Materials

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Materials and Design 29 (2008) 943–951

& Design

The tempering of glass and the failure of tempered glass plateswith pin-loaded joints: Modelling and simulation

Q.D. To a,b,*, Q.-C. He a, M. Cossavella b, K. Morcant b, A. Panait b, J. Yvonnet a

a Universite de Marne-la-Vallee, Laboratoire de Mecanique, 5 Boulevard Descartes, F-77454 Marne-la-Vallee Cedex 2, Franceb Centre Scientifique et Technique du Batiment (CSTB), 84 Avenue Jean Jaures, 77447 Marne-la-Vallee Cedex 2, France

Received 4 December 2006; accepted 28 March 2007Available online 25 April 2007

Abstract

Tempering is a thermal process to strengthen glass by generating superficial compressive stresses. These residual stresses must bedetermined and accounted for in the design of tempered glass structures. The present work is concerned with tempered glass platesassembled by pin-loaded joints. In such a structure, a hole in a glass plate is reinforced by a steel ring glued to the glass plate by meansof a thin soft resin layer. To determine the residual stresses in a holed tempered glass plate, the tempering process of the latter is firstmodelled and numerically simulated. In addition, the residual stresses thus determined are then compared with those issued from thephotoelasticity measurement. Next, the mechanical behavior of the soft resin is also modelled and experimentally identified. Finally,the failure process of tempered glass plates with pin-loaded joints is analyzed numerically and experimentally, in which unilateral contact,friction, damage and residual stresses are involved. The numerical results obtained by the finite element method turn out to be in goodagreement with the experimental ones from real-size tests.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Heat treatments; Glass; Mechanical fastening

1. Introduction

Glass is a widely used material owing to its transpar-ency, aestheticism and durability. In terms of its mechani-cal properties and usage, glass can be classified into twotypes: float glass and tempered glass. Float glass is easyto produce and widely employed for the manufacture oflow load-bearing elements. Because of microdefects, floatglass is fragile and vulnerable to stress corrosion attacks[1,2]. The strength of a float glass sheet ranges from 14 to70 MPa while that of a glass fiber almost free frommicron-sized defects is of the order of 3–7 GPa [3]. Aneffective way to improve the strength of float glass is thethermal tempering which consists in cooling glass suddenly

0261-3069/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.matdes.2007.03.022

* Corresponding author. Address: Universite de Marne-la-Vallee, Lab-oratoire de Mecanique, 5 Boulevard Descartes, F-77454 Marne-la-ValleeCedex 2, France. Tel.: +33 (0) 160 957 781; fax: +33 (0) 160 957 799.

E-mail address: quy-dong.to@univ-mlv.fr (Q.D. To).

from a liquid state temperature down to the ambient tem-perature. The tempering process generates residual com-pressive stresses that strengthen the glass surface whosemicrodefects are mostly responsible for breakage. Glassthat has undergone thermal tempering is called temperedglass. Nowadays, tempered glass is strong and safe enough(see [4–6]) to be used as a structural material to manufac-ture high load-bearing elements such as beams, columns,floors or facades (see Fig. 1). However, the questionremains open on how to determine the strength of tem-pered glass and to qualify the reliability of structuresdesigned with tempered glass.

From the mechanical point of view, the design of tem-pered glass structures should be based on their reliabilityanalysis. This analysis is complex for two reasons. First,it necessitates determining the residual stresses of temperedglass due to the thermal tempering which is a quite compli-cated process. Second, strongly nonlinear phenomena, suchas unilateral contact, friction and damage, are involved in

Fig. 1. A roof system made of tempered glass.

944 Q.D. To et al. / Materials and Design 29 (2008) 943–951

the joint systems used to assemble the elements of temperedglass structures. The objective of the present work is tomodel and simulate the mechanical behavior of temperedglass structures with reinforced pin-loaded joints. This is acontinuation of our previous studies on glass structureswith friction-grip joints [7,8] and for pin-loaded joints[9,10] in which no account was taken of residual stress. Atypical reinforced pin-loaded joint (see Fig. 2) comprises afixed part and a moving part. The fixed part is formed ofan outer steel ring, a resin layer and a glass plate whichare glued together. The moving part is composed of aninner ring and a bolt. In particular, the inner ring helpsadjusting the erection axis, the outer ring serves as rein-forcement for the glass plate, and the resin acts as a gluematerial.

