RESIDUAL STRESS MEASUREMENTS BY NEUTRON ...5 Residual stress measurements by neutron diffraction at...

RESIDUAL STRESS MEASUREMENTS BY NEUTRON DIFFRACTION

AT THE IBR-2 PULSED REACTOR

G.D. BOKUCHAVA, I.V. PAPUSHKIN, A.V. TAMONOV, A.A. KRUGLOV

Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

E-mail: [email protected]

Received September 22, 2015

Neutron diffraction is widely used for investigations of residual stresses in various

constructional materials and bulk industrial components due to the non-destructive

character of the method and high penetration depth of neutrons. Therefore, to study

residual stresses, the Fourier stress diffractometer FSD has been constructed at the

IBR-2 pulsed reactor (Dubna, Russia). Using a special correlation technique high

resolution level of the instrument has been achieved: d/d ≈ 2÷4·10–3. The FSD

design satisfies the requirements of high luminosity, high resolution and specific

sample environment. In this paper, the design and current status of FSD

diffractometer is reported.

Key words: neutron diffraction, time-of-flight method, residual stress, microstrain.

PACS: 61.05.F-, 07.10.Lw

1. INTRODUCTION

To investigate internal stresses in materials, various non-destructive methods, including X-ray diffraction, ultrasonic scanning, a variety of magnetic methods (based on the measurement of magnetic induction, penetrability, anisotropy, Barkhausen effect, magnetoacoustic effects) have been used for many years. All of them, however, are of limited application. For example, X-ray scattering and magnetic methods can be only used to investigate stresses near surfaces because of their low penetration depth. Besides, the application of magnetic methods is restricted to ferromagnetic materials. Also, magnetic and ultrasonic methods are greatly influenced by the texture in a sample. The neutron diffraction method of mechanical stress investigations appeared about 20 years ago. Since then it has been widely used because of a number of advantages. In contrast to traditional methods, neutrons can non-destructively penetrate into the material to a depth of up to 2–3 cm in steel and up to 5 cm in aluminum. For multiphase materials (composites, reinforced materials, ceramics, alloys) neutrons give separate information about each phase. Internal stresses in materials cause deformation of the crystalline lattice leading to Bragg peak shifts in the diffraction spectrum. Therefore neutron diffraction can be used for non-destructive stress evaluation as well as for calibration of other non-destructive techniques. The use of neutron diffraction in combination with the time-of-flight (TOF) method is important because of the possibility to measure mechanical stresses simultaneously for different (hkl) directions in the crystal.

Rom. Journ. Phys., Vol. 61, Nos. 3–4, P. 491–505, Bucharest, 2016

mailto:[email protected]

492 G.D. Bokuchava et al. 2

For these reasons experiments for residual stress studies start to occupy a

noticeable position in the research programs of leading neutron centers. To conduct

such experiments, specialized neutron diffractometers are being constructed. The

strain caused by internal stresses is of the order 10-3

–10-5

and requires a quite high

resolution of the diffractometer, i.e. d/d 0.2–0.3%. A special feature of the

neutron experiment to study internal stresses is the scanning of the investigated

area in the bulk sample by means of a small scattering (gauge) volume separated

using special diaphragms in the incident and scattered neutron beams, which

requires a high luminosity of the diffractometer. During last year’s a great number

of experiments were performed on IBR-2 reactor in order to approve the method

and to define potential application domain. These investigations were conducted

using the correlation Fourier technique at the high-flux IBR-2 reactor, which is a

long-pulse type source with a pulse width of about 350 µs for thermal neutrons. It

was shown that reverse time-of-flight (RTOF) technique is unique method

possessing sufficient resolution and luminosity for precise determination of

residual strain from relative shifts of diffraction peak as well as for reliable

detection of peak broadening with subsequent microstrain calculation. First

experiments for residual stress study with neutron diffraction in Dubna arouse vast

interest on the side of science and industry. For this reason, the specialized neutron

stress diffractometer FSD (Fourier Stress Diffractometer) – optimized for residual

stress studies – has been constructed at the IBR-2 pulsed reactor in FLNP JINR.

