Fracture Mechanics of Delamination Buckling in Laminated Composites

1. Fracture Mechanics of Delamination Buckling in Laminated Composites Kenneth Hunziker 4/28/08

2. Low Velocity Impact of a Laminated Composite Plate • Laminated composite materials have a strength-to-weight ratio advantage over many other materials • Low velocity impact causes a delamination in the plate (size determined by impactor and plate parameters) • A compressive load σo increases the delaminated area through coupled delamination and delamination buckling • The growth of the damage through delamination buckling is analyzed using fracture criterion based on energy release rate • Analyzed through 1-D and 2-D models σo l L l

3. Simplifications/Assumptions • One delamination caused by impact is analyzed • Delamination size is large compared to the laminate thickness but small compared to the laminate size • Growth of the delamination is in the original damage plane • Properties of the plate are considered to be homogeneous, isotropic and linearly elastic

4. 1-D Delamination Models* Thin Film Thick Column General * Reference [1]

5. 1-D Thin Film Model* εx = - εo εz = - νεo Shortening l h A i ii iii * Reference [1]

6. 1-D Thin Film Analysis - Deflection* Buckling strain of the film using beam/plate theory Post buckled film shape Solve for amplitude A using: * Reference [1]

7. 1-D Thin Film Analysis – Strain Energy* Strain energy in the buckled layer (case iii) Membrane Bending Gives: Energy release rate as l → (l+Δl) * Reference [1]

8. 1-D Thin Film Analysis – Energy Release Rate Results* * Reference [1]

9. 1-D Thin Film Analysis – Length of the delaminated region* * Reference [1]

10. 1-D General Analysis* h 3 t 1 2 L • Each section is treated as a beam column with compatibility and equilibrium • conditions applied at the interfaces • Gives the following deflections: * Reference [1]

11. 1-D General Analysis* Examining the overall shortening of the plate Using plane strain, stresses and strains are: * Reference [1]

12. 1-D General Analysis* The strain energy of the system is • In order to solve for the four unknowns ε1, ε2, ε3 and θ we combine the displacement equations with the equilibrium and shortening equations • The resulting four equations do not have a closed form solution • Solve numerically • The strain energy release rate can be found with a numerical differentiation • The same analysis can be preformed with the assumption that only section 3 contributes to the bending – ‘Thick Column’ case * Reference [1]

13. 1-D General Analysis* * Reference [1]

14. 2-D Delamination Model* Δb Displacement constraints: b Δa a • Two part analysis • Elastic stability – Solved through the Raleigh-Ritz method • Delamination growth after buckling – Energy approach through fracture mechanics * Reference [2]

15. 2-D Delamination Analysis* Energy release rate for the system due to a increase in delamination Gives Where * Reference [2]

16. 2-D Delamination Analysis* * Reference [2]

17. Conclusions • A one-dimensional model can be used to simplify analysis of a more complete two-dimensional model • Simplifications can be made to the two-dimensional model based on initial damage relative size parameters • Either stable or unstable growth can occur in both the one and two-dimensional model with increasing load • A “thin-film” one-dimensional approach can be used as the delamination being analyzed approaches the plate surface • The initial parameters of the damage in a structure determine the behavior of the damage as load is increased • Both stable and unstable growth can occur based on the size/area of the initial damage

18. Further Analysis • Further improvements of the 1-D model include: • Multiple delaminations • Non-homogeneous material properties • Further improvements of the 2-D model: • Delamination shape, circular and elliptical • Anisotropic material • The role of fiber direction in delamination growth • Multiple delaminations

19. References • One Dimensional Analysis • Chai, H., Babcock, C., Knauss, W., “One Dimensional Modelling of Failure in Laminated Plates by Delamination Buckling,” Int. J. Solids Structure, Vol. 17,. No. 11, pp. 1069-1083, 1981 • Two Dimensional Analysis • 2. Chai, H., Babcock, C., “Two-Dimensional Modelling of Compressive Failure in Delaminated Laminates,” Journal of Composite Materials, Vol. 19,. No. 1, pp. 67-98, 1985

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