The present work makes a complete analysis of temperedglass plates with reinforced pin-loaded joints by performingmechanical modelling, numerical simulation and experi-mental test. More precisely, to determine the residual stres-ses in a holed tempered glass plate, the tempering process ofthe latter is first modelled and numerically simulated. Inaddition, the residual stresses thus determined are thencompared with those issued from the photoelasticity mea-surement. Next, the mechanical behavior of the soft resin

Fig. 2. Composition of

is modelled and experimentally identified. Finally, the fail-ure process of a tempered glass plate with two holes andpin-loaded joints is analyzed numerically and experimen-tally, in which unilateral contact, friction, damage andresidual stresses are involved. The numerical resultsobtained by the finite element method turn out to be in goodagreement with the experimental ones from real-size tests.

2. Glass tempering and residual stress

The tempering of glass is a thermal process consisting incooling very quickly glass at high temperature (around600 �C) by air jets. Owing to this process, residual compres-sive stresses are generated on the surface so as to preventearly failure caused by superficial defects. The temperingmodeling and simulations presented in this section aimto obtain the residual stress field of tempered soda-lime-sil-icate plates with holes.

To model and simulate glass tempering, we need notonly thermal tempering parameters data but also the vis-cous response of glass at different temperatures. The lattercan be measured in the laboratory while thermal temperingparameters are much more difficult to obtain directly asthey are related to several thermal phenomena like convec-tion, radiation, etc. In the present paper, for simplicity, aneffective convection coefficient is proposed and the finalresults are validated with photoelasticity measurements.

2.1. Thermo-mechanical behavior of glass at high

temperature

2.1.1. Viscoelasticity of glass at constant temperature

At normal temperature, glass behaves as an elastic solid.However, at high temperature, for example in a quenchingprocess, glass becomes viscoelastic and its behavior can bedescribed by the following linear viscoelastic relation.

sijðtÞ ¼Z t

0

G1ðt � sÞ deijðsÞds

ds;

�rðtÞ ¼Z t

0

G2ðt � sÞ d��ðsÞds

ds: ð1Þ

a pin-loaded joint.

Fig. 3. Behavior of a thermo-rheologically simple material at differenttemperatures.

Q.D. To et al. / Materials and Design 29 (2008) 943–951 945

Above, sij and eij are the deviatoric parts of the stress andstrain components rij and �ij, �r and �� are the spherical partsof rij and �ij, which are defined by

rij ¼ sij þ �rdij; �ij ¼ eij þ ��dij; �r ¼ 1

3rii; �� ¼ 1

3�ii: ð2Þ

In Eq. (1), G1(t) and G2(t) are two stress relaxation func-tions. For glass, G1(t) and G2(t) can be represented by theProny series:

G1ðtÞ ¼ 2G0W1ðtÞ; W1ðtÞ ¼Xn1

i¼1

w1ie�t=s1i ;Xn1

i¼1

w1i ¼ 1;

G2ðtÞ ¼ 3K1 þ 3ðK0 � K1ÞW2ðtÞ;

W2ðtÞ ¼Xn2

i¼1

w2ie�t=s2i ;Xn2

i¼1

w2i ¼ 1: ð3Þ

The coefficients involved in the Prony series for soda-lime-silicate glass at the reference temperature Tref = 864 K areprovided by [5] in Table 1. In our mechanical modellingand numerical simulations, we shall use these numericalvalues and the following elastic modulus values:

� E0 = 70 GPa, m0 = 0.22,� G0 = E0/[2(1 + m0)], K0 = E0/[3(1 � 2m0)].

2.1.2. Thermo-rheological simplicity of glass and shift

function

To describe the dependence of the viscoelastic behavioron the temperature, the thermo-rheologically simple mate-rial supposition principle is used. According to this princi-ple, the forms of the relaxation functions Gi(t,T = cst) atdifferent constant temperatures remain identical when plot-ted against ln t (see Fig. 3). More precisely, each functionGi(t,T = cst) can be represented via a function Fi as follows(see, e.g., [11])

Giðt; T ¼ cstÞ ¼ F iðln t � ln UðT ÞÞ; i ¼ 1; 2: ð4ÞAbove U(T) is a shift function that verifies U(Tref) = 1 andGi(t,Tref) = Fi(ln t).

