Lecture 14

Lecture 14Fatigue & Creep in Engineering Fatigue & Creep in Engineering

MaterialsMaterials(Chapter 8)(Chapter 8)

Chapter 8 - 1

Fatigue• Fatigue = failure under applied cyclic stress.

compression on topspecimen

t i b tt

countermotor

flex coupling

bearing bearing

• Stress varies with time.-- key parameters are S m and

max

tension on bottom

key parameters are S, m, and cycling frequency

min time

mS

• Key points: Fatigue...--can cause part failure, even though max < y.

ibl f 90% f h i l i i f il

Chapter 8 - 2

--responsible for ~ 90% of mechanical engineering failures.

Fatigue: Definitions

SymmetricAsymmetric

dRandom

Chapter 8 - 3

Fatigue: Definitions

Chapter 8 - 4

Types of Fatigue Behavior• Fatigue limit, Sfat:

--no fatigue if S < Sfatcase for steel (typ.)unsafem

plitu

de

Sfat

safe

S=

stre

ss a

N = Cycles to failure103 105 107 109S

• For some materials, there is no fatigue

case for Al (typ.)unsafe

ampl

itude

limit!safe

S=

stre

ss a

Chapter 8 - 5N = Cycles to failure

103 105 107 109S

Ex: Fatigue in 7075-T6 Aluminum Alloy

Chapter 8 - 6

Rate of Fatigue Crack Growth• Crack grows incrementally

typ. 1 to 6 mKd

a

a~increase in crack length per loading cycle

mKdN

increase in crack length per loading cycle

• Failed rotating shaft-- crack grew even though

crack origin

crack grew even thoughKmax < Kc

-- crack grows faster as• increases• increases• crack gets longer• loading freq. increases.

Chapter 8 - 7

Fatigue Failure in Ductile Materials (Aluminum)

Chapter 8 - 8

Fatigue Failure in Brittle Material

Chapter 8 - 9

Importance of Mean Stress

Chapter 8 - 10

Improving Fatigue Life

Adapted fromFig. 8.24, Callister & Rethwisch 8e

1. Impose compressivesurface stresses

ampl

itude

Rethwisch 8e. (to suppress surfacecracks from growing)

N = Cycles to failure

moderate tensile mLarger tensile m

S =

stre

ss a

near zero or compressive m

N = Cycles to failure

--Method 1: shot peening

tshot

--Method 2: carburizing

C-rich gasput surface

into compression

C rich gas

2. Remove stressconcentrators. Adapted from

bad better

Chapter 8 - 11

Adapted fromFig. 8.25, Callister & Rethwisch 8e. bad better

Effect of Surface CompressiveEffect of Surface Compressive Stresses

Chapter 8 - 12

Effect of Surface Compressive Stresses

HardenedHardened Case depth byCarburization (orNitriding)

Micro-indentationIn compression

Nitriding)

marks

Chapter 8 - 13

Environmental Effects

Thermal cycle…..stress cycle…..Thermal fatigue….

Chapter 8 - 14

CreepSample deformation at a constant stress () vs. time

0 t

Primary Creep: slope (creep rate) decreases with time.

Adapted from

Secondary Creep: steady-statei.e., constant slope /t)

Tertiary Creep: slope (creep rate)

Chapter 8 - 15

Adapted fromFig. 8.28, Callister & Rethwisch 8e.

Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate.

Creep: Temperature Dependence• Occurs at elevated temperature, T > 0.4 Tm (in K)

tertiary

primarysecondary

elastic

Chapter 8 - 16

Secondary Creep• Strain rate is constant at a given T,

-- strain hardening is balanced by recoverystress exponent (material parameter)

activation energy for creep( t i l t )

RTQK cn

s exp2strain rate (material parameter)

applied stressmaterial const.

