Strain and Stress Analysis by Neutron Diffraction · · 2003-09-26Neutron Diffraction Monica Ceretti ... 2003 ECNS03 Introductory Course "Neutron Stress Analysis" 22 Measurement

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September 1-2, 2003 ECNS03 Introductory Course "Neutron Stress Analysis" 1

Strain and Stress Analysis byNeutron Diffraction

Monica CerettiLaboratoire Léon Brillouin

CEA Saclay, 91191 Gif Sur Yvette


Outline

• Introduction:• Definition and classification of residual stresses• Principles of diffraction stress measurements

• Use of neutrons• Experimental aspects• Examples• A look to the future


Residual Stresses: definition andclassification

• Residual stress of the first order (σI, macro) arenearly homogeneous across large areas (several grainsof the material)

• Residual stresses of the second order (σII, meso) arenearly homogeneous across smaller areas, of the orderof some grains or phases of a material

• Residual stresses of the third order (σIII, micro) areinhomogeneous across submicroscopic areas of thematerial, several atomic distances within a grain.

x

σ

σ I

σ I β

σ I α

σ II α

σ II β

σ III α

σ III β

xβ

α

Residual Stresses: « self equilibrating internal stresses existing in a free bodywith no external forces or constraints on its boundary » and under uniformtemperature conditions


Material processing

Casting(thermal residual stresses)

Reshaping

(inhomogeneous plastic deformation)

Cutting

(working RS: grinding, honing)

Joining

(brazing, welding)

Coating

Material properties(case hardening)

Material load

Mechanical

e.g. rolling

Thermal temperaturefields

Chemical H-diffusion

Formation of Residual Stresses

E.g. mutiphasematerials, inclusion

Material

RS superimpose to applied stressesduring service life

RS can affect the mechanicalbehaviour of a component

Their evaluation is fundamental


Methods for Stress Evaluation

σI, σII∆λ≈0.1cm-1=50MPa

< 1µm approx.< 1µmRaman

Microstructure sensitive(for magnetic materials only),σI, σII σIII

10%1 mm10 mmMagnetic (variations inmagnetic domains)

Microstructure sensitive;σI, σII σIII

10%5 mm> 10 cmUltrasonic (changes inelastic waves velocity

Non-destructiveσI, σII σIII (rather difficult)

3D-analysis

± 50 µε, from count.Statis. & reliability ofreference

500 µm200mm (Al), 30mm (Fe)4mm (Ti)

Neutrons (atomicstrain gauge)

Non-destructive σI, σII σIII; 2D analysis

± 10 µε, from grainsampling statistics

20 µm lateral; 1mmparallel to beam

50 mm (Al)Hard X-rays (atomicstrain gauge)

Non-destructive (surface),σI, σII σIII

± 20 MPa, from non-linearities in sin2ψ orsurf. cond.

1 mm laterally20 µm depth

< 50 µm (Al);< 5 µm (Ti); <1mm (iflayer removal)

X-rays diffraction(atomic strain gauge)

Semidistructive, σI ± 50 Mpa50 µm depth1.2xhole diameterHole drilling

CommentsAccuracySpatialResolution

PenetrationMethod


Neutrons vs. X-Rays

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

Tra

nsm

issi

on

Penetration path (mm)

Al

Ti

W

FeNi

2.0933116.601.05W

17.04073.731.86Ni

2.8624246.191.12Fe

7.3993815.40.45Ti

52.913169.30.10Al

t50% (µm)µ (cm-1)t50% (mm)µ (cm-1)Z

RaysX-ronsNeut


• Introduced in the 80’S

• rapid developments: it is the only technique which allows a nondestructive analysis of the stress field in bulk samples

