Keywords: exhaust manifold, random fatigue model, finite element reliability analysis, stochastic finite element.

This paper proposes a probabilistic approach to fatigue design based on the theory and methods of structural reliability. As an industrial application of such a methodology, the life cycle of a manifold before damage and gas leakage depends on several parameters: geometry, assembly with the engine, material properties and thermal as well as mechanical loading conditions. The manufacturing processes and the diversity of the customers introduce great variability in these parameter values and then influence the risk of failure of the manifold. Traditionally these variability sources are not taken into account in the assessment of the life cycle or in the justification of the structural resistance. The aim of this paper is to propose a complete probabilistic framework that allows the evaluation of the most important random variables that are of great influence on the reliability of the structure and to characterize the probability distribution function of the number of cycles to failure (e.g. lifetime) of a particular part of a manifold.

The uncertain parameters are described by random variables characterized by elementary measures or testing and the structural behavior is simulated through more or less sophisticated models in which the random variables concerning the geometry, the material and the loading conditions are involved. In particular, in order to characterize the fatigue behavior and variability under fatigue loading, we develop an appropriate statistical treatment that predicts the fatigue life under plastic strain loading considering a fatigue specimen database [1].

The reliability methods based on probabilistic considerations, developed and improved during the last years, allow the designer to take into account the different sources of variability and uncertainty in order to get an estimation of the risk and to identify the most important parameters involved in the reliability. Such an approach is used here on a manifold subjected to thermal and mechanical loadings. Its aim is to estimate the probability that the lifetime of the structure exceed a fixed threshold. The structural behavior of the manifold is simulated using a finite element model and by doing successively a non-linear thermal and a mechanical calculation. The uncertain parameters concern the temperatures of the exhausted gas at the maximum engine power and at the minimum, the geometrical properties (thicknesses), the material properties (elasticity modulus, yield limit and plastic modulus) depending on the temperature. Thirteen random variables with correlations are thus introduced in the finite element model.

The methodology used in this study is based on the structural reliability FORM-SORM approximation algorithms [2] implemented in the PHIMECA software©[3] directly combined with the finite element code. The results obtained concern the failure probability and reliability index as well as the most probable failure point and the importance factor of each random variable. An estimation of the structural failure probability and a better understanding of the relative importance of the parameters involved in the structural behavior of the manifold can lead to an optimization of the design and the manufacturing of the structure. On one hand, by identifying the parameters that are of great influence on the reliability of the structure, the efforts (quality controls, material selection, tolerances) can be focused on those that are important in order to limit the costs and to better manage the risk related to such products. On the other hand, by using the importance factor results, we select four random variables considering the other parameters as deterministic parameters in order to define a new stochastic model. This new probabilistic model is combined with the finite element model and we use recent developments of stochastic finite element method [4] to characterize the distribution of the lifetime on a specific part of the manifold.

The methodology presented in this paper shows the operational capability of a complete probabilistic fatigue framework applied to a complex structure whose behavior is described by finite element models.

1

F. Perrin, B. Sudret and M. Pendola, "Comparison of two methods of statistical treatments of fatigue data", Fatigue Design Conference, Senlis, France, 2005.

2

O. Ditlevsen and H. O. Madsen, "Structural reliability methods", John Wiley & Sons, 1996.

3

PHIMECA SA, "PHIMECA Software© User's manual", Aubiere, 2004.

4

M. Berveiller, "Elements finis stochastiques: approches intrusive et non intrusive pour des analyses de fiabilite", PhD thesis, Universite Blaise Pascal, Clermont-Ferrand, France, 2005.

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