Laminates and Laminate Theory Flashcards
What are the diffference between a layer and a ply in a laminate?
- Ply: Always refers to a single sheet of composite material.
- Layer: Can refer to a single ply or a group of plies with the same orientation.
What is a symmetric laminate?
A symmetric laminate has perfect symmetry about the mid-plane. Some examples:
* [ 0 / 90 / 0]
* [0 / 90 / -45 / 45 / 45 / -45 / 90 /0]
The B matrix is 0 for symmetric laminates.
What is a balanced laminate?
A balanced laminate is such that for every layer with orientation θ, there exists another layer with the same material and same thickness and with an orientation -θ (other that 0 or 90)
Example:
* [-45 / 45 / -45 / 45]
* [0 / 90 / 0]
A_xs = A_ys = 0 for a balanced laminate
What needs to be defined for a laminate layup?
- material properties
- thickness
- orientation angle
What are the assumptions for the laminate theory?
- The layers are perfectly bonded
- Each layer is homogeneous
- Individual layer properties can be isotropic, transverse isotropic or orthotropic
- Each layer is in a state of plane stress
- The laminate deforms according to the Kirchoff assumptions
What are the Kirchoff assumptions?
- Normals to the midplane remain straight and normal to the deformed midplane after deformation
- Normals to the midplane do not change length
What is the meaning of homogeneous layers?
A homogeneous layer has a set of properties that does not vary across the plane or through the thickness
Can a laminate be homogeneous?
No, a laminate cannot be considered homogeneous because it is composed of multiple layers with different properties and orientations
Explain the difference between plane stress and plane strain
- Plane Stress: Applicable to thin structures, assumes zero out-of-plane stresses.
- Plane Strain: Applicable to long structures, assumes zero out-of-plane strains.
Is it possible to be in a state of plane stress and plane strain simultaneously? If so, how?
No, due to the contradictory nature of their definitions:
* Plane stress: σ_z = 0 ->material is free to deform in the z-direction, thus e_z cannot be 0.
* Plane strain: e_z = 0 -> material is constrained in the z-direcion, and it has to be stresses in z-direction to prevent deformation.
What is the strain in position z (Kirchhoff assumption) in matrix form?
What are the equations for the kurvatures k_x, k_y and k_xy in Kirchhoff assumption?
What are the equations for the strains in the Kirchoff assumption?
What is the sign of the k_x-value for this curve?
k_x > 0
Which k-value
is responsible for the shape of this curve?
k_xy ≠ 0 gives the “twisting” shape.
(here k_xy>0)
What is the definition of a curvature?
Curvature (κ) is a measure of how sharply a curve bends.
κ = 1/radius
What are the relations between laminate loads/moments and midplane strans/curvatures?
What is the unit of in-plane laminate forces, N?
Force per unit length [N/m]
What is the unit of laminate moments?
Force multiplied by length (F*m)
Describe the meaning and consequences of a quazi-isotropic laminate.
- Quasi-isotropic laminates behave nearly isotropically in their plane by having plies oriented in multiple directions.
- They offer uniform in-plane mechanical properties and uniform stress distribution, making them suitable for applications with varying or uncertain load directions.
what are the effective in-plane elastic properties for symmetric and balanced laminates?
How is the effective in-plane elastic moduli E_x for a symmetric and balanced laminate found?
Finding E_x:
1. Consider the loadcase N_x ≠0 , N_y = 0, and calculate N=Aε^0
2. The stress σ_x = Nx/h
3. E_x = σ_x / ε_x
How to find the poissons ratio v_xy if the midplane-strains are known?
What is the effective flexural stiffness along x-direction (symmetric, balanced, no bend-twist coupling)
What primary idea behind sandwich structures?
To increase the flexural stiffness without adding much weight to the laminate. This is achieved by using a low-density core material sandwiched between two face sheets.
What simplifications can be made for the mechanics of sandwich beams?
- The thickness of the face sheets is much less than the thickness of the core, i.e: t_f «_space;t_c
- The modulus of the core is much less than the effective modulus of the face sheets, i.e: E_c «_space;E_f , and E_c can then be neglected when computing the bending stiffness
