230425 - Composite Materials Flashcards
What quantities are related in the kinematics equation?
The strain is related with the deformation.
Rod: only 1-dimensional deformation. First order derivative of ux
Beam: Rotation. Second order derivative of uz
Constitutive Equation?
Hooke’s Law. Stress vs. Strain
Which equations are needed in the classical laminate theory?
Kinematics, Constitutive, Equilibrium equations.
Equilibrium Equation?
Reaction between the internal reactions (Normal forces, Moments), and the distributed loads (p in x-direction, q in z-direction)
Integration of the differential values for the Moment and the normal force,
What’s the problem with trying to solve the diff eq as they are?
Numeric solution, CAE.
What other option is there instead of solving the diff. eq.?
Normal approach: input the normal reaction and the internal bending moment.
Avoids to solve the diff-eq and allows you to do the failure analysis.
Young’s Modulus units?
N/m2
Failure criteria
- Maximum stress criterion: check the three stress directions (fiber and transverse, x, y and shear).
- Maximum strain criterion.
- Tsai - Hill / Tsai-Wu: Consider the interaction of the stresses.
These are implemented in every composite Material software’s Module and you choose the worst case.
Unexpected effects on laminates compared with isotropic materials
Tension –> tension, twist, bending
Tension –> tension, bending
Bending –> bending + twist
Effects are actually visible.
Symmetric laminates
Effects disappear:
- tension-twist, bending-shear coupling
- bending-tension coupling
Symmetric cross-ply laminates
0 and 90 degrees alignment only.
Effects disappear:
- tension-twist, bending-shear coupling
- bending-tension coupling
Symmetric angle-ply laminates
+30 -30 (alternating)
Effects disappear:
- tension-twist, bending-shear coupling
- bending-tension coupling
