1. Introduction

Residual stresses have been one of the key factors

in developing new materials and structures. The X-

ray diffraction method is now widely used to measure

non-destructively 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 . In 2000, the standard method for stress

measurement in aluminum oxide and silicon nitride

has been published . These standards have promoted

greatly the practical applications of the X-ray method

in various engineering fields in Japan. The main

limitation of the conventional X-rays is that the

measured stress is the stress very near the surface,

because the penetration depth of X-rays is a few tens

of micrometers at most.

Neutrons can penetrate a thousand to ten thou-

sands times deeper than the conventional X-rays,and

can be utilized to measure the stress in the interior of

the material. During the last decade, the neutron

diffraction method has been actively used for measur-

ing not only residual stresses,but also loading stresses

in a variety of single-phase and multi-phase mate-

rials, and various components of engineering struc-

tures . The major drawback of the neutron

diffraction method is its need of intense neutron

source. The gage volume for stress measurement is

relatively large and between 1 mm and 27 mm ,

Received 22nd December,2003(Review)

Department of Mechanical Engineering, Nagoya

University,Furo-cho,Chikusa-ku,Nagoya 464-8603,

Japan.E-mail:ktanaka＠mech.nagoya-u.ac.jp

Diffraction Measurements of Residual

Macrostress and Microstress Using

X-Rays,Synchrotron and Neutrons

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s 3，B sC

Noは1，2，3が 1 4，5，6が 2 7，8，9が 3 10，11，12が 4

6，9，12月は Serie1，4，7，10月は SeriesA 2，5，8，11月は Serie

枠の縦幅を書誌データが入る大きさに調節する

because of the low flux of neutron beams. Further-

more, the near-surface measurement is difficult

because of pseudostrain introduced by partial immer-

sion of the gage volume .

Third-generation synchrotron radiation sources

provide the X-rays with extremely high intensity as

well as a narrow divergent angle. The energy level of

synchrotron X-rays ranges from the conventional X-

rays to very high energy. The higher energy of X-

rays gives the deeper penetration depth. Table 1

summarizes the penetration depth of synchrotron X-

rays with various energy levels,where the penetration

depth is the depth at which the intensity is reduced to

about 37%. The penetration depths of the conven-

tional characteristic X-rays of Cu-Ka radiation and

neutrons are also indicated. The X-rays with the

energy higher than 30 to 40 keV are called high-

energy or hard X-rays. The penetration depth of hard

X-rays is in between those of conventional X-rays

and neutrons,and has been used to measure the sub-

surface residual stresses. Besides those applications,

X-rays with energy levels of 5 to 20 keV from third-

and second-generation synchrotron sources have also

been used for accurate measurements of residual

stresses. A high intensity of synchrotron X-rays with

a narrow divergent angle enables the stress measure-

ment in a very localized area whose dimension is less

than one micrometer. By choosing an appropriate

wave length from synchrotron X-rays,it is possible to

conduct the stress measurements with high accuracy.

The above three methods are based on the same

principle of the diffraction of crystals. Each method

has its own adavantages,and has been utilized simul-

taneously to obtain a more complete picture of the

residual stress distribution in engineering materials

and structures. For composites or multi-phase mate-

rials, the stress in each constituent phase can be

measured separately,and the macrostress and micro-

stress are separated from the phase stresses using the

rule of mixture. This information is invaluable in

developing new materials and processing techniques.

In this paper, some recent developments of the

stress measurement by diffraction using X-rays,

synchrotron and neutrons especially in Japan will be

reviewed.

