PLANAR SECTIONS THROUGH THREE-DIMENSIONAL LINE-SEGMENT PROCESSES
DOI:
https://doi.org/10.5566/ias.v33.p55-64Keywords:
fibre process, fibre-reinforced materials, line-segment process, stereology, stochastic geometryAbstract
This paper studies three-dimensional segment processes in the framework of stochastic geometry. The main objective is to find relations between the characteristics of segment processes such as orientation- and length-distribution, and characteristics of their sections with planes. Formulae are derived for the distribution of segment lengths on both sides of the section plane and corresponding orientations, where it is permitted that there are correlations between the angles and lengths of the line-segments.References
Brandt AM (1985). On the optimal direction of short metal fibres in brittle matrix composites. J. Mater. Sci. 20:3831 - 3841.
Carling MJ and Williams JG (1990). Fiber length distribution effects on the fracture of short-fiber composites. Polymer Composites 11:307 - 313.
Chin WK (1988). Effects of fiber length and orientation distribution on the elastic modulus of short fiber reinforced thermoplastics. Polymer Composites 9:27 - 35.
Fu SY and Lauke B (1996) Effects of fiber length and fiber orientation distributions on the tensile strength of short-fiber-reinforced polymers. Comp. Sci. Tech. 56:1179 - 1190.
Hegler RP (1985) Phase separation effects in processing of glass-bead- and glass-fiberfilled thermoplastics by injection molding. Poly. Eng. Sci. 25:395 - 405.
Kacir L, Narkis N, Ishai O (1975) Oriented short glass-fiber composites. I. preparation and statistical analysis of aligned fiber mats. Poly. Eng. Sci. 15:525 - 531.
Li VC, Wang Y, Backer S (1991). A micromechanical model of tension softening and bridging toughening of short random fiber reinforced brittle matrix composites. J.Mech. Phys. Solids 39:607 - 625.
Maalej M, Li VC, Hashida T (1995). Effect of fibre rupture on tensile properties of short fibre composites. Journal of Engineering Mechanics 121:903 - 913.
Mecke J and Nagel W (1980). Station¨are r¨aumliche Faserprozesse und ihre Schnittzahlrosen. Elektronische Informationsverarbeitung und Kybernetik 16:475 - 483.
Mecke J and Stoyan D (1980a). A general approach to Buffon’s needle and Wicksell’s corpuscle problem. Combinatorial principles in stochastic geometry, Work Collect., Erevan , 164-171.
Mecke J and Stoyan D (1980b). Formulas for stationary planar fibre processes I - general theory. Math. Operationsforsch. Statist. Ser. Statistics 11:267 - 279.
Mecke J and Stoyan D (1980c). Stereological problems for spherical particles. Math. Nachr. 96:311 - 317.
Naaman AE and Reinhardt HW (1996). High performance fiber reinforced cement composites 2 (HPFRCC2). In: Proceedings of the Second International RILEM Workshop.
Chiu SN, Stoyan D, Kendall WS, Mecke J (2013). Stochastic Geometry and its Applications. 3rd Edition, Wiley.
Vaxman A, Narkis M, Siegmann A (1989). Short-fiber-reinforced thermoplastics. Part III: Effect of fiber length on rheological properties and fiber orientation. Polymer Composites 10:454 - 462.
Wanga C and Friedrich LF (2013). Computational model of spalling and effective fibre on toughening in fiber reinforced composites at an early stage of crack formation. In: Latin American Journal of Solids and Structures 10:707-811
