Experimental Investigation of High Strain-Rate Behaviour of Glass
7
Experimental investigation of high strain-rate behaviour of glass Marco Peroni 1, a , George Solomos 1,b , Valerio Pizzinato 1,c , Martin Larcher 2,d 1 EC Joint Research Centre, IPSC, European Laboratory for Structural Assessment ELSA, Via E. Fermi 2749, 21027 Ispra (VA) Italy 2 Institut für Mechanik und Statik, Universität der Bundeswehr München, 85577 Neubiberg, Germany a [email protected], b [email protected], c [email protected], d [email protected] Keywords: Split Hopkinson Pressure Bar, dynamic glass behaviour, laminated glass, strain-rate Abstract. The purpose of this work is to assess the dynamic mechanical behaviour of a commercial glass similar to that of the laminated glass structures used for protection and security applications in buildings. In particular, the study has been focussed on the influence of the strain-rate on the compressive (standard compression test) and tensile (splitting tensile test) strength of this glass. Tests at different strain-rates have been performed in the range between 10 -3 to 10 3 s -1 using standard test equipment for quasi-static tests and a SHPB equipped with a high-speed camera for the dynamic ones. Test data for compression tend to show that there is no substantial sensitivity to the strain-rate concerning ultimate strength and Young modulus. An appreciable increase in the ultimate tensile strength is revealed at higher strain-rate. Introduction Laminated glass panels are widely used for protection and security applications in buildings. Their dynamic behaviour, e.g. to blast loading, is influenced by the mechanical properties of the two materials normally used to build their sandwich structure: the external glass panes and the polymeric layer (usually PVB Polyvinylbutyral), which binds them together [1, 2]. The technical literature contains plenty of information about the dynamic mechanical properties of many structural materials, especially metals, obtained through different test types (such as Split Hopkinson Pressure Bar techniques, Taylor tests, flyer plate tests, etc.). However, the study of the dynamic mechanical properties of polymers and glassy materials is not as common. In addition, especially for glassy materials, many problems occur during dynamic testing due mainly to their brittle behaviour. For example in these situations it is very difficult for the specimen to reach dynamic equilibrium before crack propagation and failure, and frequently particular elaboration techniques for the experimental data must be developed in order to produce meaningful results. The purpose of this work is to assess the dynamic mechanical behaviour of a commercial glass similar to that used in laminated glass structures. In particular, the study has been focussed on the influence of the strain-rate on the compressive/tensile strength of this glass. Cylindrical specimens have been used both for compression (diameter 5 mm and height 6 mm) and splitting tensile tests (diameter 9 mm and height 5 mm). With reference to the splitting tensile test (Brazilian test) the effect of “bearing strips” has also been evaluated in order to better distribute compression loading and to avoid the propagation of initial cracks. Tests at different strain-rates have been performed in the range between 10 -3 to 10 3 s -1 using standard test equipment for quasi-static tests and a SHPB for the dynamic ones. Strain-rate reported refers to that at maximum stress. For what concerns high strain-rate tests, wave dispersion phenomena and the effect of local punching at the bar/specimen interface have been taken into account in order to improve the accuracy. Further, the deformation and cracking processes of the specimen have been monitored using a high-speed digital camera, which proves to be crucial in aiding in the interpretation of the data. Applied Mechanics and Materials Vol. 82 (2011) pp 63-68 Online available since 2011/Jul/27 at www.scientific.net © (2011) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.82.63 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 137.193.23.208-16/08/11,10:26:53)
Transcript of Experimental Investigation of High Strain-Rate Behaviour of Glass
Experimental investigation of high strain-rate behaviour of glass
Marco Peroni1 a George Solomos1b Valerio Pizzinato1c Martin Larcher2d 1EC Joint Research Centre IPSC European Laboratory for Structural Assessment ELSA
Via E Fermi 2749 21027 Ispra (VA) Italy
2Institut fuumlr Mechanik und Statik Universitaumlt der Bundeswehr Muumlnchen 85577 Neubiberg
Germany
amarcoperonijrceceuropaeu
bgeorgesolomosjrceceuropaeu
cerminiopizzinatojrceceuropaeu
dmartinlarcherunibwde
Keywords Split Hopkinson Pressure Bar dynamic glass behaviour laminated glass strain-rate
Abstract The purpose of this work is to assess the dynamic mechanical behaviour of a commercial
glass similar to that of the laminated glass structures used for protection and security applications in
buildings In particular the study has been focussed on the influence of the strain-rate on the
compressive (standard compression test) and tensile (splitting tensile test) strength of this glass
Tests at different strain-rates have been performed in the range between 10-3
to 103 s
-1 using
standard test equipment for quasi-static tests and a SHPB equipped with a high-speed camera for the
dynamic ones Test data for compression tend to show that there is no substantial sensitivity to the
strain-rate concerning ultimate strength and Young modulus An appreciable increase in the ultimate
tensile strength is revealed at higher strain-rate
Introduction
Laminated glass panels are widely used for protection and security applications in buildings
Their dynamic behaviour eg to blast loading is influenced by the mechanical properties of the two
materials normally used to build their sandwich structure the external glass panes and the polymeric
layer (usually PVB Polyvinylbutyral) which binds them together [1 2] The technical literature
contains plenty of information about the dynamic mechanical properties of many structural
materials especially metals obtained through different test types (such as Split Hopkinson Pressure
Bar techniques Taylor tests flyer plate tests etc) However the study of the dynamic mechanical
properties of polymers and glassy materials is not as common In addition especially for glassy
materials many problems occur during dynamic testing due mainly to their brittle behaviour For
example in these situations it is very difficult for the specimen to reach dynamic equilibrium before
crack propagation and failure and frequently particular elaboration techniques for the experimental
data must be developed in order to produce meaningful results
The purpose of this work is to assess the dynamic mechanical behaviour of a commercial glass
similar to that used in laminated glass structures In particular the study has been focussed on the
influence of the strain-rate on the compressivetensile strength of this glass Cylindrical specimens
have been used both for compression (diameter 5 mm and height 6 mm) and splitting tensile tests
(diameter 9 mm and height 5 mm) With reference to the splitting tensile test (Brazilian test) the
effect of ldquobearing stripsrdquo has also been evaluated in order to better distribute compression loading
and to avoid the propagation of initial cracks Tests at different strain-rates have been performed in
the range between 10-3
to 103 s
-1 using standard test equipment for quasi-static tests and a SHPB for
the dynamic ones Strain-rate reported refers to that at maximum stress For what concerns high
strain-rate tests wave dispersion phenomena and the effect of local punching at the barspecimen
interface have been taken into account in order to improve the accuracy Further the deformation
and cracking processes of the specimen have been monitored using a high-speed digital camera
which proves to be crucial in aiding in the interpretation of the data
