Fracture of materials

Classification of fractureⅠ

① Amount of plastic deformation

Vertical fracture Cup and coneType fracture

Chisel point fracture

Shear fracture（Separation of slip plane）

Fracture surface geometrySmall plastic deformation

Brittle fracture Ductile fracture

Large plastic deformation

Classification of fractureⅡ

② Transgranular and intergranular fracture

Fracture occurs along grain boundary

Intergranularfracture

Brittle fracture

Transgranularfracture

Ductile fractur

Fracture occurs in the grain

Intergranular and transgranularfracture

σ

σ

Classification of fracture III

Cleavage plane

（a） Cleavage fracture

③ Atomic level

（b） Shear fracture

τ

τ

Slip plane

Slip plane ｛111｝

｛0001｝

｛123｝

｛112｝｛110｝

｛1011｝

｛1010｝

Cleavageplane

｛0001｝｛100｝Non

MaterialsAl、Cu、NiAg、Auγsteel

Cr、Mo、VW、β-TiMild steel

Zn、MgBe、Snα-Ti

fcc bcc hcp

Relation between slip and cleavage plane

Fractography

Initiation of crack

Crack growth Final fractureFracture

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-fractographyNaked Loupe

Angle/colorAppearance

Micro-fractography

OpticalElecton

Microscopic appearance

Characteristics of ductile fracture surfaceⅠ

Tensile fracture

Plain strain

Perpendicular fracture surface

Cup and cone typeExample

Geometry of fracture surface depends onstress state.

Shear fracture Plain stressSlant type (shear) fracture surface

Color of fracture surface ： Gray

Macroscopic ～ Difference between tensile and shear

Microscopic ～ Dimple formationCharacteristics: mentioned laterShear fracture Chisel point

fracture

Characteristics of brittle fracture surfaceⅡ

CleavageGeometry

Fracture pattern

Perpendicular fracture surfaceColor ： Metal gray

Roughness

Chevron pattern

Starter notch

Brittle fracture surface

Chevron patternFatigue 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

Fatig

ueFi

nal

frac

ture

（D

uctil

e）

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

σ1σ2

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

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 fractureⅠDuctile fracture

Macro ～ Cup and cone etc.Micro ～ Dimple

a

bτ

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 ）

⎟⎠⎞

⎜⎝⎛=

bXπ

　ττ2sinmax

Ductile fractureⅡ

O X

τElastic line at X＝O

⎟⎠⎞

⎜⎝⎛==

aXG G γ　τ …（ 4.2）

10G

ab

21

max ≒π

τ G⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

…（ 4.3）

（ τ at X＝0 ）

bX2

bX2sin maxmax

πτ≒

π　ττ ⎟

⎠⎞

⎜⎝⎛=

（ For small θ ⇒ sin θ≒θ）

…（ 4.1）

◎ Whiskerー

Material without dislocation

◎ Normal materilas

1/10 ～ 1/100

Ductile fractureⅢInitiation 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 surfaceMacro ～ Chevron patternMicro ～ River pattern、Tonge

Brittle fracture

Absorbed energy : Small

Stored energy in material isconsumed to grow crack

Rapidly crack growth ⇒ Instant fracture

a0

λ／2

Balance positionDisplacement X

Stre

ssσ

Elastic line at X=0

σmax

Cleavage plane a0

X

σ

σ

Brittle fractureⅡ

（Stress-strain relation at X＝0）

⎟⎟⎠

⎞⎜⎜⎝

⎛==

0aX 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 positionDisplacement X

Stre

ssσ

Elastic line at X=0

σmax

a0 ：Distance between atoms

aE

2 0max ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=π

λσ

…（ 4.6）

◎ Whisker

Without dislocation ⇒ Near value

◎ High strength steel etc.

Difference of one order more

Brittle fractureⅢ

a0

λ／2

Balance positionDisplacement X

Stre

ssσ

Elastic line at X=0

σmax

aE

2 0max ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=π

λσ

…（4.6）

Work used delamination of atoms

γπ

λσ

λ

πσ

λ

2 X2sin max20 max ==⎟

⎠⎞

⎜⎝⎛∫ dX

Two new free surfaces…（4.7）

Energy consumes formation of new free surface

γ： Surface energy per unit area

10E

aE 2

1

0max ≒

γσ ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

…（4.8、4.9）

Brittle fracture Ⅳ （Griffith’s theory①）

UE ： Strain energy stored in plate

22

E 2EU cπ

σ×=

EU

22

Eσπc

= : Rigid solution

US ： Energy to form crack plane

cc γγ 422Us =×=

Nextσ

σ

2cρ

Free plane

Two planes

Fracture strength of perfect brittle material with crack

dcdU

dcdU SE =

Criterion of fracture

…（4.12）

Brittle fractureⅤ （ Griffith’s theory ②）

Ec

dcdUE

22 σπ=

γ4=dc

dUS

Crack length c

Rat

e of

ene

rgy

Variation of energy rate With increasing crack length

γ42 2

=Ecσπ

21

2⎟⎠⎞

⎜⎝⎛=

cE

πσ

γ

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 cracking5%

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 insideGrain 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

ττ

Bound. Bound.

