STUDY ON COMPUTERIZED TOMOGRAPHY AND STRAIN MAPPING NEAR THE INTERNAL CRACK TIP OF STEEL BAR USING SYNCHROTRON WHITE X-RAY

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1 Copyright JCPDS-International Centre for Diffraction Data 29 ISSN STUD ON COMPUTERIED TOMOGRAPH AND STRAIN MAPPING NEAR THE INTERNAL CRACK TIP OF STEEL BAR USING SNCHROTRON WHITE X-RA Jun-ichi SHIBANO 1, Kentaro KAJIWARA 2, Kouji KIRIAMA 3, Takahisa SHOBU 3, Kenji SUUKI 4, Takayuki ARAI 1, Setsuo MIURA 1 and Michiaki KOBAASHI 1 1 Dept. of Mech. Eng., Kitami Inst. of Tech., Kouen-cho, Kitami, Japan. 2 JASRI, Kouto Sayo-cho, Sayo-gun, Hyogo, Japan. 3 SPring-8 Service Co., Ltd., Kouto Sayo-cho, Sayo-gun, Hyogo, Japan. 4 Dept. of Tech. and Living Sci., Niigata Univ., 85, Igarashi-2-no-cho, Niigata, ABSTRACT Japan. A computerized tomography (CT) and a strain mapping near a crack tip in material were investigated using a white X-ray obtained from BL28B2 beam line at SPring-8 in Japan. A low-alloy and high-tensile steel was used as a specimen prepared in the tensile bar with a parallel part of 5mm diameter. A fatigue crack was introduced into the specimen under the pulsating tension load. The computerized tomography of the crack in the specimen was carried out by using the CCD camera that can detect indirectly the X-ray transmitted through the specimen. To measure the strain using the energy dispersive X-ray diffraction technique, the synchrotron white X-ray beam, which had a height of 8μm and a width of 3μm, was incident on the specimen with the Bragg angle θ of 5 degrees. As the results, the computerized tomography of the crack in the specimen under the tensile loading was practicable by using the white X-ray. The map of the internal strain near the crack tip of the specimen could be obtained using the high energy white X-ray. It was confirmed that the maximum tensile strain was distributed circularly along the crack tip estimated by CT. INTRODUCTION Since a crack produced in a structural component causes a serious failure accident, the clarification of its progress mechanism is desired strongly. Although the internal stress measurement of a material has been performed actively by using a neutron and a synchrotron-radiation, the strain measurement near the internal crack tip is few [1-2]. In our previous work, a fundamental study to measure the internal strain of a low-alloy and high-tensile steel using a high energy white X-ray obtained from synchrotron radiation was carried out at SPring-8. As a result, the internal strain of the steel of 5, 1 and 15 mm thickness could be evaluated using the white X-ray which range of energy from 5keV to 15keV [3]. Furthermore, the transmission imaging of the internal crack and the 2D map of the internal strain near it in the steel specimen of 5 mm thickness under the tensile loading could be obtained using the high energy white X-ray [4]. In order to measure the strain near the internal crack tip, it is necessary to detect correctly its position in the material. The aims of the present study are therefore to clarify the crack inside material by using a X-ray computerized tomography and then to measure the strain distribution near the estimated crack tip using the white X-ray obtained from the public beam line BL28B2 in SPring-8.

