Error analysis in some recent versions of the Fry Method

Fry method is a graphical technique that directly displays the strain ellipse in form of central vacancy on a point distribution, the Fry plot. For accurate strain estimation from the Fry plot, the central vacancy must appear as a sharply focused perfect ellipse. Diffused nature of the central vacancy, common in practice, induces a subjectivity in direct strain estimation from the Fry plot. Several alternative methods, based on the point density contrast, the image analysis, the Delaunay triangulation, or the point distribution analysis exist for objective strain estimation from the Fry plots. Relative merits and limitations of these methods are, however, not yet well-explored and understood. This study compares the accuracy and efficacy of the six methods proposed for objective determination of strain from Fry plots. Our approach consists of; (i) graphical simulation of variously sorted object sets, (ii) distortion of different object sets by known strain in pure shear, simple shear and simultaneous pure-and-simple shear deformations and, (iii) error analysis and comparison of the six methods. Results from more than 1000 tests reveal that the Delaunay triangulation method, the point density contrast methods or the image analysis method are relatively more accurate and versatile. The amount and nature of distortion, or the degree of sorting have little effect on the accuracy of results in these methods. The point distribution analysis methods are successful provided the pre-deformed objects were well-sorted and defined by the specific types of point distribution. Both the Delaunay triangulation method and the image analysis method are more time efficient in comparison to the point distribution analysis methods. The time-efficiency of the density contrast methods is in between these two extremes.