• neutron can deeply penetrate in most materials

• intensity of a neutron monochromatic beam is much lower than that ofX-ray tube

• high neutron source• long measuring time• spatial resolution of ~ 1mm3

Neutron Diffraction Applied to StressAnalysis


Stress Stress AnalysisAnalysis by Neutron Diffraction by Neutron Diffraction

Bragg ’s Law : θ=λ sinhkld2n

Strain StressElasticity law

θ∆θ∆λλ∆ ∗+= ancot

dd

hkl

hklBy differantiating Bragg ’s Law:

Strain εhkl

Positiondispersion if

∆λ=0Wavelengthdispersion if ∆θ=0

Lattice strain0

0hklhkl d

dd −=ε


Two cases:� λ is const (reactor)

� θ is const , time of flight technic

(spallation source)

Using diffraction to measure strain

Strain is given by the change in peakposition from the stress-free location

)2(cot21

ddd

00

0 θ∆θ−=−

=ε

tt

ddd

0

0 ∆=λλ∆=−=ε


Detector

Incident beam

Gauge volume

QCd masks

2θ ≈ 90°

Gauge volume


Coordinate System and Strain Relation

• In terms of the angles φ and ψ, ε in a given direction is:

εφψ = ε11cos2φ sin2ψ + ε22sin2φsin2ψ + ε33cos2ψ + ε12sin2φsin2ψ + ε13cosφsin2ψ + ε23sinφsin2ψ

ψ

φ

S3

S2

L2

S1L1

L3• Si, Li are the sample and laboratory systems,

respectively, and are related by φ and ψ.

• The diffracting planes are normal to L3


Converting strain to stress

Hooke ’s law

)(E

)2sinsinsin2sin

sin2sincossinsinsincos(E

1

zzyyxxhkl

hklyz

2xz

2xy

2zz

22yy

22xx

hkl

hkl

σσσν

ψϕσψϕσ

ψϕσψσψϕσψϕσν

εϕψ

++−++

++++

=

σij =E

1+ νεij + δij

ν1− 2ν

ε11 + ε22 + ε33( )


Procedure

• General triaxial stress state: 6 unknowns.

– Make (at least) 6 measurements Stress/Strain complete tensor

• Biaxial stress state: sin2ψ method

• 1D measurements if principal directions are known

• Errors depend on:• Counting statistics• Array of angles φ, ψ• Experimental errors


Four ideas

• It is strain that is actually measured.

• Residual strain changes interplanar spacings, whichshifts the positions of diffraction peaks.

• Strain is resolved differently in different physicaldirections in the sample.

• Engineering materials are polycrystalline, so somegrains are always oriented to diffract enabling stresstensors to be determined.


Lmin

Lmin

maxL

maxL

2θ2θ

θ < 45° 45° < θ < 90°

Lmin

maxL = W/sinθ

= W/cosθ

= W/cosθ

maxL

Lmin

= W/sinθ

Fron

t su

rfac

e Back su

rface

Gauge volume - Shape

LminFron

t su

rfac

e Back su

rface

θ = 45°

2θ

Lmax = Lmin = W/sinθ


Gage volume - issues

• Size– Small enough for spatial resolution– Large enough for sufficient intensity

• Shape– Confine measurement to region of interest– Neutron measurements around 90° 2θ

• Geometry and optics– Can be tricky


Texture - preferred orientation

• Conversion of strain to stress:– Elastic constants altered– Can change with sample orientation

• Peak intensities and shape:– Intensities can vary strongly with orientation– Shapes can also change, affecting accuracy

• Can be checked by:– Measurements of intensity versus sample orientation– Powder pattern intensity analysis

• If possible, use experimentally determined diffraction elasticconstants from same material


Stress-free standards

• Generally require peak positions for the stress-freestate (do values) to determine strains.

• Approaches:– Stress-free region– Stress-free piece– Reference powders– Use of equilibrium requirements:

• Two phases• Force/moment balance


Characteristics of a Strain DedicatedDiffractometer

• two axis diffractometer withgood instrumental resolution(∆d/d ~10-3 - 10-4) combinedwith a good luminosity

• high/medium neutron flux

• rigid mounting and adequatespace for manipulation of thesamples

• devices for the positioningand the alignment of thesamples

• translation/rotation tableXYZω

• slits for the definition of the“gauge volume”.

