Design Agains Fatigue - part Fatigue Endurance Prediction Design Agains Fatigue - part Fatigue Endurance Prediction Milan Růžička [email protected]@fs.cvut.cz.

Design Agains FatigueDesign Agains Fatigue- part Fatigue Endurance Prediction- part Fatigue Endurance Prediction

Milan Růžička

[email protected]

mailto:[email protected]

CTU in Prague, Faculty of Mechanical Engineering DAF Page 2

Contents1. Introduction: Life Prediction loop, limit states

2. Static and cyclic tests of materials

3. Categorization of Material Fatigue

4. Philosophy of Structure Design

5. Material Behaviors under Static and Cyclic Loading

6. Phases of Fatigue Process

7. Fatigue Curves

8. Stress State in Notches

9. Notch factor

10. Another Influences on Fatigue Strength Value

11. Influence of Mean Stress

12. Analysis of dynamic loading

13. Damage Accumulation

14. Fatigue Life Prediction Methods


Fatigue life prediction loop

Pre-project phase

Design phase

Prototype verification

Real service

Computational work

Experimental work

DATABASE

Fatigue curves

Loading spectraFinding of

critical places

Strains and stresscalculations

Fatigue life verification and recalculation

Service loading and critical places verification

Fatigue life prediction


CAX- analysis

Elastic, PlasticCreep

Analysis of Fatigue Damage

MISES VALUE+3.67 E+00

+2.83 E+02+1.70 E+02

+3.36 E+02+4.19 E+02+5.02 E+02

+5.85 E+02+6.68 E+02+7.51 E+02+8.34 E+02

+8.67 E+01

+9.17 E+02+1.00 E+03+1.63 E+03

1

2

3

Analysisof limit

state

CADmodel

FEManalysis


Limit states

Limit states

1. L.S. of Strength• Static Strength (Ductile

Fracture)

• Plasticity, Plast. Adaptation

• Stability, Buckling

• Brittle Fracture

• Creep (Creep Fracture)

• Low-, High-Cycle Fatigue

• Temperature Shock

• Fatigue + Creep Interaction

2. L.S. of Functional Capability

• Elastic and Plastic Deformation

• Impact Damage

• Dynamic Response

• Wearing

• Corrosion


Brittle fracture and fatigue damage of large structures


Brittle fracture and fatigue damage of large structures

Takona bridge The Latchford Bridge Failure (2003 )


Static and cyclic tests of materials

Smooth and Notched Round Bar Laboratory Tensile Specimens

Ultimate Strength, Su (Rm)

Yield Strength, Sy (Re, Rp0.2)


Material behavior under static and cyclic loading

0

100

200

300

400

500

600

700

800

0 0.002 0.004 , e [1]

0

100

200

300

400

500

600

700

800

0 0.2 0.4 0.6 0.8 1 , e [1]

, S

[MP

a]

Skutečný tah.diagram

Konvenční tah.diagram

f

Rm

Re

f

el

ll

l

l

eSl

llS

l

lS

A

AS

A

F

1ln1lnln

11

0

0

0

0

0

0

0

npK

K - monotonic strength hardening koeff.n - monotonic strength hardening exponentp - plastic strain

Engineering stress (Lagrange stress) S = F / A0,

Engineering strain of measured specimen leght e = (l - l0) / l0 force recomputation at the instantaneous section

True stress (Cauchy stress) = F / A

True (logaritmic) strain = ln(l / l0).

True stress-strain diagram

Engineering stress-strain diagram

Aproximation of the true stress-strain diagram


Stress-Life Analysis: Constant Amplitude Loading

Stress Amplitude, Sa

Mean Stress, Sm

Stress Range, ΔS

Two types of fatigue loadings regimes

stress amplitude loading control - soft loadingstrain amplitude loading control - hard loading.

