indentation damage and residual strength of glass -...
TRANSCRIPT
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Tanguy ROUXEL, Jean-Christophe SANGLEBOEUF,
and Kwadwo KESE
LARMAUR, Université de Rennes 1, France
The temperature dependence of the Flaw Sensitivity
The residual stress field
Indentation Damage and Residual Strength of Glass
PacRim 8, Vancouver 2009
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I. Temperature Dependence of the Flaw sensitivity
What « Brittleness » and « Ductility » mean?
High temperature studies
- To get insight into the nature of Brittlness
- To understand the nature of process-derived contact flaws and
simulate product handling damage
- To study the strength-controlling sites at room temperature
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«!Comme elle a l’éclat du verre, elle en a la fragilité…!»Polyeucte, Corneille
Low temperature or high rate
!
!
Pre-existing flaw
High temperature or low rate
Ductile
Brittle (Fragile)
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Indented window glass specimens loaded in bending
Brittle-Ductile transition
P
u
DuctileBrittle
Loa
d,
P
Deflection, u (mm)
J. Non-Cryst. Sol., 271 224-235 (2000)
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Mechanical analysis
(Kt=E!Y! a)
Crack tip stress intensity factor:
Relaxation function:
At fracture:
!
ˆ K = K1c
!
ˆ " ="decohesion
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10 hCopper at 20 °C
1 hCeramic composite Si3N4/SiC at 1600 °C
10 sBitumen at –5 °C
0,1 sWindow glass at 600 °C
1 msBitumen at 40 °C
1 msEpoxy resin at 20 °C
1 nsWater at 20 °C
1 dIce at –5 °C
1 dWindow glass at 500 °C
32 yWindow glass at 400 °C
120 yIce at –98 °C
106 yEarth mantle
Relaxation timeconstant,
"rel=#/µMaterials
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« Plastic » deformation zone:
Volume V $ b3 $ E1/2/H (b/a=(V/%V)3)
Elastic
deformation zone
P
a c
P!r
Lawn, Evans and Marshall (1979-81)
2c
ca
Indentation volume: %V $ a3 $ H-3/2
Unloading
!r $ K %V/V
K: bulk modulus
2b
"r # (E/H)1/2
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Watanabe et al, J.Mater.Sci., 2001
Michel et al, JNCS, 2004
Shang Rouxel, JACS, 2005
"r # (E/H)1/2
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0
5
10
15
20
25
0 100 200 300 400 500
Indentation temperature, °C
E/H
Dwell time = 60 s, Michel et al
Dwell time = 0 s, this study,
Recall that the analysis of the indentation problem assuming pure elasto-plasticity leads to:
"r # (E/H)1/2
Residual stresses are expected to increase with
temperature up to 450 °C
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!
c = "P( )2
3
EH( )
1
3
Kc
2
3
Measured crack length gives $ = 0.020
Sglavo Green, Acta Metall. Mater., 1995
0.028<$< 0.034
Rouxel Sangleboeuf, JNCS, 2000
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Window Glass : Planilux (Saint-Gobain)
air sideT
em
pe
ratu
re
Time
2 h
49 N Vickers
0.1 mm/s no hold
2°C/min ->100°C
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Calculate stresses from crack length
!
"T
= Kc
1# co
cr
$ % &
' ( ) 32
*cr
!
"c
= Kc
1# co
ct
$ % &
' ( ) 32
*ct
Zeng and Rowcliffe, Acta Metall. Mater., 1995
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Estimation of the residual stresses
RT
K. Kese et al,, J. Phys. D, App. Phys., 41 [7] 074025 (2008)
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• The nature of contact site can change from a fully crackedimprint at room temperature to a crack-free imprint athigher temperatures.
• The crack-free indent can transform into a fully crackedindent when the residual stress field is mechanicallydisturbed, as for example by another micro indent.
• The lateral cracks obtain their shape as a result of theircoupled growth with that of the radial cracks.
• Stresses are tensile in the tangential direction, andcompressive in the radial direction
• The spatial extent of the stress field decreases as afunction of temperature
Conclusion