deformation behaviour of asymmetrically f ti c l d m t lli...

Deformation Behaviour of Asymmetrically Deformation Behaviour of Asymmetrically F ti C l d M t lli M t i lF ti C l d M t lli M t i lFatigue Cycled Metallic MaterialsFatigue Cycled Metallic Materials

by

Krishna DuttaNational Institute of Technology, Rourkela, India

Krishna Dutta

and

K. K. Ray and

Indian Institute of Technology, Kharagpur, India

7th International Conference on Materials Structure and Micromechanics of Fracture, MSMF 7, July 1 – 3, 2013, Brno, Czech Republic

BrassBrassIF IF SteelSteel

Al alloyAl alloyAl alloyAl alloy

For all the abovementioned applications oneFor all the abovementioned applications one damage parameter is most important-

FATIGUEFATIGUEFATIGUEFATIGUE.

Fatigue damage may happen by SYMMETRIC or ASYMMETRIC type ofSYMMETRIC or ASYMMETRIC type of loading.

+ σ σm = 0σmax

iσ

t-

εσmin

Symmetric Loading

σ+

σmax = - σmin

σ

σ

σmax

Asymmetric σm ≠ 0

εσ t-

σmax ≠ - σmin

σminLoading

max min

εmaxεmin Max stress

σmax

tress

,σεmaxεmin σmax= Max. stress

σmin = Min. stress

σm = Mean stress

St

σa

m

σa = Stressamplitude

εr = Ratcheting εr

σm

r gstrain

Plastic Strain, εP

( )/σminεr = (εmax + εmin )/ 2

σ = (σ - σ i )/ 2σ = (σ + σ i )/ 2 σa = (σmax - σmin )/ 2σm = (σmax + σmin )/ 2


Eff t f t t lit d i tEffect of mean stress, stress amplitude, maximum stressand stress ratio on the nature of strain accumulation hasbeen studied by a few earlier investigators.y g

Year Author Control ParameterMaterial Test Parameters

1949 Lazan Copper Effect of Temperature1990 Yoshida SUS304 stainless steel Effect of Stress ratio1996 Xia et al ASTM A 516 Gr 70 steel Effect of mean stress1996 Xia et al. ASTM A 516 Gr. 70 steel Effect of mean stress.2004 Feaugas and

Gaudin316L Stainless steel Effect of maximum

stress.2005 Kang et al 25 CDV 4 11 steel and SS304 Effect of mean stress2005 Kang et al. 25 CDV 4.11 steel and SS304

stainless steelEffect of mean stress and stress amplitude.

2005 Chen and Hui Polymer General2009 Lim Copper alloy General2009 Lim Copper alloy General


SystematicSystematic informationinformation onon subsub--structurestructure formationformation duedue toto thetheaccumulationaccumulation ofof strainstrain underunderdifferentdifferent testtest conditionsconditions areare lackinglacking..

InformationInformation relatedrelated toto variationsvariations ininInformationInformation relatedrelated toto variationsvariations inindeformationdeformation behaviourbehaviour duedue totoaccumulationaccumulation ofof plasticplastic strainstrainareare lackinglacking..


gg

ToTo developdevelop anan understandingunderstanding aboutabout thethenaturenature ofof strainstrain accumulationaccumulation underunderasymmetricalasymmetrical cycliccyclic loadingloading withwith respectrespecttoto attendantattendant variationsvariations inin substructuresubstructureformationformation..

ToTo studystudy thethe eeffectffect ofof strainstrain accumulationaccumulationonon possiblepossible variationsvariations inin deformationdeformationbehaviourbehaviour ofof thethe investigatedinvestigated materialsmaterials..


Aluminum alloy

Interstitial free (IF) steel

α - brass

Materials ElementsMaterials ElementsC Mn Si P S Cr Ni Mg N Al Fe

Aluminumalloy*

– 0.04 0.610.61 – – 0.001 – 0.50 – Bal. 0.12alloy*

IF Steel** 0.0030.003 0.13 0.009 0.012 0.009 – 0.01 – 0.0034 0.06 Bal.