2. Diffraction Methods of Stress Measurement

2.1 Strain measurement

The strain measurement by the X-ray,

synchrotron and neutron methods is based on the

Bragg diffraction by crystals. The diffraction condi-

tion by crystals is given by

λ＝2 sinθ (１)

whereλis the wave length, is the spacing of the

diffraction plane,andθis the diffraction angle. The

change of the lattice spacing corresponds to the nor-

mal strain in the direction of the normal of the

diffraction plane as

ε＝－

(２)

where is the lattice spacing of stress-free material

and is that for strained materials. The value is

determined from the diffraction angle,θ,from stress-

free materials by using Eq.(１). The determination of

the stress-free value of orθis primarily significant

to obtain the accurate value of the strain. For this

purpose, the powder sample or small coupons which

contain negligible stresses have been used. For the

case of the plane stress,thesinψmethod is available

for stress measurement and does not require the

accurate value of orθ as described later.

In angle-dispersive systems where mono-

chromatic X-rays or neutrons are used, the strain is

determined from the change of the diffraction angle as

ε＝－122θ－2θ cotθ (３)

Therefore, the strain sensitivity is higher for higher

diffraction angles.

In energy-dispersive systems where panchro-

matic white rays are used,the strain is obtained from

change of energy of diffraction received at a fixed

angle. In time-of-flight (TOF)measurement of neu-

tron diffraction,the strain is given from the difference

of the time of flight.

2.2 Stress calculation

The strain measured from the peak shift of the

diffraction from polycrystals is the average of the

strains of diffracting grains and corresponds to the

macrostrain. The stress is obtained from the mea-

sured strain by using the relation of isotropic elastic-

ity. Still, the strain measured by the diffraction

method is different from the mechanical strain,so the

values of Young’s modulus and Poisson’s ratio can be

different from the mechanical values,which are called

diffraction elastic constants (DEC). The values of

DEC are identical in X-ray and neutron diffraction

measurements.

When the penetration depth is shallow as in the

Table 1 Penetration depth of X-rays,

synchrotron and neutrons

，41， 0月は Serie7，1 ，5，8，11月は SeriesB 3，6，sA 2 2月は SeriesC

Noは1，2，3が 1 4，5，6が 2 7，8，9が 3 10，11，12が 4

9，1

conventional X-rays,the stress to be measured is the

stress very near the surface;the stress state can be

approximated as the plane stress. By assuming the

plane stress, the diffraction angle 2θ at the inclina-

tion angle ψ is related to the in-plane stresses as

follows :

2θ＝－21＋ν tanθσ sin ψ

＋2ν tanθσ＋σ ＋2θ (４)

whereσ andσ are the in-plane stresses,and and

ν are the diffraction Young’s modulus and Poisson’s

ratio, respectively (see Fig.1). The stress, σ, is

proportional to the slope, , in the 2θ vs sinψ

relation as

σ＝ (５)

where is the stress constant expressed by

＝－ 21＋ν cotθ (６)

Once is known, the stress is obtained from the

measurement of the slope between2θ andsinψ. This

method is called thesinψmethod. Since the stress is

determined from the change of the diffraction angle,

the accurate value ofθ is not required.

When the stress perpendicular to the surface is

not zero,the stress value determined from Eq.(５)is

σ－σ (σ is the perpendicular stress). For general

stress states as in neutron stress measurements, the

six components of strains should be measured to

determine the stress state. When the principal direc-

tions of stresses are known,three principal strains are

enough to determine the stress state.

2.3 Techniques of measurement

The Committee of X-ray Studies on Mechanical

Behavior of Materials in the Society of Materials

Science,Japan,published the standard method for X-

ray stress measurement of ferritic and austenitic

steels first in 1973,and has revised it several times .

In 2000,the standard method for stress measurement

in aluminum oxide and silicon nitride has been publi-

shed . The method utilizes parallel beam optics for

measurement and thesinψmethod for stress calcula-

tion. The method is now widely used for residual

stress measurements due to surface treatments or

welding in various engineering fields. The develop-

ments of X-ray detectors and data processing tech-

niques enable to measure the stress in a short period

or even during cyclic loading .

With respect to the neutron stress measurement

in Japan,the equipment for stress measurement using

a stationary reactor is installed at Japan Atomic

Energy Research Institute(JAERI)in Tokai,and that

by spallation sources at High Energy Acceleration

Research Organization (KEK) in Tsukuba. The

equipment at JRR-3M of the Tokai Establishment of

JAERI is named RESA (REsidual Stress Analizer) .