There is a rich literature on the study of the shift func-tion U(T), most of which is obtained from the viscositymeasurement of materials like glasses, polymers near thetransition range (see [12] and the references cited therein).However, the available formulae are all empirical and theyare based on the authors’ measured data so that they aredifferent from each other. The most used and widely recog-nized functions are those of Arrhenius, Vogel–Fulcher–

Table 1Coefficients determining the relaxation functions G1(t) and G2(t)

i w1iG0 (GPa) s1i (s) w2i(K0 � K1) (GPa) s2i (s)

1 1.5845 6.658 · 10�5 0.7588 5.009 · 10�5

2 2.3539 1.197 · 10�3 0.7650 9.945 · 10�4

3 3.4857 1.514 · 10�2 0.9806 2.022 · 10�3

4 6.5582 1.672 · 10�1 7.301 1.925 · 10�2

5 8.2049 7.497 · 10�1 13.47 1.199 · 10�1

6 6.4980 3.292 10.896 2.033

Tamman (VFT) and their varieties like those ofTool–Narayanaswamy–Moynihan (TNM), Adam–Gibbs(AG) [12]. The recent works making use of these modelsinclude [5,13,14,16–18]. In the present work, we adopt theArrhenius equation:

UðT Þ ¼ exp D1

T� 1

T ref

� �� �: ð5Þ

According to [5], the value of the material parameter D isequal to 55000 K for the reference temperature Tref = 864 K.

When the temperature T is not constant but varies, theviscoelastic stress–strain relation becomes [11]

sijðtÞ ¼Z t

0

G1ðn� n0; T refÞdeijðsÞ

dsds;

�rðtÞ ¼Z t

0

G2ðn� n0; T refÞd

dsð��ðsÞ � �thðsÞÞds:

ð6Þ

In these two expressions, n(t) and n 0(s) are the so-called re-duced times defined by

nðtÞ ¼Z t

0

dt0

U½T ðt0Þ� ; n0ðsÞ ¼Z s

0

dt0

U½T ðt0Þ� ; ð7Þ

and �th is the thermal strain related to the volume relaxa-tion phenomenon presented below.

2.1.3. Phenomenological volume relaxation model

Consider a glass element which, equilibrated at tempera-ture T1, is cooled suddenly to T2. According to [12], thethermal expansion response comprises two parts (seeFig. 4): an immediate response �th(0) due to the atomic vibra-tion and a relaxation response �th(t) where the moleculesrearrange towards a new equilibrium state to which thestrain �th(1) is associated. This response can be expressedby using the volume relaxation function Mv(t) as follows

�thðtÞ � �thð1Þ�thð0Þ � �thð1Þ

¼ MvðtÞ; ð8Þ

where

�thð0Þ ¼ agðT 2 � T 1Þ; �thð1Þ ¼ alðT 2 � T 1Þ ð9Þwith al and ag being the linear dilatation coefficients in therespective liquid and solid states. In our simulations, we usethe numerical values of al and ag given by [5,6]: al =25 · 10�6 �C�1 and ag = 9 · 10�6 �C�1.

Fig. 4. Volume relaxation response to a temperature jump.

946 Q.D. To et al. / Materials and Design 29 (2008) 943–951

According to the assumption of Narayanaswamy (see[12,15]), Mv(t) is temperature dependent but verifies thethermo-rheological simplicity condition with the same shiftfunction U(T) as before. The volume relaxation functionMv(t) at the reference temperature Tref is also representedby a Prony series

Mvðt; T refÞ ¼Xn3

i¼1

w3ie�t=s3i ;Xn3

i¼1

w3i ¼ 1: ð10Þ

In the present paper, taking n3 = 6, six terms are used andthe parameters w3i and s3i are specified by Table 2.

For a continuously varying temperature T(t), the for-mula for the thermal strain is obtained by [12]

�thðtÞ ¼ alðT ðtÞ � T 0Þ � ðal � agÞZ t

0

Mvðn� n0; T refÞdTds

ds:

ð11Þ

2.1.4. Thermal properties of glass

In the above subsections, the mechanical behavior ofglass and its dependence on the temperature are formu-lated. However, to determine the temperature field in thetempering process, a heat transfer problem must be solvedin the first place.

Solving the heat transfer problem requires knowing thematerial thermal properties and specifying the thermalboundary conditions relative to convection and radiation.The thermal properties of soda-lime-silicate glass are tem-perature-dependent. Its thermal conductivity k [W/m �C]is modeled by

k ¼ 0:975þ 8:58� 10�4T ð12Þ

Table 2Coefficients determining the volume relaxation function Mv(t)

i w3i s3i (s)

1 5.523 · 10�2 5.965 · 10�4

2 8.205 · 10�2 1.077 · 10�2

3 1.215 · 10�1 1.362 · 10�1

4 2.286 · 10�1 1.5055 2.860 · 10�1 6.7476 2.265 · 10�1 29.63

while its specific heat Cp [J/kg �C] is described by

Cp ¼ 1:433þ 6:5� 10�3ðT þ 273Þ if T > 577 �C;

Cp ¼ 893þ 0:4ðT þ 273Þ � 1:8� 10�7ðT þ 273Þ2

if T 6 577 �C: ð13ÞThe thermal boundary conditions are discussed below.

