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Answer All Questions
2
Q1
Young's Modulus (GPa)
100%
90%
80%
70%
60%
50%
30%
40%
20%
0%
10%
0
20
40
60
80
100
120
140
0% 20% 40% 60% 80% 100%
% ±45º plies
Modulus (GPa)
Material
Fibre:
Matrix: Epoxy
Vf: 0.6
% 0º
Shear Modulus (GPa)
0%
10%
20%
30%
40%
50%
70%
60%
80%
100%
90%
0
5
10
15
20
25
30
35
40
0% 20% 40% 60% 80% 100%
% ±45º plies
Modulus (GPa)
Material
Fibre:
Matrix: Epoxy
Vf: 0.6
% (0º+90º)
Poisson's Ratio
100%
90%
80%
70%
60% 50%
30% 40%
20% 10% 0%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0% 20% 40% 60% 80% 100%
% ±45º plies
Poisson's Ratio
Material
Fibre:
Matrix: Epoxy
Vf: 0.6
% 0º plies
Fibre Modulus
(GPa)
Strain Allowable
(με – tensile)
E-glass 73 5×104
T-300 Carbon 230 1.6×104
Kevlar 149 185 3.4×104
Matrix
Epoxy 4
Lamina Transverse Tensile Strain Allowable = 0.4%
Lamina Shear Strain Allowable = 0.5%
Lamina Thickness = 0.125mm
Nx
Nxy
Ny
(a) The graphical data provided above is for laminates made from unidirectional pre-preg
tape. Determine which fibre is used in the pre-preg. [4 marks]
(b) Estimate the tensile strain allowables for a [0, 90, ±45]s laminate. [4 marks]
(c) A structural component is analysed to have a worst loading case of Nx=500kN/m,
Ny=450kN/m and Nxy=200kN/m. Find an appropriate lay-up for a laminate of less than
1.8mm thickness for this component and verify that it satisfies this loading case.
(Hint: use the carpet plot approach in the lecture notes) [50 marks]
3
Q2
A composite laminate with a layup [0°/90°/90°/0°] is made of unidirectional lamina. The
thickness of each lamina is t = 1 mm. The lamina stiffness matrix is given below:
0 0 5
3 10 0
138 3 0
Q
(GPa)
And the strengths of the lamina are:
t 1500MPa *
1 ,
c 650MPa *
1 ,
t 55MPa *
2 ,
c 140MPa *
2 , 75MPa *
12 .
(a) Find the laminate stiffness matrices [A], [B] and [D] when the mid-plane is taken as the
reference surface. [12 marks]
(b) If the laminate is subjected to the following generalised stresses:
Nx = 2N0, Ny = N0, Nxy = N0, Mx = My = Mxy =0.
Find the maximum load N0 (>0) at which no failure occurs in the laminate according to
the maximum stress failure criterion.
[30 marks]
Sample Solution