the development of analysis of glazed facades to resist blast effects
TRANSCRIPT
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
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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
others
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
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
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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 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)
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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
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
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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
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
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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 ?