Twin

Fracture analysisⅠ① Wire Rope failure to catch shark

Wire Rope ⇒Macroscopic Large Necking

Ductile fractureMicroscopic Dimple

5μm10μm

(a) Equiaxed dimple (b) Elongated dimple

図．Microscopic appearance of wire-rope

Fracture anaysisⅡ② Rail fracture surface

10μm

（a） Striation

Beach mark

(a)

(b)

Chevron pattern

（b） River pattern

15μm

(a) … Fatigue(b) … Brittle fracture

Fracture anaysisⅢ③ Bolt fracture surface for ship

Measurement of striation space

Fatigue crack growth rate

Beach mark

10μm

図．Bolt（SUS304）microscopic appearance

Striation

Under cyclic loadingFatigue 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.%

Duc

tility

Sample geometry、Stress condition

Ductile fracture model（McClintock）

Brittle fractureⅥ ①）

［Ⅰ］ Mechanical factor ①

・ Low temperature・ Loading rate・ Notch・ Thickness

Constrain of plasticdeformation

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 reductionof area

Tensile test

Brittle

Ductile

-200 -150 -50-100 0 50 100 1500

20

60

40

80

0

80

160

40

120

Temperature ℃

Red

uctio

n of

are

a％

Abs

orpt

ion

ener

gyJ

Ductile-Brittle Transition

Absorption energyImpact test

Ductile-Brittle TransitionTemperature

Brittle fractureⅧ［Ⅰ］ Mechanical factors ③

（Question） Which is the best steel for tanker?Each steel is the same strength.

（a） （b） （c）

Temperature ℃

Abs

orpt

ion

ener

gyJ

D.-B. transition temp. must be low

Temperature decreases

High risk of brittle fracrure

Ductile Brittle

OilNatural Gas Gas ⇒ Liquid

Under low temperatureMaterial must keep ductile

・ Notch effectNotch induces Stress concentration and high three axis stress condition

・ Plate thicknessThickness 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 ℃

Cha

rpy

impa

ct e

nerg

yJ

High carbon

High Transition temperature

Low absorption energy

Brittleness

C content of carbon steel

GeneralHigh strength Brittle

Fine grain

High strength Improvement of toughness＋

Creep fractureⅠ（Creep phenomenon）

（Ex.

WHeating

Under a stress and temperaturePlastic deformation is induced.

Creep?

Failure

Time t

Stra

inε

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

Stra

inε

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 100MPa103 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

Stra

in

Stress increase

Temperature increase

Temperature and stress increasesSteady creep is dominant Creep rate increases

Creep strength decreases

Time ℃

Stea

dy c

reep

rat

e％

／hr

Fcc crystal

High creep strengthLarge Activated energy

Creep fractureⅣ［Ⅲ］ Grain size

Grain size refinement

Normal temperature=Low

StrengtheningRefinement strength

Creep strength decreasesUnder high temperature

Grain boundary slip

High temperature

・ Substitutional element

Interaction between dislocation or vacancy is restrainedAnd then creep strength increases.

・ Stacking fault energy decreases, creep strength increases

Creep fractureⅤ

A

BC

A

BC

C

BA

A

BC

⇒

A

BC

⇒

C

BA

⇒

Void

ParticleCavity

Cavity

Grain boundary

W type cracking 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）

・ 高温焼戻し脆化

CrMn

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） 脆化

・ σ相脆化

高Crを持つαステンレス鋼など

700~900℃

加熱

σ相（脆性な第２相析出）

著しい脆化

脆性破面 延性破面

熱処理で性質が変化・ ４７５℃脆化

20μm

時効材

20μm

未時効材

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

（教科書 P126 図4.32）

巨視的破面の特徴Ⅳ（疲労破面②）

１mm

図．粗大結晶粒をもつ二相ステンレス鋼（25% Cr－5% Ni鋼）

（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

※ 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

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）

◎ 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