Neutron Diffraction Measurements of Residual Stresses in

$Page 1: Neutron Diffraction Measurements of Residual Stresses in$
Materials Science Research International, Vol.8, No.4 pp. 165-174 (2002)

Review paper

Neutron Diffraction Measurements of Residual Stresses

in Engineering Materials and Components

Keisuke TANAKA*, Yoshiaki AKINIWA* and Makoto HAYASHI***Department of Mechanical Engineering , Nagoya University,

Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan**Mechanical Engineering Research Laboratories , Hitachi Ltd.,

Kandatsu, Tsuchiura 300-0013, Japan

Abstract: The neutron diffraction method provides a powerful nondestructive method to measure the loading and residual stresses in the interior of the materials and has been applied to the determination of the residual stress distribution in various engineering structures such as welded and brazed joints. The neutron method also gives useful information on the microscopic stress or the intergranular stress induced in single and multiphase materials by plastic deformation and fatigue. The method is also available for the determination of texture and phase transformation inside the materials. The present paper reviews the fundamentals for stress measurements and the latest applications of the neutron diffraction method in the field of materials science and engineering. Several directions of future developments of the neutron method are suggested.

Key words: Neutron diffraction, Residual stress, Diffraction elastic constant, Plastic forming, Welded structure, Coating, Composites, Fatigue damage

1. INTRODUCTION

Residual stresses have been one of the key factors in

developing new materials and structures. The X-ray dif-

fraction method is now widely used to measure nonde-

structively the residual stress in crystalline materials. The

standard method for X-ray stress measurement of steels

was first published by the X-ray Committee in The Society

of Materials Science, Japan (JSMS) in 1973, and has been

revised several times [1]. In 2000, the standard method for

stress measurement in alumina and silicon nitride has been

published [2]. The method utilizes parallel beam optics for

measurement and the sin2ƒÕ method for stress calculation.

The residual stress measured by X-rays is the stress

very near the surface, because the penetration depth of X-

rays is a few tens of micrometers at most. On the other

hand, the neutron can penetrate the depth of about 50mm

in steel and 140mm in aluminum, and the stress in the

interior of the material can be measured. Both methods are

based on the same principle of the diffraction of crystals.

The residual stress can be measured nondestrutively. For

composites or multi-phase materials, the stress in each

constituent phase can be measured separately. The major

drawback of the neutron diffraction method is its need of

intense neutron source. The gage volume for stress mea-

surement is relatively large and between 1mm3 to 27mm3,

because of low intensity of neutron beams.

The stress measurement by neutron diffraction was

started in early 1980 in the UK, Germany, and USA. In Ja-

pan, the equipment for stress measurement was developed in 1992 at Japan Atomic Energy Research Institute (JAERI)

and Research Reactor Institute in Kyoto University

(KURRI) by using a stationary reactor. At High Energy

Acceleration Research Organization (KEK), a pulsed spall-

ation source has been used for stress measurement. Dur-

ing the last decade, the neutron diffraction method has

been actively used for measuring not only residual stresses,

but also loading stresses in various single-phase and multi-

phase materials, and many components of engineering

structures. New methods of stress analysis have been de-

veloped. The standardization of neutron stress measure-

ment was carried out by the support of VAMAS (The

Versailles Project on Advanced Materials and Standards),

and Technology Trend Assessment (ISO/TTA) documents

were published in 2001 by The International Organization

for Standardization [3].

This paper reviews the fundamentals and the latest ap-

plications of the neutron diffraction method. Several direc-tions of future developments of the method are suggested.

2. PRINCIPLES

2.1. Strain Measurements

The strain measurement by the neutrons method is

based on the Bragg diffraction of neutrons by crystals.

The neutron sources are either steady reactors or pulsed

spallation sources.

For a steady reactor, a single wave length is selected by

a monochromator as shown in Fig. 1 [3]. When a mono-

chromatic ray of the wave length ƒÉ is irradiated on the crys-

tal, the diffraction takes place at the angle ƒÆ which satisfies

the following equation:

ƒÉ =2dsinƒÆ, (1)

where d is the spacing of diffracting planes. When the

lattice spacing changes from d0 to d due to stresses, the

strain is defined by

Received April 15, 2002

Accepted August 29, 2002165

Keisuke TANAKA, Yoshiaki AKINIWA and Makoto HAYASHI

Fig. 1. Reactor-based diffractometer for stress measure-ment (Ferritic steel).

The strain can be determined by the change of the dif-

fraction angle as follows:

ƒÃ= -cotƒÆ0(ƒÆ-ƒÆ0), (3)

where ƒÆ0 is the diffraction angle from stress-free materials.

