2E5 Glass Structures L6 2014 VU

8/10/2019 2E5 Glass Structures L6 2014 VU

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ADVANCED DESIGN OF GLASS STRUCTURES

Lecture 6 Fracture strength and testingmethods

Viorel Ungureanu

European Erasmus Mundus Master Course

Sustainable Constructionsunder Natural Hazards and Catastrophic Events520121-1-2011-1-CZ-ERA MUNDUS-EMMC


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L6 Fracture strength and testing methods

European Erasmus MundusMaster Course

Sustainable Constructionsunder Natural Hazards

and Catastrophic Events

Introduction

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Glass is not able to yield plastically (no stress redistribution) thus its fracture strength is verysensitive to stress concentrations. Since surface flaws cause high stress concentrations, thecharacterization of the fracture strength of glass must incorporate the behaviour of such flaws.

Edge flaw caused by groundingSurface flaw on an accessible glazing

BEAM

Introduction

Glass FractureMechanics

Linear ElasticFracture Mechanics

Stress corrosion &SCG

Lifetime of a glass

elementTesting methods

Characteristicvalues in design


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The initial acceleration of a flaw starts on a relatively smooth surface known as the mirrorzone. As the flaw continues to accelerate, the higher stress and greater energy releaseproduce some form of micro mechanical activity close to the crack tip, producing severesurface roughening that finally causes the crack to bifurcate or branch along its front. Anelevation of the crack surface will reveal a progressive increase in the roughness of thefracture surface from mirror to mist to hackle.

The mirror radius R isapproximately 8 to 16 times larger than theinitial flaw depth a

R

a

Glass fracture mechanicsIntroduction




Lifetime of a glass




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Glass fracture mechanics

one (critical) flaw flaw population

INERT STRENGTH

LEFM (short-term) LEFM + PROB

AMBIENT STRENGTH

LEFM + SCG (long-term) LEFM + SCG + PROB

LEFM : Linear Elastic Fracture Mechanics

SCG : S ubcritical Crack Growth

PROB : Theory of Prob ability

Introduction




Lifetime of a glass




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Linear elastic fracture mechanics

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STEEL or CONCRETE:

homogenous

test strength = strength of the material

n < critical stress

n : uniform stress

TIMBER or GLASS:

not homogenous: defects

test strength


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The stress intensity factor K I : elastic stress intensity near a crack tip. Provides a means tocharacterize the material in terms of its fracture toughness.

K I : stress intensity factor [MPa.m 0.5 ]

Y : geometry factor [-]

n : stress normal to the flaws plane [MPa]

a : flaw depth [m]

aY K n I ... =

Instantaneous failure of glass occurs when the elastic stress intensity K I , due to tensilestress at the tip of a crack, reaches or exceeds a critical value. This critical value is amaterial constant known as the fracture toughness or the critical stress intensity factor K IC .

There is stress magnification near the tip of a crack.

Introduction




Lifetime of a glasselement

Testing methods



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K I : stress intensity factor [MPa.m 0.5 ]

Y : geometry factor [-]

n : stress normal to the flaws plane [MPa]

a : flaw depth [m]

aY K n I ... =

a

Y = 1.12

Y =0.80

a Cut edge flaw

Surface flaw

Ground edge flaw E n =

r E n +=

Annealed glass

Tempered glass

The fracture toughness or the criticalstress intensity factor K IC can beconsidered to be a material constantknown with a high level of precision. Itsvalue for SLSG is around 0.75 MPam 0.5 .

Introduction


Linear ElasticFractureMechanics



Testing methods



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Inert conditions

Ic I K K =

0.5MPa.m75.0... =cinert a f Y

Failure when:

MPa

c

inert aY

f ..

75.0

=

cinert a f Y

..

75.0

=

Stress causing failure of a crack of depth a c(a c : critical flaw depth)

Resistance of a crack to instantaneous failure(not triggered by sub critical crack growth)

Introduction


Linear ElasticFractureMechanics



Testing methods


K I : stress intensity factor

K IC : critical stress intensity factor


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Stress corrosion & Sub critical crack growth

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Instantaneous failure of glass occurs when the elastic stress intensity K I due to tensilestress at the tip of a crack reaches or exceeds or the critical stress intensity factor K IC.

In vacuum (inert conditions), the strength of glass is time independent. In the presence of

humidity, however, stress corrosion causes flaws to grow slowly when they are exposed toa positive crack opening stress. This happens for values of stress intensity at the crack tiplower than K IC (sub critical crack growth).

