Fracture of materials
Classification of fractureⅠ
① Amount of plastic deformation
Vertical fracture
Cup and cone
Type fracture
Brittle fracture
Small plastic deformation
Shear fracture
（Separation of slip plane）
Chisel point
fracture
Ductile fracture
Large plastic deformation
Fracture surface geometry
Classification of fractureⅡ
② Transgranular and intergranular fracture
Intergranular
Brittle fracture
fracture
Fracture occurs along grain boundary
Transgranular
fracture
Ductile fractur
Fracture occurs in the grain
Intergranular and transgranular
fracture
Classification of fracture III
③ Atomic level
σ
Relation between slip and cleavage plane
Cleavage plane
σ
（a） Cleavage fracture
fcc
bcc
hcp
Slip plane
｛111｝
｛110｝
｛112｝
｛123｝
｛0001｝
｛1010｝
｛1011｝
Cleavage
plane
Non
｛100｝
｛0001｝
τ
Slip plane
Materials
τ
（b） Shear fracture
Al、Cu、Ni Cr、Mo、V
W、β-Ti
Ag、Au
Zn、Mg
Be、Sn
γsteel
α-Ti
Mild steel
Fractography
Fractography?
Method of observation and analysis of fracture surface
which records progress of fracture.
Fracture
surface
Process of fracture
例．
Initiation of
crack
Crack growth
Final fracture
Fracture shows peculiar appearance
Macro-fractography
Naked
Angle/color
Loupe
Appearance
Micro-fractography
Optical
River pattern
Electon
Microscopic
appearance
Characteristics of ductile fracture surfaceⅠ
Geometry of fracture surface depends on
stress state.
Tensile fracture
Plain strain
Perpendicular fracture surface
Plain stress
Shear fracture
Slant type (shear) fracture surface
Example
Cup and cone type
Macroscopic ～ Difference between
tensile and shear
Color of fracture surface ： Gray
Microscopic ～ Dimple formation
Shear fracture
Chisel point
fracture
Characteristics: mentioned later
Characteristics of brittle fracture surfaceⅡ
Geometry
Cleavage
Color ： Metal gray
Fracture pattern
Perpendicular fracture surface
Roughness
Chevron pattern
Starter notch
Fatigue crack Chevron pattern
Brittle fracture surface
Shear lip
Characteristics of fatigue fracture surfaceⅢ
Ductile materials
・Low cyclic stress and thick plate
Perpendicular; fracture surface
・High cyclic stress and thin plate
Slant fracture surface
Brittle materials
Beach mark
Initiation point
◎ Color ： Gray
Fatigue
Perpendicular fracture surface
For random cyclic stress
Beach mark
Final
fracture
（Ductile）
（Brittle fatigue fracture ⇒ Metal luster
Microscopic characteristicsⅠ（Ductile①）
Microscopic characteristics of ductile fracture
Dimple
… Many dips are formed
Ripple
Wavy pattern
25μm
(a)
25μm
(b)
25μm
(c)
25μm
(d)
Tensile ductile fracture in stainless steel（28% Cr－9% Ni steel ）
（Ductility）； (a) ＜ (b) ＜ (c) ＜ (d)）
Characteristics of ductile fracture surfaceⅡ
σ1
σ1
σ1
（a） Equaxed dimple
ττ
σ2
σ2
ττ
σ1
（b） Elongated dimple
（Shear load）
M
M
（c） Elongated dimple
（Tear load）
Characteristics of brittle fracture surfaceⅣ
Characteristics of brittle fracture ①
River pattern
When crack propagates on
cleavage plane in which
dislocation exists,
River pattern is formed.
◎ Crack initiation is in grain boundary
◎ Flow of river pattern
＝ Propagation direction of crack growth
20μm
River pattern for mild steel
at low temperature impact load
Characteristics of fatigue fracture surface Ⅵ
Characteristics of fatigue fracture surface
Striation
Microscopic
Depending on loading、
point of fracture surface
2μm
Fracture mechanism changes
each stage of growth
Striation
（25% Cr－5% Ni steel）
Microscopic pattern depends on
each stage of crack growth
Always don’t observe
Ductile fractureⅠ
Ductile fracture
Theoretical shear strength
Macro ～ Cup and cone etc.
