Measures of mixing for extrusion by averaging concepts

This paper proposes modified Deformation Characteristics ( DC ) as a new deformation measure for three‐dimensional flows in extrusion. In contrast to the previous DC , the modified DC is defined by an averaged length stretch rate with the aid of two subsequent averaging concepts: firstly, average of length stretch rate of all the local elements in a shell, and secondly, average of a fluctuation of the averaged length stretch rate with time using a probability function. The modified DC was applied to the case of a two‐dimensional flow approximation based on the analysis of kinematics during one circulation including the “turning effect.” Consequently, we have proposed useful formulae to determine the modified DC for the two‐dimensional flow approximation. This involves extensive numerical calculations of the modified DC , both for the three‐dimensional flow and for the two‐dimensional flow approximation. Typical results are discussed with comparisons between the modified DC , the previous DC , and a strain proposed by Pinto and Tadmor. It is interesting to note that the Weighted‐Average Deformation Characteristics (WADC) obtained from the three‐dimensional analysis was found to be close to that from the two‐dimensional approximate analysis. Therefore, the formulae proposed for the modified DC of the two‐dimensional flow approximation seems to be useful in analyzing the mixing behavior on extrusion with a large aspect ratio, avoiding the complicated evaluation of the averaging process of the length stretch rate for the three‐dimensional flow.