Issue 39

M. Muñiz Calvente et alii, Frattura ed Integrità Strutturale, 39 (2017) 160-165; DOI: 10.3221/IGF-ESIS.39.16 161 the possibility of failure being initiated as a function of the predominant defect presence without requiring maximum values of the damage parameter, which emphasizes the need of introducing probabilistic concepts in the failure prediction analysis. The generalization of the probabilistic fatigue model of Castillo-Canteli [1] proposed by Muniz-Calvente et al. [2] allows the primary Weibull cdf of failure to be derived for any failure parameter, regardless of its distribution. In this way, any multiaxial damage value can be related to a number of cycles for a certain probability of failure. Once this relation is established, the probability of failure for any of the orientation planes can be calculated as a function of the local multiaxial damage value and, by extension, the global probability of failure for the component can be determined from the survival probabilities for all the planes assuming the weakest link principle. From a purely deterministic viewpoint, two specimens exhibiting the same maximum damage value would yield the same lifetime, what contradicts the inherent scatter of the experimental data, which must be necessarily taken into account. Moreover, a deterministic approach is insensitive to the variation of the damage parameter in planes adjacent to the critical one thus ignoring the angular interval at which failure is likely to happen. On the contrary, the probabilistic model proposed in this paper enables the failure probability to be found for any plane orientation, distinct from the one related to the maximum damage, by considering the local damage value in each plane. The main objective of this study is to determine the probability of failure resulting for each plane orientation by considering a suitable damage parameter as the generalized parameter (GP) causing failure. In order to take into account the variation of the GP for the different planes, the extension of the GLM to fatigue problems [2] is considered. The GLM stablishes that the probability of failure for a plane exhibiting a certain value of the generalized parameter (GP) can be obtained by using the primary failure cumulative distribution function (PFCDF):                          CN B GP P ) log( ) log( exp 1 (1) where N is the number of cycles and  ,  ,  , B , C are, respectively, the Weibull parameters estimated from the iterative process shown in Fig.1a and explained in the following section. The applicability of the model is elucidated by means of an example. Assuming the cdf for the local failure of the material to be known, the probability of failure is calculated for a cross shaped specimen in which shift between the principal stresses xx  and yy  ranges from 0º to 180º. P ROBABILISTIC MULTIAXIAL FATIGUE MODEL ig. 1a illustrates the iterative process applied for deriving the PFCDF that relates damage parameter exhibit at each plane studied to a certain probability of failure. In the following, each step is explained in detail: Step 1: Performing an experimental program: T o perform an experimental program using different biaxial loading ranges and to obtain the fatigue life for each experiment Step 2: Calculation of multiaxial fatigue parameter: The different biaxial loading ranges selected in the previous step are using to obtain the values of GP for each plane of the specimen. Some examples of the results of this step are found in Fig. 3. Step 3: Equivalent angle interval for each experiment: The equivalent angle interval , i eq A , , is defined as the angle interval that subject to the maximum GP value occurring at test failure would have the same probability of failure than the real distribution of the GP at failure. It is given by:                C N B GP S P A ref ref i i eq ) log( ) log( ) 1 log( int, , (2) where i P int, is the global probability of failure [3]: F