The standardization of neutron stress measurement

was carried out by the support of VAMAS (The

Versailles Project on Advanced Materials and Stan-

dards), and Technology Trend Assessment (ISO/

TTA) documents were published in 2001 by The

International Organization for Standardization .

Three sources of third-generation synchrotron

radiation are working in the world:ESRF(European

Synchrotron Radiation Facility), APS (Advanced

Photon Source)and SPring-8(Super Photon Ring-8).

High energy X-rays from synchrotron sources have

been used for residual stress analysis in the subsurface

region. The project of the standardization of the

stress measurement by high-energy X-rays has been

now started as VAMAS Project 02.

In parallel with the standardization of each

method,several new techniques have been proposed in

order to conduct accurate stress measurements for the

cases when the standard method is not applicable.

Several significant proposals will be described below.

2.4 Macrostress and microstress

For multi-phase materials, the mean stress in

constituent phase can be determined from the peak

shift of the diffraction profiles by using the DEC

values of single-phase polycrystals. The mean stress

is called the phase stress. From the phase stresses,the

macrostress and microstress are separated . Con-

sidering two-phase materials consisting ofαand β

phases with the phase stresses, σ and σ , the

macrostress σ′is given by the following rule of

mixture:

σ′＝ σ 1－ ＋ σ , (７)

where is the volume fraction of theβphase. The

difference between the phase stress and the macro-

stress is the microstress:

σ ＝σ′＋ σ , (８)

σ ＝σ′＋ σ , (９)

The microstresses satisfy the following self-balance

equation:

σ 1－ ＋ σ ＝0. (10)

2.5 DEC of engineering materials

The DEC values of single-phase polycrystals can

Fig. 1 Diffraction by crystal

be obtained from the single crystal elastic constants

by using several models of elastic deformation.

Among models proposed up to now,Kroner’s model

gives the best estimate.

Most engineering materials possess more than

one phase, even if they are called monolithic. For

example, sintered alumina are composed of the

alumina phase, the glassy phase and pores. Several

micromechanical models proposed for elastic defor-

mation of composites can be used to determine the

change in the mean stress in the diffracting phase with

the applied stress. Reuss’model assumes that the

stress in the diffracting phase is identical to the

macrostress. In Voigt’s model , the strains in the

matrix and the composite are equal. According to the

self-consistent model(SC model) ,the matrix phase

is modelled as a spherical particle embedded in a

composite having the composite elastic constants.

The stress in the particle under the applied stress is

obtained by using Eshelby inclusion mechanics . In

a two-phase model,ceramics are assumed to consist

of the matrix phase and pores. The apparent porosity

ρ′can be calculated from the bulk densityρto the

theoretical valueρ as

ρ′＝1－ρρ (11)

The theoretical prediction was compared with the

experimental values determined by the X-ray

diffraction method for sintered alumina with various

degrees of porosity . Figure 2 shows the change of

DEC of AlO 2.1.10 diffraction with the apparent

porosity. The experimental data agree very well with

the prediction based on the SC model. Reuss’model

gives an upper bound, while Voigt’s model a lower

bound. The present method based on the SC model

can be applied to other engineering materials such as

steels and aluminum alloys containing inclusions or

precipitates.

From the experimental data on diffraction plane

dependency of DEC, it is possible to determine the

elastic constants of single crystals. This method is

applied to sintered samples ofβ-silicon nitride whose

elastic constants of single crystals is not yet estab-

lished . The DEC of sintered silicon nitride deter-

mined by X-rays are plotted against cos γ(γ＝angle

between the diffraction plane normal and the -axis

of hexagonal crystal)in Fig.3. The DEC value of 1

＋ν changes as a second power function ofcos γ

as predicted by the Voigt-Reuss average and Kroner’s

models. The values of the single crystal elastic con-

stants, , , , and , were determined from

the DEC values of polycrystalline silicon nitride. This

method will be useful for measuring single crystal

elastic constants of the other new materials such as

nanocrystals,where single crystal samples are not be

available.

