Post on 02-Apr-2018
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.