The resolution of the strain measurement should be

better than 10-4, which corresponds to 20MPa in steels. In

X-ray stress measurement, the diffraction angle 20 is se-

lected close to 180deg to obtain a high sensitivity for

strain measurement. For example, the 2ƒÆ value is 156deg

for Fe 211 diffraction by Cr-Ku in the JSMS X-ray standard

[1]. In the neutron diffraction, the 20 value is normally

taken to be around 90deg in oder to maintain the same

sampling gage volume in strain measurements in different

directions. In this case, the peak shift is about 0.005deg for

a strain of 10-4. The peak position is normally determined

by Gauss fitting of diffraction profiles [3], in contrast to the

half value breadth method adapted in the X-ray standard

[1].

The time of flight (TOF) method is used for pulsed white

beam of neutrons given by a spallation source. The dif-

fracted beam is detected at a fixed angle B as shown in Fig.

2 [3]. The strain is given by the change of the wave length

as

The wave length is related to the time of flight by de Broglie relation:

Fig. 2. Spallation-source diffractometer for stress mea-surement (Ferritic steel with Reitveld fit).

where v is the speed of neutrons, h is Planck constant, m is the neutron mass, and L is the distance from the beam chopper to the detector. From Eqs. (4) and (5), the strain is measured by the change of TOF as

By the TOF method, many diffractions can be measured

simultaneously as illustrated in Fig. 2, where the lattice

spacing d is calculated from Eqs. (1) and (5), and plotted as

the abscissa. The strain is calculated from the change of

the time of flight by Eq. (6) for each diffraction.

2.2. Calculation of Stress from Strain

When the diffraction is taken from many grains of ran-

domly oriented polycrystals, the strains measured by neu-

trons correspond to macrostrains, and are related to

macrostresses by the equation of isotropic elasticity. The

principal stresses, ƒÐ1, ƒÐ2, ƒÐ3, are related to the principal strains, ƒÃ1, ƒÃ2, ƒÃ3, as follows:

where i=1 to 3. When the principal directions are not known, six values of strains need to be measured in different direc-tions to determine the stress components. The interplanar

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spacing of d0, or the diffraction angle ƒÆ0, of stress-free

material is necessary to calculate the strain and stress. The

accurate determination of the stress-free value of d0 or ƒÆ0 is

primarily significant to obtain the accurate strain value.

For this purpose, the powder sample or the small coupons

which contain negligible stresses have been used. For the

cases of plane stress, the sin2ƒÕ method can be used to

determine the stress and the accurate value of d0 or ƒÆ0 is

not required.

Since the strain measured by the diffraction method is

different from the mechanical strains, the Young's modulus

E and Poisson's ratio v in the above equation can be differ-

ent from the mechanical values and are called diffraction

elastic constants. These elastic constants are identical in

X-ray and neutron diffraction measurements.

2.3. Equipments

In Japan, the equipment for stress measurement using a

stationary reactor is installed at JAERI in Tokai, and that

by spallation sources at KEK in Tsukuba. Figure 3 shows

the equipment at JRR-3M of the Tokai Establishment of

JAERI and is named RESA(REsidual Stress Analizer) [4].

The neutron flux in the thermal neutron guide is 4•~10115n/

m2/h. The neutron beam is monochromated by a monochro-

mater made of piled carbon or bent silicon crystals. The

resulting beam has a wave length of 0.1 to 0.2nm and a

neutron flux of 4•~1013n/m2/h. After monochromation, the

neutron beam size is defined by a B4C rubber slit. The slit

is 3mm square, and is located in an aluminum guide. A

cadmium plate slit is set at the end of the beam guide. The

neutron flux at the slit is about 4•~1011n/m2/h.

The sample is mounted on a computer-controlled XYZ

translator fixed on the diffractometer, and the desired loca-

tion within the sample can be selected for measurements.

The strain measured by the neutron diffraction is the aver-

age of the gage volume of the neutron beam as shown by

the shaded area in Fig. 1. By scanning the gage volume, a

spatial map of strains can be constructed. The diffracted

beam passes through the cadmium receiving slit and is

detected by a 3He-type detector or position sensitive de-

tector. A loading devise is also mounted on the table of the

diffractometer to make in-situ measurements under load-

ing.

Fig. 3. Experimental set up for stress measurement by RESA.

3. LOADING STRESSES

3.1. Stresses in Single Phase MaterialsTo determine the diffraction elastic constants, the strain

is measured under the application of the known uniaxial stress. Figure 4 shows the changes of the strain deter-mined from different diffractions during elastic loading of steel whose yield stress is 230 MPa [5]. Under the same applied stress, the strain obtained from 200 diffraction is the largest and that by 222 diffraction is the lowest. The other diffractions are in between. The slope gives the Young's modulus. The difference in Young's modulus mani-fests the elastic anisotropy of the materials.