2. RESIDUAL STRESS MEASUREMENTS BY NEUTRON DIFFRACTION

Diffraction of thermal neutrons is one of the most informative methods when

solving many applied engineering and materials science problems, and it has a

number of significant advantages as compared to other techniques. The main

advantages of the method are deep scanning of the material under study (up to 2

cm for steel) due to high penetration power of the neutrons, non-destructive

character of the method, good spatial resolution (up to 1 mm in any dimension),

determination of stress distributions for each component of the multiphase material

separately (composites, ceramics, alloys, etc.), possibility to study materials

microstructure and defects (microstrain, crystallite size, dislocation density, etc.).

In combination with TOF technique at pulsed neutron sources, this method allows

to record complete diffraction patterns in wide range of interplanar spacing at fixed

scattering angle and to analyze polycrystalline materials with complex structures.

In addition, with TOF neutron diffraction it is possible to determine crystal lattice

3 Residual stress measurements by neutron diffraction at the IBR-2 pulsed reactor 493

strains along different [hkl] directions simultaneously, i.e. to investigate

mechanical anisotropy of crystalline materials on a microscopic scale.

The neutron diffraction method is very similar to the X-ray technique.

However, in contrast to the characteristic X-ray radiation the energy spectrum of

thermal neutrons has a continuous (Maxwellian distribution) character. The

velocity of thermal neutrons is rather small and this gives the opportunity to

analyze the neutron energy using it’s time of flight during the experiment at a

pulsed neutron source. Depending on the neutron wavelength, the peak position on

the time-of-flight scale is defined by the condition

t = L/v = mL/h = 2mLdhkl sinθ/h, (1)

where L is the total flight distance from a neutron source to detector, v is the

neutron velocity, is the neutron wavelength, m is the neutron mass, h is Planck’s

constant, dhkl is the interplanar spacing, and θ is the Bragg angle.

Internal stresses existing in a material cause corresponding lattice strains,

which, in turn, results in shifts of Bragg peaks in the diffraction spectrum. This

yields direct information on changes in interplanar spacing in a gauge volume,

which can be easily transformed into data on internal stresses, using known elastic

constants (Young’s modulus) of a material. The principle of the determination of

the lattice strain is based on the Bragg’s law

2dhklsinθ = , (2)

where is the neutron wavelength, dhkl is the interplanar spacing, and θ is the

Bragg angle.

The essence of the diffraction method for studying stresses is rather simple

and, in conventional experimental design, consists of incident and scattered neutron

beam shaping using diaphragms and/or radial collimators and definition of a small

scattering volume (gauge volume) in the bulk of the specimen (Fig. 1, a) [1]. The

incident beam is usually formed using cadmium or boron nitride diaphragms with

characteristic sizes from 1–2 mm to several cm depending on the purpose of the

experiment. To define a gauge volume of optimum shape in the studied specimen,

at the scattered beam radial collimators with many (about several tens) vertical slits

formed by Mylar films with gadolinium oxide coating are often used. A radial

collimator is placed at a quite large fixed distance (usually 150÷450 mm) from the

specimen and provides good spatial resolution of the level of 1–2 mm along the

incident neutron beam direction. The lattice strain is measured in the direction

parallel to the neutron scattering vector Q. The sample region under study is

scanned using the gauge volume by moving the sample in the required directions.


In this case, relative shifts of diffraction peaks from the positions defined by unit

cell parameters of an unstrained material are measured.

Q1

Q

2

Dete

cto

r 1

Dete

cto

r 2

n0

Fig. 1 – Scheme of the experiment for residual stress investigation in a bulk object. Incident and

scattered (at angles 2θ = ±90°) neutron beams are restricted by diaphragms shaping a gauge volume

within the specimen. Measurement of neutron diffraction spectra by ±90° detectors allows

simultaneous determination of strains in two mutually perpendicular directions.

On two-axis diffractometer at a neutron source with continuous flux, the

strain is determined by the change in the scattering angle –Δθ∙cotθ. When using the

TOF method at a pulsed source, the crystal lattice strain is determined by the

relative change in the neutron time of flight Δt/t:

cot//)( 00 hklhklhklhkl ddd , ttddd hklhklhklhkl //)(00 (3)

where hkld is the measured interplanar spacing and 0

hkld is the same interplanar

spacing in a stress-free material, and t is the neutron time of flight.