3. Measurements of Macrostress and Microstress

Residual

3.1 Textured thin films

The X-ray diffraction method is expected to be

one of the most powerful techniques to measure the

residual stress in polycrystalline thin films. The clas-

sical sin ψ method of stress measurement is not

always applicable when films have texture. Polycrys-

talline thin films of cubic crystals often possess the

fiber texture whose axis is 111>, 100> and 110>

perpendicular to the film surface. Under the assump-

tion of the equi-biaxial residual stress, several

modifications of thesin ψmethod has been proposed.

The equi-biaxial residual stresses were measured for

various multi-layered as well as single-layered thin

films . Using high-intensity synchrotron,the stress

in ultra-thin films of 10 nanometer thickness can be

measured. The change of the internal stress in copper

thin films coated on silicon wafer during heat cycling

up to 500℃ was measured in-situ using synchrotron

X-rays .

For the cases of non-equi-biaxial stresses,

Fig. 2 Change of diffraction elastic constant with appar

ent porosity of alumina (AlO 2.1.10 diffraction)-

Fig. 3 Relation between DEC and cos γ for β-SiN

ceramics

Tanaka and others proposed a new method of stress

measurement, and successfully applied the new

method to determine the residual stress in patterned

aluminum thin films with 111>fiber texture sputtered

on silicon wafers . The new method was also

applied to measure the stress in TiN thin films deposit-

ed on a steel substrate by the ion beam mixing

method. TiN thin films had a 110>fiber texture .

Four-point bending was applied to coated specimens,

and the stresses in the film and substrate were mea-

sured simultaneously by the X-ray method. The

changes of the stresses in the loading direction,σ ,

and in the perpendicular direction, σ , with the

applied strainε are shown in Fig.4,where(a)is the

stress in the thin film and (b) is the stress in the

substrate. The predictions of the stress variation

based on elasticity are also shown in the figure . The

residual stresses in the thin film and the substrates are

equi-biaxial compression at zero applied strain. As

the applied strain increases, the stress σ increases

linearly following the predicted line and then begin to

show a nonlinearity followed by leveling. The stress

in the perpendicular direction,σ , decrease with the

applied strain. The rate of decrease starts to increase

nearly at the same time when the stressσ deviates

from the linearity. According to SEM observation,

the onset of nonlinearity was coincident with the start

of cracking. The substrate is under uniaxial stress

and begins to yield at about 300 MPa. The loading

stress in the film is biaxial even under uniaxial stress

in the substrate,because of the mismatch of Poisson’s

ratio. The fracture of thin films is determined by the

sum of the residual and loading stresses. The fracture

stress of the TiN thin film determined by this method

was found to have a tendency to increase with

decreasing film thickness .

3.2 Nondestructive determination of residual

stress distribution beneath surface

The stress measured by X-rays is the weighted

average of the stress distributed beneath the surface

as

σ ＝σ

(12)

whereσ is the distributed residual stress, is the

depth, is the specimen thickness, is the penetra-

tion depth. When is much larger than , the

measured stress is the Laplace transform of the stress

distribution as

σ ＝1

σ ＝ σ (13)

When the stress distribution is steep within the

penetration depth,the relation between the diffraction

angle and sin ψbecomes nonlinear. Several methods

have been proposed to estimate the stress distribution

from the nonlinearity. Akiniwa and others were the

first to propose the constant-penetration depth

method which determine the stress value from the

sin ψ plot obtained under the constant penetration

depth . The penetration depth for the mixed case of

the iso-inclination of the tilt angleψand of the side-

inclination with the angleχis given as follows:

＝cosχ2μ

sin θ－sin ψcosψsinθ

(14)

whereμis the linear absorption coefficient. Equation

(14)withχ＝0 gives the penetration depth for the iso-

inclination method (Ω diffractometer)and that with

ψ＝0 for the side-inclination method (ψ

diffractometer). The angle between the surface nor-

mal and the normal of the diffraction plane, ψ, is

related toχandψ as

cosψ＝cosχcosψ (15)

For a given χ, the angle ψ can be determined by

keeping constant.

