Maximum likelihood estimation for the three-parameter Weibull cdf of strength in presence of concurrent flaw populations |
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Authors: | Constanze Przybilla Alfonso Fernández-Canteli Enrique Castillo |
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Affiliation: | 1. Department of Construction and Manufacturing Engineering, University of Oviedo, Campus de Gijón, 33203 Gijón, Spain;2. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain |
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Abstract: | For a correct strength characterization of brittle materials, not only the maximum stress at fracture, but also the geometry of the specimens has to be considered thus taking into account the variable stress state and the size effect. Additionally, fracture may occur due to different fracture modes, as for example surface or edge defects. The authors propose a maximum likelihood estimator to obtain the cumulative distribution functions of strength for surface and edge flaw populations separately, both being three-parameter Weibull cdfs referred to an elemental surface area or elemental edge length, respectively. The method has been applied to simulated 3-point bending test data. The estimated Weibull parameters have been used to compute the cdfs of strength for specimens with different size, providing also the confidence bounds calculated by means of the bootstrap method. Finally, fracture data of 4-point bending tests on silicon carbide have been evaluated with the proposed method. |
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Keywords: | Failure analysis Fracture Maximum likelihood Concurrent flaws Weibull statistics |
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