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Estimation of Weibull Brittle Fracture Parameters for Heterogeneous Materials

Department of Agronomy, Univ. of Kentucky, Lexington, KY 40546-0091

*Corresponding author(eperfect{at}ca.uky.edu).

ABSTRACT

Brittle fracture of heterogeneous materials such as dry soil aggregates is not well understood. The flaws in such materials occur as voids across a wide range of length scales. As a result, failure is an inherently variable phenomenon that is best analyzed using weakestlink (Weibull) theory combined with fractal geometry. According to this probabilistic approach, samples to be fractured are assumed to be exactly the same size. However, sample size variation can result in biased estimates of the model parameters, log(), ß, and D. Our objective was to derive and test an equation for eliminating this bias by adjusting survival probabilities to a common value of sample length. Rupture energies were determined on 1920 air-dry soil peds collected from three long-term tillage treatments on a Maury silt loam (fine, mixed, mesic Typic Paleudalf). Following adjustment for sample size variation, characteristic strength, as parameterized by log(), typically decreased with increasing ped size. Unbiased estimates of ß indicated a wider spread of strengths than reported previously. Unbiased estimates of D, the fractal scaling parameter, were lower than those obtained using other methods, possibly because of renormalization with respect to the distribution of fragile elements instead of voids. Tillage treatment significantly influenced all three parameters, with the strength of no-till peds decreasing more rapidly with increasing size than conventional-till peds. Analysis of the relative errors associated with parameter estimates computed using the adjusted survival probabilities indicated that at least 20 samples per sieved fraction should be used as a standard in future brittle fracture studies on heterogeneous materials.

Kentucky Agric. Exp. Stn. Contribution no. 97-06-94.

Received for publication August 11, 1997.

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