仪器压痕法断裂韧性检测方法

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2
Constraint effect
Plastic region constrained by elastic region
ahead of a crack tip
beneath an 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
Formation of equivalent fracture energy
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8
Fracture Behavior
Brittle materials Ductile materials
Fracture surface
4
Indentation fracture toughness
Analogous situation
K JC
JC E (1 2 )
5
K JC ?
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Energy concept
K JC
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
1 0 0.0
2.1
0.1 0.2 0.3 0.4 0.5 0.6
3.2
V / Vmax crack tip Triaxiality of indentation
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Ductile Fracture Model
9
Brittle Fracture Model
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10
Criterion
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
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*
c pm
y pm pi
c pm C f s ys
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Fracture toughness for brittle material
(1) Indentation testing
Indentation load-depth curve
JC E 2 (1 )
JC
= Required energy for crack propagation
Equivalent fracture energy in Indentation
Analysis of indentation process
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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
Large plastic deformation Strain controlled critical fracture strain at the crack tip (ef) When strain reached critical fracture strain
Brittle Fracture Model
Verification of the Models
- Comparison between fracture test results and IIT results - Applications at low temperature
Issue of indentation fracture toughness
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 ≈
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
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
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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h*
0
L dh Ac
17
K JC
wf E (1 2 )
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0
Indentation depth (m)
- Inserting determined Pmc into Pm-h curve
(5) Equivalent fracture energy until h*
(6) Indentation fracture toughness (KJC)
wf
Assumption
Rate of expansion