D6: Laminate - Analytical

Question 1

What are the 5 assumptions for CLA?

Answer 1

• Macroscopic scale
• Orthotropic lamina mechanical properties
• Linear-elastic layer constitutive equations
• Plane stress state (thin laminate)
• Intra-laminar failure modes

Question 2

What 2 types of loading does CLA consider?

Answer 2

Mechanical and hygrothermal

Question 3

What is the stress free temperature?

Answer 3

Temperature at which there are no residual stresses in the composite - usually just below processing temperature.

Question 4

What assumption is made about extensional deformations and flexural displacements in CLA?

Answer 4

Elasticity and small deformations

Question 5

What 2 types of strain make up total strain in CLA?

Answer 5

Membrane and bending

Question 6

What do terms on the diagonal of the ABD matrix represent?

Answer 6

Direct relations between loading and strain

Question 7

What do the terms A16 and A26 represent in the ABD matrix? What property is achieved when they = 0?

Answer 7

• Direct shear coupling
• Extensional orthotropy

Question 8

What do the B terms in the ABD matrix represent? What type of laminate has B = 0?

Answer 8

• Coupling between extensional loading and flexural strain.
• Symmetric laminates have B = 0.

Question 9

What do the D16 and D26 terms represent in the ABD matrix? What property is achieved when they = 0?

Answer 9

• Bend-twist coupling
• Flexural orthotropy

Question 10

What is a laminate with coupling terms = 0 called?

Answer 10

Specially orthotropic

Question 11

What must we ensure about the ABD for a “relatively” well behaved laminate?

Answer 11

That coupling terms (off the diagonal) are an order of magnitude smaller than the terms on the diagonal.

Question 12

How do we get the compliance matrix?

Answer 12

By inverting the ABD matrix

Question 13

What are the 6 “equivalent laminate engineering constants”? What type of laminate are they used for? What 2 types can we have? What’s different about how they’re defined?

Answer 13

• Ex, Ey, Gxy, Nuxy, Nuyx, mx, my
• Symmetric laminates
• Membrane equivalent or bending equivalent
• In terms of Hooke’s law vs in terms of general theory of bending.

Question 14

How are stresses and strains through a laminate different?

Answer 14

• Strains are continuous across plies, stresses are not.

Question 15

What are the 3 assumptions used for the thermal loading in CLA?

Answer 15

• Linear-elastic response at elevated temperatures
• Constant thermal expansion coefficients
• Uniform temperature through thickness (equal delta T for each layer)

Question 16

What’s the difference between thermal and moisture loading in CLA?

Answer 16

• Temperature change is constant through thickness, moisture change is not.

Question 17

How is strength analysis in CLA limited?

Answer 17

Limited to intralaminar failure modes

Question 18

What does stress whitening indicate?

Answer 18

When a ply is loaded transverse to its fibre direction and matrix/interface fails between fibres.

Question 19

How does CLA predict ultimate failure?

Answer 19

• Checks if a ply failure is matrix dominated (2-2 or 1-2), and if it is, it offloads onto the other plies and tries again.
• Once a ply fails in the fibre direction, it is assumed final failure has occured.