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Byline: D. Gary Harlow The Frechet cumulative distribution function (CDF) is the only CDF defined on the nonnegative real numbers that is a well-defined limiting CDF for the maxima of random variables (RVS). Thus, the Frechet CDF is well suited to characterize RVS of large features. As such, it is important for modelling the statistical behaviour of materials properties for a variety of engineering applications. Since the Frechet CDF is not commonly used, some of its properties are reviewed. Parametric estimation using both graphical and maximum likelihood methods are considered. Two examples, modelling interfacial damage in microelectronic packages and material properties of constituent particles in an aluminium alloy, are given. A third example is considered in which truncation in the upper tail is suggested. The Frechet CDF is recommended as a viable statistical model.

Byline: D. Gary Harlow A major concern with manufacturing processes using metals is the accurate prediction of the response of the material to complex forming operations that shape a blank into a component. One of the more difficult problems is springback, which is the tendency of a metal to not maintain the desired shape after the forming process is terminated. Springback is more pronounced in high-strength steel and aluminium alloys than other metals. Unless springback is accurately estimated, manufactured parts may deviate excessively from the design specifications. The purpose of this paper is to use mechanistically based probability modelling to accurately estimate variability in the dimensions of a component and the adherence to design tolerances. It is assumed that the variability in the component dimensions is due to randomness in the material properties that directly affect the magnitude of the springback. The yield stress is the primary source of randomness and is most critical in the springback prediction. In order to assess the effects of variability, a simple model for elastic springback in a straight rectangular bar bent around a circular mandrel is considered. Explicit computations are made for a commercially available aluminium alloy for which material properties are readily available. The stressstrain behaviour of the alloy is assumed to be bilinear. The effects of the stressstrain behaviour, the model parameters, and the statistical variability in material properties on springback are assessed.

Byline: D. Gary Harlow, Robert P. Wei Material ageing adversely affects the reliability of engineered structures. It impacts the costs of operation, maintenance, and warranty as well as long-term safety of complex structures, e.g. aircraft and automobiles. The typical empirically based design methodologies, which are often developed from accelerated life testing, are inadequate. These are appropriate for interpolation, but not for extrapolation. Effective extrapolation, beyond the range of conditions employed in obtaining supporting data and assessments of risk, must be based upon mechanistic models that capture the function, dependence on all the key external and internal variables. This undertaking requires multidisciplinary research, pertinent to industrial concerns, that addresses the chemical and micromechanical processes that control damage evolution in materials and quantifies the stochastic aspects of these processes. The purpose of this paper is to demonstrate the use and applicability of the mechanistically based probability methodology and to provide a framework for other applications. The approach is illustrated by the time dependent evolution and distribution of damage in aluminium alloys used in aircraft construction. The accuracy of estimates for the computed distribution of damage is demonstrated by comparisons with tear-down inspection data from a transport aircraft that had been in commercial service for about 24 years.