2.2. Thermal tempering simulation and photoelasticity

measurement

2.2.1. Thermal tempering simulation

In this subsection, the thermomechanical behavior of adoubly holed glass plate during the tempering is analyzed.This analysis contains two parts. First, a purely thermalcomputation is carried out to find the temperature fieldT(x, t). Then, the temperature T(x, t) is incorporated intothe thermo-viscoelastic analysis to calculate the residualstresses. The analysis is realized with the help of MSCMARC [19], a powerful Finite Element Method code.

The temperature field at the beginning of the analysis istaken to be uniform T(x, 0) = T0 = 620 �C and the temper-ature of cooling air is 20 �C. Three equivalent convectivecoefficients h1 = 135 W/m2 K, h2 = 115 W/m2 K, h3 =90 W/m2 K are used respectively for the main, edge andhole surfaces of the plate. The analysis stops when the tem-perature field over the plate is almost uniform and equal to20 �C.

As the plate is symmetrical with respect to three orthog-onal planes and subjected to symmetrical boundary condi-tions, the model to be analyzed can be reduced to one-eighth of the plate as in Fig. 5. The mesh of the reducedmodel is presented in Fig. 6 with the final residual hoopstress field. The plotted coordinate system is a cylindricalone whose origin O is placed at the center of the hole. Inparticular, the residual hoop stress distributions along thethickness at positions (1a–1b), (2a–2b) and (3a–3b) specifiedin Fig. 6 are presented in Fig. 7. Positions (1a–1b), (2a–2b)and (3a–3b) correspond to the middle of the plate, the edgeof the plate and at the edge of the hole, respectively.

2.2.2. Photoelasticity measurement

The photoelasticity apparatus used is an epibiascope(see Fig. 8) that allows for measuring the residual stressat any superficial point not too close to the border of theplate. The measurement indicates that the superficial resid-ual stress at point 1a is 122 MPa which is in good agree-ment with the value of 120 MPa obtained by ournumerical simulations presented above.

3. Failure analysis of a tempered glass structure with pin-

loaded joints

3.1. Elastic analysis of tempered glass accounting forresidual stress

The residual stresses rresij in tempered glass due to the

tempering process have been calculated in the above sec-

Fig. 5. Thermal boundary conditions for one-eighth of the double holed plate.

Fig. 6. Mesh of one-eighth of the holed plate and distribution of the residual hoop stresses rreshh .

Residual stress (MPa)

-130

-110

-90

-70

-50

-30

-10

10

30

50

70

0 1 2 3 4 5 6 7 8 9 10

Vertical coordinate z (mm)

Hole edgeEdgeMiddle

Fig. 7. Residual hoop stresses rreshh along the thickness at the middle of the

plate (1a–1b), at the edges (2a–2b) and at the edges of holes (3a–3b). Fig. 8. Epibiascope used to measure superficial residual stresses.

Q.D. To et al. / Materials and Design 29 (2008) 943–951 947

tion. Letting Dg denote the tempered glass domain, theresidual stress field rres

ij over Dg is self-equilibrated, so that

orresij

oxj¼ 0 in Dg; rres

ij nj ¼ 0 on oDg; ð14Þ

where nj is the outward normal vector on the surface oDg ofDg.

Next, when the tempered glass plate is assembled withother structural components (resin layer, steel ring, etc.)and subjected to external loads, the resulting total stressfield rij must satisfy the conditions including the equilib-rium equations and boundary conditions

orij

oxj¼ fi in Dg; rijnj ¼ T i on oDg ð15Þ

and the Hooke law

rij � rresij ¼ k�ext

kk dij þ 2l�extij in Dg ð16Þ

when the glass plate remains elastic. Above, fi is the volumeforce, Ti is the traction vector on the glass plate boundaryoDg, k and l are the Lame constants for glass, and �ext

ij is thestrain tensor caused by the applied external loads. Becausethe residual stress field is self-equilibrated as expressed byEq. (14), we can write