S 200

RT

• Strain rateincreaseswith increasing 40

100200

s (M

Pa) 427ºC

538ºCgT,

102040

Stre

ss

649ºC

Chapter 8 - 17

10-2 10-1 1Steady state creep rate (%/1000hr)s

A better & more informativeCreep Equation

Activation energy forMaterial constantdepending on

h igy

Self-diffusioncreep mechanism

Grain size Applied stress

Chapter 8 - 18

m & b depend on the creep mechanism

Mechanisms of CreepThe mechanism of creep depends on temperature and stress. The various methods are:

Bulk diffusion (Nabarro-Herring creep)

Dislocation climb -here the strain is actually accomplished by climb

Climb-assisted glide — here the climb is an enablingmechanism, allowing dislocations to get around obstacles, g g

Grain boundary diffusion (Coble creep)

Chapter 8 - 19

Thermally activated glide — e.g., via cross-slip

Mechanisms of Creepp“Things to know…”

Dislocations related creep……………….. m = 4-6, and b = 0. It has a strong dependence on the applied stress and no grain size dependence.Nabarro Herring Creep (B lk Diff’n) 1 and b 2 AtNabarro-Herring Creep (Bulk Diff’n)………..m = 1, and b = 2. Atoms diffuse through the lattice causing grains to elongate along the stress axis; it creep has a weak stress dependence and a moderate grain size dependence. Coble Creep (Grain boundary diffusion) m = 1 and b = 3 Atoms diffuseCoble Creep (Grain boundary diffusion)…. m 1, and b 3. Atoms diffuse along grain boundaries to elongate the grains along the stress axis. This causes Coble creep to have a stronger grain size dependence than Nabarro-Herring creep. Here, Q(grain boundary diffusion) < Q(self diffusion), Coble creep p , Q(g y ff ) Q( f ff ), poccurs at lower temperatures than Nabarro-Herring creep.

Thermally activated glide — e.g., via cross-slip

Chapter 8 - 20

Creep Failure

• Failure: along grain boundaries.

g.b. cavities

appliedstress

Chapter 8 - 21

Creep Failure in S-590 Alloy

Chapter 8 -fig_08_31

Prediction of Creep Rupture Lifetime• Estimate rupture time

S-590 Iron, T = 800ºC, = 20,000 psi

Ti t t t

LtT r )log20(

Time to rupture, tr

psi)

100

time to failure (rupture)

function ofapplied stress

temperature

ress

(103

10

20

3

Str

data for S-590 Iron

310x24)log20)(K 1073( rt103 L (K-h)

112 20 24 2816 24

Chapter 8 -

Ans: tr = 233 hr23

Estimate the rupture time forS 590 Iron T 750ºC 20 000 psiS-590 Iron, T = 750ºC, = 20,000 psi

• Solution:

psi)

100

LtT r )log20(

Time to rupture, tr

ess

(103

p

10

20

time to fail re (r pt re)

function ofapplied stress

temperature

LtT r )log20(

Stre

data for S-590 Iron310x24)log20)(K 1023( rt

time to failure (rupture)

103 L (K-h)

112 20 24 2816 24

)g)(( r

Ans: tr = 2890 hr

Chapter 8 - 2424

Ans: tr 2890 hr

To Increase Creep Rupturep pResistance:

1) Use large grain size material, highly directions grains or a single crystal.g g y

2) Use heavy alloying (grain boundary drag, dislocation drag etc.)g g )

3) Use high melting point material4) Use high modulus of elasticity ) g y

material

Chapter 8 - 25

Make sure it’s justifiable ($$$$$...)

SUMMARY• Engineering materials not as strong as predicted by theory• Flaws act as stress concentrators that cause failure at

• Sharp corners produce large stress concentrationsd t f il

Flaws act as stress concentrators that cause failure at stresses lower than theoretical values.

and premature failure.• Failure type depends on T and :

-For simple fracture (noncyclic and T < 0.4Tm), failure stressFor simple fracture (noncyclic and T 0.4Tm), failure stress decreases with:- increased maximum flaw size,- decreased T,,- increased rate of loading.

- For fatigue (cyclic :- cycles to fail decreases as increases.

Chapter 8 - 26

y- For creep (T > 0.4Tm):

- time to rupture decreases as or T increases.

ANNOUNCEMENTS

Reading: Study chapter 8 thoroughly. Study thesolutions of Chapter 8 problems very well. Do notmemorize but try understanding the conceptsmemorize but try understanding the conceptsbehind the solutions…

Chapter 8 - 27