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Materials 4 > Composites Part 2 > Flashcards

Composites Part 2 Flashcards

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1
Q

What does a composite material consist of, in the context of FRPs?§

A

High modulus reinforcing fibers embedded in a low modulus polymeric matrix.

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2
Q

In FRPs what does the matrix do?

A

Load can be transferred between fibers due to elasticity in the matrix. The matrix also serves to separate and protect the fibers.

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3
Q

What does the stiffness and strength of a FRP depend on?

A
  1. Proportions of fiber and resin
  2. Distribution and orientation of fiber
  3. Type of fiber
  4. Type of resin
  5. Length of fiber (or discontinuous fiber)
  6. Void content
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4
Q

Why do properties vary throughout an FRP structure?

A

because FRP materials are non-homogeneous and anisotropic

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5
Q

What is the stress strain behaviour of a FRP like?

A

The behaviour of an FRP under load is elastic up to the point of failure with no yield point or plastic behaviour. The strain to failure is also low with a correspondingly small amount of work done. This lack of yielding makes the material very notch or stress concentration sensitive, therefore localized stresses have to be critically analysed

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6
Q

Can you draw the stress strain graph for a FRP?

A

yes or no

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7
Q

in the numerical index system associated with orthogonal axes, what do x1, x2 and x3 coincide with?

A

x1 - coincide with fiber axis
x2 - coincide with transverse in-plane
x3 - out of plane

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8
Q

what are the symbols for longitudinal stiffness and transverse stiffness?

A

longitudinal - E1

transverse - E2

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9
Q

What do the mechanical properties of a FRP depend on?

A
  • the properties of the constituent materials, the reinforcement and matrix and in particular the quantity and orientation of the fiber
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10
Q

What are the different fiber orientations?

A
  • random (e.g. CSM)
  • bi-directional (e.g. woven)
  • unidirectional
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11
Q

For random orientation and in-plane only, what are the properties in different directions?

A
  • the FRP has equal properties in all directions (psuedo isotropic)
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12
Q

For bi-directional orientation, what are the properties in different directions?

A

the FRP has equal properties in the 2 directions

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13
Q

For unidirectional orientation, what are the properties in different directions?

A

the properties are greatest parallel to the fiber

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14
Q

If the same amount of fiber was used in each case, which FRP would have the highest mechanical properties, unidirectional or random?

A

UD would have the highest mechanical properties and random the lowest

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15
Q

How do the properties change with different directions in UD?

A

the properties of a UD FRP are only superior in the direction parallel to the fibers, just a small angle away from the fiber-axis and the mechanical properties drop off considerably to very low values. The transverse properties of the FRP, perpendicular to the fiber direction, are close to that of the base resin.

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16
Q

What are the typical fiber volume fractions obtainable for the different orientations?

A

UD - 50-70%
bi-directional - 30-55%
random - 15-35%

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17
Q

What model is used to analyse axial loading?

A

Voigt model

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18
Q

What model is used to analyse transverse loading?

A

Reuss model

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19
Q

What is the voigt estimate/ rule of mixtures equation?

A

Ec = EfVf + Em(1-Vf)

note Lc = Lf = Lm

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20
Q

What implicit assumption does the rule of mixtures make?

A

That poisson ratios of fiber and matrix are the same, thus ignoring the elastic constraints caused by differential contractions

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21
Q

What is the rule of mixtures for elastic modulus in fiber direction (including fiber efficiency factors)?

A 
E1 = A.EfVf + EmVm
E1 = A.EfVf + Em(1-Vf)

Fiber efficiency factor, A:

    • Aligned: A=1 (aligned parallel)
    • Aligned: A=0 (aligned perpendicular)
    • Random 2D: A=3/8 (2D isotropy)
    • Random 3D: A=1/5 (3D isotropy)
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22
Q

What is the Reuss estimate/ inverse rule of mixtures equation?

A

1/Ec = Vf/Ef + Vm/Em

–> Ec = EfEm/EmVf+Ef(1-Vf)

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23
Q

Why is it much easier to compare the properties of composite materials on a volume fraction basis?

A

Because the densities of the constituents need to be considered with the weight fraction basis.

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24
Q

How to convert between weight fraction and volume fraction?

A

Wf = rho_f Vf/ rho_f Vf + rho_m(1-Vf)

Wf + Wm = 1

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25
Q

Can you draw a diagram/graph comparing the predictions for longitudinal modulus (E1) and transverse modulus (E2) varying with volume fraction Vf?

A

Yes or no

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26
Q

What are the issues with Reuss model?

A

Reuss model is a simplified representation (does not describe the real composite perpendicular to the fibers)

a) it ignores constraints due to strain concentrations in the matrix between the fibers
b) it assumes that the transverse stiffness of the fiber is the same as its longitudinal stiffness
c) it does not consider packing geometry. Real packing is even less regular than either of these idealised geometries.

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27
Q

What is poissons ratio of an isotropic material defined as?

