Using Spallation Neutron Diffraction Measurements of Strain and Texture to Study Mechanical Behavior of

Structural Materials

Don Brown, Los Alamos National Lab

dbrown@lanl.gov

Why Use Neutron Diffraction ?

• Any diffraction technique is possible.– Peak position (Bragg’s law) lets us measure interatomic spacing.

• Question is which technique is optimal for the problem.

• Electron diffraction :

– Penetration depth is very small, ~1µµµµm.

– Surface technique.

– Does not determine interatomic spacing accurately enough to use for strain.– Does not determine interatomic spacing accurately enough to use for strain.

– Very effective for measuring texture over small length scales, 10µµµµm-1mm.

– Most materials science labs have TEM/SEM available.

• Conventional (bench-top) X-ray diffraction :

– Penetration small, ~10µµµµm.

– Traditional technique for surface texture and strain measurements.

– Sources are very common.

Why Use Neutron Diffraction ? (cont.)

• Thermal neutron diffraction :• Thermal neutron diffraction :

– Large Penetration, ~1cm.

– Effective measurement of bulk texture and strain.

– Neutrons sources are few and far between, not an everyday technique.

• High energy synchrotron X-ray diffraction :

– Large Penetration, ~1cm.

– Effective measurement of bulk texture and strain.

–Again, not an everyday technique

The Knock-On Effect Of Penetration Is Better Grain Statistics

• X-rays penetrate 10’s of microns, at best.

• Illuminate ~1 layer of grains.

• Even moderately grains sizes can cause problems with grain statistics.

The Knock-On Effect Of Penetration Is Better Grain Statistics

• With neutrons, we define a volume at depth.

• 3D instead of 2D

• Result is many more grains illuminated.

• Start to see grain statistic problems at 100’s of microns.

Lujan Neutron Scattering Center

Weapons Neutron ResearchFacility

Isotope ProductionFacility

Isotope ProductionFacility

Neutron Sources Do Not Sit on Desktop’s

Los Alamos Neutron Science Center : LANSCE

Proton Radiography 800 MeV Proton Linear Accelerator

Time of Flight Technique at a Spallation Source

Neutron

t=0

Neutron

sm3000750

mKE2

vn

−−−−≈≈≈≈====

Q⊥

30m

Tungsten Target

Water Moderator

Neutron Flux

Time

Neutron Flux

Time

0 10 20 30 40

Neutrons

Time of Flight (msec)

Energy (meV)361353

d-space in 90o detector (A)

2.620.87 1.75 3.50 10 15 20 25 30 35 400

0.05

0.1

0.15

0.2

0.25

Time of Flight (msec)

High Intensity Powder

HIPPOSingle Crystal

Quasi-elastic

Experimental Halls Contain ~ 16 Instruments

Target Moderator Assembly

Pair Distribution Function

SMARTS ReflectometersSoft MatterPolarized Beam

Small Angle

Protein Crystallography

Inelastic Scattering

Future High Resolution Inelastic

Advanced Diffractometers On-line at LANSCE

Translator

•LANSCE : Time-Of-Flight neutron source.

• Continuous spectrum of incident neutrons.

• Record entire diffraction pattern simultaneously.

• SMARTS : Optimized for study of lattice parameters in engineering materials.

• HIPPO : Optimized for high pressure and texture measurements.

Spatially Resolved Neutron Diffraction Measurement of Strain

Diffracted Beam

Incident BeamIncident Collimation

Weldment

Radal Collimators

What it Really Looks Like

More Interesting Example of In-Situ Friction Stir Welding

What is The Advantage Of A Spallation (White) Source?

+ 90 ° DetectorBank

Incident Neutron Beam

Q⊥Q||

0110

02110002

-90° DetectorBank Compression Axis

(002)(100)

(110)

(210)

Extrusion Direction

Inverse Pole Figure

0.0

-393-188-138186244461346291-133

471

177

-360

-428

-260-95

307

5004003002001000-100-200-300-400-500

Inverse Strain Pole Figure

dhkl

SMARTS is a 5 Million Dollar Bathroom Scale

• We measure the spacing between atoms very accurately.

• Calculate lattice strains from change in atomic spacing due to some perturbation.

• If we know the spring constants, we can calculate the stresses from the strains.

