FALL 2009

AE569

HOMEWORK #4

(45 Points)

(DUE 26.11.2009)

1-(15pt)A large size unidirectional thin composite laminawhich has a known fiber and unknown matrix material with an unknown proportion of fiber and matrix is brought to your laboratory.

In your laboratory you only have the following machines:

* A tensile test machine with tensile test fixture only and a Poisson ratio measuring kit.

* A water-jet machine with which you can cut the composite lamina in any way you like.

You are asked to predict the following information about the composite material:

  • Fiber/matrix composition
  • Elastic constants of the matrix material (Em,Gm and vm). Thus, you can identify the matrix material.
  • 3D orthotropic constants of the composite material.

Clearly describe a procedure which will allow you to predict the required parameters. Remember that you can only use the machines available in your laboratory.

2-(30pt) Consider the unit cell of a plain woven fabric shown below. Woven fabrics are composed of fill and warp yarns as shown. E1,E2, E3,G12,G23,G13,v12,v13,v23 represent the 3D elastic properties of the yarn.

1: parallel to filaments

2: transverse direction

3: thickness direction

In the undulated region of the fill and warp yarns have local out-of-plane angles and as shown in the figure below. These angles form during the knitting operation because the fill and warp yarns have to pass below and above each other continuously.

Determine expressions for the local in-plane elastic constants of the fill and warp yarns in the undulated regions in the global coordinate system x-y-z in terms of the 3D elastic properties E1,E2, E3,G12,G23,G13,v12,v13,v23 ) of the yarns and the local out-of-plane fill and warp anglesand .

That is; for the fill yarn determine :

for the warp yarn determine :

Local out of plane angle of the Local out of plane angle of the

Fill yarn: Warp yarn:

Note:

Remember for a unidirectional lamina shown in the figure below, strain-stress relation is given the the laminate axes by Eq.(1).

(1)

where are the transformedcompliance coefficients.

Eq.(1) can also be written in terms of effective elastic constants with respect to the laminate axis shwon below by Eq.(2)

(2)

Hint: For the fill and warp yarns try compare the local and global axes with the laminate axis shown below and modify Eqs.(1) and (2) accordingly to determine expressions for and .