Applied Mechanics and Materials Vol 82 (2011) pp 63-68Online available since 2011Jul27 at wwwscientificnetcopy (2011) Trans Tech Publications Switzerlanddoi104028wwwscientificnetAMM8263
All rights reserved No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTPwwwttpnet (ID 13719323208-160811102653)
Test equipment
Compression tests and splitting tensile tests on glass specimens have been performed with two
different apparatuses Static compression and splitting tensile tests have been performed on the
electro-mechanical universal testing machine Zwick Z100 (maximum force 100 kN and maximum
velocity 300 mmmin) at the Safety and Reliability Laboratory of the Politecnico di Torino High
strain-rate compression and splitting tensile tests have been carried out on a SHPB at the HopLab of
the JRCIspra where maraging steel rods of 10 mm diameter are used With reference to Fig 1a
this equipment generates a compressive pulse by loading in tension a portion of the input bar (1 m)
and rapidly releasing the left end with a fragile that breaks at an established load [3] The
compressive generated pulse travels through the pre-stressed and input bars and loads the specimen
like a conventional SHPB as shown in the Lagrangian waves diagram of the test (Fig 1b) With
this setup long duration compressive pulses can be easily created without the problems related to
projectilerod misalignment inherent in the conventional SHPB
t
x Pre-stressed bar Input bar Output bar
Strain transducers
Reflected wave Transmitted wave
Incident wave
(
(Fragile bolt
Hydraulic actuator
Fig 1 Pre-stressed SHPB setup with Lagrangian waves propagation diagram
The loaddisplacement curves of the specimen can be obtained with standard SHPB procedures
with the only difference that due the longer duration of the incident pulse normally incident and
reflected waves are not separated For this reason it is necessary to separate ascending and
descending waves with an appropriate algorithm [4] Because of the brittle behaviour of the material
tested it is essential to compensate for distortions due to dispersion phenomena [5] and to account
for the effect of local punching at the barspecimen interface [6] in order to improve accuracy To
better evaluate the specimen loading conditions also during the dynamic tests a high speed camera
synchronised with the SHPB acquisition system has been used Reduction of specimen overheating
is achieved by utilizing ldquocoldrdquo LED lights for the illumination
Fig 2 Glass specimens adopted
All experiments have been carried out on high purity optical glass specimens obtained by
grinding The glass with the trade name Optiwhite has a low iron content and in its specifications
includes the following mechanical characteristics density 2500 kgm3 Young Modulus 73 GPa
Poisson ratio 023 compression strength 700-900 MPa and bending (tensile) strength 30 MPa
Cylindrical specimens have been employed for both compression and splitting tensile tests In
64 Performance Protection and Strengthening of Structures under ExtremeLoading
particular their dimensions were for compression tests of 5 mm diameter and 6 mm length and for
splitting tensile tests of 9 mm diameter and 5 or 10 mm length (Figure 2) To obtain reliable
experimental data about 5 repetitions for each type of tests have been performed
Compression tests
Compression tests on glass specimens have been carried out at two strain-rates of about 510-4
s-1
(SC=static compression) and about 1103s
-1 (DC=dynamic compression) Due to the small specimen
sizes it has not been possible to precisely characterize the glass longitudinal elastic modulus using
strain-gages however as shown below reliable estimates of the global mechanical behaviour of the
material have been reached For the static tests deformation has been obtained through cross-head
displacement measurements which have been corrected from the errors introduced by the machine
compliance using a calibrated test In the high strain-rate tests dynamic equilibrium has been
carefully checked and as mentioned before state-of-the-art compensations have been applied to
acquire signals and to improve their accuracy Fig 3a summarizes all compression tests at both
strain-rates and includes also additional dynamic compression test curves where specimens did not
break These latter allow to evaluate the longitudinal elastic modulus with good accuracy by using
both the loading and unloading test phases (DCNF= dynamic compression no fracture)
0 002 0040
500
1000
1500
Stress (MPa)
SC
0 002 0040
500
1000
1500
Strain
DC
0 002 0040
500
1000
1500
DCNF
10-4
10-2
100
102
104
0
500
1000
1500
Strainrate (1s)
Stress (MPa)
SC
DC
DCNF
Fig 3 a) Compression stress-strain curves b) Maximum stress vs strain-rate in compression tests
As easily noted glass maintains a brittle-pure elastic behaviour at both strain-rates and the elastic
longitudinal modulus seems not to be appreciably influenced by the test speed Compression
maximum stresses show also small strain-rate sensitivity (Fig 3b) Table 1 summarizes the
experimental results in terms of maximum stress and longitudinal elastic modulus
Table 1 Experimental compression data
1 2 3 4 5 mean
Standard
deviation
SC
Strain-rate (s-1) 510
-4 510
-4 510
-4 510
-4 510
-4 510
-4 310
-5
Max stress (MPa) 1144 978 1087 1160 1070 1087 72
Young modulus (GPa) 61 58 72 66 79 67 8
DC
Strain-rate (s-1) 1342 947 1055 923 1282 1109 192
Max stress (MPa) 1326 1126 1251 1081 1109 1179 105
Young modulus (GPa) 63 69 51 50 54 58 8
When analysing experimental data both the static and the dynamic standard deviation of the
maximum stress and longitudinal elastic modulus are calculated and found to be quite small
considering the rather large scattering of data usually encountered in brittle materials In addition
since the maximum stress increase under high strain-rate testing is comparable to the standard
Applied Mechanics and Materials Vol 82 65
deviation it can be stated that the analysed glass does not present noticeable strain-rate sensitivity
To conclude the analysis of compression tests it is interesting to observe the image sequence of a
dynamic experiment recorded with the high-speed camera (50000 fps) The specimen was elastically
loaded (for the small size of the specimen the dynamic equilibrium is verified) and some radial
cracks appear in the third image
Fig 4 High speed sequence of compression test (50000 fps)
At this point the specimen loaded in compression collapses and a tensile wave starts to propagate
in the glass Due to the extremely low tensile strength of glass (compared to its compression one)
the whole specimen blows up becoming a fine glass dust as shown in the last picture At this point
the glass is no more able to transmit any compressive load and the transmitted signal vanishes
Splitting tensile test (Brazilian test)
Splitting tensile test or Brazilian test is nowadays a conventional mechanical test for the
investigation of the tensile strength of brittle materials This test is standardized only for concrete
specimens [5] but it is also adopted for other brittle materials such as rocks ceramics or glass [6]
The setup of splitting tensile test is rather simple a cylindrical specimen is loaded in compression
along two opposite generatrices as shown in Fig 5a This compression load generates a particular
stress-strain field with two peaks of compression at the cylinder surface and an interior zone of
almost constant tension (Fig 5a) For the higher compression strength of brittle material the
specimen breaks under tension and the maximum tensile stress can be easily deduced with the well
known analytical expression
Db
P
sdotsdot
sdot=π
σ2
(1)
where σ is the tensile strength P the maximum compression force during the test and b and D are
the specimen height and diameter respectively
compression
tension
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Stress (MPa)
S5
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Displacement (mm)
S5P
Fig 5 a) Brazilian test setup and typical stressstrain field b) static experimental data
For the reduction of local compression peaks small pieces of compliant materials (bearing strips
