Issue 31

J.A.F.O. Correia et alii, Frattura ed Integrità Strutturale, 31 (2015) 80-96; DOI: 10.3221/IGF-ESIS.31.07 84 Castillo and Fernández-Canteli [20] proposed a probabilistic model to describe the strain-life field of the material ( p-ε a -N field), based on Weibull distribution. The model assumes that the fatigue life, N f , and the total strain amplitude, ε a , are random variables. Based on several physical and statistical considerations, such as the weakest link principle, stability, limit behaviour, range of the variables and compatibility, Castillo and Fernández-Canteli [20] derived a strain-life model, which shows exactly the same formulation as proposed the authors for the stress-life field. The interested readers can see the detailed assumptions in Castillo et al. [27, 28], where the stress version of the model has been studied and successfully applied to different cases of lifetime problems. This leads to the Weibull strain-life model [28]:         0 0 * * 0 0 log log ( ; ) 1 exp log log f a a f a f a a N N p F N N N                                (10) where p is the probability of failure, N 0 and ε a0 are normalizing values, and λ , δ and β are the non-dimensional Weibull model parameters. Their physical meanings (see Fig. 2) are: N 0 : Threshold value of lifetime; ε a0 : Endurance limit of ε a ; λ : Parameter defining the position of the corresponding zero-percentile curve; δ : Scale parameter; β : Shape parameter. Note that the strain-life model (Eq. (10)) has a dimensionless form and reveals that the probability of failure p depends only on the product ** a f εN , where   0 * log NN N f f  and   0 * log a a a ε ε ε  , that is: * * * * * ~ ( , , ) ~ , , f a f a a N W N W                 (11) i.e., ** a f εN has a Weibull distribution. This model provides a complete analytical description of the statistical properties of the physical problem being dealt with, including the quantile curves without the need of separating the total strain in its elastic and plastic components but dealing with the total strains directly [20]. With respect to the conventional Coffin-Manson approach, the strain-life probabilistic model show some advantages: it arises from sound statistical and physical assumptions and not from an empirical arbitrary assumption; it provides a probabilistic definition of the whole strain-life field; it does not need to consider separately the elastic and the plastic strains; the run-outs can also be used in the analysis, and facilitates damage analysis. Log N f C=log ε a0 Log ε a B=log N 0 p=0  p=0.05  p=0.5  p=0.95 Figure 2: Percentile curves representing the relationship between dimensionless lifetime, N f * , and the strain amplitude, ε a * : p - ε a -N field. The SWT (= σ max .ε a ) parameter was proposed by Smith et al. [8] in order to account for mean stress effects on fatigue life prediction. Any combination of maximum stress and strain amplitude that leads to the same SWT parameter should lead