Figure 5 shows the change of the strains in the loading and transverse directions determined from three reflections of stainless steel by the TOF method [6]. The 0.2% proof stress is 252MPa. Deviations from linearity of the indi-vidual planes occur close to the onset of macroplasticity. Once plastic deformation occurs, the yielding of preferen-tially oriented grains relative to neighbors causes strain distribution, and a divergence from the hitherto linear re-sponse. The deviation from linearity above yielding is large for 200 diffraction because of large intergranular strains. The 111 and 311 diffractions are less sensitive to inter-granular strains. The deviation from linearity comes from plastic anisotropy of polycrystals [6]. The neutron method has an advantage to grasp the average behavior of the bulk materials, while the information by the X-ray method is influenced by the free-surface effect.

Since an entire diffraction spectrum is obtained in each measurement direction, the strain is usually determined from the whole diffraction pattern using Rietveld analysis. For cubic crystals, the strain is determined from the change of the lattice constant as

ƒÃ=a-a0/a0 (8) Fig. 4. Relation between applied stress and X-ray strains

for several diffraction planes of steel (JIS S25C).

167


where ao is the lattice constant of stress-free samples of the material. The strain obtained by the Rietveld method is also shown in Fig. 5. For the axial direction, the agreement of the Rietveld results with the macroscopic strain is good, because the average of the strains for many diffractions is close to the macroscopic strain.

Table 1 presents the recommended and problemativ dif-fractions for stress measurements in ISO/TTA [3]. The former diffractions do not show a large deviation from lin-earity above yielding because of small intergranular strains.

Kroener model is used to evaluate the diffraction elas-tic constants from the single crystal elastic constants. Most

Table 1. Recommended and problematic diffractions for stress measurement.

(a) Parallel to the tensile axis.

(b) Perpendicular to the tensile axis.

Fig. 5. Relation between applied stress and X-ray strains for stainless steel.

(a) Phase stress in Al.

(b) Phase stress in SiC.

Fig. 6. Relation between applied stress and phase stresses of aluminum alloy reinforced by SiC particles.

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of engineering materials contain secondary phases which

influence the value of diffraction elastic constants. For

those materials, the self-consistent model is used to ac-

count for secondary phases [7]. Since the diffraction elas-

tic constants are the function of the single-crystal elastic

constants, the single-crystal elastic constants in turn can

be evaluated from the data of the diffraction elastic con-

stants of polycrystals determined by powder diffraction

[8]. This method is very useful to estimate the single-crys-tal elastic constants of materials whose values have not

yet been measured otherwise.

3.2. Phase Stresses in Multi-Phase Materials

For multi-phase materials, the mean stress in constitu-

ent phase can be determined from the peak shift of the

diffraction profiles by using the diffraction elastic con-

stants of single-phase polycrystals. The mean stress is

called the phase stress.

Figure 6 shows the change of the phase stress of SiC

particulate reinforced aluminum alloy due to loading [9]. The macrostress ƒÐ'i is given by the following rule of mix-

ture:

(9)

where <ƒÐi>p is the mean stress in inclusions (SiC phase)

and <ƒÐi>m is that for the matrix (Al phase), i=1•`3, and f is

the volume fraction of inclusions. The difference between

the phase stress and the macrostress is the microstress:

(10)

(11)

The microstresses, <ƒÐi>pƒÊ and <ƒÐi>mƒÊ, satisfy the following

self-balance equation:

(12)

Furthermore, the microstress consists of two compo-

nents: the one due to stiffness mismatch under macrostress,

<ƒÐ>pƒÊE, and the other due to the eigen strain such as trans-

formation or the mismatch of the coefficient of the thermal

expansion, <ƒÐ>pƒÊT.

13)

They are proportional to the macrostress, ƒÐ'i, and the eigen

strain, ƒ¢ƒÃ*i, as

where Aij and Dij are the tensor which can be estimated from the mean stress theory by Mori and Tanaka [10] based on the Eshelby inclusion mechanics [11]. This model is called EMT model in this review. The slopes of the lines shown in Fig. 6 agree very well with the predictions based on EMT model.

4. RESIDUAL STRESSES

4.1. Plastically Deformed ComponentsFigure 7 shows the distribution of the residual tangen-

tial stress in a plastically bent plate [4]. The strains in the tangential, radial and axial directions were measured and then the stress was calculated by Eq. (7). The stress is compression near the convex side of the plate and tension near the concave side. The stress distribution agrees well with the distribution calculated by elementary beam theory.