The components of the residual stress tensor can be determined from the

measured residual strain according to the Hooke’s law:

))(21

(1

ZYXiiii

E

, (4)

where ii = X, Y, Z, ii and ii are components of the stress and strain tensors, respectively, E is Young’s modulus and ν is Poisson’s ratio.

Based on known values of the Young’s modulus, the required interplanar

spacing measurement accuracy can be estimated, so that the σ determination error


would not exceed, e.g., 20 MPa, which is, as a rule, quite sufficient for engineering

calculations. For aluminum, Е ≈ 70 GPa, hence, it is sufficient to measure Δa/a0

with an accuracy of 3·10–4

; for steel, Е ≈ 200 GPa, and the accuracy should be

better than 1·10–4

. These requirements appreciably exceed the capability of

conventional neutron diffractometers whose resolution, as a rule, is ~1%, i.e., the

diffractometer for measuring internal stresses should have high resolution. Existing

practice showed that a required accuracy can also be achieved for diffractometers

with monochromatic neutron beams, operating at stationary reactors, and for TOF

diffractometers operating at pulsed neutron sources. Without going into details of

experimental design in these two cases, we only note that a main advantage of the

former version is a larger luminosity and, hence, the possibility of sample scanning

with good spatial resolution. In the latter case, a fixed and most optimal 90°

experimental geometry is easily implemented and, in contrast to the former case,

several diffraction peaks are simultaneously measured, which allows analysis of

stress anisotropy.

An analysis of the shape (width in the simplest case) of diffraction peaks can

yield information on lattice distortions in individual grains (microstrain) and their

sizes. This is especially convenient to do that using a TOF diffractometer with the

functional dependence of the peak width on the interplanar spacing,

W2 = C1 + C2 d

2 + C3 d

2 + C4 d

4, (5)

where W is the peak width, C1 and C2 are the constants defining the diffractometer

resolution function and known from measurements with a reference sample,

C3 = (a/a)2 is the unit cell parameter dispersion (microstrain), and C4 is the

constant related to the crystallite size.

The neutron diffractometer TOF resolution in a first approximation is

defined by three terms,

R = d/d = [(t0/t)2 + (/tg)

2 + (L/L)

2]

1/2, (6)

where t0 is the neutron pulse width, t = 252.778L is the total time of flight (μs),

L is the source–detector flight distance (m), λ is the neutron wavelength (Å), and θ

is the Bragg angle. The first term is the time of flight uncertainty, the second term

includes all geometrical uncertainties associated with scattering at various angles,

and the third term is the uncertainty in the flight path length. The resolution will

improve as the Bragg angle approaches 90°, as the pulse width decreases, and as

the flight distance increases. For pulsed neutron sources with short fast neutron

pulses, the thermal neutron pulse width can be decreased to ~20 μs/Å; as the flight

path length increases to 100 m, the resolution can be improved to 0.001 and, if

required, to 0.0005.

For neutron sources with long pulses, e.g., the IBR-2, such a way to achieve

high resolution is a priori unacceptable; the only practical way is the use of the


reverse time-of-flight (RTOF) method in combination with a Fourier chopper [2],

which provides a higher luminosity of experiments in comparison with other

correlation techniques. In the RTOF method, the spectrum acquisition is performed

at continuous variation of the rotation frequency of the Fourier chopper from zero

to a certain maximum frequency ωm. In this case, the time component of the

resolution function is defined by the resolution function of the Fourier chopper RC,

which depends on a particular frequency distribution g(ω) and can be written as

dtgtt

0

0 )cos()(~/ dω, (7)

where Ω = Nωm is the maximum frequency of neutron beam intensity modulation

and N is the number of Fourier chopper slits. At a reasonable choice of g(ω), the

full width ∆t0/t at half maximum is -1

; at N = 1024 and ωm = 100 kHz, it is ~10 μs.

This means that even at a chopper–detector flight distance of ~6.5 m and scattering

angle 2θ = 90°, the contribution of the time component to the resolution function

can be ∆t0/t ≈ 2·10–3

at d= 2 Å.

