Case Study:

Residual Stress Measurement

Life Prediction/Prognostics

106102

intact (no residual stress)

with opposite residual stress

Fatigue Life [cycles]104 108

0

500

1000

1500

endurancelimit

service load

life timenatural

life timeincreasedA

ltern

atin

g St

ress

[MPa

]

Residual stresses have numerous origins that are highly variable.Residual stresses relax at service temperatures.

lowindirect

highsemi-direct

excellentdirect

selectivityrelationshipstress measurement

Load stress (LS) versus residual stress (RS)

0 (1 )M M≈ + ε

τ23F3Δ

AΔ

A

AΔA

FΔn

external loads L( )

x1

x2

x3

x1

x2

x3

F2ΔF1Δ

τ33

τ32

τ13

τ31

τ12τ11

τ22τ21

0 (1 ... )M M≈ + ηε +

LS

AdA = ∑∫∫T L

RS

AdA =∫∫T 0

0lim i

iA

F TAΔ →

Δ=

Δ

i ij jT n= τ

ij ijkl klCτ = ε

LS

AM A dA≈ τ = ∫∫ T

Potential NDE Techniques

directstiffness

vibration analysis

etc.

semi-directhole drilling

contour mapping

x-ray or neutron diffraction

etc.

indirectmagnetic

ultrasonic

eddy current

thermoelectric

etc.strain rosettestress relief hole

Time

Am

plitu

de

H

B noise

T T = Aτ τρv ≈

Sources of Residual Stress

material-related

multi-phase microstructure

composites

inclusions

etc.

processing-related

casting

quenching

cold working

cutting

joining

case hardening

surface treatments

etc.

service-related

mechanical

thermal

chemical

etc.

Surface-Enhancement TechniquesLow-Plasticity Burnishing (LPB)Shot Peening (SP) Laser Shock Peening (LSP)

Depth [mm]0 0.2 0.4 0.6 1.0 1.2

200

0

-200

-400

-600

-800

-1000

Res

idua

l Stre

ss [M

Pa]

SP Almen 12ASP Almen 4A

LSPLPB

Ti-6Al-4V

0 0.2 0.4 0.6 1.0 1.2Depth [mm]

Col

d W

ork

[%] 40

30

20

10

0

50

SP Almen 12ASP Almen 4A

LSPLPB

Ti-6Al-4V

X-ray Bragg Diffraction

2 2 2

3 4

2 sin

( ) = (cubic)

2 10Å, 0.5 5Å

10 10

BD n

aD hklh k l

a

DD

− −

θ = λ

+ +

≈ − λ ≈ −

Δε = ≈ −

incident beam diffracted beam

D(001) = a

θB θB

incident beamdiffracted beam

Θ(εp)“cold work”

θB(ε)

Main Challenge:

low penetration depth (≈1-10 µm)

before (solid circles) and after full stress relaxation (empty circles) at 900 °C, 24 hrs

XRD Measurements on Shot-Peened Waspaloy Specimens

electrochemical etching

-2000

-1500

-1000

-500

0

500

0 0.2 0.4 0.6 0.8Depth [mm]

Res

idua

l Stre

ss [M

Pa]

Almen 4AAlmen 8AAlmen 12AAlmen 16A

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8

Col

d W

ork

[%]

Almen 4AAlmen 8AAlmen 12AAlmen 16A

Depth [mm]

peeningintensity

Almen strip

Synchrotron Radiation and Neutron Diffraction

Main Advantage and Disadvantage:

good penetration depth (≈1-5 cm)

availability of source

2θB

incident beam diffracted beam

s ≈ 0.5 mm

isotope reactor (ORNL) synchrotron (Univ. Dortmund)

shot-peened turbine alloy (Ezeilo et al., 1992)

x and y directionsz direction

Distance from Surface [mm]20 1 3 4 5

400

200

-400

-200

-800

-600

0

Res

idua

l Stre

ss [M

Pa]

Indirect NDE Methods for Near-Surface Residual Stress Assessment

thermoelectric

fluxgate

nozzles

specimen

specimenheat

thermoelectric current

magnetometer

ultrasonic

SAW

laser

specimen

interferometer

transducer

eddy current specimen

eddy currents

probe coil

magnetic field

Nonlinear Acoustoelastic Effect

Normalized Lattice Distance

Pote

ntia

l Ene

rgy

[a. u

.]

0 1 2

typical

parabolic

potential well

Al-2024 T351

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.2 -0.1 0 0.1 0.2Uniaxial Strain [%]

Rel

ativ

e V

eloc

ity C

hang

e [%

]

parallel polarization

normal polarization

Normalized Lattice Distance (Strain)

Elas

tic S

tiffn

ess [

a. u

.]

