damage mechanics in composite materials - iran … … ·  · 2012-10-16damage mechanics in...

Damage Mechanics in Composite Materials

Dr. Bijan MohammadiSchool of Mechanical Engineering

Iran University of Science and Technology

Inter-laminar stresses

• The inter-laminar stresses in the boundary layer can be critical in structural applications because they can lead to delamination-type failure at loads well below those corresponding to in –plane failure.

Equilibrium Considerations

• Equilibrium considerations – To provide the justification for the existence of inter-laminar

stresses in free edges.

Inter-laminar Fyz Shear Force

• Partial Free-Body Diagrams

Inter-laminar Forces and Moments for Strain Loading

• Cross-Ply Laminates

Inter-laminar Forces and Moments for Strain Loading

• Cross-Ply Laminates

Inter-laminar Forces and Moments for Strain Loading

• Cross-Ply Laminates

Inter-laminar Forces and Moments for Strain Loading

• Angle-Ply Laminates

Inter-laminar Forces and Moments for Strain Loading

• Angle-Ply Laminates

Inter-laminar Forces and Moments for Strain Loading

• Quasi-Isotropic Laminates

Inter-laminar Forces and Moments for Strain Loading

• Quasi-Isotropic Laminates

Inter-laminar Forces and Moments for Bending

• Cross-ply Laminates

Mismatch Considerations

• The presence of inter-laminar stresses is the result of the mismatch in material properties between layers. (The mismatch in properties at the micromechanical level is ignored in this discussion.)

• Th two properties of primary interest for laminated composites are Poisson’s ratio, νxy and coefficient of mutual influence ηxy,x.

• Poisson's ratio is defined as the negative ratio of the induced lateral strain εy to the axial strain εx under the application of axial stress σx.

• The coefficient of mutual influence ηxy,x is defined to be the ratio of the induced in-plane shear strain γxy to the axial strain εx for applied axial stress σx .

Mismatch Considerations

• off-Axis Poisson's Ratio and Coefficient of Mutual Influence

(b) (a)

Mismatch Considerations

• Mismatch in Properties for +θ/-θ Angle-Ply Laminates

Mismatch Considerations

• The curve for the mismatch in coefficients of mutual influence for +θ/-θ layers exhibits much higher values than the maximum Poisson mismatch for the laminates considered.

• The mismatch in coefficients of mutual influence shows a strong maximum at 11.5° for the +θ/-θ combination.

• The mismatch in ηxy,x for θ/90 and θ/0 interfaces is exactly half that of the +θ/-θ configuration because ηxy,x for the 0° and 90°layers is identically zero and ηxy,x is an odd function of θ.

Displacement Continuity

Deformed Quasi-Isotropic Laminates

Deformed Quasi-Isotropic Laminates