(positive) influence of shot-peening and the (negative) effect of the mechanical layer on the failure probability are shown in Fig. 3. Suspension arms Fatigue tests and observations Fatigue tests on suspension arms were carried out with a mechanical system that allows one to prescribe biaxial loading along two axes X and Y in the suspension arm plane, at point E (Fig. 5). To test only the fatigue resistance, its surroundings are simplified: neither its knee joint, nor its bond with the antiinclination bar are used. Moreover, to have access to a cyclic frequency of 10 Hz, arms are mounted without the elastic bonds. Displacement boundary conditions are prescribed at two points A and B (Fig. 5); apart from a free rotation about the Z-axis, the other degrees of freedom are suppressed. The analysis of fatigue results shows a scatter in an FX-N diagram. The failures are essentially located along the AB segment, close to the knee joint (Fig. 5). By SEM analysis, microshrinkage cavities are observed as well as degenerated graphite nodules close to the free surface. As a first approximation, we consider that the flaw size distribution is identical in both machined samples and suspension arm because the degenerated graphite nodules are located in the shot-peened layer. Numerical computations To assess the predictive capacity of the probabilistic approach, a comparison between fatigue tests carried out on double shot-peened suspension arms and numerical simulations is now performed. A programme, ASTAR, was developed to evaluate the reliability of components subjected to cyclic loading. It allows one to integrate volume and stress field heterogeneity, with the flaw size distribution identified in the first section. The prediction of the local failure probabilities and the global failure probability of a structure is possible. This programme is divided into two parts: ASTAR-SURF for the surface layer and ASTAR-VOL for the remaining volume. The post-processor uses an elastic (FE) analysis to determine the stress field in structures: at each integration point, the equivalent stress is computed (e.g., maximum principal stress). To this equivalent stress corresponds an initial flaw size ac0 for a given number of cycles of failure NF. This flaw size is computed by integration of Eqn. 2 through a Newton method. The failure probability Fj P of an element j in a structure can be calculated: Fj P depends on the element volume j V , the number ng of integration points for this element and the weight wi associated with each integration point ( ) ( ) i n i Fi j Fj P w V V P g Σ = − − = 0 1 ln1 ln1 (8) where Fi P denotes the cumulative failure probability at point i, evaluated by using Eqn. 5. The failure probability k FP of one entity of the structure (viz. surface layer or remaining volume) is then computed ( ) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − = − Σ = k F n j F j k P P 1 ln1 1 exp (9) where kn is the number of elements of one part of whole structure and k stands for either the surface layer or the remaining volume. Lastly, the failure probability FP of the whole structure is computed as follows
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