A

The negative ratio of the lateral strain, e2, when a stress is applied in the longitudinal (x1) direction, divided by the longitudinal strain, e1, ie v=e2/e1

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28
Q

What are the two in plane poissons ratios for composites?

A
  • v12, called the major poisson ratio (relating to the lateral strain, e2, when a stress is applied in the longitudinal x1 direction), v12 = e2/e1
  • v21, the minor poissons ratio (relating to the strain in the x1 direction when a stress is applied in the x2 direction).
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29
Q

does major poissons ratio obey the rule of mixtures?

A

yes

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30
Q

What is anisotropic?

A

When the properties of a material vary with different crystallographic orientations, the material is said to be anisotropic

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31
Q

What is isotropic?

A

When the properties of a material are the same in all directions, the material is said to be isotropic

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32
Q

What is hookes law?

A

E = stress/strain

33
Q

what are the equations for the 3D relation between stress, strain, stiffness and complaince?

A 
stress_ij = C_ijkl*strain_kl
strain_ij = S_ijkl*stress_kl
where
C_ijkl - stiffness tensor
and
S_ijkl - compliance tensor
34
Q

Can you write the compliance relation between stress and strain in full matrix form?

A

yes or no

35
Q

How is a unidirectional reinforced lamina in a plane stress state defined ?

A

stress_3 = 0
shear stress_23 =0
shear stress_31 = 0

Stress_1 /= 0
stress_2 /= 0
Shear stress_12 /= 0

36
Q

Why do we expect to load a lamina only in plane stress?

A

Because carrying in-plane stresses is its fundamental capability. That is the reason why we develop laminated composites.

37
Q

For a thin laminate with plane stress condition (i/e. through thickness stresses are zero), what is the matrix equation?

A

see pg 36

38
Q

What are Q11 etc in the matrix equation for thin laminate with plane stress condition?

A

Q11 etc are called reduced stiffnesses.
Q11 = C11
etc

39
Q

What is G?

A

modulus of rigidity

40
Q

What is the equation for G?

A

G = E/2(1=v)

41
Q

what is the matrix equation relating stresses and strains for an isotropic laminate?

A

pg 38
.. stress = D*strain
where D = S^-1 is the stiffness matrix

42
Q

What is the material said to be when E1/=E2/=E3?

A

Orthotropic

43
Q

What is common for the properties in the plane transverse to the fiber direction?

A

For them to be isotropic to a good approximation (E2 = E3): such a material is called transverse isotropic

44
Q

What is the matrix equation relating stress and strain for transversely isotropic materials?

A

pg 40

45
Q

What is the matrix equation relating stress and strain for orthotropic laminate*? – specially orthotropic lamina - orthotropic lamina whose principal material axes are aligned with the natural body axes

A

pg 41

46
Q

What is the eqn for poissons ratio along the fibers?

A

v21 = -31/e2 = v12*E2/E1

47
Q

What is poissons ratio across the fibers?

A

v12 = -e2/e1

e is strain

48
Q

At any angle theta, the elastic constants will be what? And what do we need to determine their actual values? draw?

A

Will be variable

need experimental curves to determine their actual values. (draw the shape of these, pg 43)

49
Q

What is the transformation equation for relating stresses in 1-2 coordinate system to stresses in an x-y coordinate system?

A

pg 48

50
Q

Conversely, what is the transformation equation for relating stresses in x-y coordinate system to stresses in an 1-2 coordinate system?

A

pg 49

51
Q

What are the transformation eqns relating strains in 1-2 coordinate system to strains in x-y coordinate system and vice versa?

A

pg 50

52
Q

How can the transformation equation then be used to relate stress to strain? (both in x-y coordinate system)

A

pg 53

53
Q

What is the transformed stiffness matrix?

A

pg 53 & 54, Qbar.

54
Q

what is laminate made up of?

A

laminate is made up of stacks of lamina

55
Q

What assumptions are made for analysis of mechanical properties of laminates?

A
  1. The laminate thickness is very small compared to its other dimensions
  2. The lamina of the laminate are perfectly bonded
  3. Lines perpendicular to the surface of the laminate remain straight and perpendicular to the surface after deformation
  4. The laminae and laminate are linear elastic
  5. the through-thickness stresses and strains are negligible
56
Q

When are the assumptions made for analysis of mechanical properties of laminates good ones?

A

When the laminate is not damaged and undergoes small deflections

57
Q

Suppose a laminate has n identical orthotropic laminae; the laminate thickness is h/n, the stiffness matrix is?

A

Aij = h/n* sum(from k=1 to n)(Qbar_ij)k

where k refers to the kth ply and Qbar_ij is the transformed stiffness matrix

58
Q

Why are the directions of stress and strain important in orthotropic materials like UD lamina?

A

Important because the principal stress and strain may not coincide

59
Q

what are X, Y and S?

