Inverse method for identifying the underlying crack distribution in plateswith random strengths

In the current investigation we seek to identify the underlying crack numbe r and crack length distributions in brittle plates with a known strength di stribution. The inverse problem in probabilistic fracture mechanics is defi ned, and the numerical procedure to solve the inverse problem is constructe d. The simulation process of generating simulated plates containing simulat ed random cracks is elaborated. The maximum strain energy release rate crit erion (G(max)) is applied to each simulated random crack to find the crack strength. The strength of the simulated plate is equated to the strength of the weakest simulated crack in the plate based on the weakest link notion. The underlying crack number and crack length distributions are obtained by minimizing the difference between the simulated plate strengths and the kn own plate strengths. The gamma lognormal and two-parameter Weibull distribu tions are employed for the underlying crack length distribution, and are co mpared in order to identify the best choice. Numerical examples demonstrate that the three PDFs are all acceptable for reasons to be explained. In the appendix, the direct problem in probabilistic fracture mechanics is presen ted as part of the demonstration of a method for using the crack distributi on identified in the inverse problem to predict the strength and the probab ility of fracture in a practical application.