Sensitivity of Failure Prediction to Flaw Geometry

The assumption of ellipsoidal flaw geometry has been widely used in calculations of the probability of structural failure conditioned on nondestructive (ND) measurements. Clearly, in most cases the flaw geometry is not ellipsoidal and in the particular case of cracks the actual geometry may deviate significantly from a degenerate ellipsoid (i.e., a planar crack with an elliptical plan-view shape). We have investigated the sensitivity of a late stage of the evolution of fatigue failure to model errors of the latter type (i.e., deviations from elliptical shape for planar cracks) by considering two different overall theoretical processes. In the first, we start with a non-elliptical crack and calculate its geometry after a given large number of cycles of uniaxial stress applied perpendicular to the crack plane. In the second process, we start with the same crack but perform a simulated set of NO measurements coupled with an inversion procedure based on the assumption of elliptical geometry and then calculate the geometry of this initially elliptical crack after subjection to the above stress history. A measure of sensitivi~ to model error is then provided by a comparison of the two terminal geometries. Results for several choices of non-elliptical crack shapes and sets of NO measurements will be discussed. NATURE OF THE PROBLEM As is well known, the calculation of the probabilities of failure, both unconditional and conditioned on NO measurements, is based on a set of mathematical models, most of which are seriously oversimplified in several respects. The set consists of models of (a) the measurement process, (b) the failure process (including a model of the stress environment), and (c) the a ~riori statistics of defect properties. It is c ear that the modelling of each type of defect underlies all three of the above models and thus the errors in this modelling are a crucial issue. It is thus obvious that the errors in the defect model affect the interpretation of the NO measurements (in terms of an oversimplified state) and the calculation of conditional probability of failure. The former and latter entail the use of measurement and failure models, respectively, and both entail the use of the a priori statistics model. In any case, we may ask if the effects of the defect model errors in the measurement interpretation and the failure probability calculation tend to compound or compensate for each other. To throw light on this question we have investigated several "theoretical experiments" involving synthetic test data based on defect models that are more complex than the defect model used in the interpretation of NO measurements and the calculation of failure probability.