仪器压痕法断裂韧性检测方法

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h*
0
L dh Ac
17
K JC
wf E (1 2 )
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Hertzelasticcontact th eory
Expandingcavitymodel(elastic- plastic theory)
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13
Hertz elastic contact theory
0
Indentation depth (m)
- Inserting determined Pmc into Pm-h curve
(5) Equivalent fracture energy until h*
(6) Indentation fracture toughness (KJC)
wf
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
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sr
1 2 p
2
m
By Von Mises’ yield criterion
y pm C1 s ys
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14
Expanding cavity model (E-P theory)

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
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15
c C2 a
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Ductile Fracture Model
9
Brittle Fracture Model
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10
Criterion
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
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
JC E 2 (1 )
JC
= Required energy for crack propagation
Equivalent fracture energy in Indentation
Analysis of indentation process
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Similar constraint effect
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3
Constraint effect
SENB
loading R=250m Indenter
Indentation
[Material : API X70]
Evaluation of Fracture Toughness of Materials Using Instrumented Indentation Technique: Ductile/Brittle Fracture Models
2013. 08. 30.
Won Je Jo
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Formation of equivalent fracture energy
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8
Fracture Behavior
Brittle materials Ductile materials
Fracture surface
Onset of formation to a fully-developed plastic zone = Formation of Equivalent fracture energy
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12
Application of indentation theories
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*
Contents
Introduction
Basic concept of indentation fracture toughness
Indentation Fracture Toughness Models
- Brittle fracture model - Ductile fracture model
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
4
Indentation fracture toughness
Analogous situation
K JC
JC E (1 2 )
5
K JC ?
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Energy concept
K JC
c pm
y pm pi
c pm C f s ys
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16
Fracture toughness for brittle material
(1) Indentation testing
Indentation load-depth curve
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
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2
Constraint effect
Plastic region constrained by elastic region
ahead of a crack tip
beneath an indenter
Large plastic deformation Strain controlled critical fracture strain at the crack tip (ef) When strain reached critical fracture strain
Brittle Fracture Model
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
6
Indion of a plastic zone to the surface
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7
a
Expansion of plastic zone (c/a increase)
reliability?whenaradialstressattheedgeofthecontactarearasatisfiedyieldingcriterion??mrp???22?1??byvonmisesyieldcriterionysymcp????114expandingcavitymodeleptheoryexpandingcavitymodeleptheorystresswithinplasticzonearcip????31ln2?????rcyy???????32ln2????rcyr?corefastamp
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?
Verification of the Models
- Comparison between fracture test results and IIT results - Applications at low temperature
Issue of indentation fracture toughness
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
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 ≈
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
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c m
11
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
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