For the case of silicon nitride, the relation

between the penetration depth and sin ψis shown in Fig. 4 Change of stresses in TiN film and steel substrate

under external loading

(b) Steel substrate

(a) TiN film

Fig.5,where the 411 diffraction by Cr-Kαradiation is

used for stress analysis . The solid line indicates the

penetration depth for the side-inclination method and

the dashed line for the iso-inclination method. The

marks indicates the points of measurements. Figure

6 shows thesin ψdiagram obtained for silicon nitride

which was peened by fine particles of high-speed steel

with the diameter of 50 m. The sin ψ relation is

linear because the penetration depth is constant. The

residual stress determined is plotted against the pene-

tration depth in Fig.7. The stress very near the

surface is a very large compression of about －900

MPa, while the conventional sin ψ method gives

about －200 MPa. The inverse Laplace transform of

the distribution gives the residual stress a function of

depth from the surface .

The above method is especially useful for the

stress measurement using high-energy synchrotron

radiation,where the diffraction angle is low and the

difference in the penetration depth between iso-and

side-inclination methods is large. This method is

successfully applied to determine the subsurface resid-

ual stress distribution about 300 m beneath the sur-

face introduced by shot peening . The constant

penetration method is improved to be applicable to

non-equi-biaxial stress state . The method is only

applicable for the materials which do not have strong

texture. If the materials have a strong texture such as

textured thin films,the useful method to determine the

distribution of strains or stresses is the scattering

vector method and the in-plane strain measurement

method by grazing incidence arrangement .

High-energy synchrotron X-rays are extremely

powerful to measure the interface stress of coated

layers because of its large penetration depth. Figure

8 shows the distribution of the residual stress in the

top and under coatings of thermal barrier coatings

(TBC),where ZrO diffractions is used for top coating

and NiAl diffraction for undercoating . The values

of the in-plane stress,σ,and perpendicular stress,σ,

were determined by the new hybrid method proposed

by Suzuki and others . The stress components were

Fig. 7 Distribution of residual stress beneath the surface

ofβ-SiN peened by fine steel particles

Fig. 6 Sin ψdiagram for the constant-penetration-depth

method forβ-SiN 411 diffraction by Cr-Kαradi

ation

-

Fig. 5 Change of penetration depth with sin ψfor iso-

and side-inclination method for β-SiN 411

diffraction by Cr-Kαradiation

Fig. 8 Residual stress distribution in thermal barrier

coating measured by hybrid method of the conven

tional and synchrotron X-rays

-

determined from the measurements by the conven-

tional X-rays with those of high-energy synchrotron

X-rays. The perpendicular stress in the top coating

near the interface is a tension which gives rise to the

delamination cracking.

3.3 Local stress measurement

The diffraction of microbeam X-rays from a

local area is recorded by a two-dimensional detector,

such as an imaging plate,and used for stress determi-

nation. Two-dimensional detectors are effective for

microbeam diffraction because the intensity is low

and the diffraction image is spotty. Figure 9 illus-

trates the detection of diffraction by an imaging plate,

where the incident beam is inclined by angleψ with

respect to the specimen normal( -axis). The infor-

mation of the whole ring is used for stress determina-

tion. The strain, ε, can be determined from the

change of the diffraction angle given by the radius of

the Debye ring at an angleαshown in Fig.9 . The

following quantity is obtained from the measurements

of the strain in four directions,α,π＋α,－α,π－α.

ε＝ ε－ε ＋ ε －ε 2 (16)

This value is related to the stress for the case of the

plane stress as follows:

ε＝－1＋ν

σ sin2ψsin2ηcosα (17)

whereσ is the in-plane stress andηis equal to90－θ.

