A New Approach to Assessing the Reliability of Applying Laboratory Fracture Toughness Test Data to Full-Scale Structures

In this paper, we propose a two-step approach to addressing the question of how reliable the practice of applying laboratory data on fracture toughness to full-scale structures and components is. In the first step, we construct a two-level eight-factor 16-run-plus-a-center-point fractional factorial orthogonal design of experiments and conduct an analysis using literature fracture toughness and parameter data, where the eight factors are: (1) the Young’s modulus, E, (2) a material property constant, α, as defined in a Ramberg-Osgood stress-strain model, (3) the work hardening exponent, n, of the same model, (4) the yield stress, σy , (5) the critical local fracture stress, σf , (6) a chemical composition parameter in the form of the ratio of manganese to carbon content, Mn/C, (7) the crack depth/width ratio, a/W, and (8) the critical microstructural distance, rc , from the crack tip. Based on the 17-run data and the design of experiments analysis, we first obtain a ranking of the relative importance of those eight factors and then select two most important ones, to be named “key parameters”, to perform a multi-linear least square fit of the fracture toughness data as a function of those two key parameters. This simplification allows us to calculate, for the number of tests equal to N (= 17), the best estimate of the fracture toughness with 95% confidence prediction intervals. In the second step, we apply the statistical concept of a tolerance interval for a fixed sample size N and three coverages, 90%, 95%, and 99%, to a conversion of the results of the first step (the prediction intervals) to a set of tolerance intervals for the fracture toughness of a full-scale structure. Significance and limitations of this novel approach to answering the question of reliability from laboratory data to full scale structures are discussed at the end of this presentation.© 2008 ASME