When using thin detectors, the third term in (6) becomes negligible, and the

geometrical contribution can be optimized proceeding from the desirable relation

between resolution and intensity. A typical solution is the choice of focusing

geometry in the arrangement of detector elements with parameters providing a

geometrical contribution equal to the time contribution to the complete resolution

function.

To increase the luminosity of the TOF diffractometer and decrease the

background level, the primary neutron beam is formed using a curved mirror

neutron guide. In this case, the neutron spectrum is cut off from the side of short

wavelengths due to the neutron guide curvature radius chosen from the condition of

the absence of line of sight of the neutron moderator. A calculation shows that, at a

total flight path length from the source to the sample of ~20 m and a horizontal

cross section of the neutron guide of ≤1cm, the curvature radius can be sufficiently

large to pass neutrons up to λ ≈ 1 Å. In this case, the number of simultaneously

observed diffraction peaks, even for materials with small unit cell sizes (steel,

aluminum), is about ten, which is sufficient to analyze stress anisotropy.

Furthermore, a sample place should be specially organized in the diffractometer for

measuring internal stresses, i.e., the possibility of installing large and heavy

equipment (goniometer, loading machine, etc.).

3. FSD DIFFRACTOMETER AT THE IBR-2 PULSED REACTOR

The basic functional units of the FSD diffractometer are the neutron source –

IBR-2 reactor with grooved water moderator – generating thermal neutron pulses

~320 μs long with a frequency of 5 Hz; the long mirror neutron guide purifying the


beam from fast neutrons and γ-rays; the fast Fourier chopper providing neutron

beam intensity modulation; the straight mirror neutron guide shaping the thermal

neutron beam on the sample; the detector system consisting of detectors at

scattering angles of ±90° and a backscattering detector; a mechanical system,

including a stage for placing goniometric and loading machines and a collimation

devices setting primary beam divergence and separating the gauge volume in the

sample; and data acquisition electronics including a RTOF analyzer (Fig. 2a) [3, 4,

5]. The FSD diffractometer automation system [6] allows local or remote control of

experiment.

3,400 19,000

0,184

5,500

Moderator

Ni Guide Tube

"ISOMER" Instrument

Fourier Chopper Full Circle

Goniometer

Detectors

VME

VME control

and operative

visualization/analysis

VME Station (OS/9)

Data Acquisition

EtherNet

Data Transfer

IBR-2

F L N P

F S D

Fourier Stress Diffractometer

Slit width 0.7 mm

RotorStator

Transmission function

Binary signals

a) b)

Fig. 2 – a) Layout of FSD diffractometer (Fourier Stress Diffractometer) at the IBR-2 pulsed reactor

(FLNP JINR, Dubna). b) Design of the Fourier chopper, consisting of a rotating rotor and a stationary

stator. Outer circumference of the rotor disk is a system of interleaving slits transparent and opaque

for thermal neutrons. The diagram below shows a saw tooth function of transmission of such chopper

system and its approximating sequence of positive and negative binary (pick-up) signals.

Mirror neutron guide. The neutron beam on the sample is formed by the

mirror neutron guide made of high-quality borated (14% boron) K8 glass 19 mm

thick with a Ni coating. The neutron guide consists of two parts: one 19 m long is

bent with curvature radius R = 2864.8 m; the other is straight and 5.01 m long. The

neutron guide is cone-shaped in the vertical plane with cross sections: of 10155

mm at the curved part input, 1091.8 mm at the curved part output and at the

straight part input, and 1075 mm at the straight part output. At the Fourier

chopper removed from the beam, the total thermal neutron flux at the sample

position is 1.8106 neutron/cm

2s

–1; it decreases to 3.710

5 neutron/cm

2s

–1 due to a

finite transmittance of the Fourier chopper.

Fourier chopper. The Fourier chopper consists of a rotor disk 540 mm in

diameter, installed on the motor axis, and a stator plate fixed on the stage (Fig. 2b).

The disk and plate are made of high-strength aluminum alloy. At disk periphery, on


the radius of 229 mm, there are 1024 radial slits 60 mm long and 0.7026 mm wide,

filled with a Gd2O3 layer 0.8 mm thick. Similar slits are made on the stator plate.

