Workshop II MicMac Jan11[1]

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COMPOSITES DESIGN WORKSHOP II

MIC-MAC TOOL

Pranav Dhoj Shah, PhD

SESSION C: JANUARY 11, 2010

CO-ORDINATE AXES

N1

N2

N2

N1

N6

N6

1

3 2

x

y

q

2

Application: Mic-Mac Inplane

Material: T300/N5208 [SI]

Ply: [0]s --------------- Rotate the laminate from -15to 90 degrees

Chart-Quick:

Set laminate to [0]s

Cell [I4] to Input

Output 1 = [Cell S15]

Output 2 = [Cell F7]

ENGINEERING CONSTANTS AND PLY STIFFNESS

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STIFFNESS: INVARIANTS OF TRANSFORMATION

Like isotropy, anisotropic properties (stiffness) have limits as well.

There exist certain linear combinations of stiffness [Q] which remain constant in magnitude with changing ply angle orientation. Same applies to compliance [a].

The invariants are (Eq. 3.9):

I1 = Qxx + Qyy + 2Qxy = Q11 + Q22 + 2Q12

I2 = Qxx + Qyy + 2Qss = Q11 + Q22 + 2Q66

J2 = Sxx + Syy + Sss/2 = S11 + S22 + S66/2

For a given ply material, there is a limit to the stiffness potential to be achieved.

Increase in the stiffness in one direction is at the expense of that in some other

direction. The number of independent variables we can choose for a material is limited

to two; this limit is imposed by the invariants. How?

Say, we choose Q11 and Q66. Due to I1 and I2, other terms, Q12 and Q22 are fixed for that

particular set of Q11 and Q66. Same applies if we choose other sets of combinations.

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Invariants of transformation for stiffness

EXAMPLE

Application: Mic-Mac Inplane


Ply: [0]s : Rotate the laminate from 0 to 90 degrees

Variables: Q11, Q11 + Q22 (= I1- 2Q12: 2Q12 is plotted inverted) and

Q11+Q22+2Q12 (= I1)

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Invariants of transformation for stiffness

EXERCISE

Application: Mic-Mac/Inplane


Ply: [0]s : Rotate the laminate from 0 to 90 degrees

Variables: Q11, Q11 + Q22 (= I2 - 2Q66: 2Q66 is plotted inverted) and

Q11+Q22+2Q66 (= I2)

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MIC-MAC/ Duplex

FOR SIDE BY SIDE COMPARISON OF SYMMETRIC LAMINATES

UNDER IN-PLANE LOADS.

Laminate 1 Laminate 2

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Comparison using Duplex

MIC-MAC/ DUPLEX: EXAMPLES

Compare the effect of rigid body rotation on stiffness A*11 of

[0/90]s and [(0)2/90]s laminates.

Material : T300/5208 [SI]

Rigid body rotation: 0 to 180 degrees

Application: Duplex

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Comparison using Duplex

MIC-MAC/ DUPLEX: EXERCISE

Compare the stiffness A*11 of [0/90/45/-45]s and [±ɸ]s laminates.


Application: Duplex

Can we obtain equal of better longitudinal stiffness using less ply angles?

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MIC-MAC/ HYBRID

FOR SYMMETRIC LAMINATES UNDER IN-PLANE LOADS

N1

N2

N2

N1

N6

N6

Material 1

Material 2

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HOMEWORK 1

What will be the optimal range of ɸ in terms of A*11 and A*66 for a [0/±ɸ]s laminate if

both of the properties should be equal to or greater than that of Al.


For Al:

A*11 = 75.71 GPa

A*66 = 26.50 GPa

Application: Inplane

Hint: For Chart-Quick output, consider both A*11 and A*66

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Workshop II MicMac Jan11[1]

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