0.9 0.95 1 1.05 1.1

typical

parabolic potential function

unstrained

Surface Acoustic Wave Dispersion

0.8

0.9

1

1.1

0.01 0.1 1 10 100Normalized Frequency

Nor

mal

ized

SA

W V

eloc

ity

stiff coating layer

compliantcoating layer

uncoated

λd << d >> λd ≈ λ

surface wave

-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0

0 5 10 15 20Frequency [MHz]

Rel

ativ

e V

eloc

ity C

hang

e [%

] a

300 °C250 °C225 °C200 °C

150 °Cintact

Al 2024 Almen 8A

Rel

ativ

e V

eloc

ity C

hang

e [%

]

-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0

0 5 10 15 20Frequency [MHz]

225 °C200 °C150 °Cintact

Al 2024 Almen 6A

Indirect NDE Methods for Near-Surface Residual Stress Assessment

thermoelectric

fluxgate

nozzles

specimen

specimenheat

thermoelectric current

magnetometer

ultrasonic

SAW

laser

specimen

interferometer

transducer

eddy current specimen

eddy currents

probe coil

magnetic field

parallel

-0.004

-0.002

0

0.002

0.004

-0.001 0 0.001 0.002τua / E

Δσ /

σ 0

normal

Copper

Ti-6Al-4V

parallel

-0.004

-0.002

0

0.002

0.004

-0.002 0 0.002 0.004τua / E

Δσ /

σ 0

normalparallel

-0.004

-0.002

0

0.002

0.004

-0.001 0 0.001 0.002τua / E

Δσ /

σ 0

normal

Al 2024

parallel

-0.004

-0.002

0

0.002

0.004

-0.001 0 0.001 0.002τua / E

Δσ /

σ 0

normal

Al 7075

Piezoresistive Measurements in Different Metals

Waspaloy

parallel

-0.004

-0.002

0

0.002

0.004

-0.002 0 0.002 0.004τua / E

Δσ /

σ 0

normal

IN718

parallel

-0.004

-0.002

0

0.002

0.004

-0.002 0 0.002 0.004τua / E

Δσ /

σ 0

normal

Almen 8A, repeated 24-hour heat treatments at increasing temperatures

0.1 0.16 0.25 0.4 0.63 1 1.6 2.5 4 6.3 10

Frequency [MHz]

0

0.1

0.2

0.3

0.4

0.5

0.6

App

aren

t Con

duct

ivity

Cha

nge

[% ] intact

300 °C350 °C400 °C450 °C500 °C550 °C600 °C650 °C700 °C750 °C800 °C850 °C900 °C

The excess apparent conductivity gradually vanishes during thermal relaxation!

Thermal Stress Relaxation in Waspaloy

Inversion of Measured AECC in Low-Plasticity Burnished Waspaloy

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.01 0.1 1 10Frequency [MHz]

AEC

C C

hang

e [%

]

eddy current

0.0 0.5 1.0 1.5Depth [mm]

Col

d W

ork

[%]

.

0

5

10

15

20XRD

.

-1400

-1200

-1000

-800

-600

-400

-200

0

200

0.0 0.5 1.0 1.5Depth [mm]

Res

idua

l Stre

ss [M

Pa]

eddy currentXRD

Indirect NDE Methods for Near-Surface Residual Stress Assessment

thermoelectric

fluxgate

nozzles

specimen

specimenheat

thermoelectric current

magnetometer

ultrasonic

SAW

laser

specimen

interferometer

transducer

eddy current specimen

eddy currents

probe coil

magnetic field

Magnetic Signatures Produced bySemi-Spherical Inclusions and Cavities

milled pressed

before annealing

after annealing

plastic zone

C11000 copper, ∇T ≈ 0.6 °C/cm, 2 mm lift-off distance, 3" × 3“

0.25“-diameter tin inclusion, 33 nTp 0.375“-diameter cavity, 18 nTp

T TT = 0

0.375“-diameter tin inclusion, 104 nTp

Noncontacting Thermoelectric Inspectionin Shot-Peened C11000 Copper

before relaxationrelaxation at 235 ºCrelaxation at 275 ºCrelaxation at 315 °C2nd relaxation at 315 °C3rd relaxation at 460 °Crecrystallization at 600 °C

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16Almen Intensity (A)

Mag

netic

Sig

natu

re [n

T]

T

thermoelectric current

fluxgategradiometer

Position [20 mm/div]

Flux

Den

sity

[5 n

T/di

v]

Almen 4A

Position [20 mm/div]

Flux

Den

sity

[5 n

T/di

v]

Almen 8A

Position [20 mm/div]

Flux

Den

sity

[5 n

T/di

v]

Almen 12A

before stress release after partial stress release (30 min, 315 °C)

Conclusion

Essentially the same destructive method works in every material.

Very different nondestructive methods are needed in different materials.