usually made of plywood for concrete specimens) are used to better distribute compression loading
and to avoid the propagation of initial cracks For the current tests the effectiveness of bearing strips
66 Performance Protection and Strengthening of Structures under ExtremeLoading
to loading the specimens has been evaluated in a preliminary phase For this reason two series of
tests have been performed splitting tests on specimen without (S5) and with paper bearing strips
(S5P)
Table 2 Experimental splitting tensile data
1 2 3 4 5 mean Standard
deviation
S5 Velocity (mms) 0009 0009 0009 0009 0009 0009 1410
-4
Max stress (MPa) 756 546 382 523 861 614 192
S5P
Velocity (mms) 0010 0010 0010 0009 0009 0010 7710-4
Max stress (MPa) 667 473 505 509 574 545 77
D5 Velocity (ms) 550 483 698 599 528 572 064
Max stress (MPa) 998 773 348 475 621 643 254
D5P
Velocity (ms) 767 673 84 742 81 772 067
Max stress (MPa) 871 917 7614 981 947 895 851
As presented in Fig 5b and in Table 2 the series without bearing strips shows a higher scatter of
data results probably due to the effect of damage induced by compression loading plates Using the
paper bearing strips the standard deviation is three times smaller and allows to evaluate more
effectively the mechanical properties of the glass tested
Dynamic tests have been performed directly by loading the specimen with the SHPB bars as in a
standard compression test In this kind of tests specimen-bar alignment is essential to correctly
transfer the compression pulse from the bars to the specimen Also in this case two series of
experiments have been carried out with and without bearing strips (made of papers)
0 01 02 03 040
20
40
60
80
100
120
Stress (MPa)
D5
0 01 02 03 040
20
40
60
80
100
120
Displacement (mm)
D5P
10-6
10-4
10-2
100
102
0
20
40
60
80
100
120
Test speed (ms)
Stress (MPa)
S5
S5P
D5
D5P
Fig 6 a) Dynamic tensile data b) maximum stress vs strain-rate in splitting tensile tests
Preliminary tests have been conducted to ensure dynamic equilibrium and this condition has
been verified for all specimens Fig 6a summarizes the data results obtained by the dynamic
splitting tensile tests Also in dynamic tests data obtained without the bearing strips present high
scattering and this fact prevents the correct evaluation of the glass tensile strength (standard
deviation of D5 is three times greater than standard deviation of D5P) Contrary to the compression
data the tensile strength seems to be substantially influenced by strain-rate with an increase of about
30 MPa when the strain-rate grows by six magnitude orders This phenomenon has also been
noticed in the high strain-rate behaviour of concrete where the tensile strength is more strain-rate
influenced than the compressive strength
Applied Mechanics and Materials Vol 82 67
Fig 7 presents a sequence of images of a dynamic splitting test without bearing strips recorded at
50000 fps It is interesting to observe the initial cracks due to compression loading (picture two) and
the tensile damage zone next to the barloading axis (picture three to five) This sequence confirms
that the specimenrsquos failure is due to tensile stresses generated along the diameter of the loading axis
as depicted in Fig5a
Fig 7 High speed sequence of splitting tensile test (50000 fps)
Further numerical and experimental investigations would be required to verify the actual stress-
strain field in the specimen during static and dynamic tests and to evaluate the accuracy of Eq 1
Summary
A study of the strain-rate influence on the compressive and tensile behaviour of commercial glass
has been conducted The experimental results try to cover the gap in literature concerning
mechanical behaviour of glassy materials at medium-high strain-rate To obtain reliable data state-
of-the-art compensations for SHPB tests have been adopted and concerning splitting tensile test
different testing setups have been evaluated Compression test results indicate that this glass does
not present any substantial sensitivity to the strain-rate concerning ultimate strength and Young
modulus With reference to tensile data glass tensile mechanical behaviour seems to be influenced
by strain rate and tensile strength increases by about 30 MPa when the strain-rate grows by six
magnitude orders Further numerical and experimental investigations will be suitable to verify the
accuracy of tensile properties deduced by splitting tensile tests on brittle materials like glass
especially under dynamic loading conditions Further it will be interesting to evaluate sizescale
effects also in dynamic tests using the high loading capability of the SHPB or simply to achieve
more representative specimen volumes
References
[1] HS Norville EJ Conrath Journal of Architectural Engineering Vol 7 (2001) p 80
[2] M Larcher N Gebbeken M Teich G Solomos Simulation of laminated glass loaded by air
blast waves Proc4th
ISAAG Munich (2010)
[3] E Cadoni G Solomos C Albertini Mag Concrete Res Vol 60 (2008) p221
[4] H Zhao G Gary J Mech Phys Solids Vol 45 (1997) p 1185
[5] A Tyas AJ Watson Int J Impact Eng Vol 25 (2001) p 87
[6] G Gary K Safa Accounting for the effect of local punching at the barspecimen interface in
SHPB experiments Proc DYMAT 2009 Bruxelles (2009)
[7] ASTM C496-96 Standard test method for splitting tensile strength of cylindrical concrete
specimens ASTM standard
[8] CS Chen E Pan B Amadei Int J Rock Mech Sci Vol 35 (1998) p 43
[9] C Rocco GV Guinea J Planas M Elices Cement Concrete Res Vol 31 (2001) p73
[10] C Johnstone C Ruiz Int J Solids Structures Vol 32 (1995) p2647
[11] T Holmquist G Johnson D Grady C Lopatin E Hertel High strain rate properties and
constitutive modelling of glass Proc 15th
International Symposium on Ballistics Israel (1995)
68 Performance Protection and Strengthening of Structures under ExtremeLoading
Performance Protection and Strengthening of Structures under Extreme Loading doi104028wwwscientificnetAMM82 Experimental Investigation of High Strain-Rate Behaviour of Glass doi104028wwwscientificnetAMM8263
Test equipment
Compression tests and splitting tensile tests on glass specimens have been performed with two
different apparatuses Static compression and splitting tensile tests have been performed on the
electro-mechanical universal testing machine Zwick Z100 (maximum force 100 kN and maximum
velocity 300 mmmin) at the Safety and Reliability Laboratory of the Politecnico di Torino High
strain-rate compression and splitting tensile tests have been carried out on a SHPB at the HopLab of
the JRCIspra where maraging steel rods of 10 mm diameter are used With reference to Fig 1a
this equipment generates a compressive pulse by loading in tension a portion of the input bar (1 m)
and rapidly releasing the left end with a fragile that breaks at an established load [3] The
compressive generated pulse travels through the pre-stressed and input bars and loads the specimen
like a conventional SHPB as shown in the Lagrangian waves diagram of the test (Fig 1b) With
this setup long duration compressive pulses can be easily created without the problems related to
projectilerod misalignment inherent in the conventional SHPB
t
x Pre-stressed bar Input bar Output bar
Strain transducers
Reflected wave Transmitted wave
Incident wave
(
(Fragile bolt
Hydraulic actuator
Fig 1 Pre-stressed SHPB setup with Lagrangian waves propagation diagram
The loaddisplacement curves of the specimen can be obtained with standard SHPB procedures
with the only difference that due the longer duration of the incident pulse normally incident and
reflected waves are not separated For this reason it is necessary to separate ascending and
descending waves with an appropriate algorithm [4] Because of the brittle behaviour of the material
tested it is essential to compensate for distortions due to dispersion phenomena [5] and to account
for the effect of local punching at the barspecimen interface [6] in order to improve accuracy To
better evaluate the specimen loading conditions also during the dynamic tests a high speed camera