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3 Copyright JCPDS-International Centre for Diffraction Data 29 ISSN EXPERIMENTAL PROCEDURE Specimen. A low-alloy and high-tensile steel WEL-TEN 78E (JIS G3128 SH685) was used as a specimen prepared in the tensile bar with a parallel part of 5mm diameter as shown in Fig. 1. The notch of.23mm in width and.37mm in depth on the center of parallel part of the specimen was made by the wire electric discharge machining. Residual stress of the specimen due to machining was removed by the annealing which is done at 54 for one hour followed by slow furnace cooling under the argon gas atmosphere. oung's modulus, Poisson's ratio and the yield stress of the specimen obtained from a tensile test were 2GPa,.29 and 779MPa, respectively. A fatigue crack was introduced into the notch root of the specimen by the pulsating tension load of 588N with the sine wave having a frequency of 2Hz. The fatigue crack of length about 1mm from the notch root on the surface of the specimen was produced after the number of cycles of Compact tension equipment. The compact tension equipment, as shown in Fig. 1, was used for the computerized tomography and the strain measurement near the crack in the specimen. To apply a tension load to the specimen with a threaded part, the nut on a thrust bearing was screwed down so that it may not act a torsional moment to the specimen. The acrylics circular cylinder of 6mm thickness was used to support the applied load to the specimen and to enable the synchrotron radiation to transmit through the equipment. Visualization of internal crack by CT. A computerized tomography of the internal crack of the specimen carried out at the public beam line BL28B2 in Super Photon Ring-8 (SPring-8). The air-cooling CCD camera with 1 by 124 picture elements in the photoreceptor (Hamamatsu Photonics C A) and the beam monitor (Hamamatsu Photonics AA4P) were used for CT. A resolution of photographic image obtained with the camera is 5.83 micrometers. The CCD camera was mounted in a rear direction about 53mm of the specimen, and detected the X-ray transmitted through the specimen of 5mm diameters. The transmission images near the crack of the specimen applied to the tensile load of about 29N was exposed by rotating from degree to 18 degrees at.5-deg. step with exposure time of.2 sec. Reconstruction of the images was accomplished using the specific software. Strain measurement near the crack tip. The experimental setup of strain mapping using high energy white X-ray at BL28B2 is shown in Fig. 2. For the strain measurement, -axis on the notch root center of the specimen was coincided with the optical axis of synchrotron radiation beam. The Ge-type Solid State Detector (SSD) was fixed at the diffraction angle 2θ = 1 degrees in the - plane. The longitudinal axis of the specimen was set on the -axis, the measurement direction of strain therefore inclined 5 degrees to the -axis. However, the Screw Thrust bearing Nut for the application of tensile load to specimen Cylinder SSD (Solid State Detector) Strain gauge Incident white X-ray Diffracted X-ray of acrylic Specimen Specimen X Fig.1 Compact tension equipment for CT and internal strain measurement using synchrotron white X-ray. Fig.2 Experimental setup of strain mapping using high energy white X-ray at BL28B2 in SPring-8.

4 Copyright JCPDS-International Centre for Diffraction Data 29 ISSN difference of the strain due to the measurement direction is very small. A multi-channel analyzer (MCA) with 496 channels was used for the discrimination of the diffracted X-ray energy detected by an energy dispersive technique. To determine the energy calibration equation in this experiment, fluorescence X-rays of Pb-Kα1 ( keV) and Pb-Kα2 (72.842keV) from a lead material and a radioisotope of Co-57 (122 kev) were measured, then it was obtained as Eq.1, En =.541xCH [kev] (1) where, CH is a channel number of MCA. The energy range per channel was therefore 54.1eV, and the discrimination of energy to about 221 kev was possible at 496 channels. Figure 3 shows the schematic diagram of cross section of the gauge volume by using the transmission diffracted X-ray. The strain in only orthogonal direction to the crack face was measured because of the limitation of our machine time. The measurement was performed under the tensile load of about 29 N. Applied load was estimated by the strain gauge cemented on the parallel part of the specimen, and it was adjusted so that it might be set to 748x1-6 as strain value. The irradiated time of the synchrotron white X-ray was set to 36 seconds per measured point. The diffraction angle 2θ was set to 1 degrees. The height of both divergence and receiving slits was 1μm, and the width of divergence slit was 1μm. The width of receiving slit was set to 5μm because the number of crystal grains concerned with the diffraction would be increased. The measurement strain therefore becomes an average value in a very long and slender parallelepiped volume with length of 1.14mm, width of.1mm and height of.1mm. The number of crystal grain with mean size of 13 μm observed by an optical microscope was about 26 in this gauge volume. The strain ε is given by Eq. 2 using the energy dispersive method. ε ΔE E E n n = =, (2) E En where E n and E n are the diffracted X-ray energies detected from a non-strained and a strained specimen, respectively. In this experiment, E n was obtained by measuring the same material treated with the stress relief annealing. Here, to calculate the stress intensity factor K I in the mode I of a tensile bar which has a single-sided crack under the uniform tensile load, the specimen approximates a plate. In this case, the stress intensity factor K I is defined as follows by Tada et al. [5], K = σ πaf( ξ), ξ = a/ W, (3) I H=1μm Incident white X-ray πξ ξ sin 2 πξ 2 F ( ξ ) tan, (4) πξ 2 πξ cos 2 where, W is a width of a plate, a is a crack length and σ is a tensile stress. W was set at the diameter of the parallel part of the specimen. The crack length a was obtained from the CT 3 B=H/tanθ =1143μm Gauge volume Crack 5mm in diameter Diffracted X-ray 2θ=1 Specimen Fig.3 Setup of specimen for strain measurement and schematic diagram of gauge volume using transmission diffracted X-ray.

