Fracture of materials

破壊事故破面解析事例Ⅳ

④ （破壊の実例）

◎ ジェット戦闘機 「F‐111」の破壊事故 （1969年）

◎ 日航ジャンボ機墜落事故 （1985年）

◎ 高速増殖炉「もんじゅ」のナトリウム漏洩事故 （1995年）

◎ 京福電鉄事故、ブレーキ制御棒の破断 （2000年）

◎ 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。

⇒ 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

⇒ 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

⇒ 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

⇒ ブレーキ制御棒の金属疲労が進み破断に至った

Actual fracture accidents

Classification of fracture

Static fracture

13%

Corrosion

3%

Delay fracture、

Stress corrosion cracking 5%

Themal fatigue

Corrosion fatigue

Fretting fatigue

11% Fatigue

60%

Low cycle fatigue

8%

Ductile fracture

Classification of fractureⅠ

① Amount of plastic deformation

Vertical fracture Cup and cone

Type fracture

Chisel point

fracture

Shear fracture

（Separation of slip plane）

Fracture surface geometry Small plastic deformation

Brittle fracture Ductile fracture

Large plastic deformation

Classification of fractureⅡ

② Transgranular and intergranular fracture

Fracture occurs along grain boundary

Intergranular

fracture

Brittle fracture

Transgranular

fracture Ductile fracture

Fracture occurs in the grain

Intergranular and transgranular

fracture

Microstructure types

Brittle fracture

σ

σ

Classification of fracture III

Cleavage plane

（a） Cleavage fracture

（b） Shear fracture

③ Atomic level

τ

τ

Slip plane

Slip plane ｛111｝

｛0001｝

｛123｝

｛112｝ ｛110｝

｛1011｝

｛1010｝

Cleavage

plane ｛0001｝ ｛100｝ Non

Materials

Al、Cu、Ni

Ag、Au

γsteel

Cr、Mo、V

W、β-Ti

Mild steel

Zn、Mg

Be、Sn

α-Ti

fcc bcc hcp

Relation between slip and cleavage plane

Fractography

Initiation of

crack

Crack growth Final fracture Fracture

surface

Fractography?

Method of observation and analysis of fracture surface

which records progress of fracture.

例．

River pattern

Process of fracture

Fracture shows peculiar appearance

Macro-fractography

Naked

Loupe

Angle/color

Appearance

Micro-fractography

Optical

Electon Microscopic

appearance

Characteristics of ductile fracture surfaceⅠ

Tensile fracture

Plain strain

Perpendicular fracture surface

Cup and cone type

Example

Geometry of fracture surface depends on

stress state.

Shear fracture Plain stress

Slant type (shear) fracture surface

Color of fracture surface ： Gray

Macroscopic ～ Difference between

tensile and shear

Microscopic ～ Dimple formation

Characteristics: mentioned later Shear fracture

Chisel point

fracture

Characteristics of brittle fracture surfaceⅡ

Cleavage Geometry

Fracture pattern

Perpendicular fracture surface

Color ： Metal gray

Roughness

Chevron pattern

Starter notch

Brittle fracture surface

Chevron pattern Fatigue crack Shear lip

Characteristics of fatigue fracture surfaceⅢ

・Low cyclic stress and thick plate

Slant fracture surface

Perpendicular; fracture surface

・High cyclic stress and thin plate

Ductile materials

Brittle materials

Perpendicular fracture surface

Color ： Gray

（Brittle fatigue fracture ⇒ Metal luster

◎

For random cyclic stress

Beach mark

Fati

gu

e F

ina

l

fract

ure

（D

uct

ile）

Initiation point

Beach mark

Microscopic characteristicsⅠ（Ductile①）

25μm 25μm 25μm 25μm

(a) (b) (c) (d)

Tensile ductile fracture in stainless steel（28% Cr－9% Ni steel ）

（Ductility）； (a) ＜ (b) ＜ (c) ＜ (d)）

Microscopic characteristics of ductile fracture

Dimple … Many dips are formed

Ripple

Wavy pattern

σ1

σ1

σ1 σ2

σ1

τ

τ

σ2

M

M

σ1

σ1 τ

τ M

M

（a） Equaxed dimple （b） Elongated dimple （c） Elongated dimple

（Shear load） （Tear load）

Characteristics of ductile fracture surfaceⅡ

When crack propagates on

cleavage plane in which

dislocation exists,

River pattern is formed.

Characteristics of brittle fracture surfaceⅣ

20μm

River pattern for mild steel

at low temperature impact load

Characteristics of brittle fracture ①

River pattern

◎ Flow of river pattern

＝ Propagation direction of crack growth

◎ Crack initiation is in grain boundary

Fatigue cracks

Fatigue crack Fatigue crack Fatigue crack

Fatigue fracture Fatigue crack

Characteristics of fatigue fracture surface Ⅵ

2μm

Striation

（25% Cr－5% Ni steel）

Characteristics of fatigue fracture surface

Striation

Microscopic

Always don’t observe

Depending on loading、

point of fracture surface

Fracture mechanism changes

each stage of growth

Microscopic pattern depends on

each stage of crack growth

Ductile fractureⅠ

Ductile fracture

Macro ～ Cup and cone etc.

