Analysis of glazing under blast loading Dr Colin Morison Technical - PowerPoint PPT Presentation

Analysis of glazing under blast loading Dr Colin Morison Technical Director, Security & Explosion Effects, TPS Urban habitat constructions under catastrophic events Naples 16-18 September 2010

Analysis of glazing under blast loading  Blast loading  Theoretical basis of blast waves  Measurement of blast pressure histories  Numerical analysis of blast  Dynamic response  Single degree of freedom (SDOF) analysis  Geometric and material non-linearity  Experimental evaluation and measurement  Current trends & future developments www.tpsconsult.co.uk

Why does analysis of glazing matter? Annealed glass – large jagged fragments at high velocity www.tpsconsult.co.uk

Theory of sound and blast waves Poisson 1803 &1823  Wave progression (1 dimensional)  Adiabatic gas law  Accurate sound speed – but wave breaks down to shock front for finite  amplitude Stokes 1848  Equations for sound wave breakdown, but do not conserve energy  Breakdown of sound waves prevented by viscosity  Rankine 1870 & Hugoniot 1889  Equations for shock front with energy conservation from thermodynamics  Shock front is not adiabatic – some energy irreversibly converted to heat  Rankine – Hugoniot equations applied to blast waves, reflection etc. only  in 20 th century www.tpsconsult.co.uk

Measurement of blast waves from high explosives Fox & Harris 1939   Foil gauges allow measurement of blast pressure histories  Measurement of blast from individual weapons at different ranges  Bombs and shells are cased charges  Bursting of casing rather than blast from bare explosives  Positive phase blast impulse reduced by casing  Negative phase measured as greater than positive phase www.tpsconsult.co.uk

Measurement of blast waves from high explosives Kingery and Bulmash 1984   Best fit curves from many series of blast trials  Bare charges (adjust later for casing if appropriate)  Airburst or ground burst  Cube root scaling of blast for charge size  Peak pressure and impulse  Incident and reflected  Time of arrival and duration  Positive phase only by K&B, but negative phase data added later by others  Gives simplified pressure histories for simple geometry www.tpsconsult.co.uk

Numerical analysis of blast Hydrocode analysis  Rankine-Hugoniot equations for shock front  Adiabatic gas equations for wave behind shock front (usually ideal gas)  Iterative numerical calculation to track blast waves through 1D, 2D or 3D grids  using difference equations in small time steps Bode 1954  1D spherical expansion models air burst  Calculations for 1kT nuclear blast energy and then scaled, but results since  adapted for cube root scaled high explosives Peak pressure curve with scaled range most frequently quoted  0 . 975 1 . 455 5 . 85 P 0 . 019 bar s 2 3 Z Z Z However, results included curve fits for   Positive & negative pressure histories behind the shock  Density, particle velocity, wave velocity and dynamic pressure  Time of arrival and duration of positive and negative phases for pressure and velocity  Positive and negative impulses www.tpsconsult.co.uk

Numerical analysis of blast 3D hydrocode modelling  www.tpsconsult.co.uk

Numerical analysis of blast Pure Hydrocode – e.g.Air3D and others (SHMRC, GRIM …)  Memory efficient algorithms  3D model of reasonable resolution on normal PC  Run in core memory so reasonable execution time  Improve performance & accuracy with 1D to 2D to 3D remaps  Hydrocode – Explicit structural analysis – e.g. Autodyn, LSDyna  Blast & structural response in single ALE model or linked Euler & Lagrange models  More variables so less memory efficient and larger models, or reduction in resolution &  accuracy Runs on clusters or supercomputers, or very slowly with virtual memory on PC or Unix  workstation Autodyn supports remaps, but LSDyna does not, requiring finer mesh around detonation for  similar accuracy Computational Fluid Dynamics – e.g. Fluent and many others  Combines Rankin- Hugoniot equations with Navier-Stokes equations for supersonic  wave and flow effects More variables so less efficient, affecting speed and model size  Remapping not available, so fine mesh required around detonation, or substantial loss of  accuracy Requires clusters or supercomputers to run blast problems  www.tpsconsult.co.uk

