Damage Characterisation and Modelling in Rigid Polyurethane Foam Lewys Jones 16th June 2009

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

Background – CMC Turbine Blades Crack face debonding offers a means to increase toughness. Porous matrix CMCs being investigated to facilitate novell processing routes not requireing fibre coatings. Modelling of porous ceramics not yet fully understood. Image credit: Developments in Oxide Fibre Composites, Zok, J. Am, Ceram. Soc. 89 ( [11]

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.

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

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), Poisson’s ratio, Coefficient of friction.

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 = σc0/pc0 and kt = pt/pc0 Hardening shifts pc but not pt.

Experimental Methods 1 2 3 4 5 6 7 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. 1 2 3 4 5 6 7

Experimental Results - Uniaxial Compression

Experimental Results - Compressive Strain Rate Analysis

Experimental Results - Anisotropic Deformation All blocks compressed to ε = 0.9. Black and blue orientations show barrelling / crumpling. Red orientation remains cuboidal.

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

Experimental Results - Anisotropic Stiffness

Experimental Results - Uniaxial Tension Clear values of E, σy, εy and εfailure identifiable.

Experimental Results - Hydrostatic Compression 19 tests performed. 9 tests ‘successful’. Failure reasons include: Leakage, Rupture, Yield stress range 625 - 775 kPa. Average σy = 702 ± 55 kPa. Result fed into yield surface evaluation.

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

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

Simulation Results - Foam Hardening Profile U1 plot, ε2 ≈ 75% Comparison used to determine the volumetric foam hardening profile. Profile adjusted until results match. FH profile then fed into all future simulations.

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.

Top Appearance (PE - all) 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)

Dynamic Impact Simulation

Simulation Results - Push-in Plug Height = 20.1 mm Shaft Diameter = 12.3 mm Push-in = 28.1 mm Base Diameter = 6.0 mm FE Push-in QS Push-in

Experimental Results - QS Push-in Tearing start and end Divergence of push-in plug Growth of push-in plug Yield start 6.2 mm (≈ 98% rb) 0.6 mm

Increasing computaional time 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)

Experimental Results - QS Push-in

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.

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.

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