Modeling the effective elastic properties of materials pressed from a unidirectional hexagonal fiber strand

Abstract

The paper studies the interrelation between the effective elastic properties and the size of contact areas in the unit cell in modeling a unidirectional hexagonal fiber strand under isostatic and uniaxial pressing in a plastic flow. For a range of relative densities (0.907-1), it is shown that effective Young's modulus and Poisson's ratio correlate well with the integral projection of the contact areas relative to the corresponding cell size. For pore channels with cross-sectional shapes close to a three-beam hypocycloid with unequal beams, the elastic properties in the plane perpendicular to the fiber axis are anisotropic because the cross-sectional projections of the pore channel have different sizes.

Modeling the effective elastic properties of materials with parallel pore channels with Y-shaped cross-sections

“…The dashed curves correspond to the effective moduli [5] assessed for a cellular material with pore channels (cracks) whose sizes were determined in modeling uniaxial pressing of a fiber strand under plastic deformation [4]. The curves demonstrate how changes in the ranges of crack sizes differ in [5] and our analysis. If crack sizes change symmetrically relative to the cell center, the elastic modulus E y increases with the region of the total projection corresponding to the cracks a and d, whose normals agree with the direction of the modulus.…”

“…(7), and 0.775 (8). The dashed curves correspond to the effective moduli [5] assessed for a cellular material with pore channels (cracks) whose sizes were determined in modeling uniaxial pressing of a fiber strand under plastic deformation [4]. The curves demonstrate how changes in the ranges of crack sizes differ in [5] and our analysis.…”

“…Only do cracks b and c whose normals make 30° with the axis X have projections onto the axis Y. According to [5], effective Young's modulus X (E x ) and effective Poisson's ratio ν xy were found as functions of the length of cracks b (c) and their total length (total projection onto the axis Y). We similarly determined Young's modulus Y (E y ) and Poisson's ratio ν yx depending on the length of all cracks and their total projection onto the axis X.…”

“…Effective Young's moduli E x and E y and effective Poisson's ratios ν xy and ν yx were calculated using Hooke's law for orthotropic materials. Based on the paper [5], E z needed for the calculations was taken equal to E 0 (Young's modulus of a fiber material) and ν zx and ν zy = ν 0 = 0.3 (Poisson's ratio of a fiber material).…”

“…The formation of this material under isostatic and uniaxial pressing was modeled to obtain dependences of the morphologic microstructural properties on relative density over the range 0.907 ≤ θ ≤ 1.0 [4]. The effective elastic properties were assessed on the assumption of perfect contact at fiber boundaries to show that Young's modulus and Poisson's ratio correlated well with the total projection of pore channels onto the transverse deformation direction in the plane perpendicular to the fiber axis [5]. If we replace the pore channel with a hypocycloid cross-section by a Y-shaped crack with the same arm sizes, effective Young's modulus and Poisson's ratio remain practically unchanged in the plane perpendicular to the fiber axis.…”