diameter, and shape. The experimental data is fitted to a newly developed fatigue model, capable of describing the S-N-field in a probabilistic manner accounting for both the specimen geometry and the variable stress state of the specimens. As the estimated Wöhler field is referred to an elemental surface, loaded by a constant stress level Δσ, the extrapolation of the fatigue resistance to different specimen geometries is possible. Additionally, problems encountered due to scatter of the material properties are discussed. Keywords SN curves, Size effect, Probabilistic modelling, Transferability, Specimen geometry 1. Introduction It has been observed that fatigue lifetime depends on the size of the structural element, whereby larger specimens present lower fatigue lifetime than smaller ones when loaded by the same stress range. This so-called size effect stems from the higher probability of larger specimens to contain a critical crack, capable of initiating the fatigue process, compared to smaller specimens. Investigations on the size effect in fatigue have been done, amongst others, by Weibull [1] on ball bearing steel, by Picciotto [2] on yarn, by Köhler [3] on wires and flat specimens, by Fernández-Canteli et al. [4] on prestressing wires and by Shirani et al. [5] on wind turbine castings. Understanding the size effect is crucial to extrapolate fatigue data from small specimens tested in the laboratory to real structures. Additionally, specimen geometries used in fatigue experiments sometimes present a cross-section with varying diameter along their lengths (see Fig. 2). The experimental results (∆σ versus lifetime N) obtained from testing these specimens are usually evaluated considering the maximum nominal stress range ∆σ0 acting in the smallest cross section and the stress ratio R=σmin/σmax. While the stress ratio R is the same for all cross sections, ∆σ varies along the specimen length. Thus, even if a specimen is likely to fail in the section with the highest ∆σ, the remaining sections with lower ∆σ influence the overall failure probability. That is why for a specimen as depicted in Fig. 2 it is statistically not correct to refer the results only to the surface or volume with the smallest radius (central section). Though there are models to account for the pure length effect, e.g. [6], the variable stress in the specimen is in general not accounted for. The present investigation proposes a new model to evaluate fatigue test data considering both size effect and variable stress state of the test specimens. This allows, on one hand, a comparison of fatigue data obtained for different specimen sizes and, on the other hand, to establish a new method to extrapolate fatigue life results from laboratory tests to different specimen sizes and real structures. The applicability of the model is checked by evaluating three experimental fatigue data
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