The strain is determined from the slope in the relation

betweenε and cosαas

σ＝－1＋ν

1sin2η

1sin2ψ

εcosα

(18)

This method was proposed by Tanaka and others

and called thecosαmethod. It has been used for the

stress determination in a local area by using an imag-

ing plate as a two-dimensional detector of X-rays .

A simpler method is adapted by Withers and

others . They simply measured the change of the

size of Debye rings to obtain strain in the synchrotron

measurement of a SiC single fiber reinforced Ti alloy.

From the measurements of the change of the distribu-

tion of the fiber strain under increasing load, they

detected the fracture of the fiber and also determined

the interfacial stress distribution associated to a fiber

breakage.

In fine-grained polycrystalline materials,the ordi-

nary sin ψ method is applicable to determine the

stress in a localized area of 100 m. The residual

stress distribution around a fatigue crack in a fine-

grained steel was measured by using high intensity

synchrotron X-rays. Figure 10 shows the stress dis-

tribution measured around a 3 mm long fatigue crack

at the zero stress and at the stress intensity factor

＝9.5 MPam . The dotted line indicates the

results of the simulation by the Newman’s method .

The compressive stress on the crack line gives the

crack closure,and the crack opening stress obtained

from the compressive stress distribution agreed well

with the measured opening stress.

3.4 Stress measurement of single crystal

The stress measurements of single crystals will

be important for micro-electro-mechanical systems

(MEMS), and also necessary when the strain in a

single grain within polycrystals is measured by using

the microbeam X-rays from synchrotron radiation.

To determine the stress in a single crystal,the lattice

strains in six different directions should be measured.

For the cases of the plane stress,the strain measure-

ments in three different directions are enough to

determine the stress.

For silicon single crystals,several methods have

been proposed to determine the stresses . Figure

11(a)shows the coordinate systems for a specimen

made of silicon single crystal,where P1 axis( -axis)

is［110］direction,P2 axis( -axis)is［110］direction,

Fig. 9 Thecosαmethod to determine the stress using the

information of the whole circumference of Debye

ring recorded on a imaging plate

Fig. 10 Stress distribution around a fatigue crack mea

sured at the stress intensity factor ＝0and 9.5

MPam in fine-grained steel measured by

synchrotron radiation

-

and P3 axis ( -axis)is［001］direction. The stereo-

graphic projection of the specimen is shown in Fig.11

(b). The values of the lattice spacing of 115 and 333

planes are the same in the stress-free state. The

diffraction angle 2θis related to the stresses,σ and

σ ,in the and directions for the case ofφ＝0as

follows:

2θ＝－tanθ ＋ σ＋ σ sin ψ

－2tanθ σ＋σ ＋2θ (19)

and for the case ofφ＝90°

2θ＝－tanθ σ＋ ＋ σ sin ψ

－2tanθ σ＋σ ＋2θ (20)

where ＝ － － 2and are the compliances of

single crystals. From the measurements of the

diffraction angle of 115 and 333 diffractions in the

direction ofφ＝0 and 90 deg, the stress components

can be determined from the slope of the relation

between 2θ and sin ψ as in the ordinary sin ψ

method .

Suzuki and others have proposed a more sophisti-

cated method . For the case of the plane strain,the

strain is a linear function of the stress. By using Eq.

(３)the diffraction angle is expressed as

2θ＝ σ＋ σ＋ σ＋2θ (21)

where , ,and are the known functions of the

diffraction plane and the angles ofφandψ. When we

measure the diffraction angles of 311 family of

diffractions such as 313,313,133,133,331 shown in Fig.

11 (c)by using Cr-Kαradiation, the stress compo-

nents can be determined by the least square regression

method . Figure 12 shows the results of the mea-

surements of applied stresses by four-point bending

and the stress-free diffraction angle. Theσ value is

equal to the applied stress and the other stresses are

nearly zero.

