D4: Lamina - Analysis

Question 1

What are the assumptions for micro to macro analysis?

Answer 1

• Linear elastic response
• Perfect bonding between fibre and matrix
• Poisson strains are negligible

Question 2

What is the source of error in RoM transverse modulus and how is it reduced?

Answer 2

Error due to the neglect of Poisson’s ratio effects, reduced by using an “effective matrix modulus”

Question 3

How do the coefficients of thermal expansion for fibres and matrix differ and what effect does this have?

Answer 3

• Very small CTE for fibres, often negative, much larger and positive for matrix.
• Means that the matrix shrinks during cure while fibres do not
• Gives rise to clamping force around fibres, which helps with load transfer but creates internal stresses and leaves the matrix susceptible to cracking.

Question 4

What are the 2 terms commonly used to describe metallic material properties?

Answer 4

• Homogeneous (properties constant throughout)
• Isotropic (properties equal in all directions)

Question 5

What are the 3 terms used to describe composite properties?

Answer 5

• Heterogeneous (properties change from point to point)
• Anisotropic (properties different in all directions)
• Orthotropic (mutually perpendicular planes of material symmetry)

Question 6

What can we assume for shear stresses but not for shear strengths?

Answer 6

Shear stresses are complimentary (TAUij = TAUji), but strengths are not (material may fail at a lower shear stress in one direction)

Question 7

What is the assumption about our material that can reduce the stiffness matrix from 36 to 21 constants?

Answer 7

Assume that the material’s response is independent of the order of loading (reciprocal)

Question 8

What is the assumption that can reduce the stiffness matrix to 9 constants?

Answer 8

That the material is orthotropic, which allows us to eliminate shear coupling terms.

Question 9

What is the assumption that reduces the stiffness matrix to 4 constants?

Answer 9

Assume that the laminate is very thin, so we can neglect through-thickness stresses and strains. The resulting matrix is the “reduced stiffness matrix”, or Q matrix.

Question 10

What are the 4 independent material properties that we need to make the reduced stiffness and compliance matrices? What is other property, that isn’t independent?

Answer 10

• E1, E2, nu12 (major poisson’s ratio), and G12. - nu21 (minor poisson’s ratio)

Question 11

What is the Qbar matrix? How is it formed? How does it differ from the Q matrix?

Answer 11

• Transformed Q matrix, for transforming from xy axes to 12 axes.
• Formed using a transformation matrix (cos and sin), and a Reuters matrix (provides engineering shear strain)
• Qbar is fully populated (no zero terms). This means that it has transverse coupling (or Poisson) terms Qbar12, and shear coupling terms Qbar16 and Qbar26.

Question 12

What’s the difference between intra and inter laminar?

Answer 12

• Intra: within the layer
• Inter: between layers

Question 13

What are the 6 factors that affect the mode of intralaminar failure?

Answer 13

• Direction and sense of loading
• Fibre: matrix failure strains
• Matrix stress-strain response
• Fibre interface bond strength
• Vf and fibre packing
• Voids

Question 14

What are the 5 basic intralaminar failure modes?

Answer 14

• Longitudinal tension 1-1t
• Longitudinal compression 1-1c
• Transverse tension 2-2t
• Transverse compression 2-2c
• In-plane shear 1-2

Question 15

What assumption do we make for 1-1t strength? What is its limitation?

Answer 15

• Assume fibres have uniform strength
• In reality fibres have varying strengths due to flaws, so they fail progressively instead of all at once.

Question 16

What are the common failure mechanisms for mode 1-1c in materials with high Vf?

Answer 16

• Shear (common in CF) or in-phase fibre buckling (common in kevlar)

Question 17

What is a critical feature of composites that affects the 1-1c mechanism?

Answer 17

• Matrix support of fibres in buckling. Buckling is a lower energy failure mode than shearing, so we want to avoid it by increasing buckling strength with increased matrix support.

Question 18

How does temperature affect the 1-1c failure mode for CFRP?

Answer 18

Increasing temperature softens the matrix, meaning that it provides less support to the fibres against buckling. Past a certain temp, the matrix softening causes a change from shear to buckling failure, and the 1-1c strength drops rapidly as temp increases.

Question 19

Why are laminates so weak in the 2-2t mode? How is it affected by interface bond strength?

Answer 19

• Because the fibres essentially provide negative reinforcement.
• For a weak interface bond, fibres act as cylindrical holes, reducing the matrix cross section and generating stress concentrations.
• For a strong interface bond, the stress concentration effect is magnified, which increases as Vf increases.

Question 20

Why is Vf limited to 60%?

Answer 20

Because higher Vf means smaller gaps between fibres, which causes greater stress concentration. Higher than 60% is deemed too great.

Question 21

How does 2-2c failure tend to occur, physically?

Answer 21

Shear failure along a diagonal plane across the fibres. Sometimes through fibres, as they are relatively weak in the transverse direction.

Question 22

What governs the failure of orthotropic materials? How does this differ from isotropic materials?

Answer 22

• Orthotropic material failure is governed by the direction of weakest strength.
• Isotropic material failure is governed by the direction of largest stress (because strength is equal in all directions)

Question 23

What’s the difference between an interactive and non-interactive failure theory?

Answer 23

Interactive takes into account the effects of stresses and strains other than the principal direction of the lamina. Non-interactive only accounts for the independent effects of stresses and strains in the principal direction.

Question 24

What are failure envelopes used to show?

Answer 24

What combination of stresses will cause failure (in biaxial loading)