Statistical characterization of bimodal behavior

Recently a variety of materials subjected to rather diverse loading conditions have exhibited bimodal behavior for damage accumulation and failure. Traditional statistical modeling for such data has been relatively simplistic. Usually a mixtures or competing risks model is selected as the appropriate way in which to characterize bimodal data. With the development of advanced experimental testing procedures, more situations and more statistically complicated bimodal characteristics have been observed. The purpose of this paper is to demonstrate the use of standard and innovative statistical modeling methodologies for bimodal damage growth and failure in materials. Building upon classical methods, illustrations for modeling bimodal behavior are developed from data from diverse materials used in various applications. The damage mechanisms primarily result from fatigue crack growth; however, other loading conditions are presented as well. The main focus in this effort is on investigating standard and alternative cumulative distribution functions (cdfs) for bimodal statistics. While the methodology for constructing appropriate cdfs is applicable for all classes of underlying cdfs, the examples that are investigated will utilize of the two-parameter Weibull cdf for subpopulations.