Curve fitting of mixed-mode isopachics

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Description/Abstract

Recent work has focused on exploiting the observation that the stress-sum contours
(isopachics), obtained from TSA, in the vicinity of the tip take the form of a simple curve – the
cardioid. The analysis made use of the cardioid nature of the isopachics by deriving
expressions for the SIFs in terms of the cardioid area and the positions of certain tangents to
the curve. Both Genetic Algorithms (GAs) and Differential Evolution (DE) have also proved
successful for parameter estimation, but some of the curve-fits indicated that the cardioid form
was inappropriate for the base model, particularly for mixed-mode cracks. The effect of cracktip
interaction has been explored and shows this has a small effect on the cardioid form. New,
higher resolution infra-red detectors have become available since the original data was
collected, so the object of the current paper is to use new techniques to extract the cardioid
form and use a GA to perform the curve fitting.