Si-O-Si+H 2O Si-OH+HO-SiStress corrosion is the chemical

reaction of a water molecule with silicaat the crack tip.

Glass

Water

1

Si

O

Si

Si

O

H

H O

O

H

H

O

Si

Si

Si

2 3

H

H O

Stress corrosion - chemical phenomenon

Sub-critical crack growth - consequence of stress corrosion

Introduction





Testing methods



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Stress corrosion & Sub critical crack growth

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The growth of a surface flaw depends on the properties of the flaw and the glass, the stresshistory and the relationship between crack velocity and stress intensity.

Stress intensity factor, K I

KIC Fracture toughness (material constant = 0.75Mpa m 0.5 for SLSG)).

Kth Threshold below which no crack growth occurs

0.55 Mpa m 0.5 for SLSG.

In region III, close to K IC is independent of theenvironment and approaches a characteristicpropagation speed very rapidly ( 1500m/s).

In region II the kinetics of the chemical reactionat the crack tip are no longer controlled by theactivation of the chemical process but by thesupply rate of water (water rate cant keep upwhen the crack speed increases very fast)

For usual conditions, only region I (extremelyslow sub-critical crack growth) is relevant fordetermining the design life of a glass element.

Parameters affecting the relation between and stress intensity facroe K I :

Humidity, temperature, PH value.

Loading rate (if it is too fast the water supplysuffer a shortage and the stress corrosion isslow down).

Chemical composition of glass (affects all theparameters in sub critical crack growth).

The crack velocity scales with the kinetics of the

chemical equation for the stress corrosion (region I).

n, v 0 - crack velocity parameters for structural design n=16is reasonable and v 0 =6mm*/s should be conservative

Used for lifetimepredictions

Introduction





Testing methods



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Integration of the crack growth law,

considering a constant stress history, constant n and

yields:

)(.).(. t at Y K n I

=

n

Ic

I

K K

vdt da

).(0=

( ) ( )

n

ni

n

Ic f

ct aK Y vnt

f

/ 1

2 / )2-(0 . / ...2-.

2

=

Risk integral or Browns integral(to characterize damageaccumulation in glass)

Given a stress story enables the calculation of:

the lifetime of a crack given its initial depthor the allowable initial crack depth given its required lifetime

Lifetime of a glass elementsingle flaw

This is asymptotic to inertstrength, i.e.( t f t r ) 0 as a i a f , and asymptotic to thethreshold strength,i.e. ( t f t r ) as a i a TH

Introduction





Testing methods



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The single flaw model is adequate when the critical flaw is known and it is sure that it willlead to failure. In situations other than that a random surface flaw population has to be

considered.

Lifetime of a glass elementrandom surface flaw population (RSFP)

If the physical characteristics of the surfacecracks are unknown, the characteristictensile strength of glass is evaluatedstatistically, from the 2-parameter Weibull

distribution of test specimens.

= exp1 f P

P f - Cumulative probability of failure

Failure stress of specimens which the surface area A is exposed to tensile stress.

Scale parameter (depends on A)

Shape parameter of the Weibull distribution

Introduction





Testing methods



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one(critical) flaw flaw population

INERT STRENGTH

LEFM (short-term) LEFM + PROB

AMBIENT STRENGTH

LEFM + SCG (long-term) LEFM + SCG + PROB

LEFM : Linear Elastic Fracture Mechanics

SCG : S ubcritical Crack Growth

PROB : Theory of Prob ability

Introduction





Testing methods



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Flaw characteristics known Flaw and environment characteristics known

One flaw Flaw population One flaw Flaw population

Flaw characteristics known and environment characteristics not known

finert P f,inert(Weibull)

fambientP f,ambient

(Weibull)

Testing Testing Testing

Inert + micr. ambient

Y, a:flawparameters

n, 0 :crack velocityparameters

Inert or ambient

Test results(fitting Weibull)

P f,inert

Test results(fitting Weibull)

P f,ambient

Introduction





Testing methods



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Testing methodsThe (characteristic) strength of glass can be estimated experimentally with the coaxialdouble ring (CDR) or the four point bending (4PB) test setup.