synchronised with the SHPB acquisition system has been used Reduction of specimen overheating
is achieved by utilizing ldquocoldrdquo LED lights for the illumination
Fig 2 Glass specimens adopted
All experiments have been carried out on high purity optical glass specimens obtained by
grinding The glass with the trade name Optiwhite has a low iron content and in its specifications
includes the following mechanical characteristics density 2500 kgm3 Young Modulus 73 GPa
Poisson ratio 023 compression strength 700-900 MPa and bending (tensile) strength 30 MPa
Cylindrical specimens have been employed for both compression and splitting tensile tests In
64 Performance Protection and Strengthening of Structures under ExtremeLoading
particular their dimensions were for compression tests of 5 mm diameter and 6 mm length and for
splitting tensile tests of 9 mm diameter and 5 or 10 mm length (Figure 2) To obtain reliable
experimental data about 5 repetitions for each type of tests have been performed
Compression tests
Compression tests on glass specimens have been carried out at two strain-rates of about 510-4
s-1
(SC=static compression) and about 1103s
-1 (DC=dynamic compression) Due to the small specimen
sizes it has not been possible to precisely characterize the glass longitudinal elastic modulus using
strain-gages however as shown below reliable estimates of the global mechanical behaviour of the
material have been reached For the static tests deformation has been obtained through cross-head
displacement measurements which have been corrected from the errors introduced by the machine
compliance using a calibrated test In the high strain-rate tests dynamic equilibrium has been
carefully checked and as mentioned before state-of-the-art compensations have been applied to
acquire signals and to improve their accuracy Fig 3a summarizes all compression tests at both
strain-rates and includes also additional dynamic compression test curves where specimens did not
break These latter allow to evaluate the longitudinal elastic modulus with good accuracy by using
both the loading and unloading test phases (DCNF= dynamic compression no fracture)
0 002 0040
500
1000
1500
Stress (MPa)
SC
0 002 0040
500
1000
1500
Strain
DC
0 002 0040
500
1000
1500
DCNF
10-4
10-2
100
102
104
0
500
1000
1500
Strainrate (1s)
Stress (MPa)
SC
DC
DCNF
Fig 3 a) Compression stress-strain curves b) Maximum stress vs strain-rate in compression tests
As easily noted glass maintains a brittle-pure elastic behaviour at both strain-rates and the elastic
longitudinal modulus seems not to be appreciably influenced by the test speed Compression
maximum stresses show also small strain-rate sensitivity (Fig 3b) Table 1 summarizes the
experimental results in terms of maximum stress and longitudinal elastic modulus
Table 1 Experimental compression data
1 2 3 4 5 mean
Standard
deviation
SC
Strain-rate (s-1) 510
-4 510
-4 510
-4 510
-4 510
-4 510
-4 310
-5
Max stress (MPa) 1144 978 1087 1160 1070 1087 72
Young modulus (GPa) 61 58 72 66 79 67 8
DC
Strain-rate (s-1) 1342 947 1055 923 1282 1109 192
Max stress (MPa) 1326 1126 1251 1081 1109 1179 105
Young modulus (GPa) 63 69 51 50 54 58 8
When analysing experimental data both the static and the dynamic standard deviation of the
maximum stress and longitudinal elastic modulus are calculated and found to be quite small
considering the rather large scattering of data usually encountered in brittle materials In addition
since the maximum stress increase under high strain-rate testing is comparable to the standard
Applied Mechanics and Materials Vol 82 65
deviation it can be stated that the analysed glass does not present noticeable strain-rate sensitivity
To conclude the analysis of compression tests it is interesting to observe the image sequence of a
dynamic experiment recorded with the high-speed camera (50000 fps) The specimen was elastically
loaded (for the small size of the specimen the dynamic equilibrium is verified) and some radial
cracks appear in the third image
Fig 4 High speed sequence of compression test (50000 fps)
At this point the specimen loaded in compression collapses and a tensile wave starts to propagate
in the glass Due to the extremely low tensile strength of glass (compared to its compression one)
the whole specimen blows up becoming a fine glass dust as shown in the last picture At this point
the glass is no more able to transmit any compressive load and the transmitted signal vanishes
Splitting tensile test (Brazilian test)
Splitting tensile test or Brazilian test is nowadays a conventional mechanical test for the
investigation of the tensile strength of brittle materials This test is standardized only for concrete
specimens [5] but it is also adopted for other brittle materials such as rocks ceramics or glass [6]
The setup of splitting tensile test is rather simple a cylindrical specimen is loaded in compression
along two opposite generatrices as shown in Fig 5a This compression load generates a particular
stress-strain field with two peaks of compression at the cylinder surface and an interior zone of
almost constant tension (Fig 5a) For the higher compression strength of brittle material the
specimen breaks under tension and the maximum tensile stress can be easily deduced with the well
known analytical expression
Db
P
sdotsdot
sdot=π
σ2
(1)
where σ is the tensile strength P the maximum compression force during the test and b and D are
the specimen height and diameter respectively
compression
tension
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Stress (MPa)
S5
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Displacement (mm)
S5P
Fig 5 a) Brazilian test setup and typical stressstrain field b) static experimental data
For the reduction of local compression peaks small pieces of compliant materials (bearing strips
usually made of plywood for concrete specimens) are used to better distribute compression loading
and to avoid the propagation of initial cracks For the current tests the effectiveness of bearing strips
66 Performance Protection and Strengthening of Structures under ExtremeLoading
to loading the specimens has been evaluated in a preliminary phase For this reason two series of
tests have been performed splitting tests on specimen without (S5) and with paper bearing strips
(S5P)
Table 2 Experimental splitting tensile data
1 2 3 4 5 mean Standard
deviation
S5 Velocity (mms) 0009 0009 0009 0009 0009 0009 1410
-4
Max stress (MPa) 756 546 382 523 861 614 192
S5P
Velocity (mms) 0010 0010 0010 0009 0009 0010 7710-4
Max stress (MPa) 667 473 505 509 574 545 77
D5 Velocity (ms) 550 483 698 599 528 572 064
Max stress (MPa) 998 773 348 475 621 643 254
D5P
Velocity (ms) 767 673 84 742 81 772 067
Max stress (MPa) 871 917 7614 981 947 895 851
As presented in Fig 5b and in Table 2 the series without bearing strips shows a higher scatter of
data results probably due to the effect of damage induced by compression loading plates Using the
paper bearing strips the standard deviation is three times smaller and allows to evaluate more
effectively the mechanical properties of the glass tested
Dynamic tests have been performed directly by loading the specimen with the SHPB bars as in a
standard compression test In this kind of tests specimen-bar alignment is essential to correctly
transfer the compression pulse from the bars to the specimen Also in this case two series of
experiments have been carried out with and without bearing strips (made of papers)
0 01 02 03 040
20
40
60
80
100
120
Stress (MPa)
D5
0 01 02 03 040
20
40
60
80
100
120
Displacement (mm)
D5P
10-6
10-4
10-2
100
102
0
20
40
60
80
100
120
Test speed (ms)
Stress (MPa)
S5
S5P
D5
D5P
Fig 6 a) Dynamic tensile data b) maximum stress vs strain-rate in splitting tensile tests
Preliminary tests have been conducted to ensure dynamic equilibrium and this condition has
been verified for all specimens Fig 6a summarizes the data results obtained by the dynamic
splitting tensile tests Also in dynamic tests data obtained without the bearing strips present high
scattering and this fact prevents the correct evaluation of the glass tensile strength (standard
