Fracture Mechanics of Delamination Buckling in Laminated Composites

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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

• 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 so 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

so
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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 Film
Thick Column
General
Reference 1
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1-D Thin Film Model
ex - eo ez - ?eo
Shortening
l
h
A
i
ii
iii
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)
Membrane
Bending
Gives
Energy release rate as l ? (l?l)
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
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
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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 e1, e2,
  e3 and ? 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
Displacement constraints

• Two part analysis
• Elastic stability Solved through the
  Raleigh-Ritz method
• Delamination growth after buckling Energy
  approach through fracture mechanics

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