仪器压痕法断裂韧性检测方法
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In the case of metals,
Fracture test
IIT
Indenter
Crack propagation and fracture
No crack and no fracture
What is a correlation between fracture test and IIT?
p sr 2 c 2 ln i s ys 3 a s ys
2 c pi 2 ln s ys a 3
c 1 a
Fast & Precise Solutions for Quality & Reliability
15
c C2 a
Fast & Precise Solutions for Quality & Reliability
2
Constraint effect
Plastic region constrained by elastic region
ahead of a crack tip
beneath an indenter
Formation of equivalent fracture energy
Fast & Precise Solutions for Quality & Reliability
8
Fracture Behavior
Brittle materials Ductile materials
Fracture surface
Onset of formation to a fully-developed plastic zone = Formation of Equivalent fracture energy
Fast & Precise Solutions for Quality & Reliability
12
Application of indentation theories
Contents
Introduction
Basic concept of indentation fracture toughness
Indentation Fracture Toughness Models
- Brittle fracture model - Ductile fracture model
Stress within plastic zone (a ≤ r ≤ c)
core
s s c 1 2 ln( ) sy sy r 3 sr c 2 2 ln( ) sy r 3 pi s r
pm pi
Change of the core pressure (r = a) until forming the fully-developed plastic zone
Deformation Criterion Formation of fracture energy
Relatively little or no deformation Stress controlled critical fracture stress at the crack tip (sf) When stress reached critical fracture stress
Stress outside the contact area (r ≥ a)
( 1 2 )a 2 s r s pm 2 2r
sz 0
When a radial stress at the edge of the contact area (r = a) satisfied yielding criterion
h*
0
L dh Ac
17
K JC
wf E (1 2 )
Fast & Precise Solutions for Quality & Reliability
a
h*
c
Step 1
Yielding right outside the contact area → Formation of a plastic zone to the surface
Step 2
Expansion of the plastic zone → Formation of fully-developed plastic zone
6 5 --- y=3.01177[1-exp{-4.57486(x+0.31229)}] 4
6 5 4
3.0
--- y=3.29831[1-exp{-3.65099(x+0.27357)}]
tmax
tmax
3.2 3 2
3 2 1 0 0.0
2.3
0.1 0.2 0.3 0.4 0.5 0.6
3.0
by K.E. Puttick (1977)
Criterion of equivalent fracture energy
The total pressure required for equivalent fracture energy,
c y pm pm pm
Step 1 Step 2
Criterion
Critical stress(pressure) at h*
L (kgf)
εrr
Critical indentation depth (h*)
hmax (m)
pm p
Fast & Precise Solutions for Quality & Reliability
c m
11
Similar constraint effect
Fast & Precise Solutions for Quality & Reliability
3
Constraint effect
SENB
loading R=250m Indenter
Indentation
[Material : API X70]
JC E 2 (1 )
JC
= Required energy for crack propagation
Equivalent fracture energy in Indentation
Analysis of indentation process
Fast & Precise Solutions for Quality & Reliability
Fast & Precise Solutions for Quality & Reliability
Ductile Fracture Model
9
Brittle Fracture Model
Fast & Precise Solutions for Quality & Reliability
10
Criterion
Verification of the Models
- Comparison between fracture test results and IIT results - Applications at low temperature
Issue of indentation fracture toughness
1 0 0.0
2.1
0.1 0.2 0.3 0.4 0.5 0.6
3.2
V / Vmax
hmax / R
Triaxiality of crack tip Triaxiality of indentation
Fast & Precise Solutions for Quality & Reliability
c pm
y pm pi
c pm C f s ys
Fast & Precise Solutions for Quality & Reliability
16
Fracture toughness for brittle material
(1) Indentation testing
Indentation load-depth curve
6
Indentation process
Formation of a plastic zone to the surface
Fast & Precise Solutions for Quality & Reliability
7
a
Expansion of plastic zone (c/a increase)
Evaluation of Fracture Toughness of Materials Using Instrumented Indentation Technique: Ductile/Brittle Fracture Models
2wk.baidu.com13. 08. 30.