Micro ～ Dimple

a

b τ

τ

Theoretical shear strength

Perfect crystal without defect

O X

τ

Theoretical shear strength Next

Slip plane

X Elastic line in X＝O

（τmax ： Shear stress between atoms ）

b

Xπ　ττ

2sinmax

Ductile fractureⅡ

O X

τ Elastic line at X＝O

a

XG G γ　τ …（ 4.2）

10

G

a

b

2

1max ≒

πτ G

…（ 4.3）

（ τ at X＝0 ）

b

X2

b

X2sin maxmax

πτ≒

π　ττ

（ For small θ ⇒ sin θ≒θ）

…（ 4.1）

◎ Whiskerー

Material without dislocation

◎ Normal materilas

1/10 ～ 1/100

Ductile fractureⅢ Initiation and growth of void

（a） （b） （c） （d）

Cup and cone type tensile fracture process

Maximum

shear at

45 degree

Void : Initiates at inclusion and delaminate from matrix

Brittle fractureⅠ

Theoretical cleavage fracture strength

Brittle fracture surface

Macro ～ Chevron pattern

Micro ～ River pattern、Tonge

Brittle fracture

Absorbed energy : Small

Stored energy in material is

consumed to grow crack

Rapidly crack growth ⇒ Instant fracture

a0

λ／2

Balance position Displacement X

Str

ess

σ

Elastic line at X=0

σmax

Cleavage plane a0

X

σ

σ

Brittle fractureⅡ

（Stress-strain relation at X＝0）

0a

X E E ε　σ …（ 4.5）

（Sine fuction）

λ

πσ≒

λ

π　σσ

X2

X2sin maxmax

（For small θ ⇒ sin θ≒θ）

…（ 4.4）

a0

λ／2

Balance position Displacement X

Str

ess

σ

Elastic line at X=0

σmax

a0 ：Distance

between atoms

a

E

2 0

max

π

λσ

…（ 4.6）

◎ Whisker

Without dislocation ⇒ Near value

◎ High strength steel etc.

Difference of one order more

Brittle fractureⅢ

a0

λ／2

Balance position Displacement X

Str

ess

σ

Elastic line at X=0

σmax

a

E

2 0

max

π

λσ

…（4.6）

Work used delamination of atoms

γπ

λσ

λ

πσλ

2 X2

sin max2

0max

dX

Two new free surfaces …（4.7）

Energy consumes formation of

new free surface

γ： Surface energy per unit area

10

E

a

E2

1

0

max ≒γ

σ

…（4.8、4.9）

Brittle fracture Ⅳ （Griffith’s theory①）

UE ： Strain energy stored in plate

22

E2E

U cπσ

EU

22

E

σπc : Rigid solution

US ： Energy to form crack plane

cc γγ 422Us

Next σ

σ

2c ρ

Free plane

Two planes

Fracture strength of perfect brittle material with crack

dc

dU

dc

dU SE

Criterion of fracture

…（4.12）

Brittle fractureⅤ （ Griffith’s theory ②）

E

c

dc

dUE

22 σπ

4dc

dUS

Crack length c

Rat

e of

ener

gy

Variation of energy rate

With increasing crack length

42 2

E

cσπ

2

1

2

c

E

πσ

Griffith’s equation

…（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

Classification of fracture

Static fracture

13%

Corrosion

3%

Delay fracture、

Stress corrosion cracking 5%

Themal fatigue

Corrosion fatigue

Fretting fatigue

11% Fatigue

60%

Low cycle fatigue

8%

About 80% of fracture

was caused by fatigue

Impact failure

σ

t

Loading and fracture

Static, Environmental

Fatigue

Microscopic fracture surfaceⅢ（Ductile fracture③）

2μm

(a) Shallow dimple

25μm

(b) 組織

図．Two phase stainless steel （25% Cr-5% Ni steel）

Shallow

Microvoid along

grain boundary

Crack growth inside

Grain boundary

Elongated dimple

Microscopic fracture surfaceⅤ（Brittle fracture②）

20μm

図．High Cr ferrite steel（475℃ageing

Brittle fracture surface ②

Tongue appearance

… Twin deformation related

τ τ

Bound. Bound.

