A PROBABILISTIC CRITERION FOR EVALUATING THE GOODNESS OF FATIGUE-CRACK GROWTH-MODELS

The fatigue crack growth (FCG) phenomenon is usually modelled by means of a differential equation relating the crack growth rate, da/dN, to the instantaneous crack size, a(N). This equation usually contains two or more parameters, which are used to ''fit'' the model to some exper imental result given as pairs (a,N). As a rule, the fitting procedure is such that the differences between the solution of the differential equation and experimental points are minimized according to, let's say , the least square criterion. This procedure implies the interpretatio n of the differential equation as an equation for the mean growth curv e, which leads to difficulties when considering the random fluctuation s observed in the growth rate. In this paper, the meaning of the crack growth equation is reconsidered and the interpretation as a local rel ation adopted. Coherently, model parameters may no longer be fitted to experimental curves as a whole: they must be locally evaluated along the crack path. A statistical analysis of these local values can be us ed to investigate whether or not a differential equation is an appropr iate model for the FCG phenomenon. In particular, the homogeneous rand om field (HRF) criterion is shown to be very useful in the search for improved FCG equations. The improvements that can be attained with thi s criterion are demonstrated with an application to the Bogdanoff-Kozi n(BK) model, where the FCG process is represented as an equivalent Mar kov chain. Finally, conclusions about the correlation length of an inf erred random field are drawn. Considering that the magnitude of this c orrelation length is of utmost importance when the Markovian approxima tion is adopted, it is demonstrated that the FCG process can be regard ed as Markovian only if the crack tip is observed at relatively large time intervals.