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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 42
Probabilistic Assessment of Fatigue Life Using a StressBased Fatigue Criterion C. Schwob^{1}^{2}, L. Chambon^{1}, F. RondeOustau^{2} and J.P. Bernadou^{3}
^{1}EADS Corporate Research Center, Suresnes, France
C. Schwob, L. Chambon, F. RondeOustau, J.P. Bernadou, "Probabilistic Assessment of Fatigue Life Using a StressBased Fatigue Criterion", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 42, 2006. doi:10.4203/ccp.83.42
Keywords: probabilistic assessment, fatigue life, fatigue criterion, statistical evaluation.
Summary
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 stresslifetime 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 nonlocal 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 nonlocal, 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 nonlocal 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 MonteCarlo 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. References
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