A

X: strength in 1 direction
Y: strength in 2 direction
S: shear strength in 1-2 coordinates
(draw diagrams)

60
Q

E.g. a UD composite of the following properties:

X=350 MPa, Y=7MPa, S=14MPa. If stress_1=315 MPa, stress_2=14MPa and shear stress_12 = 7MPa, what will happen?

A

Max principal stress Y so the lamina must fail in the transverse direction (direction 2). The key observation is strength is a function of the orientation of stresses relative to the principal materials coordinates of an orthotropic lamina.

61
Q

In isotropic materials , for plane stress, what can the von mises stress be represented by?

A

principal stresses:

Stress_vm = sqrt(stress_x^2-stress_xstress_y+stress_y^2+3shears_xy^2)

62
Q

(Still for isotropic)For analysis and design purposes, what is von mises stress eqn in simplified form?

A

stress_x = stress_y

stress_vm = sqrt(stress_x^2 + 3shears_xy^2)

63
Q

Can you draw the diagram showing von mises and tresca yield criterion?

A

yes / no

pg 64

64
Q

What is the max stress theory for orthotropic materials?

A

The stresses acting in a material are transformed into 1 and 2 directions. The stress_1, stress_2 and shears_12 at a point on a lamina will cause failure when one or more of the following conditions are satisfied:
- longitudinal failure: stress_theta >= X/cos^2(theta)
- shear failure:
stress_theta >= S/sin(theta)cos(theta)
- transverse failure:
stress_theta >= Y/sin^2(theta)
where stress_theta is the stress along the reference axis of the lamina (could be X or Y axis)

65
Q

Can you draw diagrams showing longitudinal failure, transverse failure and shear failure

A

yes/no

pg 67

66
Q

What is TSAI-HILL theory?

A

Similar to the Von mises isotropic yield criteria, the TSAI-HILL theory predicts that failure in orthotropic materials will initiate when the magnitude of the stresses reach the following condition:

(stress_1/X)^2 - (stress_1*stress_2/X^2) + (stress_2/Y)^2 + (shears_12/S)^2 >= 1

67
Q

What are the minimum factors of safety for different loads?

A

F (factor of safety) = Ultimate strength/ working stress

static short term loads, F = 2

Static long term loads, F=4

Fatigue loads, F=6

Impact loads, F=10

68
Q

What can TSAI-Hill theory not do that max stress theory can?

A

Max stress theory limits criteria (tells you what failure mode is) but tsai-hill theory does not indicate failure mode.

69
Q

When will both max stress and tsai-hill theories give the same failure stress?

A

when you have a UD composite subject to uniaxial stress parallel to the principal direction

70
Q

what are the two main components of a sandwich structure?

A

facing and core materials

71
Q

What is the function of the core material in a sandwich structure?

A

The core material separates the faces so that the second moment of inertia is increased and hence increasing the global strength and stiffness of the section.

72
Q

What properties must the facing material have?

A
  • resists in-plane and bending loads and requires high strength and stiffness
  • must resist local loading, i.e. to be robust
  • must resist environmental attack on itself as well as the core
  • must have good adhesion properties
73
Q

Can you draw the diagram and write down the values for increasing thickness effect on relative stiffness and weight of a sandwich structure?

A

1T - relative stiffness = 1 - weight PSF=0.910

2T - relative stiffness-7 - weight PSF=0.978

4T - relative stiffness= 37 - weight PSF= 0.994

74
Q

what properties must the core of a sandwich structure have?

A
  • stabilise the facings against buckling and bending
  • provide shear strength and crush resistance
  • must meet safety, insulation, adhesion, cost and thickness requirements
75
Q

What are sandwich panels very efficient at? How does this work?

A

Very efficient way of providing high bending stiffness at low weight.
The stiff, strong facing skins carry the bending loads, while the core resists shear loads.

76
Q

Why do the faces have to be well bonded to the core?

A

The principal is the same as the traditional I beam. High bending loads require one skin to resist in compression and the other in tension.. hence they will have to be well bonded.

77
Q

What are three different core types for sandwich panels?

A
  • expanded plastic core
  • honeycomb core
  • corrugated core
78
Q

What are the typical applications/properties of honeycomb panels?

A
  1. Lightweight and highly rigid structures which demonstrates excellent strength to weight ratio: fast ships superstructures
  2. Al honeycomb: combination of strength and crush resistance: formula 1 racing cars
  3. Honeycomb structures increase the beam strength of solid composites and kraft paper used in decks/floors of marine vessels
79
Q

What are the typical applications/ properties of foam cores?

A
  1. Traditional PVC based foams are predominantly close-linked (thermoset) which makes them unyielding but may fail in later stages of life under stress, in shear or by cracking. Thermal tolerance can also be an issue.
  2. More recent foams such as PP are closed cell linear thermoplastic foams with bonds which give under stress. They are useful where shocks, fatigues and severe dynamic loads are expected.
  3. Foam filled honeycombs used in boat constructions

Materials 4 (13 decks)

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