Question 10.S.P.7: Two [02/90)2]s graphite–epoxy laminates are cured at 175°C a...
Two [0_{2}/90)_{2}]_{s} graphite–epoxy laminates are cured at 175°C and then cooled to room temperature (20°C). After cooling, one laminate is trimmed to in-plane dimensions of 300×150 mm, whereas the second is trimmed to in-plane dimensions of 3000×150 mm. Both laminates are then mounted in assemblies that provide type S1 simple supports along all four edges, and subjected to a uniform increase in temperature. Determine the temperature at which each plate will buckle. Use the properties listed for graphite–epoxy in Table 3 of Chap. 3, and assume each ply has a thickness of 0.125 mm.
| Table 3 Nominal Material Properties for Common Unidirectional Composites | |||
| Property | Glass/epoxy | Kevlar/epoxy | Graphite/epoxy |
| E_{11} | 55 GPa (8.0 Msi) | 100 GPa (15 Msi) | 170 GPa (25 Msi) |
| E_{22} | 16 GPa (2.3 Msi) | 6 GPa (0.90 Msi) | 10 GPa (1.5 Msi) |
| ν_{12} | 0.28 | 0.33 | 0.30 |
| G_{12} | 7.6 GPa (1.1 Msi) | 2.1 GPa (0.30 Msi) | 13 GPa (1.9 Msi) |
| σ_{11}^{fT} | 1050 MPa (150 ksi) | 1380 MPa (200 ksi) | 1500 MPa (218 ksi) |
| σ_{11}^{fC} | 690 MPa (100 ksi) | 280 MPa (40 ksi) | 1200 MPa (175 ksi) |
| σ_{22}^{yT} | 45 MPa (5.8 ksi) | 35 MPa (2.9 ksi) | 50 MPa (7.25 ksi) |
| σ_{22}^{yC} | 120 MPa (16 ksi) | 105 MPa (15 ksi) | 100 MPa (14.5 ksi) |
| σ_{22}^{fT} | 55 MPa (7.0 ksi) | 45 MPa (4.3 ksi) | 70 MPa (10 ksi) |
| σ_{22}^{fC} | 140 MPa (20 ksi) | 140 Msi (20 ksi) | 130 MPa (18.8 ksi) |
| τ_{12}^{y} | 40 MPa (4.4 ksi) | 40 MPa (4.0 ksi) | 75 MPa (10.9 ksi) |
| τ_{12}^{f} | 70 MPa (10 ksi) | 60 MPa (9 ksi) | 130 MPa (22 ksi) |
| α_{11} | 6.7 μ/m °C
(3.7 μin./in. °F) |
-3.6 μm/m °C
(-2.0 μin./in. °F) |
-0.9 μm/m °C
(-0.5 μin./in. °F) |
| α_{22} | 25 μ/m °C
(14 μin./in. °F) |
58 μm/m °C
(32 μin./in. °F) |
27 μm/m °C
(15 μin./in. °F) |
| β_{11} | 100 μm/m %M
(100 μin./in. %M) |
175 μm/m %M
(175 μin./in. %M) |
50 μm/m %M
(50 μin./in. %M) |
| β_{22} | 1200 μm/m %M
(1200 μin./in. %M) |
1700 μm/m %M
(1700 μin./in. %M) |
1200 μm/m %M
(1200 μin./in. %M) |
A [(0_{2}/90)_{2}]_{s} graphite–epoxy laminate was also considered in Sample Problem 1, and numerical values for the [ABD] matrix and effective thermal expansion coefficients are listed there. The aspect ratios involved in this problem are:
R = 300 mm /150 mm = 2
and
R = 3000 mm/150 mm = 20.
The temperature at which thermal buckling is predicted to occur is obtained through application of Eq. (44b). It is found that both laminates are predicted to buckle in mode [1,1]. For the laminate with aspect R = 2, thermal buckling is predicted to occur when temperature is raised to 51°C, whereas for the laminate with aspect ratio R = 20, thermal buckling is predicted at a temperature of 40°C.
T = \frac{\pi ^{2}}{b^{2} R^{4}}\left[\frac{D_{11} m^{4} + 2(D_{12} + 2 D_{66} )(mnR)^{2} + D_{22} (nR)^{4}}{n^{2} (A_{12} \overline{\alpha }_{xx} + A_{22} \overline{\alpha }_{yy}) + \left(\frac{m }{R} \right)^{2} (A_{11} \overline{\alpha }_{xx} + A_{12} \overline{\alpha }_{yy}) } \right] T_{RT} (44b)