Won Je Jo
Fast & Precise Solutions for Quality & Reliability
c
c/a
h* h
a
h*
Formation of a fully-developed plastic zone (c/a is constant)
c
Assumption
Onset of formation of a fully-developed plastic zone = Maximum strain energy beneath the indenter ≈
60 50 40
(2) Measuring σys & Determining Pmc
- σys from analyzing L-h curve c pm C f s ys
(3) Fitting Pm-h curve
- Mean contact pressure at each unloading depth
sr
1 2 p
2
m
By Von Mises’ yield criterion
y pm C1 s ys
Fast & Precise Solutions for Quality & Reliability
14
Expanding cavity model (E-P theory)
0
Indentation depth (m)
- Inserting determined Pmc into Pm-h curve
(5) Equivalent fracture energy until h*
(6) Indentation fracture toughness (KJC)
wf
Large plastic deformation Strain controlled critical fracture strain at the crack tip (ef) When strain reached critical fracture strain
Brittle Fracture Model
Indentation mean pressure(kgf/m )
2
Pm - h curve
1500
L (kgf)
30 20 10 0 0 20 40 60 80 100 120 140 160 hmax (m)
Pm
c
pm
Lmax ac 2
1000
500
h*
0 20 40 60 80
(4) Determining h*
4
Indentation fracture toughness
Analogous situation
K JC
JC E (1 2 )
5
K JC ?
Fast & Precise Solutions for Quality & Reliability
Energy concept
K JC
Assumption
Rate of expansion
final plastic zone size dc time dt
dc da c / constant dt dt a da
dt
; rate of core expansion
fully - developedplasticzone
Hertzelasticcontact th eory
Expandingcavitymodel(elastic- plastic theory)
Fast & Precise Solutions for Quality & Reliability
13
Hertz elastic contact theory
Fracture test
IIT
Indenter
Crack propagation and fracture
No crack and no fracture
What is a correlation between fracture test and IIT?
p sr 2 c 2 ln i s ys 3 a s ys
2 c pi 2 ln s ys a 3
c 1 a
Fast & Precise Solutions for Quality & Reliability
15
c C2 a
Fast & Precise Solutions for Quality & Reliability
2
Constraint effect
Plastic region constrained by elastic region
ahead of a crack tip
beneath an indenter
Formation of equivalent fracture energy
Fast & Precise Solutions for Quality & Reliability
8
Fracture Behavior
Brittle materials Ductile materials
Fracture surface
Onset of formation to a fully-developed plastic zone = Formation of Equivalent fracture energy
Fast & Precise Solutions for Quality & Reliability
12
Application of indentation theories
Contents
Introduction
Basic concept of indentation fracture toughness
Indentation Fracture Toughness Models
- Brittle fracture model - Ductile fracture model
Stress within plastic zone (a ≤ r ≤ c)
core
s s c 1 2 ln( ) sy sy r 3 sr c 2 2 ln( ) sy r 3 pi s r
pm pi
Change of the core pressure (r = a) until forming the fully-developed plastic zone
Deformation Criterion Formation of fracture energy
Relatively little or no deformation Stress controlled critical fracture stress at the crack tip (sf) When stress reached critical fracture stress
Stress outside the contact area (r ≥ a)
( 1 2 )a 2 s r s pm 2 2r
sz 0
When a radial stress at the edge of the contact area (r = a) satisfied yielding criterion
h*
0
L dh Ac
17
K JC
wf E (1 2 )
Fast & Precise Solutions for Quality & Reliability
a
h*
c
Step 1
Yielding right outside the contact area → Formation of a plastic zone to the surface
Step 2
Expansion of the plastic zone → Formation of fully-developed plastic zone