deviation of D5 is three times greater than standard deviation of D5P) Contrary to the compression
data the tensile strength seems to be substantially influenced by strain-rate with an increase of about
30 MPa when the strain-rate grows by six magnitude orders This phenomenon has also been
noticed in the high strain-rate behaviour of concrete where the tensile strength is more strain-rate
influenced than the compressive strength
Applied Mechanics and Materials Vol 82 67
Fig 7 presents a sequence of images of a dynamic splitting test without bearing strips recorded at
50000 fps It is interesting to observe the initial cracks due to compression loading (picture two) and
the tensile damage zone next to the barloading axis (picture three to five) This sequence confirms
that the specimenrsquos failure is due to tensile stresses generated along the diameter of the loading axis
as depicted in Fig5a
Fig 7 High speed sequence of splitting tensile test (50000 fps)
Further numerical and experimental investigations would be required to verify the actual stress-
strain field in the specimen during static and dynamic tests and to evaluate the accuracy of Eq 1
Summary
A study of the strain-rate influence on the compressive and tensile behaviour of commercial glass
has been conducted The experimental results try to cover the gap in literature concerning
mechanical behaviour of glassy materials at medium-high strain-rate To obtain reliable data state-
of-the-art compensations for SHPB tests have been adopted and concerning splitting tensile test
different testing setups have been evaluated Compression test results indicate that this glass does
not present any substantial sensitivity to the strain-rate concerning ultimate strength and Young
modulus With reference to tensile data glass tensile mechanical behaviour seems to be influenced
by strain rate and tensile strength increases by about 30 MPa when the strain-rate grows by six
magnitude orders Further numerical and experimental investigations will be suitable to verify the
accuracy of tensile properties deduced by splitting tensile tests on brittle materials like glass
especially under dynamic loading conditions Further it will be interesting to evaluate sizescale
effects also in dynamic tests using the high loading capability of the SHPB or simply to achieve
more representative specimen volumes
References
[1] HS Norville EJ Conrath Journal of Architectural Engineering Vol 7 (2001) p 80
[2] M Larcher N Gebbeken M Teich G Solomos Simulation of laminated glass loaded by air
blast waves Proc4th
ISAAG Munich (2010)
[3] E Cadoni G Solomos C Albertini Mag Concrete Res Vol 60 (2008) p221
[4] H Zhao G Gary J Mech Phys Solids Vol 45 (1997) p 1185
[5] A Tyas AJ Watson Int J Impact Eng Vol 25 (2001) p 87
[6] G Gary K Safa Accounting for the effect of local punching at the barspecimen interface in
SHPB experiments Proc DYMAT 2009 Bruxelles (2009)
[7] ASTM C496-96 Standard test method for splitting tensile strength of cylindrical concrete
specimens ASTM standard
[8] CS Chen E Pan B Amadei Int J Rock Mech Sci Vol 35 (1998) p 43
[9] C Rocco GV Guinea J Planas M Elices Cement Concrete Res Vol 31 (2001) p73
[10] C Johnstone C Ruiz Int J Solids Structures Vol 32 (1995) p2647
[11] T Holmquist G Johnson D Grady C Lopatin E Hertel High strain rate properties and
constitutive modelling of glass Proc 15th
International Symposium on Ballistics Israel (1995)
68 Performance Protection and Strengthening of Structures under ExtremeLoading
Performance Protection and Strengthening of Structures under Extreme Loading doi104028wwwscientificnetAMM82 Experimental Investigation of High Strain-Rate Behaviour of Glass doi104028wwwscientificnetAMM8263
particular their dimensions were for compression tests of 5 mm diameter and 6 mm length and for
splitting tensile tests of 9 mm diameter and 5 or 10 mm length (Figure 2) To obtain reliable
experimental data about 5 repetitions for each type of tests have been performed
Compression tests
Compression tests on glass specimens have been carried out at two strain-rates of about 510-4
s-1
(SC=static compression) and about 1103s
-1 (DC=dynamic compression) Due to the small specimen
sizes it has not been possible to precisely characterize the glass longitudinal elastic modulus using
strain-gages however as shown below reliable estimates of the global mechanical behaviour of the
material have been reached For the static tests deformation has been obtained through cross-head
displacement measurements which have been corrected from the errors introduced by the machine
compliance using a calibrated test In the high strain-rate tests dynamic equilibrium has been
carefully checked and as mentioned before state-of-the-art compensations have been applied to
acquire signals and to improve their accuracy Fig 3a summarizes all compression tests at both
strain-rates and includes also additional dynamic compression test curves where specimens did not
break These latter allow to evaluate the longitudinal elastic modulus with good accuracy by using
both the loading and unloading test phases (DCNF= dynamic compression no fracture)
0 002 0040
500
1000
1500
Stress (MPa)
SC
0 002 0040
500
1000
1500
Strain
DC
0 002 0040
500
1000
1500
DCNF
10-4
10-2
100
102
104
0
500
1000
1500
Strainrate (1s)
Stress (MPa)
SC
DC
DCNF
Fig 3 a) Compression stress-strain curves b) Maximum stress vs strain-rate in compression tests
As easily noted glass maintains a brittle-pure elastic behaviour at both strain-rates and the elastic
longitudinal modulus seems not to be appreciably influenced by the test speed Compression
maximum stresses show also small strain-rate sensitivity (Fig 3b) Table 1 summarizes the
experimental results in terms of maximum stress and longitudinal elastic modulus
Table 1 Experimental compression data
1 2 3 4 5 mean
Standard
deviation
SC
Strain-rate (s-1) 510
-4 510
-4 510
-4 510
-4 510
-4 510
-4 310
-5
Max stress (MPa) 1144 978 1087 1160 1070 1087 72
Young modulus (GPa) 61 58 72 66 79 67 8
DC
Strain-rate (s-1) 1342 947 1055 923 1282 1109 192
Max stress (MPa) 1326 1126 1251 1081 1109 1179 105
Young modulus (GPa) 63 69 51 50 54 58 8
When analysing experimental data both the static and the dynamic standard deviation of the
maximum stress and longitudinal elastic modulus are calculated and found to be quite small
considering the rather large scattering of data usually encountered in brittle materials In addition
since the maximum stress increase under high strain-rate testing is comparable to the standard
Applied Mechanics and Materials Vol 82 65
deviation it can be stated that the analysed glass does not present noticeable strain-rate sensitivity
To conclude the analysis of compression tests it is interesting to observe the image sequence of a
dynamic experiment recorded with the high-speed camera (50000 fps) The specimen was elastically
loaded (for the small size of the specimen the dynamic equilibrium is verified) and some radial
cracks appear in the third image
Fig 4 High speed sequence of compression test (50000 fps)
At this point the specimen loaded in compression collapses and a tensile wave starts to propagate
in the glass Due to the extremely low tensile strength of glass (compared to its compression one)
the whole specimen blows up becoming a fine glass dust as shown in the last picture At this point
the glass is no more able to transmit any compressive load and the transmitted signal vanishes
Splitting tensile test (Brazilian test)
Splitting tensile test or Brazilian test is nowadays a conventional mechanical test for the
investigation of the tensile strength of brittle materials This test is standardized only for concrete
specimens [5] but it is also adopted for other brittle materials such as rocks ceramics or glass [6]
The setup of splitting tensile test is rather simple a cylindrical specimen is loaded in compression
along two opposite generatrices as shown in Fig 5a This compression load generates a particular
stress-strain field with two peaks of compression at the cylinder surface and an interior zone of
