me 582 advanced materials science chapter 5 failure...

ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou

ME 582 Advanced Materials Science

Chapter 5 Failure, Analysis, and Design of Laminates(Part 1)

Dr. Jan GouComposite Materials Research Laboratory

Department of Mechanical EngineeringUniversity of South Alabama, Mobile, AL 36688


HW #6

5.1

5.12

Due Day: 6:00 PM, 10/25/2006, Wednesday.


Symmetric Laminates

Symmetric laminate: for every ply above the laminate midplane, there is an identical ply (material and orientation) an equal distance below the midplane

[B] = 0

The force and moment are uncoupled


Cross-Ply Laminates

Cross-ply laminate: composed of plies of either 0˚ or 90˚ (no other ply orientation)

A16= 0, A26= 0

B16=0, B26= 0

D16= 0, D26= 0

Uncoupling occurs between the normal and shear forces as well as between the bending and twisting moments


Angle Ply Laminates

Angle-ply laminate: has plies of the same material and thickness and only oriented at +θ and -θ directions

If the laminate has an even number of plies, then A16= 0, A26= 0

If the number of plies is odd and it consists of alternating +θ and -θ plies, then it is symmetric, giving [B] =0, and A16, A26, D16, and D26 becomes small.


Antisymmetric Laminates

Antisymmetric laminate: the material and thickness of the plies are the same above and below the midplane, but the ply orientation at the same distance above and below the midplane are negative of each other.

A16= 0, A26= 0

D16=0, D26=0


Balanced Laminates

Balanced laminate: for every ply at a +θ orientation, there is another ply at the – θ orientation somewhere in the laminate. The plus and minus pairs do not need to be adjacent to each other.

A16=A26 =0


Isotropic Materials


Quansi-Isotropic Laminates

Quansi-isotropic laminate: produced using at least three different ply orientations, all with equal angles between them.

Exhitbit isotropic extensional stiffness properties

A11=A22

A16=A26=0

A66 = (A11-A12)/2

The stiffnesses are independent of the angle of rotation of the laminate

[B] and [D] may not behave like isotropic materials. (Quansi-isotropic, not isotropic!)


Responses of Special Laminates

Balanced, unsymetric laminate

Tensile loading produces twisting curvature

Ex: [+θ/0/- θ]T

Symmetric, unbalanced laminate

Tensile loading produces in-plane shearing

Ex: [+θ/0/+ θ]T

Unsymmetric cross-ply laminate

Tensile loading produces bending curvatures

Ex: [0/90]T


Responses of Special Laminates

Balanced and symmetric laminate

Tensile loading produces extension

Ex: [+θ/- θ] s

Quasi-isotropic laminate

Tensile loading produces extension loading, independent of angle

Ex: [+60/0/-60] s and [-45/0/+45/90]s


Example 5.1


Solution to Example 5.1






Degradation of Stiffness and Strength


Analysis Procedures


Example 5.3





Local stress at 0°, top

Local strain at 0°, top



Tsai-Wu Failure Theory:



Maximum Strain Failure Theory:





First Ply Failure:



Degradation of [Q]:







Failure Analysis:




Example 5.4



Tsai-Wu Failure Criteria:



me 582 advanced materials science chapter 5 failure...

Documents