Tsuchiya et al. measured the residual stress distribu-tion in a jacket material, Incoloy 908, for ITER super con-ducting coil [12]. The jacket was bent three times to have the final shape. A tensile residual stress above 200MPa is detected near the inner surface of the jacket, which results in stress-assisted grain boundary cracking.

The neutron method has been applied to measure the internal distribution of the residual stress due to plastic forming such as tube drawing and cold expansion of holes [13,14]. Plastic forming introduces the preferred orienta-tion, or texture, of material, which can easily be measured by neutron diffraction. The stress measurement of textured material is not easy. Hayashi proposed a new method to account for the texture effect in stress measurements [5].

Fig. 7. Residual stress distribution in tangential direction at the center region of cross section of bend steel plate.

169


4.2. Welded and Brazed Joints

Welding residual stresses are very important for the

performance of welded structures. The neutron diffraction

method has been utilized to measure the welding residual

stress in the interior of welded joints.

Figure 8 shows eight locations of the sampling volume

and the measured residual stress distribution near socket

welded joint of steel pipes [15]. Three components of the

residual stress were determined from the measurements of

strains in axial, radial and hoop directions. The residual

stress is compression at the outer surface of the root of the

weld joint and changes to tension near the inner surface.

The stress at the root is the maximum tension of 100 to 130

MPa. The residual stress in the weld metal near the inter-

face to the outer surface of the pipe and the heat affected

zone takes a low value around •}40MPa. The stress-relief

treatment at 600•Ž for 1h removes the residual stress as

shown in Fig. 8.

Figure 9 shows the axial residual stress distribution in

butt welded steel pipes measured by the neutron, X-ray

(a) Locations of residual stress measurement.

(b) Residual stresses.

Fig. 8. Residual stresses in socket weld joint in as-welded and stress-relieved conditions.

and strain gage methods [16]. The neutron method detects

the stress in the volume of 1.5mm near the surface and the

measured value of the X-ray method is the average of 20

ƒÊm in depth and that by the strain gage method corre-

sponds to the average over the thickness. Although the

sampled volume is different, the measured values of the

residual stresses by the three methods agree well with each

other.

The neutron method have been utilized to measure the

interior distribution of the residual stress of various types

of joints, such as brazed joints [17,18], friction welded

joints [19], and claddings [20].The VAMAS TWA20 project has performed a round

robin test of shrink-fit ring and plug assembly made of

aluminum alloy A7050-T7451. The specimen consisted of a

plug with a diameter of 25.43mm, cold shrunken on a ring

Fig. 9. Comparison of residual stresses measured by neu-tron diffraction, X-ray diffraction and strain gage in butt-welded pipe.

Fig. 10. Hoop residual stress distributions in the VAMAS TWA20 round robin test specimen.

170


with outer and inner diameters of 50 and 25.4mm, respec-tively. Figure 10 shows the distribution of hoop residual stress measured by 111, 200 and 220 diffractions [5]. The measured residual stresses nearly agree with each other. The solid circles indicate the averaged residual stress dis-tribution analyzed by the finite element method (FEM). The measured residual stress in the ring agree well with the FEM results, while it is slightly smaller than the FEM com-putation in the plug. This may be caused by weak diffrac-tion intensity of the diffraction from the plug and by the texture of materials.

4.3. Coatings and Surface ModificationsThe residual stress made by surface modification and

coating has been measured by the X-ray method, and the successive removal method is used to obtain the subsur-face distribution. The neutron diffraction method was used to determine the interior distribution of the residual strain of plasma-sprayed thermal barrier coatings. Figure 11 shows the distribution of the residual normal strain in the direc-tion perpendicular to the coated surface [21]. The top coat of zirconia with 1mm in thickness was sprayed on the bondcoat of NiCoCrAlY over the copper substrate. The compressive strain measured in the top coat near the inter-face means the tensile in-plane residual stress. The strain is not uniform. The stress in the substrate is tension.

The neutron method has been applied to determine the subsurface distribution of shot-peened and carburized steels [22,23]. The spatial resolution of the neutron method is not yet satisfactory and thicker layers are necessary for measurement. High-energy X-rays from synchrotron sources are available to determine the subsurface residual stress distribution in the intermediate region [24].