almost constant tension (Fig 5a) For the higher compression strength of brittle material the
specimen breaks under tension and the maximum tensile stress can be easily deduced with the well
known analytical expression
Db
P
sdotsdot
sdot=π
σ2
(1)
where σ is the tensile strength P the maximum compression force during the test and b and D are
the specimen height and diameter respectively
compression
tension
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Stress (MPa)
S5
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Displacement (mm)
S5P
Fig 5 a) Brazilian test setup and typical stressstrain field b) static experimental data
For the reduction of local compression peaks small pieces of compliant materials (bearing strips
usually made of plywood for concrete specimens) are used to better distribute compression loading
and to avoid the propagation of initial cracks For the current tests the effectiveness of bearing strips
66 Performance Protection and Strengthening of Structures under ExtremeLoading
to loading the specimens has been evaluated in a preliminary phase For this reason two series of
tests have been performed splitting tests on specimen without (S5) and with paper bearing strips
(S5P)
Table 2 Experimental splitting tensile data
1 2 3 4 5 mean Standard
deviation
S5 Velocity (mms) 0009 0009 0009 0009 0009 0009 1410
-4
Max stress (MPa) 756 546 382 523 861 614 192
S5P
Velocity (mms) 0010 0010 0010 0009 0009 0010 7710-4
Max stress (MPa) 667 473 505 509 574 545 77
D5 Velocity (ms) 550 483 698 599 528 572 064
Max stress (MPa) 998 773 348 475 621 643 254
D5P
Velocity (ms) 767 673 84 742 81 772 067
Max stress (MPa) 871 917 7614 981 947 895 851
As presented in Fig 5b and in Table 2 the series without bearing strips shows a higher scatter of
data results probably due to the effect of damage induced by compression loading plates Using the
paper bearing strips the standard deviation is three times smaller and allows to evaluate more
effectively the mechanical properties of the glass tested
Dynamic tests have been performed directly by loading the specimen with the SHPB bars as in a
standard compression test In this kind of tests specimen-bar alignment is essential to correctly
transfer the compression pulse from the bars to the specimen Also in this case two series of
experiments have been carried out with and without bearing strips (made of papers)
0 01 02 03 040
20
40
60
80
100
120
Stress (MPa)
D5
0 01 02 03 040
20
40
60
80
100
120
Displacement (mm)
D5P
10-6
10-4
10-2
100
102
0
20
40
60
80
100
120
Test speed (ms)
Stress (MPa)
S5
S5P
D5
D5P
Fig 6 a) Dynamic tensile data b) maximum stress vs strain-rate in splitting tensile tests
Preliminary tests have been conducted to ensure dynamic equilibrium and this condition has
been verified for all specimens Fig 6a summarizes the data results obtained by the dynamic
splitting tensile tests Also in dynamic tests data obtained without the bearing strips present high
scattering and this fact prevents the correct evaluation of the glass tensile strength (standard
deviation of D5 is three times greater than standard deviation of D5P) Contrary to the compression
data the tensile strength seems to be substantially influenced by strain-rate with an increase of about
30 MPa when the strain-rate grows by six magnitude orders This phenomenon has also been
noticed in the high strain-rate behaviour of concrete where the tensile strength is more strain-rate
influenced than the compressive strength
Applied Mechanics and Materials Vol 82 67
Fig 7 presents a sequence of images of a dynamic splitting test without bearing strips recorded at
50000 fps It is interesting to observe the initial cracks due to compression loading (picture two) and
the tensile damage zone next to the barloading axis (picture three to five) This sequence confirms
that the specimenrsquos failure is due to tensile stresses generated along the diameter of the loading axis
as depicted in Fig5a
Fig 7 High speed sequence of splitting tensile test (50000 fps)
Further numerical and experimental investigations would be required to verify the actual stress-
strain field in the specimen during static and dynamic tests and to evaluate the accuracy of Eq 1
Summary
A study of the strain-rate influence on the compressive and tensile behaviour of commercial glass
has been conducted The experimental results try to cover the gap in literature concerning
mechanical behaviour of glassy materials at medium-high strain-rate To obtain reliable data state-
of-the-art compensations for SHPB tests have been adopted and concerning splitting tensile test
different testing setups have been evaluated Compression test results indicate that this glass does
not present any substantial sensitivity to the strain-rate concerning ultimate strength and Young
modulus With reference to tensile data glass tensile mechanical behaviour seems to be influenced
by strain rate and tensile strength increases by about 30 MPa when the strain-rate grows by six
magnitude orders Further numerical and experimental investigations will be suitable to verify the
accuracy of tensile properties deduced by splitting tensile tests on brittle materials like glass
especially under dynamic loading conditions Further it will be interesting to evaluate sizescale
effects also in dynamic tests using the high loading capability of the SHPB or simply to achieve
more representative specimen volumes
References
[1] HS Norville EJ Conrath Journal of Architectural Engineering Vol 7 (2001) p 80
[2] M Larcher N Gebbeken M Teich G Solomos Simulation of laminated glass loaded by air
blast waves Proc4th
ISAAG Munich (2010)
[3] E Cadoni G Solomos C Albertini Mag Concrete Res Vol 60 (2008) p221
[4] H Zhao G Gary J Mech Phys Solids Vol 45 (1997) p 1185
[5] A Tyas AJ Watson Int J Impact Eng Vol 25 (2001) p 87
[6] G Gary K Safa Accounting for the effect of local punching at the barspecimen interface in
SHPB experiments Proc DYMAT 2009 Bruxelles (2009)
[7] ASTM C496-96 Standard test method for splitting tensile strength of cylindrical concrete
specimens ASTM standard
[8] CS Chen E Pan B Amadei Int J Rock Mech Sci Vol 35 (1998) p 43
[9] C Rocco GV Guinea J Planas M Elices Cement Concrete Res Vol 31 (2001) p73
[10] C Johnstone C Ruiz Int J Solids Structures Vol 32 (1995) p2647
[11] T Holmquist G Johnson D Grady C Lopatin E Hertel High strain rate properties and
constitutive modelling of glass Proc 15th
International Symposium on Ballistics Israel (1995)
68 Performance Protection and Strengthening of Structures under ExtremeLoading
Performance Protection and Strengthening of Structures under Extreme Loading doi104028wwwscientificnetAMM82 Experimental Investigation of High Strain-Rate Behaviour of Glass doi104028wwwscientificnetAMM8263
deviation it can be stated that the analysed glass does not present noticeable strain-rate sensitivity
To conclude the analysis of compression tests it is interesting to observe the image sequence of a
dynamic experiment recorded with the high-speed camera (50000 fps) The specimen was elastically
loaded (for the small size of the specimen the dynamic equilibrium is verified) and some radial
cracks appear in the third image
Fig 4 High speed sequence of compression test (50000 fps)
At this point the specimen loaded in compression collapses and a tensile wave starts to propagate
in the glass Due to the extremely low tensile strength of glass (compared to its compression one)
the whole specimen blows up becoming a fine glass dust as shown in the last picture At this point
the glass is no more able to transmit any compressive load and the transmitted signal vanishes
Splitting tensile test (Brazilian test)
Splitting tensile test or Brazilian test is nowadays a conventional mechanical test for the
investigation of the tensile strength of brittle materials This test is standardized only for concrete
specimens [5] but it is also adopted for other brittle materials such as rocks ceramics or glass [6]
The setup of splitting tensile test is rather simple a cylindrical specimen is loaded in compression
