Issue 38

M. Kepka et alii, Frattura ed Integrità Strutturale, 38 (2016) 82-91; DOI: 10.3221/IGF-ESIS.38.11 86 Determination of resulting fatigue life distribution function The resulting fatigue life distribution function (FLDF) is to account for the random nature of loading, as well as the random nature of material properties. The input to the process of its determination consists of the quantity s of constant- length segments of the loading process, and 99 lifetime curves for individual failure probability levels. Hence, a total of k = s ×99 combinations of loads and material properties are available. The resulting FLDF is obtained by finding a set of distribution curves through process segmentation, using the lifetime curve for P = 1 %, then 2 %, and so forth until 99 % is reached. Finally, 99 distribution curves are obtained from which the resulting FLDF is generated for individual corresponding probability levels. D EMONSTRATION EXAMPLE he chosen demonstration example concerns a welded joint in an articulated bus which is located at the base of the fixed bracket of the articulated joint on the rear section (Fig. 5). In fact, some vehicles exhibited fatigue damage in this location. The purpose of the measurement was to assess the stresses in this structural detail, redesign it and validate this modification through another measurement run. For this case study, stress analysis has been carried out for the location of the R1 strain gauge rosette which is a place where two welded joints meet. Engineering strain time histories from this rosette were used for evaluating the components of principal, longitudinal, vertical and shear stresses. Road tests involved running a demanding route of approximately 13 kilometers in urban and suburban traffic: four times with the vehicle empty and four times with the vehicle loaded, although without real passengers. On this route, the frequency of failures occurring in buses was the highest. Along this route, the road is uneven with large differences in height which causes vertical excitation in the vehicle. In addition, there are many curves and upward and downward slopes which were expected to contribute to twisting loads on the joint. Figure 5 : The joint of the rear section of an articulated bus – a schematic drawing and the strain gauge rosette R1. Time histories analysis Generally, the approach for multiaxial fatigue problems depends on the type of loading involved. The solution is less complicated for structural details under proportional loading. This is the type of loading in which the ratio of principal stresses (biaxiality ratio) a = σ 2 / σ 1 and the directions of the principal stresses remain constant. Non-proportional loading involves principal stresses whose directions rotate or undergo stepwise changes. The critical location of interest – the strain gauge rosette R1 – was studied using the nCode software. The figures below show results of the analysis for one of the stress-time histories obtained from the road test of the empty vehicle in real traffic. Fig. 6 shows the dependence of the absolute maximum principal stress on its angle to the x direction. The graph indicates that the directions of principal stresses remain constant at all stress levels, except the very low ones. This is the necessary condition for considering proportional loading conditions. The other graph in Fig. 6 from the same measurement run shows the dependence of the absolute maximum principal stress on the biaxiality ratio. At higher stresses, the biaxiality ratio fluctuates about 0.25 and approaches the Poisson’s ratio, which is an indication of near-plane strain loading. T