load

loading ring

reaction ring

glassspecimen

reaction

Coaxial double ring test

Four point bending test

loadglass specimen

reaction reaction

Introduction





Testing methods



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Testing methodsThree point bending test:

one flaw is testedFour point bending test:

a flaw population is tested

Introduction





Testing methods



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Testing methodsCoaxial double ring test

standardized in EN 1288-1

large (EN 1288-2: 240000 mm) orsmall (EN 1288-5: 254 mm) test surface area

stress rate: 2 MPa/s 0,4 MPa/s

rel. humidity: 40 % to 70 %

equibiaxial stress field ( 1 = 2)

the failure strength is influenced by thesurface conditions only

Technische Universitt Darmstadt,

Germany

1 Load ring

2 Specimen

3 Supporting ring

Introduction





Testing methods



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Testing methodsFour point bending test

standardized in EN 1288-3

size of the specimens: 1100 x 360 mm

stress rate: 2 MPa/s 0,4 MPa/s

rel. humidity: 40 % to 70 %

uniaxial stress field

the failure strength is influenced by the edgeand the surface conditionsthe failure can occur from the edge or fromthe surface

the test results outside the load span areexcluded

M P A D a r m s t a

d t ,

G e r m a n y

Ls = 1000 mm L b = 200 mm

Introduction





Testing methods



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Characteristic values in design The characteristic value corresponds to a fractile of 5%, and

can be determined according to EN 1990, EN 12603 and therelevant product standards .

Glass type Characteristic bending strengthf g;k i

[N/mm 2]

Annealed glass 45 Heat strengthened glass 70

Fully tempered glass 120

Chemical strengthened glass 150 *)

*)

depends on the surface conditionsGlasbau /Wrner et al.

Introduction





Testing methods



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Characteristic values in designExample: Determination of a the characteristic value in the drilled area of a flat glass.

Parameters (specimens):Glass type: Annealed glass

Nominal size: 250 mm x 250 mm

Diameter of the central borehole: 50 mm

Nominal glass thickness: 6 mm

Parameters (testing):

Coaxial double ring test

Stress rate: 2 MPa/s 0,4 MPa/s

Rel. humidity: 50 %

Introduction





Testing methods



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Sustainable Constructionsunder Natural Hazardsand Catastrophic Events

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Characteristic values in designFrom the coaxial double ring test, the following values were obtained:

measured failurestress

N Measuredfailurestress

[N/mm 2]

N Measured failurestress

[N/mm 2]

N Measured failurestress

[N/mm 2]

1 67.70 11 69.96 21 66.67

2 74.12 12 68.29 22 72.04

3 62.05 13 55.05 23 69.86

4 73.09 14 74.24 24 69.91

5 73.99 15 72.1 25 69.8

6 71.35 16 75.32 26 72.92

7

73.84

17

66.46

27

77.63

8 70.87 18 67.34 28 69.90

9 68.18 19 60.46 29 64.57

10 83.27 20 59.88 30 70.55

MPA Darmstadt, Germany

Introduction





Testing methods



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Characteristic values in design

Histogram and 2p-Weibull fitting:

measured failurestress

Introduction





Testing methods


For brittle materials, the Weibull distribution is the mostappropriate statistical strength distribution. In Europe, thestandard EN 12603 specifies procedures on evaluation of

test results with the 2p-Weibull distribution.


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Characteristic values in designFor brittle materials, the Weibull distribution is the most appropriate statistical strengthdistribution. In Europe, the standard EN 12603 specifies procedures on evaluation of testresults with the 2p-Weibull distribution.

The cumulative distribution function of the 2p-Weibull distribution is given by:

The experimental results were fitted to the 2p-Weibull distribution, using the MaximumLikelihood Estimation method.

(The method according to EN 12603 can be used alternatively)

Using Matlab, the Weibull parameters were estimated:

= 72.18 MPa and = 13.64

) ) x

-( exp( - ) x ( F

1=

Introduction





Testing methods



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Characteristic values in designA probality plot shows the failure probability P f of the measured data, which were fittedto a 2p-Weibull distribution (large deviations at the lower bound!!!)

Introduction





Testing methods



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Characteristic values in design

A probality plot shows the failureprobability P f of the measured data, whichare fitted to a 2p-Weibull, Normal and 2p-Lognormal distribution: for these data thetail fits best to the Weibull distribution

Introduction





Testing methods



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Characteristic values in designThe probability of failure for the fitted 2p-Weibull distribution:

The characteristic strength f g;k corresponds to P f = 0.05:

= 72.18 MPa and = 13.64 are the estimated Weibull parameters.

