Composite Materials Research Progress

58
Michaël Bruyneel
Figure 3.2. Stiffness coefficients in N/mm² in the structural axes for several values of the fibers
orientation in a carbon/epoxy material T300/5208 (after Tsai and Hahn, 1980).
Based on the fact that the trigonometric functions entering the matrix in (3.5) can be
written in the following way:
4 1
cos θ = ( 3 + 4cos
2θ
+ cos 4θ
)
8
3 1
cos θ sinθ
= ( 2sin
2θ
+ sin 4θ
)
8
2 2 1
cos θ sin θ = ( 1 − cos 4θ
)
8
3 1
cosθ
sin θ = ( 2sin
2θ
− sin 4θ
)
8
4 1
sin θ = ( 3 − 4 cos 2θ
+ cos 4θ
)
8
(3.6)
Tsai and Pagano (1968) derived an alternative expression for the Q’s coefficients in the
structural axes given in (3.7):
⎡Q11
Q12
Q16
⎤
Q ( 1,
2,
3)
=
⎢
Q22
Q
⎥
26 = γ0
+ γ1
cos2θ + γ2
cos4θ
+ γ3
sin 2θ
+ γ4
sin 4θ
⎢
⎥
⎢⎣
sym Q66⎥⎦
where the parameters γ are functions of the lamina invariants U1-U5:
(3.7)