Damage Characterisation and Modelling in Rigid Polyurethane Foam

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Damage Characterisation and Modelling in Rigid
Polyurethane Foam
Lewys Jones 16th June 2009
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Background CMC Turbine Blades

• High melting point run engine hotter without
  melting (or creep),
• Oxide ceramics need no oxidation protection,
• Possibility to eliminate wasteful air cooling
  systems.

• Ceramics are brittle more susceptibe to foreign
  object damage (FOD) and catastrophic failure.

Image credit Toshihiko Sato/Associated Press
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Background CMC Turbine Blades

• Crack face debonding offers a means to increase
  toughness.
• Porous matrix CMCs being investigated to
  facilitate novell processing routes not requiring
  fibre coatings.
• Modelling of porous ceramics not yet fully
  understood.

Image credit Developments in Oxide Fibre
Composites, Zok, J. Am, Ceram. Soc. 89 ( 11
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Project Objectives

• Evaluate the experiments needed to find the input
  parameters for finite element (FE) modelling of a
  porous solid.
• Identify unnecessary experiments and other ways
  to reduce material wastage during testing.
• Design the required experiments.
• Calibrate the instruments involved in such
  experiments.

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Test Material

• Density of 107 kgm-3.
• Supplied in 5 colours, in blocks 25 x 50 x 100
  mm.

• Out of plane
• In plane short axis
• In plane long axis

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Simulation Parameters

• Bulk density,
• Elastic stiffness,
• Yield stress (quasi-static value),
• Rate-dependant yield stress,
• Crushable foam model constants k kt, (see
  later),
• Foam hardening profile (post-yield),
• Poissons ratio,
• Coefficient of friction.

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CF Model Constants
Image redrawn from Abaqus TM Theory Manual

• Yield surface (ellipse) defined in the
  hydrostatic-deviatoric stress space by two
  constants k and kt.
• k sc0/pc0 and kt pt/pc0
• Hardening shifts pc but not pt.

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Experimental Methods

• Quasi-static
• Uniaxial compression ( µ),
• Uniaxial tension,
• Hydrostatic compression,
• Push-in,
• Unconstrained shear-punch,
• Constrained shear-punch,
• Dynamic
• Small gas-gun.
• including strain rate sensitivity analysis.

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1
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Experimental Results - Uniaxial Compression
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Experimental Results -Compressive Strain Rate
Analysis
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Experimental Results - Anisotropic Deformation

• All blocks compressed to e 0.9.
• Black and blue orientations show barrelling /
  crumpling.
• Red orientation remains cuboidal.

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Experimental Results - Anisotropic Stiffness
Average Stiffness 27.09 Mpa,
Average 14.30 Mpa,
n 16
n 6
n 6
n 3
n 20
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Experimental Results - Anisotropic Stiffness
n 16
n 6
n 6
n 3
n 20
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Experimental Results - Uniaxial Tension

• Clear values of E, sy, ey and efailure
  identifiable.

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Experimental Results - Hydrostatic Compression

• 19 tests performed.
• 9 tests successful.
• Failure reasons include
• Leakage,
• Rupture,
• Yield stress range 625 - 775 kPa.
• Average sy 702 55 kPa.
• Result fed into yield surface evaluation.

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Experimental Results - Yield Ellipse Plotting

• Three unique points now known
• Uniaxial compression (18 unique readings ? static
  extrapolation)
• Uniaxial tension (20 unique values, averaged)
• Hydrostatic compression (9 unique values,
  averaged)
• k 0.93 0.08 and kt 0.098 0.008

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Experimental Results - Dynamic Impacts

• 3 damage types identified, dent, bounce-off and
  stay-in.
• Penetration depth to projectile KE relationship
  investigated.

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Simulation Results - Foam Hardening Profile
U1 plot, e2 75

• Comparison used to determine the volumetric foam
  hardening profile.
• Profile adjusted until results match.
• FH profile then fed into all future simulations.

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Experiment / Simulation Comparison

• Verify the crushable foam model.
• Allows direct visualisation of sub-surface damage
  development / processes.
• Allows for individual system energies to be
  evaluated and dominant processes identified.

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Side Profile (PE - all)
Top Appearance (PE - all)
Region I v -3.69 ms-1 (RP 23 psi) Pi 1.59 mm
Region II v -7.23 ms-1 (RP 45psi) Pi 3.22 mm
Region III v -15.26 ms-1 (RP 95 psi) Pi
7.53 mm
(All images are at 2µs)
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Dynamic Impact Simulation
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Simulation Results - Push-in
QS Push-in
FE Push-in
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Experimental Results - QS Push-in
Divergence of push-in plug
Growth of push-in plug
Yield start
0.6 mm
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Plastic Strain (PE - all)
Increasing computaional time
Axisymm. (swept 180)
3D - 90 (YZ plane mirrored)

• 3D (90 mirrored) simulation is a good compramise
  between realistic failure modelling and
  computational time.

3D - 180 (native)
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Experimental Results - QS Push-in
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Future Work

• Refine FE models.
• Include strain-rate dependent data,
• Reduce mesh size
• Discuss results with Dr. Deshpande, University of
  Cambridge currently developing anisotropic CF
  FE model.
• Testing of porous ceramics.

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Conclusions

• Key experiments / techniques were identified with
  unsuccessful experiments now not needing to be
  repeated by others.
• Equipment was calibrated for the successful
  experiments.
• Data analysis practices were developed to extract
  simulation input constants from experimental
  data.
• FE modelling techniques were learnt and several
  types of practical experiment modelled, results
  were compared with experimental observations.
• Simulations were generally in agreement with
  experimental findings, with key areas for ongoing
  work identified.
• Characterisation and modelling task timeline
  reduced from 8 months to 2 months.

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Acknowledgements
Dr. Frank Zok Kirk Fields Brett Compton Nell
Gamble
Dr. Richard Todd Dr. Ian Stone Dr. Adrian Taylor