3.5 Composite materials

Like the X-ray method,the neutron method can

detect the mean stress in each constituent phase of

composite materials. The average stress in the bulk

can be detected by the neutron method,while the X-

ray measurement detects the stress only very near the

surface. Figure 13 shows the change of the phase

stress of SiC particulate reinforced aluminum alloy

due to loading measured by the neutron method,

(a) Coordinate system of single crystal specimen

(b) Two-tilt method

(c) Multiple regression method

Fig. 11 Standard (001) stereographs for X-ray stress

measurement of silicon single crystal

Fig. 12 Stresses and diffraction angle measured by multi

ple regression method as a function of the applied

stress in silicon single crystal

-

where the thermal residual strains are not included .

The macrostress obtained by Eq.(７)is equal to the

applied stress. The phase stress in each phase is

proportional to the macrostress as expressed by

σ ＝∑ σ′ (22)

where is the tensor which can be estimated from

the mean stress theory proposed by Mori and

Tanaka based on the Eshelby inclusion

mechanics . This model is called EMT model in this

review.

The thermal stress in the composite of alumina

and zirconia measured by the neutron method is

shown in Fig.14 . The residual stress is tensile in

alumina and compressive in zirconia. The lines in the

figure are the prediction of thermal mismatch stress

based on EMT model as

σ ＝∑ ε, (23)

where is the tensor which can be estimated from

EMT model and ε is the mismatch strain. The

calculated stresses are dependent on which phase is

assumed as the matrix. The solid lines in the figure

indicate the prediction by assuming that the phase

with higher volume fraction is the matrix. Agreement

between predictions and experiments is fairly good.

For general cases, the measured residual stress

can be decomposed into the macrostress and micros-

tress by using Eqs.(７)to(10),and the microstress is

further decomposed to elastic mismatch stress and

thermal mismatch stress by using Eqs.(22)and (23).

The above measurement deals with the mean

stress in each phase in composites. By using the

microbeam of synchrotron radiation, the local stress

in each phase can be measured as described before.

3.6 Welding residual stresses

Welding residual stresses are very important to

guarantee the performance of welded structures. The

neutron diffraction method has been utilized to mea-

sure the welding residual stress in the interior of

welded joints. Figure 15 shows eight locations of the

sampling volume and the measured residual stress

distribution near socket welded joint of steel pipes .

Fig. 13 Relation between applied stress and phase stress

obtained by neutron diffraction for SiC reinforc

ed Al alloy

-

(b) SiC 116 diffraction

(a) Al 222 diffraction (a) Phase stress in ZrO

(b) Phase stress in AlO

Fig. 14 Variation of residual stresses in AlO /ZrO com

posites with zirconia content measured by neu

tron diffraction

-

-

Three components of the residual stress were deter-

mined 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

welded 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 interface to the outer surface of

the pipe and the heat affected zone takes a low value

around±40 MPa. The stress-relief treatment at

600℃ for 1 h removes the residual stress as shown in

Fig.15.

The neutron method have been utilized to mea-

sure the interior distribution of the residual stress of

various types of joints, such as butt-welded joints,

brazed joints,friction welded joints,and claddings .

4. Concluding Remarks

The macrostress and microstress in crystalline

solids can be measured by diffraction using X-rays,

synchrotron and neutrons. These three methods are

based on the same principle of the diffraction of

crystals,and have different advantages. The conven-

tional X-rays detect the stress very near the surface,

while the neutron diffraction takes the stress in the

interior of the materials. High-energy X-rays from

synchrotron sources have the penetration depth in

between and are suitable for the measurement of

subsurface stresses.

The measurement procedure has been greatly

advanced and these methods have been extensively

applied to determine the state of residual stresses in a

variety of engineering materials and structures. The

recent applications of diffraction stress measurements

cover the residual stress analysis in textured thin

films,the nondestructive determination of the subsur-

face distribution of the residual stress in shot-peened

materials, local stress measurements near the crack

tip,the stress measurements of single crystals,micro-

and macro-stress measurements in composites, and

the internal distribution of the residual stress in

welded joints.

The success of the applications of these three

diffraction methods to residual stress analysis will

promote further developments of the techniques and

open even wider field of applications.

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