In a unidirectional composite, cylindrical fibers may be packed in square or hexagonal (sometimes called triangular)...

 

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In a unidirectional composite, cylindrical fibers may be packed in square or hexagonal (sometimes called triangular) arrays, as shown in the figure. By selecting representative area elements (repeating units), show that the fiber volume fractions are Square packing: V, 4 s ; Hexagonal packing: V, = d 2352 3 3 Fiber Matrix (a) Square-packed array (b) Hexagonal (or Triangular) packed array where d is the fiber diameter and s is the distance between centers of two adjacent fibers. Theoretical maximum fiber volume fraction occurs when adjacent fibers touch each other. Calculate theoretical maximum fiber volume fraction in each case. In a unidirectional composite, cylindrical fibers may be packed in square or hexagonal (sometimes called triangular) arrays, as shown in the figure. By selecting representative area elements (repeating units), show that the fiber volume fractions are Square packing: V, 4 s ; Hexagonal packing: V, = d 2352 3 3 Fiber Matrix (a) Square-packed array (b) Hexagonal (or Triangular) packed array where d is the fiber diameter and s is the distance between centers of two adjacent fibers. Theoretical maximum fiber volume fraction occurs when adjacent fibers touch each other. Calculate theoretical maximum fiber volume fraction in each case.