• It is important to note that the lattice strain is necessarily proportional to the stress on the grain family, not the macroscopic stress.

0

0

d

ddhkl −=ε

klijklij C εσ =

SIDEBAR : Neutrons Always Struggle to Measure Reference Lattice Spacing: d0

• Measure lattice parameters in small coupon removed from sister sample.

– Relieves macroscopic stresses.

• Issues :

– Geometry of coupon should be similar to part.

– Changes in path length can give fictitious lattice strains due to absorption.due to absorption.

– Sister sample must be very similar.

– Chemistry changes will dominate stress effects.

– Often, thermo-mechanical treatment (e.g. welding) inadvertently changes chemistry within a single part

– Must measure reference lattice parameters in several positions.

– Becomes very labor intensive.

Crystal Anisotropy is Very Important

• Stiffness tensor is usually anisotropic.

• Polycrystalline yield surface can be more so.

• Texture dependent.

• How do we understand the Cijkl

Neutron Diffraction Separates Response of Grain Orientations

Polycrystalline Aggregate Stainless Steel

(002)

(111)

• Grains with plane normals parallel to the diffraction vector defined by the instrument geometry diffract into a detector.

• Each grain orientation (hkl) contributes to a distinct peak, given by the interplanar spacing.

Q

Lattice Response to Applied Stress

+ 90 ° DetectorBank

Incident Neutron Beam

-90° DetectorBank

Comp. Axis

Q⊥Q||

dd −

0 500 1000 1500 2000 2500 30000

50

100

150

200

250

300

350

111200311331a

Lattice Strain (x106)

App

lied

Str

ess

(MP

a)

Plastic Anisotropy is Also Apparent

Load

ing

Unl

oadi

ng

0 500 1000 1500 2000 2500 30000

50

100

150

200

250

300

350

111200311331a

Lattice Strain (x106)

App

lied

Str

ess

(MP

a)

Stiffness Anisotropy is Evident

0

0

d

dd −=ε

200

300

400

500 Kanthal Matrix

Tungsten Fibers

App

lied

load

[M

Pa]

Kanthal with 10% Tungsten fibers

200

300

400

500 Kanthal Matrix

Tungsten Fibers

App

lied

load

[M

Pa]

Kanthal with 10% Tungsten fibers

Understand Anisotropy in Terms of a Composite

Tungsten FibersKanthal Matrix

-0.1 0 0.1 0.2 0.3 0.40

100

Lattice strain [%]

App

lied

load

[M

Pa]

-0.1 0 0.1 0.2 0.3 0.40

100

Lattice strain [%]

App

lied

load

[M

Pa]

• Microstructure represents loading 2 constituents in parallel.

• In elastic regime, lattice strains are equivalent.

• Saturation of lattice strain in plastic regime in Kanthal indicates that it has yielded.

– Call Kanthal the “soft” phase.

– Intergranular strain = deviation from linearity.

Next Consider Anisotropic Polycrystalline Samples : “The Mother of All Composites”.

Polycrystalline Aggregate

(110)

(103)

Be in Compression-300

-250

-200

-150

-100

App

lied

Str

ess

(MP

a)

Q

• Example : Beryllium

− Yield strength when loaded along different plane normals is disparate.

− (103) is “soft orientation”; (110) is “hard orientation”.

− Difference in (hkl) strains and bulk modulus are due to “intergranular” strains.

− In situ deformation measurements provide Cijkl information.

-1200-800-4000

-50

0

(1120)(1013)

Lattice Strain (µεµεµεµε)A

pplie

d S

tres

s (M

Pa)

(110)(103)

Development of Intergranular Strains : Tensile Deformation of Be

-450

-250

-50

150

[10-10][20-21][10-11][10-12][10-14][0002]

[2-1-14]

[2-1-12]

[2-1-10]

[3-1-20]

[3-1-21][3-1-22]

[3-1-23]

0.0% Total Strain

0.16% Total Strain

Intergranular strain (contours µε)µε)µε)µε)

350

550

750

950

0.70% Total Strain

0.52% Total Strain

-194 1050

875

Intergranular Strains Are Different in Tension and Compression

Compression

Tension

-360500400

[1010][2021][3032]

[1011][2023]

[1012][1013]

[1014][0002]

[1124]

[1122]

[1120]

[2130]

[2131][2132]

[2133]

