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2018 04 18 원종호
Evaluation of material properties using IIT
2
Contents
What is IIT
Evaluation of materials properties
- Strength
- Residual stress
- Fracture toughness
3
Introduction
Deformation
Fracture
σYS UTS n E
KIC JIC δIC
Destructive
How can I measure the mechanical properties
I am working Do not touch
4
Introduction
Specimens for tensile test Specimens for fracture test
Not applicable for small scale testing
Large scale testing
5
Introduction
Convenient
In-situ amp In-field System
Non-destructive amp Local test
Simple amp fast
6
Instrumented Indentation test
A novel method to characterize mechanical properties
Hardness Elastic modulus Tensile properties Residual stress Fracture toughness
Indentation load-depth curve
Load
Depth
Loading
Unloading
7
Research history
Brinell (1900) defining as the ratio of the load to the surface area
Meyer (1908) defining as the ratio of the load to the projected area
OrsquoNeill (1944) expressing dD as the indentation strain plotting pm against dD
Tabor (1950) representing the uniaxial stress and strain
2
2
44 minus
==
m
m DdA
dLp
ππ
22 )(112
DdDLNHBminusminus
=π
Ddp
rm
r 20 == εψ
σ
bull σr εr representative stress strain bull ψ plastic constraint factor (asymp28-30)
bull L applied load bull d diameter of residual impression bull D diameter of the ball indenter
bull A material constant bull m Meyer index ( asymp n+2)
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
2
Contents
What is IIT
Evaluation of materials properties
- Strength
- Residual stress
- Fracture toughness
3
Introduction
Deformation
Fracture
σYS UTS n E
KIC JIC δIC
Destructive
How can I measure the mechanical properties
I am working Do not touch
4
Introduction
Specimens for tensile test Specimens for fracture test
Not applicable for small scale testing
Large scale testing
5
Introduction
Convenient
In-situ amp In-field System
Non-destructive amp Local test
Simple amp fast
6
Instrumented Indentation test
A novel method to characterize mechanical properties
Hardness Elastic modulus Tensile properties Residual stress Fracture toughness
Indentation load-depth curve
Load
Depth
Loading
Unloading
7
Research history
Brinell (1900) defining as the ratio of the load to the surface area
Meyer (1908) defining as the ratio of the load to the projected area
OrsquoNeill (1944) expressing dD as the indentation strain plotting pm against dD
Tabor (1950) representing the uniaxial stress and strain
2
2
44 minus
==
m
m DdA
dLp
ππ
22 )(112
DdDLNHBminusminus
=π
Ddp
rm
r 20 == εψ
σ
bull σr εr representative stress strain bull ψ plastic constraint factor (asymp28-30)
bull L applied load bull d diameter of residual impression bull D diameter of the ball indenter
bull A material constant bull m Meyer index ( asymp n+2)
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
3
Introduction
Deformation
Fracture
σYS UTS n E
KIC JIC δIC
Destructive
How can I measure the mechanical properties
I am working Do not touch
4
Introduction
Specimens for tensile test Specimens for fracture test
Not applicable for small scale testing
Large scale testing
5
Introduction
Convenient
In-situ amp In-field System
Non-destructive amp Local test
Simple amp fast
6
Instrumented Indentation test
A novel method to characterize mechanical properties
Hardness Elastic modulus Tensile properties Residual stress Fracture toughness
Indentation load-depth curve
Load
Depth
Loading
Unloading
7
Research history
Brinell (1900) defining as the ratio of the load to the surface area
Meyer (1908) defining as the ratio of the load to the projected area
OrsquoNeill (1944) expressing dD as the indentation strain plotting pm against dD
Tabor (1950) representing the uniaxial stress and strain
2
2
44 minus
==
m
m DdA
dLp
ππ
22 )(112
DdDLNHBminusminus
=π
Ddp
rm
r 20 == εψ
σ
bull σr εr representative stress strain bull ψ plastic constraint factor (asymp28-30)
bull L applied load bull d diameter of residual impression bull D diameter of the ball indenter
bull A material constant bull m Meyer index ( asymp n+2)
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
4
Introduction
Specimens for tensile test Specimens for fracture test