CuCu Zn Ni Sn

* Ti – 0.012, Zn – 0.006, Cu – 0.004, V – 0.005, ** Ti – 0.052, Nb – 0.001, Mo – 0.001, V – 0.001

CuCu Zn Ni Sn

α- brass 68.8268.82 30.6430.64 0.013 trace


50 μm 200 μmAl alloy IF steel

Material Grain size (μm)

Aluminum alloy 33 ± 3.6

200 μmα brass

IF Steel 64 ± 1.3

α - Brass 19 ± 2.4


200 μmα - brass

250250

150

200

250

ress

, MPa

150

200

250es

s, M

Pa

50

100

150

ngin

eeri

ng st

r

Material: IF Steel50

100

ng

inee

ring

stre

0 10 20 30 40 500

En

Engineering strain, %

Material: IF Steel

0 2 4 6 8 10 12 14 16 18 200

M ate ria l: A l a llo y

E n gin eerin g stra in %

En

3 0 0

3 5 0

Strain rate: 1.0x10-4s-1

Temperature: 300 K1 5 0

2 0 0

2 5 0

3 0 0

ng s

tres

s, M

Pa

Temperature: 300 KGauge length: 30 mmGauge diameter: 6 mm

0

5 0

1 0 0

1 5 0

Engi

neer

i

M a te r ia l: B ra s s


0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

E n g in e e r in g s tra in , %

MaterialMaterial YS (MPa)

UTS (MPa)

%eu %et n K (MPa)

Al llAl ll 140 220 6 8 18 2 0 10 309Al alloyAl alloy 140 220 6.8 18.2 0.10 309

IF SteelIF Steel 94 238 34.6 45.2 0.40 537IF SteelIF Steel 94 238 34.6 45.2 0.40 537

αα -- BrassBrass 103 323 88.7 96.7 0.49 608

n = strain hardening exponent, K = strength coefficient


sφ 7

Stre

ss

Time

σa

σm110

φ

1335 35

φ11

Time

σσmm >> 00Asymmetric

35 35

Specimen design

/

σσmm 00cycling

Waveform: Triangular Stress rate: 50 MPa/s

σ ≠ σσmax ≠ - σmin7th International Conference on Materials Structure and Micromechanics of Fracture, MSMF 7, July 1 – 3, 2013, Brno,

Czech Republic

MaterialMaterial σσmm (MPa)(MPa) σσaa (MPa)(MPa)10 130 140 150

Aluminium

10 130,140,150

20 130,140,150

30 130 140 15030 130,140,150

IF Steel

10 130,140,150

20 130,140,150, ,

30 130,140,150

10 90, 110, 130

α - brass 30 90, 110, 130

50 90, 110, 130 , ,


100

150 σmax = 0.62σUTS IF Steel

20

40

60

80

100M

Pa Aluminium alloyσmax = 0.64 σUTS

50

100

150 σmax = 0.62σUTS IF Steel

, MPa

50

100

MPa

-60

-40

-20

0

20

Stre

ss,

-100

-50

0

Stre

ss,

0

ress

, M-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-80

Strain, %0 1 2 3 4

-150

Strain, %

200 σmax = 0.6 σUTS

Brass

-100

-50Str

50

100

150

ess,

MPa

StrainStrain accumulationaccumulationisis insignificantinsignificant inin thetheAlAl alloyalloy upup toto thethe

0 1 2 3 4-150

100

0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2

-100

-50

0

Stre

AlAl alloyalloy upup toto thetheinvestigatedinvestigated numbernumberofof cyclescycles..