The chopper is rotated by an M2AA 132SB-2 asynchronous bipolar motor (ABB

Motors, Sweden) with a power of 7.5 kW. An incremental magnetic encoder GEL-

208 (Lenord+Bauer and Co. GmbH, Germany) is fixed on the motor axis for

measuring the disk velocity and acceleration and for generating a pick-up signal

coming to the RTOF analyzer. The motor is supplied by a VECTOR VBE750

(Control Techniques, UK) control drive with a built-in microcomputer to which

information on the disk velocity and acceleration comes (Fig. 3).

Fig. 3 – 3D model of the Fourier stress diffractometer FSD at the IBR-2 reactor (FLNP JINR, Dubna).

The basic functional units of the FSD are the long mirror neutron guide with variable diaphragms, the

fast Fourier chopper, the detector system consisting of ±90°-detectors with radial collimators and a

backscattering detector, HUBER goniometer at the sample position, auxiliary equipment (furnaces,

loading machines, etc.), specialised data acquisition electronics including RTOF analysers.

Detector system. In developing the detector system of the diffractometer for

measuring internal stresses, two mutually exclusive requirements should be

satisfied: the solid angle of the detector system should be large enough to acquire

statistics from a small sample volume for a reasonable time; and the contribution of

the detector system to the geometrical component of the resolution function should

not exceed the time component to retain high resolution.

There are two well-known versions of such a type of detectors used in TOF

diffractometers: position-sensitive systems and detectors designed by the principle

of geometrical time focusing during diffraction. However, the need to use the

correlation principle of data recording in Fourier diffractometry almost excludes


the possibility of using the position detector in this method. On the contrary, as for

time focusing, it is successfully used in all operating Fourier diffractometers. A

disadvantage of this method is a significant disproportion of the effective solid

angle of the detector with its actual geometrical sizes. Progress in the development

of relatively low-cost correlation electronics based on digital signal processors

made it possible to propose a new principle of the development of the FSD detector

system, namely, the multi-element detector with combined electronic and

geometrical focusing [7]. The schematic representation of such a detector, called

the ASTRA, is shown in (Fig. 4a). Each detector element is a counter based on an

ND (Applied Scintillation Technologies Ltd., UK) scintillation screen with a

sensitive layer thickness of 0.42 mm and several hundred square centimeters in

area. The scintillation screen consists of a powder mixture of 6LiF crystals (nuclear

active additive) and ZnS(Ag) (scintillator) fixed in a Plexiglas optical matrix. The

screen flexibility allows approximation of the time focusing surface by conical

surface portions with required accuracy. Such an approximation method excludes

dead areas on the sensitive layer and increases the geometrical focusing quality.

The detector efficiency is mostly defined by the 6Li concentration in the screen and

is ~60%.

a) b)

Fig. 4 – a) Multielement 90°-detector ASTRA assembled from seven ZnS(Ag) scintillation elements.

In front of the detector, a radial collimator is placed for gauge volume selection in a bulk sample.

b) Detector system of FSD diffractometer.

In the final version (Fig. 4b), the FSD detector system will consist of two

ASTRA detectors at scattering angles 2θ = ±90°; each detector includes seven

independent ones, i.e., with independent outputs of electronic signals of elements

[8]. The combined use of electronic and time focusing of the scattered neutron

beam allows an increase in the solid angle to ~0.16 sr for each ASTRA detector.

This sharply increases the instrument luminosity while retaining high resolution for


the interplanar spacing of Δd/d ≈ 4·10–3

. Currently, six elements (among 14

planned) of ASTRA detectors are installed and being tested on the FSD at

scattering angles of +90°and –90°. Furthermore, the backscattering detector with

time focusing, called the BS (backscattering), consisting of 16 scintillation 6Li

elements at the scattering angle 2θ = 140°, is installed on the FSD.

Electronic focusing method. An algorithm and software were developed for

electronic focusing of multi-module ASTRA detectors. This method implies the

use of scale coefficients for each measured TOF spectrum (Fig. 5a),

ki = Lisin(i) / L0sin(0), (8)

where L is the flight path length and θi and θ0 are the scattering angles for the i-th

and basic detectors, respectively. Then the spectra reduced to a unified scale are

summed. The diffraction spectrum summed in such a way is characterized by

almost the same resolution as the spectra from individual modules of ASTRA

detectors (Fig. 5b). Due to summation, a multiple increase in the intensity of the

final diffraction spectrum is achieved.

