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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