1 / 20

Fracture Mechanics of Delamination Buckling in Laminated Composites

Fracture Mechanics of Delamination Buckling in Laminated Composites. Kenneth Hunziker 4/28/08. Low Velocity Impact of a Laminated Composite Plate. Laminated composite materials have a strength-to-weight ratio advantage over many other materials

Download Presentation

Fracture Mechanics of Delamination Buckling in Laminated Composites

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

  20. Back Up

More Related