948 Q.D. To et al. / Materials and Design 29 (2008) 943–951

orij

oxj¼

oðrij � rresij Þ

oxjin Dg;

rijnj ¼ ðrij � rresij Þnj on oDg:

ð17Þ

Posing rextij ¼ rij � rres

ij , it follows from Eqs. (15)–(17) that

orextij

oxj¼ fi in Dg; rext

ij nj ¼ T i on oDg;

rextij ¼ k�ext

kk dij þ 2l�extij in Dg:

ð18Þ

The foregoing analysis shows that, whenever the glassplate is elastic, the total stress field rij in it can be calculatedin two steps: (i) determine rext

ij as the stress field producedonly by the applied external loads; (ii) compute rij bysuperposing rext

ij to the pre-existing residual stress fieldrres

ij obtained in the last section.

3.2. Tensile strength of tempered glass

The strength of float glass rfg depends on the load dura-tion due to the stress corrosion crack phenomena [1,2], thesize of the element and the surface finish quality. In thetests performed in [5,6], the average value of rfg rangesfrom 31 MPa to 56 MPa.

The failure of tempered glass is governed by the totalmaximal tensile stress rmax. According to the analysis ofthe last paragraph, we know that rmax is the maximal prin-cipal stress component associated to the total stress field rij

obtained by superposing the stress field rextij due to the

external loads to the residual stress field rresij due to the tem-

pering process. Then, the failure criterion of tempered glassis simply given by

rmax 6 rfg: ð19ÞIn the particular case where rext

ij and rresij are both uniaxial

along the same direction, the criterion (19) amounts to say-ing that the failure of tempered glass takes place when themaximal tensile stress rext

max due to the external loads reachesthe tensile strength rf of tempered glass which is equal tothe superposition of the residual compressive stresses rres

to the strength rfg of float glass. In this case, (19) reduces to

rextmax 6 rf ¼ rfg � rres: ð20Þ

The tensile hoop strength at the hole edge (3a–3b) is of spe-cial interest because there is a stress concentration whenloading. In Fig. 7, the residual compressive stress at thepoint 3b (middle of the edge) is the smallest, so it has thelowest tensile strength. The tensile strength rf at the pointranges from rfhhmin = 31 + 85 = 116 MPa to rfhhmax =56 + 85 = 141 MPa. In the paper, a reference tensilestrength 128 MPa for that point is adopted.

3.3. Resin and its mechanical behavior

The resin used in bolted connections is a cured mixtureof an Epoxy resin and a hardener, which often containsvoids. Its mechanical behavior is similar to hardened

cement paste: elastic-brittle in traction and elastoplasticin compression because of microcracking.

The uniaxial response of the material is determined bythe tests reported in [10], which can be summarized asfollows

(i) the resin remains elastic if ry < r < rcr;(ii) when ry is reached and �y > � > �c, the resin has a

hardening behavior;(iii) when r = rcr or � = �c, the failure occurs.

Above, ry and rcr are the initial yielding stress andtensile strength; �y and �c are the corresponding initialyielding and crushing strains.

A multi-axial model is constructed by combining the Ran-kine criterion and the Drucker–Prager criterion with abilinear hardening law (Fig. 9). According to [20], the latterreads:

f ¼ aI1 þffiffiffiffiffiJ 2

p� jryjð1�

ffiffiffi3p

aÞffiffiffi3p 6 0; a ¼ sin /ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3ð3þ sin2 /Þq ;

ð21Þ

where I1 and J2 are the first and second principal stressinvariants defined by

I1 ¼ r1 þ r2 þ r3;

J 2 ¼1

6ðr1 � r2Þ2 þ ðr2 � r3Þ2 þ ðr3 � r1Þ2h i

; ð22Þ

and / is the angle of friction.According to our experimental results, the material

parameter values for the resin are

� elastic properties: E = 2500 MPa, m = 0.22;� tensile strength: rcr = 11 MPa;� initial compressive yield stress and strain:

ry = �50 MPa, ey = �0.02;� maximum compressive yield stress and corresponding

strain: rmax = �65 MPa, e = �0.03;� crushing strain and corresponding stress: �c = �0.045,

r = �58 MPa.� friction angle and pressure-sensitivity index: / = 20�,

a = 0.11.

3.4. Failure analysis of a tempered glass structure

In the present paper, a structure composed of a 19 mmthick glass plate with two reinforced pin-loaded joints isconsidered (see Fig. 10). Two opposite increasing displace-ments are applied on the two bolts until the structure fails.The structure is first studied by two models which are dif-ferent in the type of interface used. The results obtainedwith these two models are then compared with the experi-mental results on the same structure. The two models areimplemented by using the finite element code MSCMARC.