Micro ～ Dimple
Perfect crystal without defect
X
Elastic line in X＝O
τ
τ
a
Slip plane
τ
⎛ 2πX ⎞
τ=τmax sin ⎜
⎟
⎝ b ⎠
O
X
b
Theoretical shear strength
（τmax ： Shear stress between atoms ）
Next
Ductile fractureⅡ
Elastic line at X＝O
τ
◎ Whiskerー
Material without dislocation
O
X
◎ Normal materilas
1/10 ～ 1/100
（ τ at X＝0 ）
…（ 4.1）
2πX
⎛ 2πX ⎞
sin ⎜
τ = τmax ≒
τ
⎟
max
b
b
⎝
⎠
（ For small θ
⎛X⎞
τ = Gγ　= G ⎜ ⎟
⎝a⎠
⇒
sin θ≒θ）
…（ 4.2）
τmax
G
⎛ 1 ⎞⎛ b ⎞
= ⎜ ⎟⎜ ⎟G ≒
10
⎝ 2π⎠⎝ a ⎠
…（ 4.3）
Ductile fractureⅢ
Initiation and growth of void
Void : Initiates at inclusion and delaminate from matrix
Maximum
shear at
45 degree
（a）
（b）
（c）
Cup and cone type tensile fracture process
（d）
Brittle fractureⅠ
σ
X
Theoretical cleavage fracture strength
Brittle fracture surface
a0
Cleavage plane
Macro ～ Chevron pattern
Micro ～ River pattern、Tonge
σ
Elastic line at X=0
Brittle fracture
Absorbed energy : Small
Stored energy in material is
consumed to grow crack
Stress σ
a0
σmax
λ／2
Displacement X
Rapidly crack growth ⇒ Instant fracture
Balance position
Brittle fractureⅡ
Elastic line at X=0
Stress σ
a0
σmax
a0 ：Distance
between atoms
◎ Whisker
Without dislocation ⇒ Near value
◎ High strength steel etc.
λ／2
Displacement X
Balance position
（Sine fuction）
Difference of one order more
…（ 4.4）
2πX
⎛ 2πX ⎞
σ = σmax sin ⎜
≒
σ
⎟
max
λ
λ
⎝
⎠
（For small θ
⇒
sin θ≒θ）
（Stress-strain relation at X＝0）
⎛X⎞
σ = Eε　= E ⎜⎜ ⎟⎟
⎝ a0 ⎠
…（ 4.5）
σmax
⎛ λ ⎞⎛⎜ E ⎞⎟
= ⎜ ⎟⎜ ⎟
⎝ 2π⎠⎝ a 0 ⎠
…（ 4.6）
Brittle fractureⅢ
Elastic line at X=0
Stress σ
a0
Work used delamination of atoms
σmax
Energy consumes formation of
new free surface
λ／2
Displacement X
γ： Surface energy per unit area
Balance position
σmax
⎛ λ ⎞⎛⎜ E ⎞⎟
= ⎜ ⎟⎜ ⎟
⎝ 2π⎠⎝ a 0 ⎠
…（4.6）
λ
2
0
∫
λσmax
⎛ 2πX ⎞
σmax sin ⎜
= 2γ
⎟ dX =
π
⎝ λ ⎠
…（4.7）
Two new free surfaces
σmax
⎛ Eγ⎞ 12 E
⎟⎟ ≒
= ⎜⎜
10
⎝ a0 ⎠
…（4.8、4.9）
Brittle fracture Ⅳ （Griffith’s theory①）
Fracture strength of perfect brittle material with crack
σ
UE ： Strain energy stored in plate
Free plane
σ2
UE =
×πc 2
2E
πc 2σ2
UE =
E
ρ
: Rigid solution
2c
US ： Energy to form crack plane
U s = 2 × 2γc = 4γc
σ
Two planes
Next
Rate of energy
Brittle fractureⅤ （ Griffith’s theory ②）
dU E 2πcσ2
=
dc
E
dU S
= 4γ
dc
Criterion of fracture
dU E dU S
=
dc
dc
…（4.12）
2πcσ2
= 4γ
E
Griffith’s equation
Crack length c
Variation of energy rate
With increasing crack length
⎛ 2 Eγ ⎞
σ= ⎜
⎟
⎝ πc ⎠
1
2
…（4.13）
（Plane stress state）
Fig. An oil barge that fractured in a brittle manner
by crack propagation around its girth
（The New York Times）
Classification of fractureⅣ
④ Loading and environment
Impact failure
Static, Environmental
Corrosion
3%
σ
Static fracture
13%
Delay fracture、
Stress corrosion cracking
5%
11%
Themal fatigue
Corrosion fatigue
Fretting fatigue
Fatigue
60%
8%
Fatigue
t
Loading and fracture
Low cycle fatigue
Classification of fracture
About 80% of fracture
was caused by fatigue
Microscopic fracture surfaceⅢ（Ductile fracture③）
Microvoid along
grain boundary
Crack growth inside
Grain boundary
Elongated dimple
2μm
(a) Shallow dimple
25μm
Shallow
(b) 組織
図．Two phase stainless steel （25% Cr-5% Ni steel）
Microscopic fracture surfaceⅤ（Brittle fracture②）
Brittle fracture surface ②
Tongue appearance
… Twin deformation related
τ
τ
20μm
Twin
Bound. Bound.
