Materials: Laminate
Description
A laminate is an ordered stack of LAYOUTS: Plies or lamina bonded together. Perfect bond is assumed between plies, which means that the thickness of the bond material is negligible and there is no relative displacement between the plies.
Each ply is assumed to be an orthotropic material with its own fibre direction, material constants and thickness. An equivalent elasticity matrix for the stack can be assembled from the ply information according to the classical laminate theory (CLT). This theory produces a matrix that is suitable for analysis using plate/shell elements.
Ply material limits may optionally be specified for the calculation of various reserve factors for post-processing.
Some typical ply material properties are tabulated below.
|
Material |
E1 (GPa) |
E2 (GPa) |
n12 |
G12 (GPa) |
|
Graphite/Epoxy |
138.0 |
14.5 |
0.21 |
6.63 |
|
Graphite/Epoxy AS/3501 |
145.0 |
9.80 |
0.30 |
4.19 |
|
GY70/Epoxy |
293.0 |
6.90 |
0.30 |
6.63 |
|
E-Glass/Epoxy (Prepreg) |
49.3 |
11.9 |
0.27 |
4.19 |
|
Boron/Epoxy |
293.0 |
14.5 |
0.21 |
5.58 |
|
Graphite/Aluminium |
125.7 |
25.1 |
0.30 |
22.4 |
|
CSM/Polyester |
9.0 |
9.0 |
0.10 |
3.25 |
|
Woven Roving/Polyester |
15.0 |
15.0 |
0.10 |
3.25 |
|
Unidirectional Glass/Polyester |
30.0 |
4.0 |
0.28 |
3.0 |
An example of a laminate using the conventional layup description, [902 / 452 / -45 / 02] s, consists of a stack with the following plies:
|
Ply Layer |
Angle (degree) |
| 1 | 90 |
| 2 | 90 |
| 3 | 45 |
| 4 | 45 |
| 5 | -45 |
| 6 | 0 |
| 7 | 0 |
| 8 | 0 |
| 9 | 0 |
| 10 | -45 |
| 11 | 45 |
| 12 | 45 |
| 13 | 90 |
| 14 | 90 |
In Strand7, the first ply is on the -z surface of the plate element and the last ply is on the +z surface.
Core Materials
Core materials can be included in the laminate definition to model a sandwich panel. These are treated the same as the rest of the plies in the laminate. There is, however, some caution required:
- Typically, the shear modulus of the core material is very low compared with that of the plies. Consequently, shear deformation can be large and this can have a significant effect on the lateral deflections and stress distribution in the sandwich. This effect is not modelled.
- Buckling is usually the primary mode of failure of the compressive plies in a sandwich. This mode of failure is not considered in the calculation of the reserve factors. These will typically be optimistic for composite sandwiches. Buckling of the sandwich facings should be checked separately.
- Cores often fail by both transverse shear and in-plane shear. These shears are not included in the determination of failure criteria. This mode of failure should be checked separately.
For a more thorough analysis of a sandwich panel with code material, a combined plate element and brick element model should be analysed, modelling the core with brick elements and the skins with plate/shell elements.
See Results Interpretation: Result Quantities for a brief description of available reserve factors.
See the Strand7 Theoretical Manual for more information.
Literature
Whitney, J.M.,Daniel, I.M. & Pipes, R.B. 1982, "Experimental Mechanics of Fibre Reinforced Composite Materials", Soc. Expt. Stress Analysis Mongraph, no. 4, Prentice-Hall.
Agarwal, B.D. & Broutman, L.J. 1980, Analysis and Performance of Fibre Composites, John Wiley & Sons.
Tsai, S.W. 1985, Composites Design, Think Composites.
Rolfes, R. and Rohwer, K. 1997, "Improved Transverse Shear Stresses in Composite Finite Elements based on First Order Shear Deformation Theory", International Journal for Numerical Methods in Engineering, vol. 40, pp. 51-60.
See Also