Laminates can be classified according to the fiber orientation.

Transcription

1 Laminates

2 Definition A laminate is an assemblage of individual lamina or plies bonded together normal to their principal plane (i.e., plies are stacked and bonded in their thickness direction). Laminates can be classified according to the fiber orientation. T L

3 Laminates classification according to the fiber orientation. Unidirectional Laminate- The fiber angle in any ply is parallel to the fiber angle in every other ply. This is a thick lamina from a mechanics point of view. Cross Ply Laminate - The fiber angle in any ply is normal to at least one other ply and parallel to any other ply or plies (i.e., contains only 0 and 90 plies). Angle Ply Laminate - Fiber angle of any ply is not restricted to parallel and normal directions.

4 Laminates classification based on stacking sequence Symmetric Laminate In a symmetric laminate all plies above the midplane have the same angle as the ply in the equivalent positio n below the midplane (i.e., the midplane of the laminate is a plane of symmetry). Antisymmetric Laminate - All plies above the midplane have the opposite (negative) angle as the ply in the equivalent position below the midplane. (The midplane is a plane of antisymmetry) Asymmetric Laminate - The midplane is not a plane of symmetry or antisymmetry. Quasiisotropic Laminate - Three or more plies in which the orientation of constituent are increments of p n where n is the total number of plies.

5 Examples of quasiisotropic laminates

6 LAMINATE CODE To avoid the ambiguity based on fabrication direction, the angle naming convention is with respect to the loading direction. Remember the loading direction is called the arbitrary direction (the x direction). Each ply is considered to have the same thickness. The naming convention is reflected in the laminate code. Consider the laminate with 6 plies: 0º, +45º, 90º, 90º, +45º, 0º in the sequence indicated. Since there is an even number of plies the laminate code is written The subscript, s, indicates a plane of symmetry in the laminate. [0/45/90] S For the laminate with 5 plies: 0º, +45º, 90º, +45º, 0º stacked in the sequence indicated. There is an odd number of plies in laminate and the code is written [0/45/90] S The bar indicates that the plane of symmetry passes through 90 ply. For negative angles the sign is displayed in front of the angle. Positive and negative pairs are indicated by ±. For the ply sequence: 0º, 45º, -45º, 90º, 90, -45º, 45º,0º the laminate code is [0/±45/90] S Consider the stacking sequence: 0º, 90º, 0º, 0º, 0º, 0º, 45º, 45º, 0º, 0º, 0º, 0º, 90º, 0º with repeat plies on both sides of the midplane; the laminate code is [0/90/0 4 /45] S For repeat pairs: 0º, +45º, -45º, +45º, -45º, +45º, -45º, 0º, 0º, 0º, 0º, -45º, +45º, -45,+45º, -45º, +45º, 0º the code is written [0/(±45 3 )/0 2 ] S If an extra 0 ply is inserted at the midplane in the code becomes [0/(±45 3 )/0 2 /0] S If the ply sequence is antisymmetric the subscript S is replaced with A.

7 Plate assumptions Flat plate of several individual layers Laminate thickness negligible with respect to the other dimensions (i.e., the interlaminar stresses far from the edges can be neglected) Layers are perfectly bonded together, therefore displacements are continuous across boundaries Deformations in the z directions can be neglected (i.e., ε z 0) Stress components along z can be neglected (σ z 0) Kirchoff-Love hypothesis: Normals to the center line remain normal to center line after deformation -- this neglects through the thickness shears

8 A generic deformation applied to the laminate: stretching-bending

9 Assume to deform the laminate. The displacement u along the x axis of a point C at a distance z from the middle plane is: Where: The subscript 0 refers to the middle plane

10 Analogously, for the displacement v in the y direction one can write : The displacement w in the z direction is the sum of the displacement of the middle plane and of the elongation of the perpendicular to the middle plane. If we assume this last one as neglectable, it holds:

11 The deformations ε x, ε y and γ xy are therefore equal to: ε and k are the deformations and the curvatures of the middle plane, respectively