Interval-based uncertainty models for micromechanical properties of composite materials

Abstract

Extensive work has been done in the past few decades to quantify the uncertainties associated with the micromechanics of composite materials in the presence of uncertainties in constituent material properties using probabilistic approaches. However, the probabilistic approaches require a knowledge of the probability distributions of the input parameters which are not known in most cases. This work presents interval-based uncertainty analysis using probabilistic approach with three sigma band about the mean, interval analysis method and the universal grey system (number) theory. Since the interval analysis predicts wider ranges and, in some cases, might violate the physical laws of the problem, the truncation-based interval analysis is presented to overcome the overestimation caused in the computed quantities by the so-called dependency problem associated with the interval analysis. The uncertainties exhibited in the micromechanics characteristics of composite materials due to the presence of uncertainties in the constituent material properties are investigated. The propagation of these uncertainties to the response characteristics of an angle-ply lamina is also studied. In the numerical study, two types of composite materials are considered – the graphite/epoxy and glass/epoxy systems – to demonstrate and compare the influence of the uncertainty models on the results. This work shows that improved and more meaningful results can be obtained using the universal grey system theory compared to the interval analysis, truncation-based interval analysis and probabilistic method for the micromechanics of composite materials and the response of an angle-ply lamina when the fiber and matrix properties are uncertain.