ENGIN-X (ISIS), SMARTS (Los Alamos), DIANE (LLB), POLDI(SINQ), D1A (50%, ILL), E3 (HMI)


Spallation Source

tt∆

=λλ∆

=ε • good gauge volume definition

• Diffraction angle fixed, wavelength varies

• Peaks from many planes recordedsimultaneously

• Useful for anisotropic systems


2θ0

2θ

∆2θ

Steady State Reactor

• One peak analysis;

• data analysis quite simple

• Wavelengths from about 1-2 Å(2-5 Å for cold neutrons)

• Resolution adequate, throughputvaries.

)2(cot21

0 θ∆θ−=ε

2θ0

2θ

∆2θ


Measurement Measurement of radial of radial strain strain in in the the crosscrosssection of a section of a railway wheel hooprailway wheel hoop

• Recent railway disasters are essentially caused bymaterial failure of the wheel

• a better understanding of failure mechanism isneeded

The life time of railway wheels is limitated by:

• Accumulation plastic strains and formation of micro-cracks due to cyclic loading

• Manufacturing engineering and structuralmodifications «local cold work hardening» inducesresidual stresses formation


Strain Scanning

• Diffractomètre G52, λ = 3A

• Fe-α (110)

• résolution spatiale: 2x2x10 mm3

0,1

1

10

100

1000

0 5 10 15 20 25depth in mm

coun

ting

rate

of t

he 1

10 --

re

flexi

on in

cps

MaterialMaterial:: • perlitic steel

• Sector (35°) of an ICE train

• used 1.400.000 Km (life limit)


Results

Tension

Compression

ConclusionConclusion• Compression in the central region, tension in the regions

near the wheel-rail contact regions

• Correlation between strain distribution and fracturemechanism

• the stress re-distribution during the wheel service life isfundamental.


Residual Stress Analysis in Metal MatrixComposites

MMC

Diffraction methods give access to phase stresses

• Wearing resistance

• high temperature resistance

• Stiffness

• Improved combination of mechanicalcharacteristics

• Bad ductibility

• Misfit Stress between phases due to≠ CTE and elastic properties

MMC

v Aim of the study: effects of plasticity on the residual stresses of thermal origin

v Material: Al 2124 + 17% SiCp (505°C 2h, cold water quench) : before and after bending

mEi

mTi

Mi

Ti σ+σ+σ=σ

MmE

TM

TP

M

mTM

mTP

B

)f1(f

0)f1(f

σ=σ

σ−+σ=σ

=σ−+σv Theoretical model :

v Neutron diffraction stress measurements

X

Y

Z


Results

-600

-400

-200

0

200

0 2 4 6 8 10 12 14

Measured Al stressMeasures SiC macroAl thermal mismatchSiC thermal mismatch

Position z (mm)

Al

SiC

Unbent bar• Dominance of the thermal expansionmisfit on the residual stressesevolution before bending

-600

-400

-200

0

200

0 2 4 6 8 10 12 14

Measured Al stressMeasured SiC stressMacroAl thermal mismatchSiC thermal mismatch

Position z (mm)

Al

SiC

Bent bar

•After bending the mismatch in thecentre of the bar remain unchanged, butthe plasticity in the surface region has alarge effect relaxing the misfit stresses


Residual Stresses and MicrostrainInvestigation in Fatigued Specimen

PLASTICREGION

CRACK

70 mm

10 mm

45 mm

AISI 316LCompact Tension specimens

• CT_1: R=0.1, 26000 cycles ∆K=30.48MPa mm 1/2

• CT_2: R=0.5, 20000 cycles ∆K=30.48MPa mm 1/2

• CT_3: tension up to 5mm crack opening(10000N)