-186-249-313-332-274-1352237121126

49

-305

-307

-204-226

-269

875

700

525

350

175

0

-175

-350

0.70% Total Strain-0.70% Total strain

0.0

-393-188-138

186244

461346

291-133

471

177

-428

-260-95

307

4003002001000-100-200-300-400-500

Compression : Contour Interval 60 µεµεµεµε Tension : Contour Interval 175 µεµεµεµε

As always, difficulties lead to oppurtunities…

Neutron Diffraction Manifests “Indicators” of Plasticity

-200

-100

0

100

200

300

103Inte

rgra

nula

r S

trai

ns (

x10

6 )

-400

-300

0 0.002 0.004 0.006 0.008

103

110

Inte

rgra

nula

r S

trai

ns (

x10

Plastic Stain

• Intergranular Strains and the Anisotropy Strain are Empirical “Indicators” of Plasticity.

( )I Ip 1120 101310.4ε = ε − ε

Example of Welded Beryllium Rings

• Girth Welded Be Rings.

• Beryllium has hexagonal crystal structure.

• Aluminum-Silicon Weldment.

• Objectives of the Neutron Diffraction Studies

– Measure Residual Stresses Post-Weld.

– Understand Development of Residual Stresses.

– Verify or Improve FEM.

– Optimize Weld Procedures.

Development of Residual Stresses During Welding

Hot material contracts

•When hot, material near weld flows to accommodate thermal gradient.

•As it cools and strength increases residual stresses develop due to constrained thermal contraction near the weld.

• In autogeneous welds, typically yield level tensile residual stresses near weld.

Cold material constrains thermal contraction

-100

0

100

200

FEM(110)(103)

Strain µεµε µεµε (N

eutron Diffraction)

Primary Stress Component is in the Hoop Direction

-300

-200

-20 -10 0 10 20

(Neutron D

iffraction)

Distance From Weld (mm)

Radial Strain

(110)(103)

0

200

400

hkl -

Spe

cific

Str

ain

( µεµε µεµε)

Axial Strain

Expect Little Or No Residual Strain in Axial and Radial Directions

-20 -10 0 10 20

-200

hkl -

Spe

cific

Str

ain

(

z (mm)-20 -10 0 10 20

z (mm)

Observed residual strains are (hkl) dependent, even in sign !!!

0.001

0.002

0.003

0.004Plastic Strain

Pla

stic

str

ain

Intergranular Strains Allow Us To Estimate Plastic History

-300

-200

-100

0

100

200

300

103

110

Inte

rgra

nula

r S

trai

ns (

x10

6 )

0

-20 -10 0 10 20z (mm)

-4000 0.002 0.004 0.006 0.008

Plastic Stain

( )I Ip 1120 101310.4ε = ε − ε

We estimate the amount of plastic strain from the difference in orientation dependent (hkl) strain.

But What About the Macroscopic Residual Stressess?

-300

-200

-100

0

100

200

300

400

a

c

Str

ain

(x10

6 )

-300

-200

-100

0

100

200

300

400average

Str

ain

(x10

6 )

-40

-20

0

20

40

60Stress

Res

idua

l Str

ess

(MP

a)

-400-20 -10 0 10 20

Distance From Weld Centerline (mm)

-400-20 -10 0 10 20

Distance From Weld Centerline (mm)

• Pick an (hkl) that is relatively insensitive to intergranular stresses, e.g. 311 in steel.

• Because we have a full pattern we can use Rietveld refinement to find lattice parameters, instead of single hkl’s.

– “Empirical” averaging over different orientations.

• Texture weighted average over multiple orienations.

– Hexagonal case (no texture) : ε ε ε ε = (2εεεεa+εεεεc)/3

• In the case of beryllium, relatively easy to go from strain to stress.

-60-20 -10 0 10 20

Distance From Weld Centerline (mm)

Summary

• Neutrons provide bulk stress/strain measurements with increased grain sampling.

• Integration volume on the order of 1mm.

• Geometry allows for measurement of several components of strain.

• Crystal anisotropy can make macroscopic strain • Crystal anisotropy can make macroscopic strain determination difficult.

– More so in lower symmetry crystal structgures.

• Spallation ND (white beam) allows for the determination of strains from many orientations simultaneously..

–Allows us to probe the part more deeply…