ICRS-8/DENVER, AUG/06/08

RESIDUAL STRESS MEASUREMENTS BY X-RAY DIFFRACTION:CRITICAL EVALUATION OF ERROR SOURCES

Rogério Machado1,

Alexei Kuznetsov1,

Carlos Alberto Achete1, 2

Thomas Hirsch3

1 Divisão de Metrologia de Materiais (DIMAT), Inmetro, CEP 25250-020, Xerém, Duque de Caxias, RJ, Brazil

2 Programa de Engenharia Metalúrgica e de Materiais (PEMM), Universidade Federal do Rio de Janeiro, Cx. Postal 68505, CEP 21945-970, Rio de Janeiro, RJ, Brazil

3 Institut fuer Werkstofftechnik, Bremen, Germany

ICRS-8/DENVER, AUG/06/08

Definition of experimental parameters(Evaluation of influence of experimental conditions)

Definition of the method of data processing

Sample(s) choice

MOTIVATION

NACIONAL ROUND ROBIN FOR RESIDUAL STRESS MEASUREMENTS

PRELIMINARY STUDY

ICRS-8/DENVER, AUG/06/08

INTERCOMPARISON IWT-INMETRO (NOV/2007) [Sample A0b][5 analysis per instrument]

IWT#1

IWT#4

IWT#5

INMETRO

-270

-265.5

-262

-264

ICRS-8/DENVER, AUG/06/08

ELASTIC CONSTANTS (+/- 5% RELATIVE)

AISI 1070, 1/2S2 = 5.7 10-6 MPa; S1 = -1.235 10-6 MPa

PRESENCE OF CRYSTALLOGRAPHIC TEXTURE

Quasi ideally random texture

MICROSTRUCTURE

Homogeneous tempered martensite with small carbides

PRESENCE OF STRESS/STRAIN GRADIENTS

A little gradient at surface showed by Cu radiation measurements

SAMPLE SHAPE (PLANE, CILINDER, …)

Sample properties (partially defined by sample preparation methods)

Plates of 20mm X 25mm (s11 direction)

ICRS-8/DENVER, AUG/06/08

Sample properties (partially defined by sample preparation methods)

0 1 2 6 7 8 9

a

b

c

Row A

Row B

Row C

e.g.B2b

Sand Blasting:Mean grain size: 0,6 mmair pressure: 3 barMax. time per B2b sample: 30secNozzle to sample distance 50 mmNozzle diameter: 6 mm

200 mm

225 mm

6mm

Scheme ofnozzle move-ments

0 1 2 6 7 8 9

a

b

c

Row A

Row B

Row C

e.g.B2b

Sand Blasting:Mean grain size: 0,6 mmair pressure: 3 barMax. time per B2b sample: 30secNozzle to sample distance 50 mmNozzle diameter: 6 mm

200 mm

225 mm

6mm

Scheme ofnozzle move-ments

MANUFACTURED AT IWT/BREMEM/GERMANY (Dr. Thomas Hirsch)

Chemical Composition C=0,73, Mn=0,64, P=0,010, S=0,001, Si 0,19, Cr=0,18, V=0,01 Ni=0,02 Mo=0,030 Al=0,041

Average hardness of 270 HV0,5. Microstructure: homogeneous tempered martensite with small carbides.

ICRS-8/DENVER, AUG/06/08

NUMERICAL METHOD FOR PEAK POSITION DETERMINATION

Method of data processing

Numerical fitting of Ka1 and Ka2 (and Kb) with symmetrical Pseudo Voight function.No convolutions applied. Linear Background Subtraction.