Internal Elastic Stresses by NeutronDiffraction and FE calculation

-400

0

400

800

1200

-2 0 2 4 6 8 10 12 14 16 18

Str

ess

(MP

a)

Distance from the crack tip (mm)

crack tip

σxxσ

yy

σzz

-400

0

400

800

1200

-2 0 2 4 6 8 10 12 14 16 18

Str

ess

(MP

a)

Distance from the crack tip (mm)

crack tip

σxxσ

yy

σzz

Neutrons�q 3D measurements

�q Spatial resolution:

1x1x1 mm3

FE calculation• 3D

• Elastic-plastic behaviour

o In all the three specimens a 3D stress stateis observed.

o CT_1: the residual stresses obtained arerather weak.

o CT_2: higher tensile stresses with amaximum at 1.5 mm from the crack tip.

o CT_3: the maximum stress level is at 2 mmfrom the tip. At 8mm from the tip, σxx and σyyare very low, whereas σzz becomes large andcompressive


Steep gradients at a surface

Detector finds peak athigher angle = apparentcompressive strain

Wavelength longer, on averageCenter of scattering mass is shifted in space

Sampling volumeSampling volume

Specimen


Z

Y

X

50 mm5 mm

• Ni Superalloy

• shot-peening

• high spatial resolution :

0.3x0.3x20 mm3

-1000

-800

-600

-400

-200

0

200

400

0 0.5 1 1.5 2 2.5 3

σy corrected

σz correctedσy exp

σz exp

Depth z (mm)

Stre

ss (M

Pa)

Example: Shot-peening


Residual Stresses in Notches Resultingfrom Impacts

Aim of the study: determine the effect of a high-energy projectile impact on thefatigue life of the target material.

To validate the elasto-plastic Finite Element calculation, neutron diffraction has beenused to determine the evolution of the residual stresses under the notch

(spatial resolution: 1x1x1mm3)

-1000

-800

-600

-400

-200

0

200

400

1 2 3 4 5 6 7 8

σrr (calc)

σzz

(calc)

σzz

(exp)

σrr (exp)

Z (mm)

σ (MPa)

COMPRESSION

TRACTION

XC38 STEEL

Impa

ct o

f pr

ojec

tile

with

a s

peed

of

100k

m/h

Disagreement under theimpact notch, due to theadiabatic heating of the steeland the formation of adiabaticshear bands made by veryhigh energy impact;

residual stress relaxation


Recommandations

• Experience is really feasible?• Path length, spatial resolution, number of samples ….

• Define an efficient strategy:– How large are the stress gradients? Dimensions of the gauge volume

– Are D vs sin2ψ linear (or approx.)? Yes measurements in the 3 principal directions

– What is the ratio of macro- to microstress? Use of single reflection line or several

– Define meaningfull region of the sample to be investigated

– Choise of an adeguate {hkl} reflection

• Reference sample for determining d0


A look to the future

• Triaxial measurements• Anisotropic materials• Small strain systems (e.g. ceramics)• Real time (parametric) studies• Small gage volumes (e.g. gradients, buried interfaces)• Higher temperature and stress• High Z materials

High flux, highresolution

3rd high flux neutronsources: SNS, JNS,ESS


Neutrons vs. Synchrotron Radiation

Minutes-seconds½ h – 1hCounting time

NoYesIndustrial realcomponent study

YesNoCoarse grain probleme

With problemsYesStress complete tensor

2D3DStrain maps

µm in one direction, mm in theother (0.1mm3)

1mm3

Spatial resolution

Qq. mm 10-20 mm

10-20 mm 40-60 mm

Penetration•? Steels• Al alloys

Synchrotron RadiationNeutrons

Documents

Strain and Stress Analysis by Neutron Diffraction · · 2003-09-26Neutron Diffraction Monica Ceretti ... 2003 ECNS03 Introductory Course "Neutron Stress Analysis" 22 Measurement