0 500 1000 1500 2000

0

1x105

2x105

Inte

nsity

TOF Channels

0 500 1000 1500

0

1x105

2x105

3x105

4x105

5x105

6x105

Inte

nsity

TOF channels

1540 1560 1580 1600 1620 1640

TOF channels

a) b)

Fig. 5 – a) Diffraction spectra from individual elements of the ASTRA detector. b) Diffraction spectra

from individual elements of the ASTRA detector, reduced to a unified TOF scale and the final total

spectrum.

Gauge volume definition with radial collimator. To form the incident

neutron beam, a diaphragm (Huber GmbH, Germany) with a variable aperture

(0÷10 mm for width and 0÷24 mm for height) was installed on the FSD neutron

guide end. The motion of the diaphragm is provided by precision step motors. At

present the scattered neutron beam is formed using a composite multislit radial

collimator [5]. It allows definition of the gauge volume (gauge volume) in the

sample under study. The radial collimator is assembled from four independent

modules with apertures of 7° and 10°, arranged on a supporting alignment frame.


Each module consists of Mylar films coated with gadolinium oxide with a total

thickness of ~50 μm. The spatial arrangement of collimator modules corresponds

to positions of individual elements of ASTRA detectors. The performed

experiments showed that the radial collimator provides a spatial resolution of

~2 mm and precisely forms a required gauge volume within the sample under

study. However, essential drawback of this system is difficulty of its adjustment

and insufficient transmission.

In order to improve gauge volume definition recently a new wide-aperture

radial collimator with spatial resolution of 1.8 mm and acceptance angle of ±20 °

was designed and is being manufactured at the present time (Fig. 6a). This

collimator is a single module with an improved neutron transmission capacity

(Fig. 6b). It is expected that such a wide-aperture radial collimator will possess

higher transmission function and ease of alignment.

Transmission Distribution a) b)

Fig. 6 – a) Design of new wide-aperture radial collimator with spatial resolution of 1.8 mm and

acceptance angle of ±20 °. b) Calculated transmission map for the new wide-aperture radial

collimator.

Using neutron scanning, the gauge volume position can be easily determined

with respect to the sample surface; then its position in the sample bulk can be accurately positioned in further strain measurements as well. The neutron scanning method consists in the plotting of the dependence of the intensity of material diffraction peaks on the gauge volume position center. The sample is sequentially displaced so that the gauge volume is gradually immersed into the sample (Fig. 7a). The initial point in the plot corresponds to the gauge volume position outside the sample; in this case, the diffraction peak intensity is zero (there is no diffraction on the sample). Then the gauge volume gradually enters the sample, hence, the diffraction peak intensity, which is proportional to the scattering material volume,


begins to increase. The point of the maximum in the plot approximately corresponds to the position at which the gauge volume is completely immersed into the sample. During further motion to the sample depth, the scattering material volume remains unchanged; however, neutron absorption in a material begin to appear, and the intensity begins to slowly decrease according to the exponential dependence

)exp(0 DII , (9)

where μ is the material attenuation cofficient and D is the total neutron path in the sample. Thus, neutron scanning allows the determination of the gauge volume in the sample with high enough accuracy (~0.1 mm).

Sample environment. Available supplementary equipment integrated into the experiment control system makes it possible to provide various conditions (load, temperature, etc.) at the sample. It includes a four axis (X, Y, Z, Ω) HUBER goniometer (Fig. 7b) for positioning the sample with an accuracy better than ~0.1 mm and with the maximal carrying capacity of 300 kg; an LM-20 loading machine (Fig. 8a) with a maximal load of 20 kN and maximal temperature of 800 °C for uniaxial tension/compression of samples in the neutron beam (the main advantage of this machine is almost slack-free load transfer to the sample; samples 30–100 mm long with a screwed cylindrical head can be studied; and the sample elongation is measured by a mechanical strain gage); and an MF2000 water-cooled mirror furnace (Fig. 8b) based of halogen lamps with a maximal temperature of 1000°С and with temperature control by an Euroterm controller.