along two opposite generatrices as shown in Fig 5a This compression load generates a particular
stress-strain field with two peaks of compression at the cylinder surface and an interior zone of
almost constant tension (Fig 5a) For the higher compression strength of brittle material the
specimen breaks under tension and the maximum tensile stress can be easily deduced with the well
known analytical expression
Db
P
sdotsdot
sdot=π
σ2
(1)
where σ is the tensile strength P the maximum compression force during the test and b and D are
the specimen height and diameter respectively
compression
tension
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Stress (MPa)
S5
0 01 02 03 040
10
20
30
40
50
60
70
80
90
100
Displacement (mm)
S5P
Fig 5 a) Brazilian test setup and typical stressstrain field b) static experimental data
For the reduction of local compression peaks small pieces of compliant materials (bearing strips
usually made of plywood for concrete specimens) are used to better distribute compression loading
and to avoid the propagation of initial cracks For the current tests the effectiveness of bearing strips
66 Performance Protection and Strengthening of Structures under ExtremeLoading
to loading the specimens has been evaluated in a preliminary phase For this reason two series of
tests have been performed splitting tests on specimen without (S5) and with paper bearing strips
(S5P)
Table 2 Experimental splitting tensile data
1 2 3 4 5 mean Standard
deviation
S5 Velocity (mms) 0009 0009 0009 0009 0009 0009 1410
-4
Max stress (MPa) 756 546 382 523 861 614 192
S5P
Velocity (mms) 0010 0010 0010 0009 0009 0010 7710-4
Max stress (MPa) 667 473 505 509 574 545 77
D5 Velocity (ms) 550 483 698 599 528 572 064
Max stress (MPa) 998 773 348 475 621 643 254
D5P
Velocity (ms) 767 673 84 742 81 772 067
Max stress (MPa) 871 917 7614 981 947 895 851
As presented in Fig 5b and in Table 2 the series without bearing strips shows a higher scatter of
data results probably due to the effect of damage induced by compression loading plates Using the
paper bearing strips the standard deviation is three times smaller and allows to evaluate more
effectively the mechanical properties of the glass tested
Dynamic tests have been performed directly by loading the specimen with the SHPB bars as in a
standard compression test In this kind of tests specimen-bar alignment is essential to correctly
transfer the compression pulse from the bars to the specimen Also in this case two series of
experiments have been carried out with and without bearing strips (made of papers)
0 01 02 03 040
20
40
60
80
100
120
Stress (MPa)
D5
0 01 02 03 040
20
40
60
80
100
120
Displacement (mm)
D5P
10-6
10-4
10-2
100
102
0
20
40
60
80
100
120
Test speed (ms)
Stress (MPa)
S5
S5P
D5
D5P
Fig 6 a) Dynamic tensile data b) maximum stress vs strain-rate in splitting tensile tests
Preliminary tests have been conducted to ensure dynamic equilibrium and this condition has
been verified for all specimens Fig 6a summarizes the data results obtained by the dynamic
splitting tensile tests Also in dynamic tests data obtained without the bearing strips present high
scattering and this fact prevents the correct evaluation of the glass tensile strength (standard
deviation of D5 is three times greater than standard deviation of D5P) Contrary to the compression
data the tensile strength seems to be substantially influenced by strain-rate with an increase of about
30 MPa when the strain-rate grows by six magnitude orders This phenomenon has also been
noticed in the high strain-rate behaviour of concrete where the tensile strength is more strain-rate
influenced than the compressive strength
Applied Mechanics and Materials Vol 82 67
Fig 7 presents a sequence of images of a dynamic splitting test without bearing strips recorded at
50000 fps It is interesting to observe the initial cracks due to compression loading (picture two) and
the tensile damage zone next to the barloading axis (picture three to five) This sequence confirms
that the specimenrsquos failure is due to tensile stresses generated along the diameter of the loading axis
as depicted in Fig5a
Fig 7 High speed sequence of splitting tensile test (50000 fps)
Further numerical and experimental investigations would be required to verify the actual stress-
strain field in the specimen during static and dynamic tests and to evaluate the accuracy of Eq 1
Summary
A study of the strain-rate influence on the compressive and tensile behaviour of commercial glass
has been conducted The experimental results try to cover the gap in literature concerning
mechanical behaviour of glassy materials at medium-high strain-rate To obtain reliable data state-
of-the-art compensations for SHPB tests have been adopted and concerning splitting tensile test
different testing setups have been evaluated Compression test results indicate that this glass does
not present any substantial sensitivity to the strain-rate concerning ultimate strength and Young
modulus With reference to tensile data glass tensile mechanical behaviour seems to be influenced
by strain rate and tensile strength increases by about 30 MPa when the strain-rate grows by six
magnitude orders Further numerical and experimental investigations will be suitable to verify the
accuracy of tensile properties deduced by splitting tensile tests on brittle materials like glass
especially under dynamic loading conditions Further it will be interesting to evaluate sizescale
effects also in dynamic tests using the high loading capability of the SHPB or simply to achieve
more representative specimen volumes
References
[1] HS Norville EJ Conrath Journal of Architectural Engineering Vol 7 (2001) p 80
[2] M Larcher N Gebbeken M Teich G Solomos Simulation of laminated glass loaded by air
blast waves Proc4th
ISAAG Munich (2010)
[3] E Cadoni G Solomos C Albertini Mag Concrete Res Vol 60 (2008) p221
[4] H Zhao G Gary J Mech Phys Solids Vol 45 (1997) p 1185
[5] A Tyas AJ Watson Int J Impact Eng Vol 25 (2001) p 87
[6] G Gary K Safa Accounting for the effect of local punching at the barspecimen interface in
SHPB experiments Proc DYMAT 2009 Bruxelles (2009)
[7] ASTM C496-96 Standard test method for splitting tensile strength of cylindrical concrete
specimens ASTM standard
[8] CS Chen E Pan B Amadei Int J Rock Mech Sci Vol 35 (1998) p 43
[9] C Rocco GV Guinea J Planas M Elices Cement Concrete Res Vol 31 (2001) p73
[10] C Johnstone C Ruiz Int J Solids Structures Vol 32 (1995) p2647
[11] T Holmquist G Johnson D Grady C Lopatin E Hertel High strain rate properties and
constitutive modelling of glass Proc 15th
International Symposium on Ballistics Israel (1995)
68 Performance Protection and Strengthening of Structures under ExtremeLoading
Performance Protection and Strengthening of Structures under Extreme Loading doi104028wwwscientificnetAMM82 Experimental Investigation of High Strain-Rate Behaviour of Glass doi104028wwwscientificnetAMM8263
to loading the specimens has been evaluated in a preliminary phase For this reason two series of
tests have been performed splitting tests on specimen without (S5) and with paper bearing strips
(S5P)
Table 2 Experimental splitting tensile data
1 2 3 4 5 mean Standard
deviation
S5 Velocity (mms) 0009 0009 0009 0009 0009 0009 1410
-4
Max stress (MPa) 756 546 382 523 861 614 192
S5P
Velocity (mms) 0010 0010 0010 0009 0009 0010 7710-4
Max stress (MPa) 667 473 505 509 574 545 77
D5 Velocity (ms) 550 483 698 599 528 572 064
Max stress (MPa) 998 773 348 475 621 643 254
D5P
Velocity (ms) 767 673 84 742 81 772 067
Max stress (MPa) 871 917 7614 981 947 895 851
As presented in Fig 5b and in Table 2 the series without bearing strips shows a higher scatter of
data results probably due to the effect of damage induced by compression loading plates Using the
paper bearing strips the standard deviation is three times smaller and allows to evaluate more
effectively the mechanical properties of the glass tested
Dynamic tests have been performed directly by loading the specimen with the SHPB bars as in a
