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

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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

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Why does analysis of glazing matter?

Annealed glass – large jagged fragments at high velocity

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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 20th century

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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

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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

• thers

 Gives simplified pressure histories for simple geometry

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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

bar Z Z Z P

s

019 . 85 . 5 455 . 1 975 .

3 2



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

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Numerical analysis of blast



3D hydrocode modelling

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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

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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

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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

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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

• nly (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)

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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

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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

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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

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Post cracking behaviour of laminated glass



Similar approach based on multiple sources used by European Laboratory for Structural Assessment (2009)

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Non-linear resistance of laminated glass



Finite element membrane with strain hardening

 Initial elastic membrane with near

cubic curve

 Transition as plastic yield extends

• ver 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%

• f span from failure in water bag tests

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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

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Glazing hazard levels



Based on debris locations in test cubicles



Locations indicate extent

• f 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

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Glazing fragility curves



Glazing hazard level lines plotted for positive phase pressure- impulse combination



Overlaid with charge and standoff combination for face-on loading of large façade



For laminated glass low/high hazard strongly influenced by nature of glass support



Fragility curves for two standard sizes of test panels



Difficult to extrapolate to other sizes and aspect ratios, but can also be produced by multiple SDOF analysis

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Commercial blast testing



Testing of glazing systems, curtain walling and glass doors



Almost all laminated glass or laminated double glazing



May be to ISO, GSA or project specific threat levels

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Commercial blast testing



Tests may be of multiple panes to justify glazing structure and glass support



Manufacturer tests for product development and to demonstrate performance levels for future projects – generally to standard threat levels



Project specific proof tests for bespoke designs for large and or high threat projects

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Current practice in analysis



Developments of SDOF



Up to 5DOF simultaneous analysis of curtain wall units

 Double glazing, mullion & transom and deforming bracket  Reactions load supports  Glazing and framing response affected by support motions



Non-linear glazing parameters & elastic-plastic framing



Irregular, multi-bay framing by linear implicit FEA

 Loading by reactions from 2-5DOF analysis



Nonlinear FEA solutions



Explicit transient analysis – non-linearity easier than in implicit



Full model of multiple bays of glass, framing and support structures



Framing members modelled in shell elements allows buckling



Simplified glazing material models

 Layered shell models with linear/ cracking glass and linear PVB

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Trends and developments in blast resistant glazing



Alternative materials



Anchored anti-shatter films for retrofits to monolithic glass



Ionoplast interlayers are stiffer than PVB and less sensitive to temperature, but require stronger supports, which are being developed



Poured resin materials e.g. PBT bond direct to glass and can provide substantial blast and ballistic resistance

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Trends and developments in blast resistant glazing



Yielding supports to reduce reactions



Yielding connection of frame to structure for punched windows



Yielding brackets for curtain walling

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Analysis of glazing under blast loading

Any Questions ?