Keywords: probabilistic assessment, fatigue life, fatigue criterion, statistical evaluation.

Fatigue crack initiation is usually assessed through the use of stress criteria. We denote, in a general way, such a criterion. Here represents the stress state of the specimen after cycles and represents a set of material parameters (typically the fatigue limit) which are determined on simple coupons at a given number of cycles . The general idea of a fatigue criteria is then to separate the stress-lifetime space in two areas: a safe one where , and an unsafe one where . However it is well known that the fatigue phenomenon is not a deterministic one. Probabilistic criteria have been proposed recently (see for example Sudret [1], or Flacelière [2]) but they are usually either formulated using classical (local) fatigue criterion, which restricts their range of application, or hard if not impossible to generalize to more complex cases where numerous sources of uncertainty may interact. We propose here an approach integrating an advanced non-local stress fatigue criterion in a general probabilistic framework. The general purpose of this research is to obtain "random" fatigue life predictions with statistical properties similar to actual fatigue test data.

The fatigue model used has been developed at the EADS CCR (EADS Corporate Research Centre France). It is a non-local, multiaxial fatigue criterion, and it has been shown to provide relatively robust estimates of the mean fatigue life for various coupons geometry. Several factors contribute to the random output of a fatigue test, but geometrical uncertainties, material variability and manufacturing variability may be considered as major contributors for simple coupon tests. In our study, as we mainly analyse simple material coupons, a single source of uncertainty is considered, which could be labelled as the "material fatigue resistance" of the material (denoted ). It is thus assumed that manufacturing, geometry and loads are consistent from test to test and of secondary importance, which is debatable but achievable to the first order with (much) experimental care.

The paper is organised as follows. In the first section, the formulation of our proposed non-local criterion is briefly presented, together with a procedure to determine the parameters of the criterion. In the next section, a procedure to determine the statistical distribution of the material fatigue resistance (which is the only stochastic variable in our analysis) is then proposed. This evaluation procedure has been carried out on an aluminium alloy for which a dedicated fatigue database (tensile tests on open hole specimen) has been created. An additional fatigue database (tensile tests on plain specimens) has also been created to question the relevance of the single uncertainty source hypothesis: applying the evaluation procedure to this new database yields the same estimation of the random variable, thus increasing our confidence in the model.

In the final section, the propagation of the uncertainties is performed by the use of a Monte-Carlo related method, which needs very few computer resources, providing us with probabilized curves as the output of the method. In the field of classical fatigue, it is customary to assume that the fatigue criterion calibrated on some tests (i.e. given loads on a given geometry) allows the prediction of the fatigue life of any other configurations (provided the damage mechanisms are identical). It is of interest to check whether this assumption is also valid for the scatter in a stochastic model. Additional dedicated fatigue databases have therefore been created (using the same batch of material) for other coupon geometries and load cases. The predictions of the stochastic model in terms of scatter are compared successfully to the experimentally observed dispersion.

1

B. Sudret, Z. Guede, P. Hornet, J. Stephan, M. Lemaire, "Probabilistic assessment of fatigue life including statistical uncertainties in the SN curve", Transactions of the 17th Internationnal conference on Structural Mechanics in Reactor Technology, Prague, p. 17-22, 2003

2

L. Flacelière, F. Morel, "Approche Fiabiliste en Fatigue Multiaxiale Polycyclique: critère probabiliste et endurance limitée", in proceedings of the 23ie Journées de Printemps, 2004

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