Issue 33

M. Vormwald, Frattura ed Integrità Strutturale, 33 (2015) 253-261; DOI: 10.3221/IGF-ESIS.33.31 258 0 0 κ ( ) exp( ( / ) ) P a a a    (10) The distribution parameter a  and the Weibull-exponent  are determined based on a statistical evaluation of the scatter of the initial crack depths from scatter of strain-life data. The initial crack depth for a component with any highly stressed surface A can be calculated by 1/ 0 0,ref ref ( / ) a a A A   (11) Here a 0,ref and A ref are the initial crack depth and the highly stressed surface of the reference or material specimen. The variables a 0 and A are the initial crack depth and the highly stressed surface of the structure under investigation. The component’s fatigue life therefore differs from material specimen’s fatigue for identical local stress and strain histories. S in MPa -200 0 200 -200 0 200 -200 0 200 -400 0 400 -0.8 -0.4 0.0 0.4 0.8 -0.5 0 0.5  in % Experiment T in MPa  in MPa  in MPa  in % pseudo-strain-app. pseudo-stress-app. FE-Calculation strain-energy-app. Figure 5 : Local, notch root stress,  , and strain,  , states for a notched shaft under load controlled butterfly loading with tension- compression (nominal stress S ) and torsion (nominal stress T ), S460N, Hertel et al. [27]. S EQUENCE EFFECTS IN VARIABLE AMPLITUDE LOADING wo major sources of sequence effect have been identified, either cyclic plastic deformation or geometric issues like a changing geometry of the structure during the fatigue process [30]. Some of the sequence effects are severe. Mean stress re-arrangement and plasticity induced crack closure as well as the continuous decrease of the technical endurance limit very strongly influence variable amplitude fatigue lives. Challenge 9: Sequence effects due to plasticity induced crack closure In the section on challenge 2 the determination of effective ranges for constant amplitude loading has been described. The crack opening strain  x,op (or  x,cl , respectively) discriminates effective and non-effective portions of a cycle. Under variable amplitude loading the crack opening strain is considered to depend on the load sequence. Two main cases are distinguished. If the constant amplitude crack opening strain of a cycle is smaller than the crack opening strain of previous cycles the crack opening strain is set to its constant amplitude value. This case is typical for large cycles following small cycles. If, however, the constant amplitude crack opening strain of a cycle is greater than the crack opening strain of previous cycles, the effective range of the actual cycle is computed using the old, lower crack opening strain. This case is typical for small cycles following large cycles. In this case effective ranges and crack growth increments of the proceeding small cycles are larger than they would be under constant amplitude conditions. An accelerating sequence effect is modeled. The small cycles following a large cycle continuously restore their constant amplitude crack opening strain level. The algorithm is described in more detail in reference [1]. It relies on rainflow cycle counting of the strain sequence. Challenge 10: Sequence effects due to increasing crack size A major issue in the assessment of variable amplitude loading is to realistically account for the damage contribution of load cycles with amplitudes smaller than the constant amplitude endurance limit. A fracture mechanics based assessment offers a natural solution of this problem. The threshold condition discriminates between growing and non-growing cracks. T