Under the assumption, that the count of specimens is high, the characteristic strength

f g;k can be calculated approximately:

) ) f

-( exp( -P g f

1=

) ) f

-( exp( -. k g;

1=050

MPa0658=050MPa1872= 64131 . )).--ln(1( *. f . / k ;g

Introduction





Testing methods



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ReferencesAnderson, T.L. , Fracture mechanics, Fundamentals and Applications, Taylor & Francis Group, 2005.

Evans A.G. , A method for evaluating the time-dependent failure characteristics of brittle materials and its application topolycrystalline alumina. Journal of materials science 7: 1137-1146, 1972.

Fink A. , Dissertation D17: Ein Beitrag zum Einsatz von Floatglas als Dauerhaft tragender Konstruktionswerkstoff imBauwesen. Technische Universitt Darmstadt, Institut fr Statik, Bericht Nr. 21, 2000.

Griffith A. A., The Phenomena of Rupture and Flow in Solids. Philosophical Transactions, Series A, 1920, 221: 163-198.

Haldimann M. , Thse n 3671: Fracture strength of structural glass elements analytical and numerical modelling, testing anddesign. EPFL, Lausanne, 2006.

Haldimann M, Luible A, Overend M., Structural Engineering Document 10: Structural use of glass. IABSE / ETH Zrich,Zrich, 2008.

Irwin G. , Analysis of Stresses and Strains near the End of a Crack Traversing a Plate. Journal of Applied Mechanics, 1957,24: 361-364.

Irwin, G.R. , Crack-extension force for a part-through crack in a place. Journal of Applied Mechanics, 1962, pp. 651-654.

Porter M. , Thesis: Aspects of Structural Design with Glass. Trinity, Oxford, 2001.

Schneider, J., Schula, S., Weinhold, W.P. (2010) Characterisation of the scratch resistance of annealed and temperedarchitectural glass. Thin Solid Films - article in press, doi:10.1016/j.tsf.2011.04.104.

Schneider, J., Schula, S., Burmeister, A. (2011) Two mechanical design concepts for simulating the soft body impact atglazings Part 1: Numerical, transient Finite Element simulation and simplified concept with equivalent static loads. Stahlbau

Spezial 2011 Glasbau/Glass in Building 80 (1) pp. 81 87.Veer F.A., Rodichev Y.M. , The structural strength of glass: hidden damage. Strength of materials, May 2011, Vol. 43, nr. 3.

Weller B., Nicklisch F., Thieme S., Weimar T. , Glasbau-Praxis: Konstruktion und Bemessung. 2 Aufl. Berlin: Bauwerk, 2010.

Wiederhorn S.M., Bolz L.H. , Stress corrosion and static fatigue of glass. Journal of the American Ceramic Society, 1970,Vol. 53, p. 543 548.

Wrner, J.-D., Schneider, J., Fink, A. (2001) Glasbau: Grundlagen, Berechnung, Konstruktion. Springer, Berlin.


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ReferencesEN 1288-1 Glass in building - Determination of the bending strength of glass - Part 1: Fundamentals of testing glass

EN 1288-3 Glass in building - Determination of the bending strength of glass - Part 3: Test with specimen supported at twopoints (four point bending)

EN 1288-5 Glass in building - Determination of the bending strength of glass - Part 5: Coaxial double ring test on flat

specimens with small test surface areasEN 1990 Eurocode: Basis of structural design

EN 12600 Glass in building - Pendulum tests - Impact test method and classification for flat glass EN 12603 Glass in building Procedures for goodness of fit and confidence intervals for Weibull distributed glass strenghtdata

DIN 18008-1 Glass in Building - Design and construction rules - Part 1: Terms and general bases

DIN 18008-2 Glass in Building - Design and construction rules - Part 2: Linearly supported glazings

DIN 18008-3 Glass in Building - Design and construction rules - Part 3:Point fixed glazing

DIN 18008-4 Glass in Building - Design and construction rules - Part 4: Additional requirements for anti-drop deviceDIN 18008-5 Glass in Building - Design and construction rules - Part 5: Accessible glazing


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This lecture was prepared for the 1st Edition of SUSCOS(2012/14) by Prof. Sandra Jordo (UC).

Adaptations brought by Prof. Viorel Ungureanu (UPT) for2nd Edition of SUSCOS

2E5 Glass Structures L6 2014 VU

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