The development of analysis of glazed facades to resist blast effects

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

www.tpsconsult.co.uk

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


Why does analysis of glazing matter?

Annealed glass – large jagged fragments at high velocity


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


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


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



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

barZZZ

Ps 019.085.5455.1975.032

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



3D hydrocode modelling



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


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


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


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)


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


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


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


Post cracking behaviour of laminated glass

Similar approach based on multiple sources used by

European Laboratory for Structural Assessment (2009)


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


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


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


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


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


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


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


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


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


Analysis of glazing under blast loading

Any Questions ?

The development of analysis of glazed facades to resist blast effects

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