Twin

Fracture analysisⅠ

① Wire Rope failure to catch shark

Wire Rope ⇒ Macroscopic Large Necking

Ductile fracture Microscopic Dimple

5μm 10μm

(a) Equiaxed dimple (b) Elongated dimple

図．Microscopic appearance of wire-rope

Fracture anaysisⅡ

② Rail fracture surface

10μm

（a） Striation

Beach mark

(a)

(b)

Chevron pattern

（b） River pattern

15μm

(a) … Fatigue

(b) … Brittle fracture

Fracture anaysisⅢ

③ Bolt fracture surface for ship

Measurement of striation space

Fatigue crack growth rate

Beach mark

10μm

図．Bolt（SUS304）microscopic appearance

Striation

Under cyclic loading

Fatigue facture

Ductile fractureⅣ

◎ Microstructure effect

Void formation ⇒ Inclusion

・Content

・Distribution

・Size, Geometry

● Globular martensite

○ Ferriteト‐globular perrite

Sulfide

△ Ferrite‐layer perrite

Inclusion(2 phase) Vol.%

Duct

ilit

y

Sample geometry、Stress condition

Ductile fracture model

（McClintock）

Brittle fractureⅥ ①）

［Ⅰ］ Mechanical factor ①

・ Low temperature

・ Loading rate

・ Notch

・ Thickness

Constrain of plastic

deformation

Locally stress increases

Brittle

Sharpy impact tester

Hammer

α β

h1

h2

Measure

Notched specimen

Potential energy of Hammer

Toughness evaluation

Sharpy impact test

Remained Energy after impact

Absorbed energy of material

＋

＝

（Toughness）

Brittle fractureⅦ

［Ⅰ］ Mechanical factors ② （Ductile-Brittle Transition Behavior）

Rate of reduction

of area

Tensile test

Brittle

Ductile

-200 -150 -50 -100 0 50 100 150

0

20

60

40

80

0

80

160

40

120

Temperature ℃

Red

uct

ion

of

are

a ％

Ab

sorp

tion

en

ergy

J

Ductile-Brittle Transition

Absorption energy

Impact test

Ductile-Brittle Transition

Temperature

Brittle fractureⅧ ［Ⅰ］ Mechanical factors ③

（Question） Which is the best steel for tanker?

Each steel is the same strength.

（a） （b） （c）

Temperature ℃

Ab

sorp

tio

n e

ner

gy

J

D.-B. transition temp. must be low

Temperature decreases

High risk of brittle fracrure

Ductile Brittle

Oil

Natural Gas Gas ⇒ Liquid

Under low temperature

Material must keep ductile

・ Notch effect

Notch induces Stress concentration and high three axis stress condition

・ Plate thickness

Thickness increases, Three axis stress condition becomes high.

（Ex. ： Titanic sinked in 1912.4.14）

Brittle fractureⅨ

P, C, O, H etc.

Low toughness

σ

σ

Cleavage plane

［Ⅱ］ Microstructure effect ① （Crystal structure, Chemical composition）

bcc crystal （Mild steel）

fcc crystal

（Cu、Al、Ni、18%Cr-8%Ni stainless steel）

Difficult brittle

Low temperature brittle

LiquidO2 orLiquidN2 vessel

C、P

Transition temp.

Ni、Mn

Brittle

Increase Urge

Decrease Restraint

Brittle fractureⅩ ［Ⅱ］ Microstructure ② （Carbon steel）

Temperature ℃

Ch

arp

y i

mp

act

en

erg

y

J

High carbon

High Transition temperature

Low absorption energy

Brittleness

C content of carbon steel

General

High strength Brittle

Fine grain

High strength Improvement of toughness ＋

Creep fractureⅠ（Creep phenomenon）

（Ex.

W Heating

Under a stress and temperature

Plastic deformation is induced.

Creep?

Failure

Time t

Str

ain

ε

Accelerated creep

Softening

Transient creep

Work hardening

Steady creep

Deformation depends on time

and loading

Work hardening Softening） Cancellation

Deformation ～ Stress and Time

High temperature

Creep fractureⅡ（Creep strength）

Failure

Time t

Str

ain

ε

Steady creep

Creep rate

Creep rate at steady creep stage

Small creep rate

Time to tolerance strain

=long using period

Creep strength

A constant stress of 100MPa

103 Hours

Strain=0.01%

（例）

Creep strength =100MPa at 0.01% ／ 103 h

Creep fractureⅢ ［Ⅰ］ Effects of temperature and stress ［Ⅱ］ Microstructure effect

Time

Str

ain

Stress increase

Temperature increase

Temperature and stress increases

Steady creep is dominant

Creep rate increases

Creep strength decreases

Time ℃

Ste

ad

y c

reep

ra

te ％／

hr

Fcc crystal

High creep strength

Large Activated energy

Creep fractureⅣ

［Ⅲ］ Grain size

Grain size refinement

Normal temperature=Low

Strengthening

Refinement strength

Creep strength decreases

Under high temperature

Grain boundary slip

High temperature

・ Substitutional element

Interaction between dislocation or vacancy is restrained

And then creep strength increases.

・ Stacking fault energy decreases, creep strength increases

Creep fractureⅤ

A

B C

A

B C

C

B

A

A

B C

⇒

A

B C

⇒

C

B

A

⇒

Void

Particle Cavity

Cavity

Grain boundary

W type cracking r type cracking

Two type intergranural cracking at high temperature creep