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

3500

4000

4500

5000

5500

6000

6500

7000

7500

Sample surface

Region 3Region 2

Measured

Calculated

Inte

nsity

X, mm

Region 1

a) b)

Fig. 7 – a) Sample surface scan using the radial collimator: diffraction peak intensity vs. gauge volume position in the material depth. b) Sample place at FSD: end part of the neutron guide with incident beam diaphragm, 4-axis HUBER goniometer (max. capacity 300 kg) and multi-sectional

radial collimator are visible.


a) b)

Fig. 8 – a) Uniaxial mechanical loading machine LM-20 (Fmax = 20 kN, Tmax = 800°C).

b) Water-cooled mirror furnace (P = 1 kW, Tmax = 1000°C).

4. INSTRUMENT PERFORMANCE

To study main characteristics of the FSD diffractometer, a number of test

experiments were performed to estimate the instrument resolution, sensitivity to the

spatial distribution of strains, and the possibility of studying typical structural

materials under external loads. The spectral distribution of the incident neutron

beam intensity on the FSD allows efficient operation at λ ≥ 1 Å. This makes it

possible to measure diffraction spectra in the ranges dhkl = 0.63÷6.71 Å at 2θ = 90°

and dhkl = 0.51÷5.39 Å at 2θ = 140°, which is an optimum range for most structural

materials used in industry. The typical high resolution diffraction spectra measured

on the α-Fe reference sample at a maximum rotation speed of the Fourier chopper

Vmax = 6000 rpm is shown in (Fig. 9).

An analysis of the diffractometer resolution function showed that FSD

detectors indeed have a necessary resolution level in the interplanar spacing: Δd/d

≈ 2.310–3

for the backscattering detector BS and Δd/d ≈ 410–3

for both ASTRA

detectors at a maximum rotation rate of the Fourier chopper Vmax = 6000 rpm

(Fig. 10). Furthermore, the dependence of the shape of an individual diffraction

peak on the maximum speed of the Fourier chopper and resolution function for all

detectors were investigated (Fig. 10). According to expectations, the effective

neutron pulse width decreases as 1/Vmax, reaching a minimum of ~10 μs. Thus, the

diffractometer parameters can be optimized proceeding from a required accuracy of

the determination of the diffraction peak position and from a scheduled beam time.


Fig. 9 – Neutron diffraction patterns measured from -Fe standard sample using BS (left) and 90°–

detector ASTRA (right) at the maximal Fourier chopper speed Vmax = 6000 rpm. Shown are the

measured data points, full profile calculated by Rietveld method [9] and the difference curve.

0.5 1.0 1.5 2.0 2.5 3.01x10

-3

2x10-3

3x10-3

4x10-3

5x10-3

6x10-3

7x10-3

d

/d

d, Å

FSD

Backscattering

2 = +90°

2 = –90°

a) b)

Fig. 10 – a) Diffraction peak shape dependence vs. maximal Fourier chopper speed Vmax.

b) FSD resolution function measured on -Fe powder at maximal Fourier chopper speed

Vmax = 6000 rpm for backscattering detector (2θ = 140) and both ASTRA detectors (2θ = ±90).

5. CONCLUSIONS

The experiments demonstrated that the FSD performance parameters

correspond to the expected ones. Achieved resolution level of the instrument is

suitable for residual stress investigations in most constructional materials with

required accuracy of 20–30 MPa. Available auxiliary equipment (loading machine,

mirror furnace, Huber goniometer, etc.) make it possible to vary experimental

conditions in a wide range. At present the regular experiments for residual stress

and microstrain studies in bulk industrial components [10, 11] and in new


advanced materials [12] are successfully performed on FSD diffractometer. The

future plans of the FSD development include further improvement of the detector

system, electronics, and software.

Acknowledgements. This work was partially supported by the Romania-JINR Programme

2014-2015, by the Russian Foundation for Basic Research (RFBR) within the project No. 15-08-

06418_a and jointly by RFBR and the Moscow Region Government within the project No. 14-42-

03585_r_center_a.

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RESIDUAL STRESS MEASUREMENTS BY NEUTRON ...5 Residual stress measurements by neutron diffraction at...

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