Page 98 - 3D Fibre Reinforced Polymer Composites

Micromechanics Models for Mechanical Properties 87

c,, = CLVT + c;vB. c,, =CLVT +c,BvB

(4.45)

C,'C," CST c,,
c,, = c5, =
VTC, B+ VBCUT v .I c,, B+ v "c,,
+
c, = c&vT CLV

where VT and are, respectively, the volume fractions for the top fibre ply (i.e., warp
yarn in Figure 4.1 l(b)) and bottom fibre ply (i.e., weft yarn in Figure 4.1 l(b)), Cur, C,"
and Cij are, respectively, the stiffness constants for the top fibre ply, bottom fibre ply
and the micro-block SCPMIB.
For the micro block UMIB shown in Figure 4.1 l(b), the stiffness constants Cij under
its local coordinate system can be evaluated using equations (4.45), and then its stiffness
constants Cij' under the global coordinate system can be obtained by:

where [Cg] is the stiffness matrix referred to the local coordinate system and [CuJ is the
stiffness matrix in the global coordinate system. [rJ is the Hamiltonian tensor
transformation matrix, namely

2 2
/I2 m1 n1 2m1n1 2h 21,m,
2 2
122 m2 n2 2m2n2 212n2 212m2
2 2 2
13 9 123 2m3n3 213% 213m3 (4.46b)
[TI =
1,1, m2m3 n2n3 m2n3+m3n2 12n3+13n2 12m3+13m2
1,1, mlm3 n,n3 m,n3+m3nl lln,+13n, l,m,+l,m,
1,1, mlm2 n,n2 mln2+m2n, l,n2+12n, l,m2+12m,

where Zi = cos(i, x). mi = cos(i, y) and ni = cos(i, z) for i=1,2,3.
When micro-blocks are assembled in the warp or x direction to form the warp
stripes, the average properties for a warp stripe can be given by:

NAC,2AVA
+
GIA
C,,S = c C;2 = NACAVA + NBC&VB