Fig. 9. Uniaxial behavior and biaxial tensile failure – compressive yield surface.

Fig. 10. A tempered glass plate with two pin-loaded joints, model and test devices.

Fig. 11. Finite element mesh of the reduced model (view near the joint).

Q.D. To et al. / Materials and Design 29 (2008) 943–951 949

All the structural components, i.e. glass plate, bolts,resin, inner and outer rings, are meshed by 3D isoparamet-ric solid elements with 8 nodes. Owing to the fact that theproblem is symmetrical with respect to 3 orthogonalplanes, each model is further reduced to one-eighth withappropriate boundary conditions (see Fig. 11). The exter-nal load is an increasing displacement applied on the headsurface of each of the two bolt at a small constant rate.

The mechanical properties of the materials involved inthe analysis and other than the resin are provided asfollows:

� bolt (stainless steel): E = 200000 MPa, m = 0.3;� inner ring (copper): E = 70000 MPa, m = 0.22;

Fig. 12. Resin failure followed by failure in tempered glass.

Fig. 13. Cracked zone in the resin and stress concentration in glass.

Maximal stress in the glass

0

20

40

60

80

100

120

0 20 40 60 80

Applied force [kN]

Str

ess

[Mp

a]

interfacew/o interface

Fig. 14. Numerically determined relation between the applied force andthe maximal stress in the glass by the two models.

950 Q.D. To et al. / Materials and Design 29 (2008) 943–951

� outer ring (stainless steel): E = 200000 MPa, m = 0.3;� frictional coefficient between stainless steel and polished

copper in normal environment: l = 0.2.

In terms of interface, we considered two models

(i) Model 1: the interface is perfect.(ii) Model 2: the interface is imperfect. The material near

the interface is modeled by a finite thickness layerwith a tensile strength lower than the resin. Here itstensile strength is taken to be rcr = 9 MPa.

The failure mechanisms of the structure evidenced by theforegoing two models are little different and in good agree-ment with those from the experimental test. More precisely,it can described as follows (see Figs. 12 and 13):

� The first crack is initiated in the resin near the interfacein the first model and inside the interface layer in thesecond model at lower load level.� After the first crack, the cracked zone then develops

quickly inside the resin and along the interface, tendingto separate the left part from the ring. The right partremains glued to the ring but highly compressed andexhibits irreversible plastic strain.� The glass becomes heavily stressed and fails when the

maximal total stress attains the tensile strength rf atthe middle point 3b of the hole edge. It is noted that

the residual stress state and the stress state at point 3bis almost uniaxial and their principal direction almostcoincides with the hoop direction so that the criterion(20) can be applied. According to numerical results,given the reference strength rf = 128 MPa, the globalfailure load is equal to 72 kN in the first model and to76 kN in the second model, see Fig. 14. These valuesare quite close to the global failure load 65 kN providedby the experimental test.

Maximal stress in the glass

mu=0.0mu=0.2mu=0.4

0

20

40

60

80

100

120

0 20 40 60 80

Applied force [kN]

Str

ess

[Mp

a]

Fig. 15. Influence of the friction coefficient.

Q.D. To et al. / Materials and Design 29 (2008) 943–951 951

3.5. Influence of the frictional coefficient

To study the influence of the friction coefficient betweenthe stainless steel and copper on the failure load, a varia-tion in the coefficient from 0 to 0.4 is considered. Fig. 15illustrates the inconsiderable dependence of the failure loadon the coefficient. This can be explained by the fact that thefailure takes place far from the contact zone.

4. Conclusions

In this paper, the failure process of tempered glass struc-tures with pin-loaded joints has been systematically studiedby a coupled experimental–numerical method. Firstly, thetempering process is simulated numerically and validatedby photoelasticity measures. As a result, the residual stressas well as tensile strength field can be both precisely deter-mined. Secondly, the mechanical characteristics of the resinused in the joint are experimentally identified, and a dam-age model is proposed for it. Thirdly, a numerical proce-dure is elaborated to analyze the mechanical behavior oftempered glass structures with pin-loaded joints up to fail-ure. Finally, a real-size structure is experimentally testedand numerically simulated. The experimental and numeri-cal results obtained for this structure are compared. Ourpresent study completes our previous ones [7–10], so thata complete and efficient approach is now available bothfor the design and optimization of glass structures withfriction-grip joints or pin-loaded joints.

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