Source:http://fatiguecalculator.com


Different mean stress


Cyclic stress-strain curve

saturated hysteresis loops

cyclic stress-strain curve

The materials deformation during a fatigue test is measured in the form of a hysteresis loop. After some initial transient behavior the material stabilizes and the same hysteresis loop is obtained for every loading cycle. Each strain range tested will have a corresponding stress range that is measured. The cyclic stress strain curve is a plot of all of this data


Hysteresis loop

-300

-200

-100

0

100

200

300

-0.01 -0.005 0 0.005 0.01

[1]

[M

Pa

]

a

ap

ae

a

napa K

naa

apaea KE

1

K’ - cyclic strain hardening koeff.n’ - cyclic strain hardening exponentE - Young’s modulus of elasticity (tension)

Aproximation of the cyclic stress-strain curve


Changing of Cyclic Material Behavior

t

t

t

t

t t

t

t

t

a

b

c

d

e

0

A

B

C

DD

C

B

A

0

C´

E

Re

laxa

tion

Ha

rde

nin

gS

oft

en

ing

Cre

ep

Me

mo

ry

hardening

softening

deformationcurves:

cyclic

static


Fatigue Testing Machines http://www.kuleuven.ac.be


Fatigue Testing Machines


Stress- Life Curves

www.tu-berlin.de

www.ncode.com


Quasistatic and Fatigue Design, Fatigue categories

Rm

range Re

C

Quasi-static Strength

Low-cycle Fatigue

High-cycle Fatigue

Lifetime Limited Unlimited

Stre

ngth

Per

man

ent

Fat

igue

1. Quasi-static strength (N<102 cycles)

2. Low-cycle fatigue (102<N<5·105 cycles)

3. High –cycle fatigue (5·105< N<2·106 cycles)

Fatigue categories

• fatigue of material

• fatigue of elements

• fatigue of structural parts

• fatigue of structures


Phases of a Fatigue Process

•Phase of cyclic behaviors changing, there is change of metal structure in all of volume. Generally it takes only few percentages of specimen life.

•Phase of fatigue crack nucleation, includes local changes in surface layers of material caused by dislocation effect.

•Phase of crack propagation, includes stage of micro-crack growing in major crack and further crack growth.

•Phase of final fracture, involving high-speed quasi-brittle crack of residual section when fracture toughness is exceeded or ductile crack at yield and strength limit exceeding.

1 A

102 A

1 102 1 mm 102 mm

AtomicDistance

Grain Sizeof Austenite

Micro-crack Formation

GlissileDislocation

Macro-crack Creation

Macro-crack Growth


Fatigue Crack Nucleation

Fat

igue

Cra

ck g

row

thQ

uasi

-br

ittl

e F

ract

ure

Intruses

Slip bands

Initiation


Fracture surfaces


Fatigue Design methods

COMPONENTFATIGUEBEHAVIOR

CRITERIA OFFATIGUE DESIGN

PERMANENTSTRENGHT(UNLIMITEDFATIGUE LIFE)

FATIGUESTRENGHT(LIMITEDFATIGUE LIFE)

SAFE-LIFESTRUCTURE

FAIL-SAFESTRUCTURE DAMAGE-TOLERANCE

STRUCTURE

SLOW CRACKGROWTH-STRUCTURE


S-N curve (stress-life curve, Wöhler curve )

100

1000

1,E+04 1,E+05 1,E+06 1,E+07

N [1]

a [

MP

a]

100

1000

1,E+04 1,E+05 1,E+06 1,E+07

N [1]

a [

MP

a]

100

1000

1,E+04 1,E+05 1,E+06 1,E+07

N [1]

a [

MP

a]

structural steel

• stress amplitude loading control - soft loading• R=const., or Sm=const.•Enduramce limit, Fatigue limit SFL

•Probability of fracture P [%]

Fatigue limit


100

1000

1,E+04 1,E+05 1,E+06 1,E+07

N [1]

a [

MP

a]