6 5 --- y=3.01177[1-exp{-4.57486(x+0.31229)}] 4
6 5 4
3.0
--- y=3.29831[1-exp{-3.65099(x+0.27357)}]
tmax
tmax
3.2 3 2
3 2 1 0 0.0
2.3
0.1 0.2 0.3 0.4 0.5 0.6
3.0
by K.E. Puttick (1977)
Criterion of equivalent fracture energy
The total pressure required for equivalent fracture energy,
c y pm pm pm
Step 1 Step 2
Criterion
Critical stress(pressure) at h*
L (kgf)
εrr
Critical indentation depth (h*)
hmax (m)
pm p
Fast & Precise Solutions for Quality & Reliability
c m
11
Similar constraint effect
Fast & Precise Solutions for Quality & Reliability
3
Constraint effect
SENB
loading R=250m Indenter
Indentation
[Material : API X70]
JC E 2 (1 )
JC
= Required energy for crack propagation
Equivalent fracture energy in Indentation
Analysis of indentation process
Fast & Precise Solutions for Quality & Reliability
Fast & Precise Solutions for Quality & Reliability
Ductile Fracture Model
9
Brittle Fracture Model
Fast & Precise Solutions for Quality & Reliability
10
Criterion
Verification of the Models
- Comparison between fracture test results and IIT results - Applications at low temperature
Issue of indentation fracture toughness
1 0 0.0
2.1
0.1 0.2 0.3 0.4 0.5 0.6
3.2
V / Vmax
hmax / R
Triaxiality of crack tip Triaxiality of indentation
Fast & Precise Solutions for Quality & Reliability
c pm
y pm pi
c pm C f s ys
Fast & Precise Solutions for Quality & Reliability
16
Fracture toughness for brittle material
(1) Indentation testing
Indentation load-depth curve
6
Indentation process
Formation of a plastic zone to the surface
Fast & Precise Solutions for Quality & Reliability
7
a
Expansion of plastic zone (c/a increase)
Evaluation of Fracture Toughness of Materials Using Instrumented Indentation Technique: Ductile/Brittle Fracture Models
2wk.baidu.com13. 08. 30.
Won Je Jo
Fast & Precise Solutions for Quality & Reliability
c
c/a
h* h
a
h*
Formation of a fully-developed plastic zone (c/a is constant)
c
Assumption
Onset of formation of a fully-developed plastic zone = Maximum strain energy beneath the indenter ≈
60 50 40
(2) Measuring σys & Determining Pmc
- σys from analyzing L-h curve c pm C f s ys
(3) Fitting Pm-h curve
- Mean contact pressure at each unloading depth
sr
1 2 p
2
m
By Von Mises’ yield criterion
y pm C1 s ys
Fast & Precise Solutions for Quality & Reliability
14
Expanding cavity model (E-P theory)
0
Indentation depth (m)
- Inserting determined Pmc into Pm-h curve
(5) Equivalent fracture energy until h*
(6) Indentation fracture toughness (KJC)
wf
Large plastic deformation Strain controlled critical fracture strain at the crack tip (ef) When strain reached critical fracture strain
Brittle Fracture Model
Indentation mean pressure(kgf/m )
2
Pm - h curve
1500
L (kgf)
30 20 10 0 0 20 40 60 80 100 120 140 160 hmax (m)
Pm
c
pm
Lmax ac 2
1000
500
h*
0 20 40 60 80
(4) Determining h*
4
Indentation fracture toughness
Analogous situation
K JC
JC E (1 2 )
5
K JC ?
Fast & Precise Solutions for Quality & Reliability
Energy concept
K JC
Assumption
Rate of expansion
final plastic zone size dc time dt
dc da c / constant dt dt a da
dt
; rate of core expansion
fully - developedplasticzone
Hertzelasticcontact th eory
Expandingcavitymodel(elastic- plastic theory)
Fast & Precise Solutions for Quality & Reliability
13
Hertz elastic contact theory