Not applicable for small scale testing
Large scale testing
5
Introduction
Convenient
In-situ amp In-field System
Non-destructive amp Local test
Simple amp fast
6
Instrumented Indentation test
A novel method to characterize mechanical properties
Hardness Elastic modulus Tensile properties Residual stress Fracture toughness
Indentation load-depth curve
Load
Depth
Loading
Unloading
7
Research history
Brinell (1900) defining as the ratio of the load to the surface area
Meyer (1908) defining as the ratio of the load to the projected area
OrsquoNeill (1944) expressing dD as the indentation strain plotting pm against dD
Tabor (1950) representing the uniaxial stress and strain
2
2
44 minus
==
m
m DdA
dLp
ππ
22 )(112
DdDLNHBminusminus
=π
Ddp
rm
r 20 == εψ
σ
bull σr εr representative stress strain bull ψ plastic constraint factor (asymp28-30)
bull L applied load bull d diameter of residual impression bull D diameter of the ball indenter
bull A material constant bull m Meyer index ( asymp n+2)
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
5
Introduction
Convenient
In-situ amp In-field System
Non-destructive amp Local test
Simple amp fast
6
Instrumented Indentation test
A novel method to characterize mechanical properties
Hardness Elastic modulus Tensile properties Residual stress Fracture toughness
Indentation load-depth curve
Load
Depth
Loading
Unloading
7
Research history
Brinell (1900) defining as the ratio of the load to the surface area
Meyer (1908) defining as the ratio of the load to the projected area
OrsquoNeill (1944) expressing dD as the indentation strain plotting pm against dD
Tabor (1950) representing the uniaxial stress and strain
2
2
44 minus
==
m
m DdA
dLp
ππ
22 )(112
DdDLNHBminusminus
=π
Ddp
rm
r 20 == εψ
σ
bull σr εr representative stress strain bull ψ plastic constraint factor (asymp28-30)
bull L applied load bull d diameter of residual impression bull D diameter of the ball indenter
bull A material constant bull m Meyer index ( asymp n+2)
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
6
Instrumented Indentation test
A novel method to characterize mechanical properties
Hardness Elastic modulus Tensile properties Residual stress Fracture toughness
Indentation load-depth curve
Load
Depth
Loading
Unloading
7
Research history
Brinell (1900) defining as the ratio of the load to the surface area
Meyer (1908) defining as the ratio of the load to the projected area
OrsquoNeill (1944) expressing dD as the indentation strain plotting pm against dD
Tabor (1950) representing the uniaxial stress and strain
2
2
44 minus
==
m
m DdA
dLp
ππ
22 )(112
DdDLNHBminusminus
=π
Ddp
rm
r 20 == εψ
σ
bull σr εr representative stress strain bull ψ plastic constraint factor (asymp28-30)
bull L applied load bull d diameter of residual impression bull D diameter of the ball indenter
bull A material constant bull m Meyer index ( asymp n+2)
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
7
Research history
Brinell (1900) defining as the ratio of the load to the surface area
Meyer (1908) defining as the ratio of the load to the projected area
OrsquoNeill (1944) expressing dD as the indentation strain plotting pm against dD
Tabor (1950) representing the uniaxial stress and strain
2
2
44 minus
==
m
m DdA
dLp
ππ
22 )(112
DdDLNHBminusminus
=π
Ddp
rm
r 20 == εψ
σ
bull σr εr representative stress strain bull ψ plastic constraint factor (asymp28-30)
bull L applied load bull d diameter of residual impression bull D diameter of the ball indenter
bull A material constant bull m Meyer index ( asymp n+2)
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
8
Strength
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
9
Algorithm for strength evaluation
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
diams Step 1Determining contact areataking into considerationplastic pile-upsink-in
SphericalIndentation
Stress and StrainState in Material
=
Rhnf
hh max
ITc
pile
diams Step 2Defining stress and strain statein materials underneath spherical indenteras representative stress and strain
c
maxT A
F1Ψ
σ = θξε tan=T
diams Step 3 amp 4Fitting to constitutive equation andevaluating tensile properties
True strain εΤ
True
stre
ss σ
Τ
σ=E(ε-0002) σ=Kεn