standard compression test In this kind of tests specimen-bar alignment is essential to correctly
transfer the compression pulse from the bars to the specimen Also in this case two series of
experiments have been carried out with and without bearing strips (made of papers)
0 01 02 03 040
20
40
60
80
100
120
Stress (MPa)
D5
0 01 02 03 040
20
40
60
80
100
120
Displacement (mm)
D5P
10-6
10-4
10-2
100
102
0
20
40
60
80
100
120
Test speed (ms)
Stress (MPa)
S5
S5P
D5
D5P
Fig 6 a) Dynamic tensile data b) maximum stress vs strain-rate in splitting tensile tests
Preliminary tests have been conducted to ensure dynamic equilibrium and this condition has
been verified for all specimens Fig 6a summarizes the data results obtained by the dynamic
splitting tensile tests Also in dynamic tests data obtained without the bearing strips present high
scattering and this fact prevents the correct evaluation of the glass tensile strength (standard
deviation of D5 is three times greater than standard deviation of D5P) Contrary to the compression
data the tensile strength seems to be substantially influenced by strain-rate with an increase of about
30 MPa when the strain-rate grows by six magnitude orders This phenomenon has also been
noticed in the high strain-rate behaviour of concrete where the tensile strength is more strain-rate
influenced than the compressive strength
Applied Mechanics and Materials Vol 82 67
Fig 7 presents a sequence of images of a dynamic splitting test without bearing strips recorded at
50000 fps It is interesting to observe the initial cracks due to compression loading (picture two) and
the tensile damage zone next to the barloading axis (picture three to five) This sequence confirms
that the specimenrsquos failure is due to tensile stresses generated along the diameter of the loading axis
as depicted in Fig5a
Fig 7 High speed sequence of splitting tensile test (50000 fps)
Further numerical and experimental investigations would be required to verify the actual stress-
strain field in the specimen during static and dynamic tests and to evaluate the accuracy of Eq 1
Summary
A study of the strain-rate influence on the compressive and tensile behaviour of commercial glass
has been conducted The experimental results try to cover the gap in literature concerning
mechanical behaviour of glassy materials at medium-high strain-rate To obtain reliable data state-
of-the-art compensations for SHPB tests have been adopted and concerning splitting tensile test
different testing setups have been evaluated Compression test results indicate that this glass does
not present any substantial sensitivity to the strain-rate concerning ultimate strength and Young
modulus With reference to tensile data glass tensile mechanical behaviour seems to be influenced
by strain rate and tensile strength increases by about 30 MPa when the strain-rate grows by six
magnitude orders Further numerical and experimental investigations will be suitable to verify the
accuracy of tensile properties deduced by splitting tensile tests on brittle materials like glass
especially under dynamic loading conditions Further it will be interesting to evaluate sizescale
effects also in dynamic tests using the high loading capability of the SHPB or simply to achieve
more representative specimen volumes
References
[1] HS Norville EJ Conrath Journal of Architectural Engineering Vol 7 (2001) p 80
[2] M Larcher N Gebbeken M Teich G Solomos Simulation of laminated glass loaded by air
blast waves Proc4th
ISAAG Munich (2010)
[3] E Cadoni G Solomos C Albertini Mag Concrete Res Vol 60 (2008) p221
[4] H Zhao G Gary J Mech Phys Solids Vol 45 (1997) p 1185
[5] A Tyas AJ Watson Int J Impact Eng Vol 25 (2001) p 87
[6] G Gary K Safa Accounting for the effect of local punching at the barspecimen interface in
SHPB experiments Proc DYMAT 2009 Bruxelles (2009)
[7] ASTM C496-96 Standard test method for splitting tensile strength of cylindrical concrete
specimens ASTM standard
[8] CS Chen E Pan B Amadei Int J Rock Mech Sci Vol 35 (1998) p 43
[9] C Rocco GV Guinea J Planas M Elices Cement Concrete Res Vol 31 (2001) p73
[10] C Johnstone C Ruiz Int J Solids Structures Vol 32 (1995) p2647
[11] T Holmquist G Johnson D Grady C Lopatin E Hertel High strain rate properties and
constitutive modelling of glass Proc 15th
International Symposium on Ballistics Israel (1995)
68 Performance Protection and Strengthening of Structures under ExtremeLoading
Performance Protection and Strengthening of Structures under Extreme Loading doi104028wwwscientificnetAMM82 Experimental Investigation of High Strain-Rate Behaviour of Glass doi104028wwwscientificnetAMM8263
Fig 7 presents a sequence of images of a dynamic splitting test without bearing strips recorded at
50000 fps It is interesting to observe the initial cracks due to compression loading (picture two) and
the tensile damage zone next to the barloading axis (picture three to five) This sequence confirms
that the specimenrsquos failure is due to tensile stresses generated along the diameter of the loading axis
as depicted in Fig5a
Fig 7 High speed sequence of splitting tensile test (50000 fps)
Further numerical and experimental investigations would be required to verify the actual stress-
strain field in the specimen during static and dynamic tests and to evaluate the accuracy of Eq 1
Summary
A study of the strain-rate influence on the compressive and tensile behaviour of commercial glass
has been conducted The experimental results try to cover the gap in literature concerning
mechanical behaviour of glassy materials at medium-high strain-rate To obtain reliable data state-
of-the-art compensations for SHPB tests have been adopted and concerning splitting tensile test
different testing setups have been evaluated Compression test results indicate that this glass does
not present any substantial sensitivity to the strain-rate concerning ultimate strength and Young
modulus With reference to tensile data glass tensile mechanical behaviour seems to be influenced
by strain rate and tensile strength increases by about 30 MPa when the strain-rate grows by six
magnitude orders Further numerical and experimental investigations will be suitable to verify the
accuracy of tensile properties deduced by splitting tensile tests on brittle materials like glass
especially under dynamic loading conditions Further it will be interesting to evaluate sizescale
effects also in dynamic tests using the high loading capability of the SHPB or simply to achieve
more representative specimen volumes
References
[1] HS Norville EJ Conrath Journal of Architectural Engineering Vol 7 (2001) p 80
[2] M Larcher N Gebbeken M Teich G Solomos Simulation of laminated glass loaded by air
blast waves Proc4th
ISAAG Munich (2010)
[3] E Cadoni G Solomos C Albertini Mag Concrete Res Vol 60 (2008) p221
[4] H Zhao G Gary J Mech Phys Solids Vol 45 (1997) p 1185
[5] A Tyas AJ Watson Int J Impact Eng Vol 25 (2001) p 87
[6] G Gary K Safa Accounting for the effect of local punching at the barspecimen interface in
SHPB experiments Proc DYMAT 2009 Bruxelles (2009)
[7] ASTM C496-96 Standard test method for splitting tensile strength of cylindrical concrete
specimens ASTM standard
[8] CS Chen E Pan B Amadei Int J Rock Mech Sci Vol 35 (1998) p 43
[9] C Rocco GV Guinea J Planas M Elices Cement Concrete Res Vol 31 (2001) p73
[10] C Johnstone C Ruiz Int J Solids Structures Vol 32 (1995) p2647
[11] T Holmquist G Johnson D Grady C Lopatin E Hertel High strain rate properties and
constitutive modelling of glass Proc 15th
International Symposium on Ballistics Israel (1995)
68 Performance Protection and Strengthening of Structures under ExtremeLoading
Performance Protection and Strengthening of Structures under Extreme Loading doi104028wwwscientificnetAMM82 Experimental Investigation of High Strain-Rate Behaviour of Glass doi104028wwwscientificnetAMM8263
Performance Protection and Strengthening of Structures under Extreme Loading doi104028wwwscientificnetAMM82 Experimental Investigation of High Strain-Rate Behaviour of Glass doi104028wwwscientificnetAMM8263
