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Abstract: 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. [Copyright &y& Elsevier]

Abstract: Engineering prognosis and life cycle management have increasingly become dependent on probabilistic methods and material microstructure. Due to variability in microstructural properties produced by differences in alloys and processing conditions, scientifically based probability modeling for life prediction and reliability is a challenging problem. For several years, probabilistic and statistical methodologies have been available to address prognosis issues, and there has been significant progress in computational methods for engineering applications. Their utility has been greatly limited by the lack of well developed physically and mechanistically based models for many of the complex applications. Without a reasonably accurate description of the damage process at a scale that is pertinent to the desired application, probabilistic computations have minimal value for prognosis and life cycle assessment. In this paper, the major methods in computational probability are reviewed, and their efficacy is illustrated through two engineering examples. One example is corrosion and corrosion fatigue crack growth for 7075-T6 aluminum alloy, which is used commonly for structural components in commercial and military aircraft. The other example is very high cycle S–N behavior of SUJ2 bearing steel for which multiple modes of failure are manifest in the high cycle regime. Their application to other critical engineering problems is discussed. [Copyright &y& Elsevier]

Probability analyses are increasingly being used for reliability and durability assessments for life prediction of engineered components and systems. Nevertheless, many of the current analyses are predominately statistical rather than probabilistic. Fatigue life prediction has historically been based on the safe-life or the crack growth approaches, both of which are empirically based. Consequently, they do not adequately reflect long-term operating conditions, or identify the sources and extent of their contributions to variability. A comparison between probability and statistical approaches for fatigue life prediction is developed herein. Using simple crack growth models, the variability inherent in S-N response can be related to key random variables that are readily identified in the models. The identification and quantification of these variables are paramount for predicting fatigue lives. The effectiveness of probability modeling compared to statistical methodologies is shown through the analysis of an extensive set of S-N data for 2024-T4 aluminum alloy. Subsequently, the probability approach is demonstrated with S-N data for SUJ2 steel, in which two distinct failure modes are operative. Variability associated with manufacturing and material variables are considered. The adoption of this technique to put life prediction on a sound scientific and probabilistic basis is recommended. [ABSTRACT FROM AUTHOR]

Focuses on designing a model of a platform crane. Examination of Hooke's Law which deals with how materials behave under tensile loading; Use of equilibrium in the design; Combination of springs that would support the maximum weight for minimum cost.