Representative stress-strain points
E
Instrumented indentation testwith a spherical indenter
Tensile propertiesTensile properties
σy IT σu IT nIT EIT
Force-depth curveof multiple unloadings
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
10
Contact Area
Reference plane
Elastic deflection
dh-Plastic pile-upsink-in
pileh+
R
h c h d
h max
h pile
piledc hhhh +minus= max
SLhd
maxε= ) ( max
Rhnfhpile =
-WC Oliver amp GM Pharr J Mater Res (1992) -SH Kim et al Mater Sci Eng A (2006)
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
11
Representation
Indentation depth increases Stress and strain increase
γ γ
Representative Stress Definition
Ψ=σR
mPΨ Constraint Factor (about 3)
2max
cm a
LPπ
=
Representative Strain Definition
γααε tan)(1 2
=minus
=Ra
Rac
c
R
-DTabor The Hardness of Metals (1951) -JH Ahn et al JMR (2000)
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
12
Representation
Continuous
indentation
test
Load depth data
at each unloading
step (15th)
Stress strain
determination
at each step
(15 points)
Flow curve fitting
from stress-strain
points (K n determination)
Extrapolation of flow curve
up to yield strain and
uniform strain
Yield strength(YS)
Ultimate tensile strength (UTS)
Extrapolation for YS UTS
Stress strain determination
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
13
Determination
)0020( minus= yny EK εε
True
stre
ss
True strain
Yield strength
AL σ=
εdA
dAd=minus=
ll
σσd
AdA
=minus
σεσ=
dd
Tensile strength
nu =ε
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
14
Residual stress
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
15
Concept
0S LLL minus=∆
ht
ΔL
ΔL
LT
L0
Indentation depth
L o a d Compressive Tensile
Stress free
LC
Tensile stress
Indentation Load-Depth Curves
CLTL or
Vickersindenter
136
119923119923119931119931
119923119923119914119914
Compressive stress
Condition same indentation depth
High load is needed to reach to the same indentation depth
Less load is needed to reach to the same indentation depth
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
16
Stress tensor
Non-equibiaxial residual stress state
xres
yresp
σσ
=
σ+
σ+
σ+
xres
xres
xres
)p(
)p(
)p(
3100
03
10
003
1
σ+
minus
σminus
σminus
xres
xres
xres
)p(
)p(
)p(
3100
03
120
003
2
σσ
0000000
yres
xres
σσ
0000000
xres
xres
p
hydrostatic stress deviatoric stress
xresσ
yresσ
x
y
z
Stress Ratio
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
17
Evaluation
xresσ
3p)(1+
S
xres A
L1p)(1
3σ ∆Ψ+
=
S
xres A
L1σ3
p)(1 ∆Ψ
=+
=
σσ
= AreaContactp xres
yres A S
Deviatoric stress along Z direction Indentation stress
intσ
Ψ
=SA
ΔL1
where = constraint factor (30) Ψ
L σxres ∆prop
Residual Stress Indentation Load
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
18
Fracture toughness
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
19
Approach
How to correlate flat punch indentation with crack tip behavior in CRB test
isotropic
Virtual crack
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
20
concept
Scibetta (1999)
ldquoMaximum load can be evaluated by limit load in case of cracked round bar geometryrdquo
Limit load
For cracked round bar geometry
Von mises yield criterion a crack length b ligament radius R specimen radius
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
21
Fracture toughness calculation
J-integral formula from fracture mechanics
119869119869119868119868119868119868 = 119869119869119890119890 + 119869119869119901119901 =(1 minus 1205841205842)1198701198701198681198682
119864119864+ 120578120578119901119901119901119901
1198601198601199011199011199011199011205871205871198861198862
Apl area under force versus displacement record ηpl factor for specimen geometry and crack size πa2 ligament area
119870119870119869119869119868119868 =119869119869119868119868119868119868 ∙ 1198641198641 minus 1205921205922
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
22
Research Extension
High temp Low temp
MicroNano
Non-metallic material
scale
temp
material
bull Indentation size effect
bull Creep behavior bull Ductile to brittle transition
bull Ceramic bull Polymer
(RT Macro Metal)
23
Nanoindentation
24
Adhesion concept
25
23
Nanoindentation
24
Adhesion concept
25
24
Adhesion concept
25
25
