Acta Mechanica Solida Sinica

, Volume 29, Issue 1, pp 59–77 | Cite as

Analytical Solutions for Predicting Tensile and Shear Moduli of Triaxial Weave Fabric Composites

Article

Abstract

Novel micromechanical curved beam models were presented for predicting the tensile and shear moduli of triaxial weave fabric (TWF) composites by considering the interactions between the triaxial yarns of 0° and ±60°. The triaxial yarns in micromechanical representative unit cell (RUC) were idealized as curved beams with a path depicted using the sinusoidal shape functions, and the tensile and shear moduli of TWF composites were derived by means of the strain energy approach founded on micromechanics. In order to validate the new models, the predictions were compared with the experimental data from literature. It was shown that the predictions from the new model agree well with the experimental results. Using these models, the tensile and shear properties of TWF composites could be predicted based only on the properties of basic woven fabric.

Key Words

triaxial weave fabric (TWF) composite elastic properties tension modulus shear modulus 

Nomenclature

A

cross-section area of yarns, mm2

w

width of yarn, mm

Bi

transformation variable

Ci

transformation variable

E1

elastic modulus of yarn in longitudinal direction, MPa

ET

tension modulus of TWF composites, N/mm

F1

internal force on 0° yarn, N

F2

internal forces on ±60. yarns, N

G12

in-plane shear modulus of yarn, MPa

Gs

in-plane shear modulus of TWF composites, N/mm

h

thickness of yarn, mm

Iyi

inertia moment of yarn relative to y i axis, mm4

Izi

inertia moment of yarn relative to z i axis, mm4

Ipi

polar inertia moment of yarn, mm4

Ji

transformation variable

Ki

transformation variable

L

half undulation length of yarn, mm

M1

bending moment on yarn, Nmm

M2

bending moment on yarn, Nmm

N

interaction force between angularly interlacing yarns, N

N1

restraining force from yarn torsion along the direction of x i axis, N

N2

restraining force from yarn torsion along the direction of z i axis, N

N3

restraining forces from yarn torsion along the direction of z i axis, N

Nxi

axial force on yarn in the direction of x i axis, N

PT

external tension force, N

PS1

external shear force in longitudinal direction, N

PS2

external shear force in transverse direction, N

Qi

transformation variable

T1

torque moment on yarn, Nmm

T2

torque moment of yarn, Nmm

σT

tension force per unit length on RUC, N/mm

εT

tension strain of RUC

τL

longitudinal shear force per unit length on RUC, N/mm

τT

transverse shear force per unit length on RUC, N/mm

δPT

relative shift of RUC in the direction of external force PT, mm

δPS1

relative shift of RUC in the direction of external shear force PS1, mm

γ

shear strain of RUC

FE

finite element

RUC

representative unit cell

TWF

triaxial weave fabric

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2016

Authors and Affiliations

  • Jiangbo Bai
    • 1
  • Junjiang Xiong
    • 1
  • Meng Liu
    • 1
  • Ziyu Man
    • 1
  1. 1.School of Transportation Science and EngineeringBeihang UniversityBeijingChina

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