図．High Cr ferrite steel（475℃ageing
Fracture analysisⅠ
① Wire Rope failure to catch shark
Macroscopic
Wire Rope ⇒
Microscopic
Large Necking
Dimple
Ductile fracture
5μm
10μm
(a) Equiaxed dimple
(b) Elongated dimple
図．Microscopic appearance of wire-rope
Fracture anaysisⅡ
② Rail fracture surface
Beach mark
(a) … Fatigue
(b) … Brittle fracture
(a)
Chevron pattern
(b)
10μm
（a） Striation
15μm
（b） River pattern
Fracture anaysisⅢ
③ Bolt fracture surface for ship
Striation
Beach mark
10μm
図．Bolt（SUS304）microscopic appearance
Under cyclic loading
Fatigue facture
Measurement of striation space
Fatigue crack growth rate
Ductile fractureⅣ
◎ Microstructure effect
・Content
Void formation ⇒ Inclusion
・Size, Geometry
・Distribution
● Globular martensite
Sample geometry、Stress condition
○ Ferriteト‐globular perrite
Ductility
△ Ferrite‐layer perrite
Sulfide
Inclusion(2 phase) Vol.%
Ductile fracture model
（McClintock）
Brittle fractureⅥ
①）
［Ⅰ］ Mechanical factor ①
・ Low temperature
・ Loading rate
・ Notch
・ Thickness
Locally stress increases
Constrain of plastic
deformation
Brittle
Toughness evaluation
Hammer
Sharpy impact test
Measure
Potential energy of Hammer
＝
h1
α
Remained Energy after impact
＋
Absorbed energy of material
（Toughness）
β
h2
Notched specimen
Sharpy impact tester
Brittle fractureⅦ
80
Rate of reduction
of area
160
Tensile test
60
120
40
80
Impact test
Absorption energy
20
40
0
0
-200
-150
-100
-50
0
50
100
150
Ductile
Absorption energy J
Reduction of area ％
［Ⅰ］ Mechanical factors ② （Ductile-Brittle Transition Behavior）
Ductile-Brittle Transition
Temperature
Temperature ℃
Brittle
Ductile-Brittle Transition
Brittle fractureⅧ
Absorption energy J
［Ⅰ］ Mechanical factors ③
（Question） Which is the best steel for tanker?
Each steel is the same strength.
Oil
Natural Gas
Gas ⇒ Liquid
Temperature decreases
（a）
（b）（c）
Ductile
Brittle
High risk of brittle fracrure
Under low temperature
Material must keep ductile
Temperature ℃
D.-B. transition temp. must be low
（Ex. ： Titanic sinked in 1912.4.14）
・ Notch effect
Notch induces Stress concentration and high three axis stress condition
・ Plate thickness
Thickness increases, Three axis stress condition becomes high.
Brittle fractureⅨ
［Ⅱ］ Microstructure effect ① （Crystal structure, Chemical composition）
bcc crystal （Mild steel）
σ
Low temperature brittle
Cleavage plane fcc crystal
（Cu、Al、Ni、18%Cr-8%Ni stainless steel）
Difficult brittle
σ
LiquidO2 orLiquidN2 vessel
P, C, O, H etc.
Low toughness
Transition temp.
