Measures describing curvilinear short fiber distributions
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O R I G I NA L
Stefan Hartmann
· Teresa Liese
Measures describing curvilinear short fiber distributions
Received: 9 February 2020 / Accepted: 24 August 2020 © The Author(s) 2020
Abstract In this article, we discuss measures for fibers having a curvilinear shape. This is the case, for example, for man-made cellulose fibers having a weak stiffness. The fibers are bent during the injection molding process of short fiber reinforced plastics. For this purpose, μ-CT data can be evaluated and several measures can be introduced defining the geometrical orientation of the fibers. These measures are the length, a mean curvature, and the mean torsion. Furthermore, a mean orientation of a fiber and a mean deviation to a straight line can be defined. Additionally, to these measures, which are based on a continuous interpolation of given data points, discretized quantities only considering the data points are compared. Finally, the distributions of these measures at real μ-CT data are provided. Keywords Short fibers · Composite · Fiber orientation · CT analysis · Natural fibers 1 Introduction Natural fibers are of particular interest in view of sustainability developments, see [6]. Man-made cellulose fiber reinforced injection molded components are an interesting alternative to glass fiber reinforced plastics for certain applications due to their high mechanical properties (elongation at break: 13%) and lower density (1.5 g cm−3 ). They also have a lower bending stiffness than glass fibers. Man-made cellulose fibers are bent during the injection molding process which leads to faster fiber entanglement and a lower fiber preferred orientation, see [9]. In other words, the lower bending stiffness does also not imply alignment as a straight fiber resulting in an anisotropy of the component properties. Furthermore, it is known, see, for example [14], that a fiber reinforced specimen has different material properties over its thickness, which is caused—apart from the melt flow behavior of the thermoplastic—by the spatial distribution of the fiber orientation. Applications from glass fiber reinforced plastic, where the short fibers are straight lines, are discussed in a number of publications, see, for example [7,8,13,18]. In these publications, the fiber orientation of glass fiber reinforced samples has already been extensively investigated. There, the fiber orientation and the fiber length are mainly evaluated. However, a curved fiber has no unique orientation. Furthermore, it can reach various geometrical forms. Thus, measures, principally describing the specific form, are of particular interest. Since μ-CTs can provide coordinates of each fiber, these can be drawn on to apply interpolation concepts so that a continuous function is assigned to each fiber. These functions can be evaluated, i.e. geometrical measures S. Hartmann (B) Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Str. 2a, 38678 Clausthal-Zellerfeld, Germany E-mail: [email protected] T. Liese Institute of Materials En
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