ICRS-8/DENVER, AUG/06/08

ALGORITHM OF ANALYSIS (SOFTWARE)

Method of data processing

Based on traditional least-square fit of d x sen2PSi curves to experimental data (isotropic case)

( )ψτψσεε ϕϕψϕ 2sin21sin

21

22

200hklhklhklhkl SS ++=

MPaE

Shkl

hkl 61 10235.1 −−=⎟

⎠⎞

⎜⎝⎛−=

ν

MPaE

Shkl

hkl 62 107.51

21 −=⎟

⎠⎞

⎜⎝⎛ +

=ν

( ) 332332211100

00 21 σσσσε hklhkl

hklunstrained

hklunstrained

hklhkl SS

ddd

+++=−

=

( ) 332

22122

11 sin2sencos σ−ϕσ+ϕσ+ϕσ=σϕ

ϕσ+ϕσ=τϕ sincos 2331

ICRS-8/DENVER, AUG/06/08

ALGORITHM OF ANALYSIS (SOFTWARE)

Method of data processing

Additional assumption:

hklunstrained

hkl dd ≅00

( )⎟⎟⎠

⎞⎜⎜⎝

⎛ψτ+ψσ⎟

⎠⎞

⎜⎝⎛ ν+

+= ϕϕψϕ sinsinE

11dd 2hkl

hkl00

hkl

( )ψτ+ψσ⎟⎠⎞

⎜⎝⎛ ν+

=ε ϕϕψϕ sinsinE

1 2hkl

hkl

ICRS-8/DENVER, AUG/06/08

Method of data processingALGORITHM OF ANALYSIS (SOFTWARE)

Traditional d x Sin2PSI plot

ICRS-8/DENVER, AUG/06/08

INSTRUMENTAL MISALIGNMENTS (SERIOUS SOURCE OF ERROR)

2THETA RANGE USED FOR BACKGROUND SUBTRACTION

GEOMETRY (PSI,OMEGA,LINE FOCUS, POINT FOCUS,…)

COUNTING TIME (STEP TIME/SCAN VELOCITY)

NUMBER OF PSI TILTS AND PSI MAX

X-RAY ENERGY (ABSORPTION EFFECTS)

OPERATOR REPRODUCIBILITY

Experimental conditions

ICRS-8/DENVER, AUG/06/08

Effect of Counting Time

1 2 3 4 5 6 7 8 9 10-280

-270

-260

-250

-240

-230

-220

-210

-200

acceptable region

Experimental Mean Value +/- 5% +/- 10%

Res

idua

l Str

ess

(MPa

)

Counting Time (sec)

Experimental conditions

ICRS-8/DENVER, AUG/06/08

15 20 25 30 35 40 45 50 55 60

-550-525-500-475-450-425-400-375-350-325-300-275-250-225-200-175-150-125-100

acceptable region

Res

idua

l Str

ess

(MPa

)

ψmax

ψ>=0 ψ>=0 + ψ<=0

Experimental conditionsThe Choice of PSI MAX

ICRS-8/DENVER, AUG/06/08

5 10 15 20-280

-270

-260

-250

-240

-230

-220

-210

-200

-190

acceptable region

ψmax = 60o

Res

idua

l Str

ess

(MPa

)

Δψ (Degrees)

ψ>=0 ψ>=0 + ψ<=0

Experimental conditionsNumber of PSI Tilts

ICRS-8/DENVER, AUG/06/08

135

-170

142

-170

144

-168

146

-166

148

-164

150

-162

152

-160

154

-158

-250

-240

-230

-220

-210

-200

-190

-180

-170

-160

-150

-140

acceptable region

R

esid

ual S

tres

s (M

Pa)

2θ Range (degrees)

ψ>=0 ψ>=0 + ψ<=0

2Theta Ranges

Experimental conditions Cr: Fe (211), 2Theta ≅ 1560

ICRS-8/DENVER, AUG/06/08

Ω Ψ-260

-255

-250

-245

-240

-235

-230

-225

-220

-215

-210

-205

-200Instrument Code: 8

ψmax=+/-60o

Δψ=5o

Δt=5sec

ψmax=+/-60o

Δψ=5o

Δt=2sec

Res

idua

l Str

ess

(MPa

)