Brittle
C、P
Increase
Urge
Ni、Mn
Decrease
Restraint
Brittle fractureⅩ
［Ⅱ］ Microstructure ② （Carbon steel）
C content of carbon steel
High Transition temperature
Low absorption energy
Brittleness
General
High strength
Charpy impact energy J
High carbon
Brittle
Temperature ℃
Fine grain
High strength
＋
Improvement of toughness
Creep fractureⅠ（Creep phenomenon）
Creep?
Under a stress and temperature
Plastic deformation is induced.
Failure
Strain ε
（Ex.
Accelerated creep
Steady creep
Heating
W
Transient creep
High temperature
Deformation ～ Stress and Time
Work hardening Cancellation
Softening）
Deformation depends on time
and loading
Work hardening
Softening
Time t
Creep fractureⅡ（Creep strength）
Creep rate at steady creep stage
Strain ε
Failure
Small creep rate
Creep rate
Time to tolerance strain
=long using period
Creep strength
（例）
A constant stress of 100MPa
Steady creep
Strain=0.01%
103 Hours
Creep strength =100MPa at 0.01% ／ 103 h
Time t
Creep fractureⅢ
Stress increase
Strain
Temperature increase
Steady creep rate ％／hr
［Ⅰ］ Effects of temperature and stress ［Ⅱ］ Microstructure effect
Time
Time ℃
Temperature and stress increases
Steady creep is dominant
Creep rate increases
Creep strength decreases
Fcc crystal
Large Activated energy
High creep strength
Creep fractureⅣ
［Ⅲ］ Grain size
Normal temperature=Low
Strengthening
Refinement strength
High temperature
Grain size refinement
Creep strength decreases
Under high temperature
Grain boundary slip
・ Substitutional element
Interaction between dislocation or vacancy is restrained
And then creep strength increases.
・ Stacking fault energy decreases, creep strength increases
Creep fractureⅤ
Void
A
A
⇒
B
B
C
C
Cavity
A
A
⇒
B
C
C
A
B
C
Grain boundary
B
A
⇒
Cavity
Particle
B
W type cracking
C
r type cracking
Two type intergranural cracking at high temperature creep
脆性破壊ⅩⅠ（脆性破壊に及ぼす諸因子の影響⑥）
［Ⅱ］材料学的因子の影響 ③ （熱処理）
・４７５℃脆化
熱処理で性質が変化
（教科書 P126 図4.32）
・高温焼戻し脆化
Cr
Mn
添加
高温焼戻し
粒界偏析
脆化
・青熱脆化
軟鋼を200~350℃で負荷
ひずみ時効
（転位の固着作用の促進）
20μm
20μm
時効材
未時効材
脆性破面
延性破面
図．35% Cr-5% Niフェライト鋼の
４７５℃時効の引張破面形態に及ぼす影響
脆化
・ σ相脆化
高Crを持つαステンレス鋼など
700~900℃
σ相
（脆性な第２相析出）
加熱
著しい脆化
巨視的破面の特徴Ⅳ（疲労破面②）
（教科書 P100, 図4.6）
疲労破壊
微視組織の影響
大
結晶粒ごとに
き裂の進展方向が変化
組織の痕跡が破面上に残る
１mm
※ 脆性破面も巨視的には類似
微視的な特徴（破壊機構）が異なる
破面の色彩
図．粗大結晶粒をもつ二相ステンレス鋼
（25% Cr－5% Ni鋼）
破壊事故破面解析事例Ⅳ
④ その他（破壊の実例）
◎ ジェット戦闘機「F‐111」の破壊事故（1969年）
⇒ 主翼の金具に疲労き裂が発生し、
このき裂のわずかな進展により早期運転中に破壊
◎ 日航ジャンボ機墜落事故（1985年）
⇒ 機体後部圧力隔壁が金属疲労により破壊し、機体もろとも御巣鷹山に墜落
◎ 高速増殖炉「もんじゅ」のナトリウム漏洩事故（1995年）
⇒ 温度計さやの金属疲労が原因で、大量のナトリウムが漏洩
◎ 京福電鉄事故、ブレーキ制御棒の破断（2000年）
⇒ ブレーキ制御棒の金属疲労が進み破断に至った
◎ 中華航空機墜落事故（2002年）
⇒ 金属疲労による機体の空中分解による墜落。