Page 106 - 3D Fibre Reinforced Polymer Composites

Micromechanics Models for Mechanical Properties 95
As shown in Figure 4.17, an “X assembly” is assembled with NA blocks of material A
and NB blocks of material B in the x direction. The overall material properties are given
via the following equations:

c,,s =c C22 =NAC22AVA+NBC2?VB,

CB =NAC23AVA+NBC23BVB, C33 =NAC33AVA+NBC33BVB,

CM =NACaAVA+NBC44BVB,

C,,S = C55AC55B c,,s = ‘66 (4.50)
+
NAVACSSB + NBVBCSsA ’ NAVACMB NBVBC66A

where NA and NB are the numbers of micro-blocks A and B within a strip respectively,
and VA and VB are the volume fractions of a micro-block A and a micro-block B in a
strip respectively, CuA, C<, Ciy are the stiffness constants for a micro-block A, a micro-
block B and a strip respectively.
The overall material properties for the Y assembly block are given by the following
equations:

ClZS
cI1 =N~c~~~v~+N~c~~~v~, =c22

C 13 =NAC I jAVA+NBC 13BVB, C,,S = C22AC22B
NAVACZZB + NBVBCZzA ’

S
+ NBc23~vB], c33 ,NAc~~AvA+NBc~:vB,
‘23‘ =‘22
c22
CaACaB
c,s = Css =NAC5SAVA+NBCs:VB,
+
’
NAVACUB NBVBCMA
C6,S = c66 c66 (4.5 1)
+
’
NAVAC66B NBVBC66A
The equations required to calculate the overall material properties for the 2 assembly
are given as follows: