Progress in 3D/4D Material Science toward Ferrous Materials
3D/4D マテリアルサイエンスの鉄鋼材料への展開
Hiroyuki Toda
Professor, Department of Mechanical Engineering, Toyohashi University of Technology,
Toyohashi, Aichi 441-8580, Japan

Introduction
Over the past decade, attempts have been made to apply synchrotron X-ray
microtomography (XMT) to ferrous materials, as the importance of 3D observation has beenrecognized. XMT performed on light materials has generally enabled the reconstruction of
volumes with maximum spatial resolution close to the physical limit of the projection-type setup (approximately 1 µm) 1,2). However, in the case of ferrous materials, difficulties arise withrespect to X-ray transmission. Since photoelectric absorption is dramatically enhanced withincreasing atomic number, high energy X-rays are needed to realize X-ray imaging for ferrous
materials. This can lead to spatial resolution degradation, in addition to image quality
degradation due to poor photon statistics. For example, Everette et al. and Lame et al. have
utilized white X-rays to observe steel at a spatial resolution of 3 and 2.7 µm (not on ferrous
materials, but on Cu), respectively 3,4). Cheong et al. (90 keV X-ray was used for field of view of
4.34 mm) and Shobu et al. (66.4 keV X-ray was used for field of view of 5.97 mm) usedmonochromatic X-rays from undulators 5,6); and although no measurement or description of
spatial resolution is presented in their papers, spatial resolutions of 19 and 35 µm, respectively,
are expected at best, according to the descriptions of sample size and the number of projections.
This technological limitation prevents us from utilizing advanced applications of XMT, such asmeasurements of 3D/4D crack-tip displacement/strain fields 7), local crack driving forces 8), andthe spatial distribution of chemical concentrations 9), which have been developed mainly using
light materials. It would therefore be of significant value to attain the best achievable spatial
resolution level for ferrous materials.
The past decade has also witnessed an explosive growth in the XMT technique using large
synchrotron sources (e.g., SPring-8, ESRF) for studying the fracture and fatigue behaviour ofengineering materials 10). The development of techniques such as 3-D strain mapping 11), K-edge
subtraction 12) and local crack driving force mapping 8) from the reconstructed images obtained
from the in-situ XMT experiments in synchrotron radiation facilities have provided new insights
on the failure of alloys, foams and composites 8,9,13-16). The availability of 3-D images containing
internal microstructural information provides the unique opportunity for investigating thedevelopment of cavities during creep of material. Recent investigation on the development of
creep damage (voids and cracks) in a Fe-Ni-Cr fully austenitic steel using synchrotron beamline at Spring-8 provided quantitative characterization of the void content in the as-cast and exservice variants of the material 5).
In the present study, an XMT study was performed at a synchrotron radiation facility to
examine the effects of various experimental parameters on spatial resolution. Fatigue crack
opening behaviors were then evaluated, and advanced analysis performed, by applying the
optimal experimental conditions obtained. Study on the evolution of voids due to creep
deformation in 9-12%Cr tempered martensitic steels was also carried out with the subsequent
quantitative analysis concerning the creep stress and holding time dependent behaviors.

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2. Experimental procedure
2.1 XMT setup
XMT was performed at the undulator beamline BL20XU of the SPring-8. A
monochromatic X-ray beam, produced by a liquid nitrogen-cooled Si (511)-(333) double crystal
monochromator, was used. The image detector consisted of a cooled 4000 (H) × 2624 (V)element CCD camera (pixel size of the camera: 5.9 µm square) in 2×2 binning mode, ascintillator (Lu2SiO5:Ce), and an optical microscope (OM) objective lens (×20). Thickness of
the LSO scintilllator was 10 and 26 µm for 40 and 55/70 keV, respectively. In total, 1500
radiographs, scanning 180 degrees, were obtained in 0.12 degree increments. As mentioned
above, the theoretical limit of the projection-type XMT is approximately 1 µm, which isdetermined primarily by inevitable image blurring caused by Fresnel diffraction, the diffraction
limit of visible light, and the spatial resolution of a scintillator 17). Isotropic voxels (a volume
element in 3D space) with 0.5 µm edges, that were requisite to achieve the 1 µm spatial
resolution, were achieved in the reconstructed slices. In order to realize high-resolution imaging
for ferrous materials, high photon energies of 40~70 keV were used in this study.
2.2 Spatial resolution evaluation
First purpose of this study was to optimize the spatial resolution of the XMT setup at high
X-ray energies, by varying experimental parameters. Test patterns were designed to test spatial
resolution. The test patterns consisted of pairs oflateral and vertical gratings with increasing line
pitch between 1.36~2.65 µm and 1.32~2.47 µm,
respectively, as shown in Fig. 1. The test
patterns were machined on a stainless steel wireof about 497 µm in diameter using the focusedion beam milling technique. The modulationtransfer function (MTF) derived from an edge
response function (ERF) at the outer contour of
the wire (i.e., the steel/air interface) was alsomeasured, to determine the spatial resolution at
5 % contrast ratio. This measurement
corresponds to the lateral direction, which is thecircumferential direction with respect to theFig. 1 A resolution test object that has been
stainless steel wire axis. The test-pattern wire
prepared on a stainless-steel wire of about
was scanned at 40, 55 and 70 keV, with varying
497 µm in diameter using the focused ion
sample/detector distance. The results of thebeam technique. The three arrows indicate
interface-based MTF calculations and thethree directions along which spatial
subjective inspection of the test patterns
resolution was measured.
suggested fundamentally reasonable agreement.
2.3 Fatigue crack observation
Material used in this section was S15C carbon steel, which exhibits a ferritic-martensitic
structure with comparatively large areas of martensite due to a special heat treatment. Its
chemical composition was 0.15C-0.15Si-0.41Mn-0.014P-0.008S and balance Fe in mass %. A
specimen of 22 mm L × 0.48 mm W × 0.48 mm B with a corner fatigue crack was prepared in
the form of an I-shaped specimen. The values of W and B are within a 0.6 mm long gauge
length. The fatigue pre-crack was introduced with a load ratio Pmin/Pmax of 0.1 and maximum
stress of 350 MPa.

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Photon energy of 40 keV and sample/detector distance of 110 mm were adopted. The entire
cross-section of the specimen and a region of about 650 µm-high around the crack were
captured on the CCD camera. An in-situ loading rig, which had been specially designed for thein-situ XMT observation, allowed specimens to be scanned under cyclic loading with a load
resolution of 0.1 N and a displacement stability of about 0.1~0.2 µm. A first scan of thetomography was performed without loading (2.4 N). Subsequent scans were performed at 6.7,
13.4, 20.2, 26.9, 33.6 and 60.0 N, after the relaxation behavior of the material was stabilized.
Image slices were reconstructed from the series of projections, based on a conventional filtered
back-projection algorithm 18). The gray value in each dataset was calibrated so that the linear
absorption coefficient of 3~50 cm-1 fell within an 8-bit gray scale range between 0 and 255.
To calculate the gravity center of each particle and pore with sub-voxel accuracy,
pentagonal facetted iso-intensity surfaces were computed from the volumetric data set using theconventional marching cubes algorithm 19). To suppress inaccuracies originating from image
noise, only particles over 27 voxels in volume were counted for particle tracking. The particles
were tracked throughout the tensile loading by employing a matching probability parameter(MPP) method, called the modified spring model which we had previously developed 11,20). The
optimal values of coefficients α, β and γ in the MPP were identified as 0.8, 0.1, and 0.1,
respectively. Tetrahedra with all the particles and pores as vertices in the 3D image were createdby the Delaunay tessellation technique to calculate internal strain in 3D in high density 20,21). All
the strain components were calculated from the displacement of the vertices of the tetrahedrons,
assuming that the displacement in a given tetrahedron is a linear function. Crack-tip opening
displacement (CTOD) was also measured on each slice.
2.4 Void observation in creep samples
Typical 9-12% Cr heat resistant steel with nominal chemical compositions of 12Cr-2W1Cu-0.6Mn-0.4Mo-0.2V-0.1C-0.1Si-bal.Fe (in mass%) was selected for this investigation. The
samples have been crept after quenched and tempering treatment involving austenitizing at 1373
K for 8 h, followed by aging at 1003 K for 36 h. The stress rupture tests were carried out withperiodic interruptions to measure their elongations until failure at 873 K. Applied nominal
stresses were ranged within 120~180 MPa. Coupon samples with a square cross-section of
about 300×300 µm2 were extracted from the each crept specimen to investigate their voids
evolution using synchrotron XMT in Spring-8. The undulator beamline BL20XU was tuned to
produce a beam of energy 40 keV and a detector distance was 110 mm from sample. To evaluate
the creep cavities, a local threshold of grey value was assigned and only those greater than
3×3×3 connected voxels were selected. A marching cubes algorithm was utilized to determine
the number, volume, surface area and gravity center of voids in the reconstructed region ofinterest.

3. Results and discussion
3.1 Spatial resolution
Fig. 2 shows the virtual cross-sections captured at a sample/detector distance of 110 mm.
Even the narrowest grating was resolved with each of the three X-ray energies used. The
variations in lateral (radial with respect to the stainless-steel wire axis) and vertical resolution
with sample/detector distance are shown in Figs. 3(a) and 3(b), respectively. It can be confirmedthat the vertical resolution exceeds the lateral resolution, at least at 55 and 70 keV. The lateral
resolution results further reveal that spatial resolution worsens when the sample is closer to thedetector. This is probably due to the effects of X-ray scattering. It is well known that at a
relatively low X-ray energy range (~20 keV) the X-ray scattering distribution is approximately
isotropic, while increasing the X-ray energy causes a preferential forward scattering 22). The X-－ 129 －

ray photons that are forward directed are
more apt to be detected by the image
detector when the sample/detector distanceis small, thereby reducing spatial resolution.
Fig. 3(c) shows the variations in lateral(circumferential with respect to thestainless-steel wire axis) direction withrespect to the spatial resolution that wereobtained by means of MTF. Although thelateral resolution appears to differ between
Figs. 3(b) and 3(c), it should be noted thatthe measuring directions differ between
Figs. 3(b) (circumferential direction) and(c) (radial direction) with respect to thestainless-steel wire axis. Comparisons of all
the resolution data shown in Fig. 3 indicatethat the spatial resolution is unexpectedly
highest in all three directions when the Xray energy is 70 keV. This may be
associated with the characteristics of the Fig. 2 Virtual cross-sections captured at
Lutetium-based scintillator employed. The sample/detector distance of 110 mm, showing
size of the volume in the scintillator in how the lateral gratings for vertical resolution
which X-rays are absorbed and scintillation evaluation can be resolved at the three X-ray
photons are produced is generally energies. Note that even the narrowest grating
dependent on the X-ray energy. If this was resolved with the three X-ray energies used.
volume is less than the diffraction-limited
resolution of the optical system used, the spatial resolution of the system is not limited by the Xray absorption process. It is however reasonable to assume that the absorption mean free path of
X-ray radiation depends on photon energy at high X-ray energies. Hence, it may be assumed
that the lower the photon energy is, the better the resolution achieved in the image. This isbecause the spreading of the visible photons produced in the scintillator acts to blur the image. It
is however interesting to note that Lu has K absorption edge at 63.314 keV and this inevitablycauses the smallest absorption mean free path at 70 keV among the three X-ray energies
employed, thereby resulting in beneficial effects on spatial resolution.

Fig. 3 Variation in spatial resolution in (a) lateral (circumferential), (b) vertical and (c) lateral(radial) directions with respect to the rotation axis; (a) and (b) were obtained through subjective
evaluation of the resolution test object, while (c) was determined with MTFs derived from ERFs
at the outer contour of the wire. Spatial resolution was defined at modulation transfer functionof 5 %. Original line spread functions were fitted with a sigmoid function.

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Fig. 4 shows edge response functions
revealing the degree of blurring at the sharp
air/steel interface. Obvious overshoot andundershoot may be observed in the profiles.
Since these are caused by X-ray refraction at
the interface, the extent of the overshoot andundershoot increases with the increase indistance. And, it is qualitatively evident thatspatial resolution is not significantly different
among the three conditions. A total of eightmeasurements were averaged for each ERF. A
line spread function (LSF) was obtained bytaking the first derivative from each ERF that
had been fitted with a sigmoid function. MTF
was then derived by applying discrete Fouriertransform to the LSF.
3.2 Fatigue crack visualization

Fig. 4 ERFs (which indicate how original
images are spread out) at X-ray energy of 55
keV according to various sample/detector
distances, used to calculate MTFs of 3Dimages.

Owing to the superior spatial resolution level attained, both cracks and somemicrostructural features of the underlying steel could be clearly visualized. In total, 1,249
dispersion particles and 1,687 micropores were confirmed in the entire rendered volume. The
particle volume fraction was 0.04 % and the mean equivalent diameter was 4.3 µm, while thosefor the micropores were 0.11 % and 5.4 µm, respectively, as shown in Fig. 5. The particles andpores are limited to those larger than 27 voxels in volume. It may be inferred that the number ofvisible microstructural features is somehow enough to derive various internal mechanicalquantities such as stress/strain and local crack driving forces. In Fig. 5, only crack images wereextracted from the tomographic volume captured at 2.4 N, and the underlying metal and othermicrostructural features are not displayed. They are shown as 3D perspective images viewed in
the mode I loading direction in Fig. 5(a) and the crack mouth direction in Fig. 5(c). Fig. 5(b) isan OM image that corresponds to Fig. 5(c). Fig. 5(a) reveals the distribution of some fatigue
crack closure patches (indicated by black arrows), that don’t completely disappear even at
relatively high load levels. It has been well documented in the literature that such scatteredclosure patches contribute effectively to fatigue crack growth resistance 23,24).

Fig. 5 3D perspective views of a fatigue crack. Only cracks have been extracted from thetomographic volume as shown in (a) and (c); (b) is an OM image that corresponds to (c).

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Crack extension varied to some extent along the crack front line. A few retarded sections of
the crack front are seen periodically, as indicated by white arrows in Fig. 5(a), together withsome fracture surface roughness. Other noteworthy features are the significant crack deflection
and tilting caused by the occurrence of modes II and III driving forces, respectively, which canbe more obviously identified in Fig. 5(c). In fact, the underlying phases have been identified, as
shown in Fig. 5(b), as the ductile ferrite phase and the less ductile martensite phase 25), which
can be associated with the significant mode III tilting shown in Fig. 5(c). Frequent changes intilting direction are confirmed at martensite/ferrite interfaces together with somemartensite/ferrite interfacial crack extension where the crack front line becomes more
complicated. A typical example is indicated by the arrows in Figs. 5(b) and 5(c). It can beinferred that the retarded sections of the crack front might be associated with the existence ofthe martensite grains.
Fig. 6(a) shows the variations in measured CTOD along the crack front line at an applied
load of 60 N. The CTOD value tends to roughly increase when going from left to right. It
appears to increase locally four to five times over intervals of approximately 10 to 50 µm along
the crack front line, probably because of the crack/microstructure interaction that was shown in
Fig. 5. This is because the length range over which the CTOD values are locally elevatedcorresponds to the dimensions of the ferrite/martensite grains that are shown in Fig. 5(b). The
local CTOD elevation can also be associated with the occurrence of local crack deflection
shown in Fig. 6(b), providing evidence for the effects of the underlying grain dual phasestructure.
Fig. 7 shows examples of crack-tip strain field shown on three different virtual crosssections that has been calculated between applied loads of 33.6~60.0 N. It is clear that the strain
distribution is far different from that obtained in typical elastic-plastic fracture mechanics.
Although the measurement does not provide an exceedingly high spatial density in displacement
markers, due to the relatively small number of microstructural features visible that can beutilized as strain markers, it appears most likely that the strain distribution has been affectedsignificantly by the underlying microstructure. Fig. 7 also shows how the crack-tip strain field
varies from place to place. In Fig. 7(c), vertical elongation of the crack-tip strain field isobserved in both upper and lower directions. This characteristic geometry of the crack-tip strain
field can be associated with the existence of considerably elongated inclusion particles in thevicinity of the crack-tip. Such particles can be clearly recognized in Fig. 5(c) as ten to twelve
needle-like inclusions that align in the vertical direction.

Fig. 6 Distribution of CTOD along the crack front line in (a) and corresponding deflection angle
distribution in (b).

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Fig. 7 The examples of crack-tip strain field shown on three different virtual cross-sections.
Equivalent strain is shown in the figure.

3.3 Effect of creep stress on the void evolution

ElongationtD/ tF

From the 3-D rendering of the
0.4
reconstructed slices obtained from XMT on
the crept samples, it is clear that the creep
0.3
damage that is in-homogenously distributedin the re-constructed volume of interest was
progressively increased with increase of
0.2
creep stress and holding time. The series ofcreep tests reveal that the cavitation damage
0.1
Time
was dominated issue in the creep failure.
The inset in Fig. 8 shows the method used
to identify the onset of damage phase from
0.0
120
130
140
150
160
170
180
the elongation-time curves obtained via theStress (MPa)creep tests. The tangent intersection fromthe secondary and tertiary stages separates
Fig. 8 A plot of the variation of the fraction of
the tertiary part of creep elongation-time
creep life expended in cavitation with stress forcurve into coarsening dominated andthe 12%Cr tempered martensitic steel. The inset
cavitation dominated regions. Fig. 8 shows
shows the procedure followed to delineate thethe stress dependence of the life fraction
period of cavitation damage from theconsumed in the damage phase for the steel.
elongation-time obtained from the creep test.
There seems to be a transition in thefunctional dependence of the ratio of time expended in damage to its corresponding creep life in
the tested stress range. As the applied stress during creep decreases the ratio sharply decreases
until about 155~160 MPa, after which the fall is arrested with a slight increase in the stressrange 120~135 MPa. In order to explain these trends, the quantitative analysis of cavitation
behavior from the 3-D rendered volumes has been carried out. The analysis results are shown in
Fig. 9, in terms of variation of number density, size and volume fraction of voids with theapplied creep stress. While a steady rise in the number density of voids is seen with decreasing
creep stress, correspondingly a significant rise in the void volume fraction is observed only forthe lowest stress. An increasing number density of voids without significant variation in its
volume fraction and average void size in creep stress range 135~180 MPa implies an increase innucleation rate of voids. At the lowest stress, however, there has been nearly a three-foldincrease in volume fraction along with slight increase in the average diameter of voids and atDtF－ 133 －

significant upswing in the number density curve, which implies the growing influence of void
coalescence/growth mechanism. This is also corroborated by the presence of many of complex
shaped large voids at the lowest stress. The analysis of the void size distribution shown in Fig.
9(d) also confirms the trend of increasing nucleation rate sustained even at long creep time,along with increasing influence of void coalescence. This interpretation stems from theobservation that the size distribution shifts to the right only after increasing peak frequency to adefined level with increase in creep exposure times.
3.4 Effect of creep holding time
Creep behavior of the steel shows an extended damage period before failure above a stressof 155~160 MPa as compared with those at lower stresses. It is significant to note that at thesehigh stresses the void nucleation rates seems to be lower as evidenced by its low number density,
volume fraction and peak frequencies in void size distribution. Further from the 3-D images thespatial distribution of the voids seems to be in-homogenous. In order to understand the nature of
the distribution rendering near to the areas of high number density of voids have been carriedout. The rendered 3-D volume expanded near to these regions is shown for three types of creep
time in Figs. 10(a), 10(b) and 10(c). It is clearly seen that with increasing creep time theappearance of aligned voids increase. The probable loci of the alignment of the voids areemphasized by the black lines in the images. It is well known that internal interfaces are thepreferred locations for nucleation of creep voids in materials 26). Tempered martensitic steels
contain both prior austenitic boundaries as well as packet and lath boundaries, which are known
to initiate creep voids. It is thus evident from nature of the curves that the aligned voids are apart of the various boundaries present in a tempered martensitic structure. In order to investigate
the association of the boundaries to these aligned voids, the specimen crept at 15216 h was
6

-5

1.0

0.8

0.6

Void diameter (μm)

(a)

−3

Number Density (10 μm )

1.2

(b)

5
4
3
2
1

0.4
120

140

160

0

180

Stress (MPa)

120

140

160

180

Stress (MPa)

(c)

400

300

1000

Frequency

Void Volume Fraction (ppm)

1500
51406 hours(180 MPa )29466 hours(135 MPa )(d)15316 hours(150 MPa )200 2825 hours(180 MPa )5006779 hours(165 MPa )

100

0

0

120

140

160

180

0

Stress (MPa)

5

10

15

Void Size (Eq. pixels)

20 50 55

Fig. 9 Plots showing the variation of (a) number density (b) void diameter (c) void volume
fraction with stress. (d) The void size distribution as a function of creep exposure time.

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investigated by combined serial sectioning and OM. The twenty serial sections with a 3 µm
interval were imaged and digitized using OM. The slices were merged to create a volumedataset. One polished section of the selected sample about 9 µm from the top was etched todelineate the prior austenitic grain boundary, which was then traced out on the corresponding
digitized image of the polished slice. The volume dataset thus generated was matched with thecorresponding tomography dataset on the basis of the registration of the images of voids seen in
the two 3-D rendered images. Fig. 10(d) shows the result of the near matching of the 3-D
rendered image. The prior austenite grain boundary located 9µm below the surface is seen withthe voids in the tomography image. From the Fig. 10(d) it appears that void cluster marked as‘A’ is associated with the prior austenite grain boundary. As it is the dominant cluster type in thevolume, it may well be that in this case that voids show preference to nucleate at the prioraustenite boundary as compared with packet or lath boundary located in the grain interior.

Fig. 10 An expanded 3-D rendering of the regions of high number density of voids for sample
exposed to creep times of (a) 2825 h (b) 15316 h and (c) 51406 h. The black lines are the loci of
the alignment of the voids. (d) The composite image of the region characterized by optical
microscopy within the reconstructed, rendered and thresholded image obtained fromtomography scan. The dark line within the OM characterized region is the prior austenite
boundary located 9 µm below surface. The dominant void cluster is indicated as A.

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4. Conclusions
X-ray microtomography was employed to observe a fatigue crack in S15C steel and a void
evolution by creep stress in 12%Cr alloy. A high-resolution experimental configuration enabled
surprisingly superior spatial resolution of better than 1.3 µm after optimizing experimental
parameters. The spatial resolution level achieved in the present study is clearly advantageouscompared to the limited past trials on ferrous materials. Owing to the high spatial resolution
achieved, the details of a crack were readily observed, along with evidence of the interaction
between the crack and a dual phase microstructure. After preliminary investigation of theobtained images were used to quantify crack-tip opening displacement and crack-tip strain.
From the 3D visualization of voids in the crept samples, it can be considered as one ofeffective methodologies to understand the in-homogenous nature of the spatial distribution ofvoids and its relation to the variation of the damage period with stress and time in the creep lifeof the steel. Due to the break-down of martensitic structure in the boundary vicinities, further
precipitate coarsening can lead to acceleration of void nucleation. Therefore, there is large scale
appearance of aligned voids at prior austenite boundaries that subsequently grow and coalesce.
In case of the stress range 155~180 MPa, together with less cavitation inside grains, a rapid
decline of the damage phase was observed as a fraction of total creep life due to the greater
contribution of void growth.
It may be concluded that the use of 4D microtomography observation, combined with anadvanced image analysis techniques, might offer a highly effective means of investigating
various issues relating to ferrous materials. The high-resolution XMT observation achieved in
the present study is of crucial importance to the development and application of such techniques.

Acknowledgements
This work was partly undertaken as a technical research aid project of the JFE 21st Century
Foundation for FY 2010. The synchrotron radiation experiment was performed with theapproval of JASRI through proposal number 2010A1247.

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