Strain, %0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2

Strain, %

6 σm = 10MPa, σa = 130 MPa

0 3

0.4

0.5

stra

in, %

σa=130 MPa σa=140 MPa σa=150 MPa

σm= 20 MPa

4

6 σm 10MPa, σa 130 MPa

σm = 10MPa, σa = 140 MPa

σm = 10MPa, σa = 150 MPa

g st

rain

, %

0.1

0.2

0.3

Rat

chet

ing

2

R

atch

etin

g

0 20 40 60 80 100Number of cycles

0 20 40 60 80 1000

Number of cycles

2

3

4

g st

rain

, %Al alloyAl alloy IF SteelIF Steel

0

1

2

σm = 50MPa, σa = 90 MPa σm = 50MPa, σa = 110 MPa σm = 50MPa, σa = 130 MPaR

atch

etin

g

BrassBrass


0 20 40 60 80 1000

Number of cycles

σa = 130 MPa σa = 150 MPa

Strain accumulation increases due to increased dislocation densityincreased dislocation density


σa = 130 MPaσa = 90 MPa

Strain accumulation increases due to increased dislocation densityincreased dislocation density


300

Pa Ratcheted

200

250tr

ess,

MP

100

150

erin

g St Undeformed

0

50 σm = 10MPa, σa = 130 MPa σm = 10MPa, σa = 140 MPa σm = 10MPa, σa = 150 MPaEn

gine

e

0 2 4 6 8 10 12 14 160 m a

Engineering Strain, %

Loading condition*

Tensile strength (MPa)

% Increase

in strength

% Uniform

elongation

% Decrease in uniform elongation

%Total elongation

%Decrease in total

elongation

Unratcheted 220 - 6.8 - 18.2 -

M10A130 261 18.6 4.6 32.4 13.9 23.6

M10A140 263 19 5 3 7 45 6 16 1 11 5M10A140 263 19.5 3.7 45.6 16.1 11.5

M10A150 268 21.8 5.0 26.5 15.3 15.9

M20A130 266 20.9 4.5 33.8 15.9 12.6

M20A140 262 19.1 3.5 48.5 16.2 11.0

M20A150 263 19.5 4.5 33.8 15.5 14.8

M30A130 268 21.8 3.9 42.6 16.9 7.1

M30A140 261 18.6 3.7 45.6 16.1 11.5

M30A150 270270 22 722 7 4 7 30 9 15 1 17 0M30A150 270270 22.722.7 4.7 30.9 15.1 17.0

280280

200

240

, MPa

200

240

280

, MPa

120

160

Stre

ngth

YSUTS 120

160

200

Stre

ngth

YSUTS

80

120

Mean stress MPa302010

UTS

Stress amplitude: 140 MPa

Un-ratcheted80

120

Stress amplitude MPa150140130

UTS

Mean stress: 30 MPa

Un-ratcheted

Mean stress, MPa Stress amplitude, MPa

60 60

50

60

n, M

Pa 50

60

n, M

Pa

30

40

Elon

gatio

n

% uniformation elongation % total elongation 30

40

Elon

gatio

n

% uniformation elongation % total elongation

Mean stress: 30 MPa

20

30

302010

%E

Stress amplitude: 140 MPa

Un-ratcheted

20

150140130%

EUn-ratcheted

Mean stress, MPa Stress amplitude, MPa

200 N = 100N = 80N = 2 N = 6 N = 48N = 24

100

150

Pa

0

50

ress

, M

-100

-50

20 M P 140 M P

St

1 .5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5-150 σ m = 20 M Pa, σ a = 140 M Pa

Strain, %,

Accumulation of ratcheting strain (εr) increases with increasingstress amplitude (σa) at any constant mean stress (σm) in all theinvestigated materials. The observed increase in straininvestigated materials. The observed increase in strainaccumulation can be qualitatively correlated with increaseddislocation density in the ratcheted samples.

Accumulation of ratcheting strain leads to improved yield andtensile strength of the investigated materials associated withreduction in their %uniform elongation, compared to that ofunratcheted samples. The increase in strength can be correlatedwith increased cyclic damage as well as cyclic hardening of thematerials.

On the other hand, %total elongation of the samples aregoverned by characteristic post-necking elongation dictated bythe substructural features of the ratcheted material.


deformation behaviour of asymmetrically f ti c l d m t lli...

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