100

1000

1,E+04 1,E+05 1,E+06 1,E+07

N [1]

a

[M

Pa

]

alloy steel

S-N curve (stress-life curve, Wöhler curve )


Aproximation of the Fatigue Stress-Life Curves (S-N)

100

1000

1.E+04 1.E+05 1.E+06 1.E+07počet kmitů N [1]

amp

litu

da

nap

ětí

a [M

Pa]

ocel slitinováocel konstrukčnídural 2024 T3

1

1/ w

CNwa

2b

a f N

bfC1

2

1

bw

1

Alloy SteelStructural SteelDural 2024 T4

Load Cycles

Str

ess

Am

pli

tud

eAproximation

Basquin

fatigue strength coefficient

fatigue strength exponent

f

b


Strain-Life Curve (-N), Manson-Coffin‘s curve

0.0001

0.001

0.01

0.1

1

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

počet půlkmitů 2N [1]

ampl

ituda

pom

. def

orm

ace

a [1

]

ae

ap

a

f '

f ' /E

b

c

1

1

cf

bfapaea NN

E22

6,06,012,05,32 NNE

Rf

ma

general tangent method

Number of Half-Cycles

Str

ain

Am

pli

tud

e

Aproximation

fatigue ductility coefficient

fatigue ductility exponent

f

c


Hysteresis loop

-300

-200

-100

0

100

200

300

-0.01 -0.005 0 0.005 0.01

[1]

[M

Pa

]

a

ap

ae

a

napa K

naaapaea KE

1

K’ - cyclic strain hardening koeff.n’ - cyclic strain hardening exponentE - Young’s modulus of elasticity (tension)

Aproximation of the cyclic stress-strain curve


Relations Between Coefficients

naaapaea KE

1

K’ cyclic strain hardening koeff.n’ cyclic strain hardening exponent

2b

a f N fatigue strength coefficient

fatigue strength exponent

f

b

cf

bfapaea NN

E22

fatigue ductility coefficient

fatigue ductility exponent

f

c

ncnf

bfa NKN

22 nf

fK

c

bn

cbnK ff ,,,,, 6 material parameters, 4 independent:


Relations between the strength and the fatigue limit

STEELS:Sf in tension 0,35 Rm in bending = 0,43 Rm

in torssion 0,25 Rm .

http://fatiguecalculator.com


Example http://fatiguecalculator.com


Questions and problems I

.

1. What is difference between static design and fatigue design of structures?

2. What are typical attributes for low cycle fatigue and for high cycle fatigue?

3. Draw a hysteresis loop and describe on it elastic and plastic part of strain.

4. Specify phases of damage and fatigue progress in metals. 5. What is main difference between safe-life and fail-safe design

philosophy?6. What are main attributes of the damage tolerance design

philosophy?7. Define the fatigue limit of a given material8. What type of fatigue curve describes high cycle fatigue primary?

Draw this curve.9. What type of fatigue curve describes low cycle fatigue? Draw this

curve.10.Could be fatigue limit higher as yield strength?11.How many percent of ultimate strength could you predict the fatigue

limit of carbon steel?


Questions and problems I

.

1. Example 1: Approximation of a stress amplitude is napa K . Derive equation for

the total strain amplitude of a hysteresis loop apaea ?

2. Example 2: Approximation of the fatigue curve is CNwa or b

fa N2 .

Derive relations between parameters .,,, wbC f

3. Example 3: There are 6 material fatigue parameters cbnK ff ,,,,, , only

are 4 independent. Derive relations between these parameters. 4. Example 4: There is special number of cycles ( tN ) in the Strain-life curve,

where apae . Derive equation to calculate this number tN .

Design Agains Fatigue - part Fatigue Endurance Prediction Design Agains Fatigue - part Fatigue Endurance Prediction Milan Růžička [email protected]@fs.cvut.cz.

Documents

fatigue curves

stresslife analysis

fatigue strength value

stress state

fatigue life prediction

phases of fatigue process

cyclic loading

corrosion slide