Single degree of freedom analysis Analytical SDOF models applied to glazing 1940-46   Linear analysis used for resistance and natural period  “Equivalence” by matching measured & calculated natural period  Rebound of uncracked glass greater for some T/ t ratios Negative phase loading important for many cases   Glass analysis using small deflection theory gave variable results Newmark develops elastic-pure plastic SDOF solution in 1950s   Computer numerical analysis used to create charts  No of variables limited for single chart  Elastic-pure plastic resistance  Simple positive phase loading only – justified for plastic yielding structure, but not for elastic  Main interest in RC bunkers and nuclear blast www.tpsconsult.co.uk

Equivalent single degree of freedom analysis Amman & Whitney, MIT and US Army Corps of Engineers in 1950s  Energy equivalence based on the incremental deflected shape  Mass equivalence based on kinetic energy  Load equivalence based on work done  Resistance equivalence based on internal strain energy, but gives same factor  as load equivalence Analysis of the equation of motion of the equivalent lumped mass –  spring system gives the response of the centre of the pane www.tpsconsult.co.uk

Large deflection non-linearity of glass panes  Timoshenko for square panels of steel with in-plane restraint  Experimental equivalent for square panels with transverse restraint only (from 1960s)  Numerical analysis – glass Poisson’s ratio and different aspect ratios Moore 1980 JPL  finite element produced simple curves for non-linear  resistance of glass panes Meyers 1986 used Moore for blast resistance  SDOF factors still based on small deflection  Popularised by use in TM5-1300 (1990)  www.tpsconsult.co.uk

Non-linear factors & coefficients for glass By Morison (2003)  Variations with aspect ratio  Full range of aspect ratio from 1 to 4, to  match range of resistance data Variations with deflection  Transformation factors  Dynamic reaction coefficients  Reaction concentration at peak location  Migration of location of peak reaction  www.tpsconsult.co.uk

Post cracking behaviour of PVB laminate glass BRE waterbag tests 1991-2  Low strain rate  “S” shaped resistance curve  indicates nonlinear PVB material properties in membrane Failure deflections up to 50% of  span 90% characteristic failure  deflection 27.8% of span for 1.52 mm thick interlayers Failure by cutting of PVB by glass  fragments may not be strain rate sensitive www.tpsconsult.co.uk

Post cracking behaviour of PVB laminate glass PVB membrane after cracking   Observed properties bi-linear (like elastic-plastic)  Low strain rate  High strain rate  Non-linear viscoelastic  Transition between glassy and hyperelastic  Strain rate sensitive  Temperature sensitive  Abrupt reduction in stiffness  Extension fully recoverable over time  Simplified material models  Elastic – plastic with strain hardening  Elastic stiffness possibly reduced on rebound www.tpsconsult.co.uk

Post cracking behaviour of laminated glass Similar approach based on multiple sources used by  European Laboratory for Structural Assessment (2009) www.tpsconsult.co.uk

Non-linear resistance of laminated glass Finite element membrane with strain  hardening  Initial elastic membrane with near cubic curve  Transition as plastic yield extends over the whole membrane  Near linear resistance as material hardening opposes geometric softening of a plastic membrane Idealised non-linear resistance for  SDOF analysis of laminated glass  Variable SDOF coefficients used for the different deflected shapes for best accuracy in the analysis  Lower bound failure taken as 27.8% of span from failure in water bag tests www.tpsconsult.co.uk

Testing of glazing under blast Philips, 1940 - 45   UK trials during WW2  Back analysis of damage by single bombs in urban areas  Predominantly plate and sheet annealed glass  Conclusions limited by analysis capability PSA / HOSDB, 1978 onwards   UK trials to assess hazards from terrorist bombs  Annealed float glass, toughened glass, laminated glass  Standardized test panes and glazing hazard levels  Fragility curves for different glazing make-up  Double glazing combinations, particularly toughened outer leaf and laminated inner leaf  Incorporated with US and Israeli tests in database of 1000+ tests www.tpsconsult.co.uk

Glazing hazard levels Based on debris  locations in test cubicles Locations indicate extent  of hazard and velocity of fragments Developed by UK  Adopted with variants by  GSA, ASTM and ISO Used in EN ISO 16933  and EN ISO 16934 for arena and shock tube testing of glass In performance  specifications low hazard is often acceptable but high hazard is not www.tpsconsult.co.uk