MethodR 5 8

-280-275-270-265-260-255-250-245-240-235-230-225-220-215-210-205-200

ψMAX = +/-60o

Δψ = 5o

Δt = 2sec

ψMAX = +/-60o

Δψ = 10o

Δt = 2sec

ψMAX = +/-34o

Δψ ~ 7o

Δt = 10sec

Res

idua

l Str

ess

(MPa

)

INSTRUMENT CODE

OMEGA GEOMETRY Cr Radiation

Geometries

Experimental conditions

ICRS-8/DENVER, AUG/06/08

F 6-1 6-2

-145

-140

-135

-130

-125

-120

-115

-110

-105

Mean Value = -130MPa!

R

esid

ual S

tres

s (M

Pa)

INSTRUMENT CODE

OMEGA GEOMETRY Cu Radiation Secondary Monochromator

Cu Radiation

Experimental conditions

ICRS-8/DENVER, AUG/06/08

Operator

Experimental conditions

AK CL RM TH-255

-250

-245

-240

-235

-230

-225

R

esid

ual S

tres

s (M

Pa)

Operator (random choice)

Operator

ICRS-8/DENVER, AUG/06/08

X-raysource

Focusingcircle

Sample

ReceivingSlit

Detector

Anti-scatterSlit

DivergenceSlits 2Θ

Θ

Goniometer2Θ circle

Instrument MisalignmentsExperimental conditions

Diffractometer Geometry

ICRS-8/DENVER, AUG/06/08

Lab System

Tube System

Detector System

Eulerian System

1st Monochr. System1st Soller SlitAperture Slit

Shulz Slit

XYZ System

AntiScatter Slit

2nd Soller SlitFilter Slit

Receive Slit

2nd Monochr. System

Sample

2nd Crystal Detector Slit

Focus System1st Crystal

Exit Slit

AnodeInstrument MisalignmentsExperimental conditions

Diffractometer Components

ICRS-8/DENVER, AUG/06/08

20 40 60 80 100 120 140 160 180

5000

10000

15000

20000 Experiment Calculated ,Ψ=00

Calculated ,Ψ=700

Calculated ,Ψ=800

Inte

ncity

(cou

nts)

2Θ (deg.)

Instrument MisalignmentsExperimental conditions

LaB6 Case

ICRS-8/DENVER, AUG/06/08Zero peaks shift means ideal alignment

140 160

5000

10000 Experiment Calculated ,Ψ=00

Calculated ,Ψ=700

Calculated ,Ψ=800

In

tenc

ity (c

ount

s)

2Θ (deg.)

Instrument MisalignmentsExperimental conditions

LaB6 Case (zoom)

ICRS-8/DENVER, AUG/06/08

0 20 40 60 80

-0.02

0.00

0.02

0.04

0.06

Δ2Θ

(0 )

Ψ (0)

Hypothetical 2Θ shift Fe (211)

0 20 40 60 80-1x10-4

-1x10-4

-8x10-5

-6x10-5

-4x10-5

-2x10-5

0

2x10-5

4x10-5

6x10-5

Δd (A

)

Ψ (0)

Hypothetical d-spacing shift Fe (211)

Instrument MisalignmentsExperimental conditions

LaB6 sample displacement

Criterion for well aligned diffractometer: |Δdmax| less than ~ 10-4A

ICRS-8/DENVER, AUG/06/08

PSI>=0

60o

Influence on Final Results (example)

-219

PSI<=0 + PSI>=0

80o

-185

-238

-202

ICRS-8/DENVER, AUG/06/08

Conclusions

1.The selected material is suitable for national round robin (homogeneity, surface state).

2.Scattering of the results in the acceptable range can be expected in PSI geometry for wide range of experimental conditions.

3.Comparison of the data processing method with the method based on fundamental parameter approach to peak fitting (TOPAS) showed small differences in residual stress values.