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

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Low Velocity Impact of a Laminated Composite Plate l L l 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 σ o 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 σoσo

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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

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1-D Delamination Models * Thin FilmThick ColumnGeneral * Reference [1]

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1-D Thin Film Model * Shortening l hA ε x = - ε o ε z = - νε o iiiiii * Reference [1]

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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]

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

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

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

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

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

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1-D General Analysis * The strain energy of the system is In order to solve for the four unknowns ε 1, ε 2, ε 3 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]

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1-D General Analysis * * Reference [1]

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

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

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2-D Delamination Analysis * * Reference [2]

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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

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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

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References One Dimensional Analysis 1.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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