4.4. Composite MaterialsLike the X-ray method, the neutron method can detect

the mean stress in each constituent phase of composite materials. Figure 12 shows the change of the phase strains in aluminum alloy reinforced with 5% SiC whisker as a func-tion of applied loading, where the thermal residual strains are not included [25]. In the elastic range (<50MPa), Eshleby's model gives good agreement for strain partition-ing. With the onset of matrix plasticity (>50MPa), the phase strain deviates from linearity as load is transferred towards the reinforcement, increasing the whisker stress and de-creasing matrix stress. This gives rise to compressive re-sidual strains in the matrix and tensile strains in the rein-forcement upon unloading. The compressive strains in the matrix lower the yield stress in the reversed loading. This induces the Bauschinger effect and has been reported for multiphase materials such as steels consisting of ferrite and cementite phases [26].

The measured residual stress can be decomposed into the macrostress and microstress, and the latter further de-composed to elastic mismatch stress and thermal mismatch stress by using Eqs. (9) to (15). Figure 13 shows the re-sidual stress distribution of Al/20 wt%SiCp plate with T4 heat-treatment [27]. The macrostress is compression near the surface. The thermal mismatch stress is tension in alu-minum and compression in the reinforcement.

The thermal stress in the composite of alumina and zir-

conia measured by the neutron method is shown in Fig. 14 [28]. The residual stress is tension in alumina and com-pression in zirconia. The lines in the figure are the predic-tion of thermal mismatch stress based on EMT model. Agree-ment is fairly good.

4.5. Fatigue Damaged and Cracked ComponentsFigure 15 shows the residual stress distribution along

the midthickness of the fatigue-cracked compact-tension specimen of steel measured by the neutron method [29], wherex andy axes are along the crack line and perpendiculer to the crack face, respectively. The gage volume was 1mm3. The tensile peak stress at a small distance from the crack tip in the relaxed state. Similar observation was re-ported for Al/SiCp composite [30]. A small change in the residual stress due to crack growth was hardly measured

Fig. 11. Rresidual strain of plasma-sprayed thermal barrier coatings.

Fig. 12. Realtion between applied stress and lattice strain in aluminum alloy reinforced.

171


(a) Phase stress in Al. (b) Phase stress in SiC.

Fig. 13. Residual stress distribution in aluminum alloy reinforced with SiC particle.

(a) Phase stress in ZrO2.

(b) Phase stress in Al2O3.

Fig. 14. Residual stress in Al2O3/ZrO2composites.

Fig. 15. Rresidual stress distribution in a fatigue-cracked compact-tension specimen.

by the neutron method because of the limited spatial reso-lution [31]. The neutron method was successfully applied to the detection of the development of the residual stress near the notch root by fatigue cycling [32].

5. MATERIALS EVALUATION

5.1. Line BroadeningThe microstress induced by plastic deformation gives

172


rise to the line broadening of the diffraction profiles [33,34,35]. Figure 16 shows the change of the line broaden-ing as a function of the applied strain in stainless steel (JIS SUS316NG) [35]. The degree of broadening depends on the

Fig. 16. Change of HVB with tatal strain for stretched SUS316NG stainless steel.

(a) Poling direction.

(b) Diffraction pattern.

Fig. 17. Diffraction pattern of tetragonal PZT.

diffraction planes. Like the X-ray method, the line broaden-ing can be used to estimate the dislocation density or fa-tigue damage in polycrystals. The scatter of microstresses in mutiphase materials such as WC-Co alloys [36] is also responsible for the line broadening.

5.2. TextureThe preferred orientation or texture of polycrystals is

easily measured by the neutron method because there is no need to thin the sample. Figure 17 shows the neutron diffraction profiles of 200 and 002 of poled piezoelectric ceramics (PZT) [35]. The direction of 002 is the spontane-ous polarization direction of the tetragonal crystals of PZT, and is aligned along the poling direction.

5.3. Phase TransformationThe phase transformation inside the samples is detect-

able by the neutron method. Several in-situ measurements have been reported with respect to the martensitic trans-formation of NiTi shape memory alloys in smart materials and structures [37,38].

6. CONCLUDING REMARKS

The neutron diffraction method has been used to mea-sure the loading and residual stresses in the interior of the materials and gives valuable information on materials sci-ence and engineering applications. Especially, the neutron method has been applied to the measurements of interior distributions of the residual stress in various welded and jointed structures. The neutron and X-ray methods comple-ment each other in many practical determinations of re-sidual stresses. Several problems are to be solved for fur-ther extensive applications. The determination of the stress-free lattice constants is one of significant subjects to im-prove the accuracy of the strain determination. The effect of the texture on the conversion from strains to stresses is the subject of the future study. The improvement of the spatial resolution is necessary. A joint project of high-in-tensity proton accelerators planed by KEK and JAERI will be a solution to the spatial resolution problem.

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Neutron Diffraction Measurements of Residual Stresses in