5 Copyright JCPDS-International Centre for Diffraction Data 29 ISSN X SR Crack Measurement area Fig.4 Distribution of diffracted X-ray energy along the direction orthogonal to the notch root. Fig.5 Measurement area for strain mapping near the crack tip. image. The nominal stress due to maximum tensile load in this experiment was used as σ. Substitution of W of 5 mm, a of 1.9 mm and σ of 15 MPa into Eqs. (3) and (4) yields the stress intensity factor K I as shown below, KI = MPa m. (5) The size of the monotonic plastic zone, 2r p, in the plane stress state is given by 2 1 K I 2rp =. (6) π σ Substituting the yield stress σ of 779 MPa of the specimen and the K I of Eq. (5) into Eq. 6, 2r p will be about.282mm. The value of 2r p in the plane strain state is set to one third of Eq. (6), and will be about.94mm. Before the internal strain measurement near the crack tip, the strain distribution from the central axis of the specimen to the notch root on the diameter was measured to recognize the internal crack distribution. The diffracted X-ray energy of α-fe321 plane from the central axis of the specimen to the notch root on the diameter is shown in Fig. 4. The area of the sudden changes in the diffracted X-ray energy appeared at the location of.4mm from the axial center. It was therefore confirmed that the crack tip propagated near the axial center of the specimen. The measurement areas near the crack therefore were set up as shown in Fig points in 1 x 12 micrometers area in the X- section (at = ) and 71 points in 14 x 25 micrometers area in the X- section (at = ) were measured with the measuring time of 36 seconds per point. RESULTS AND DISCUSSION CT image of the internal crack. CT image of the internal fatigue crack in X- section (at = ) of the specimen is shown in Fig. 6. It was found that the fatigue crack propagated deeply in the specimen. The crack tip position estimated by CT was in close agreement with it observed by the heat tinting method. It was therefore confirmed that the synchrotron white X-ray was useful for the computerized tomography of the internal crack. Strain distribution near the internal crack. The diffracted X-ray profile of the specimen used in this experiment is shown in Fig. 7. Although a background noise was a little high, the intensity of each diffraction peak was sufficiently strong to measure. The peak energy of the diffracted X-ray was calculated by approximating the diffraction profile to the Gaussian

6 Copyright JCPDS-International Centre for Diffraction Data 29 ISSN X 38 notch crack tip 1mm Fig. 6 CT image of the fatigue crack at X- section (at =) Fig. 7 Diffraction profile of specimen using high energy white X-ray. curve. Figures 8 and 9 show the strain εz distributions of α-fe321 plane superimposed upon the CT images in the X- section (at = ) and the X- section (at = ), respectively. It was found in Fig. 8 that the large tensile strain occurred at the position of about.4mm from the axial center. The compressive strain due to the compressive residual stress produced during Gauge volume Measurement position mm.2 Crack.1 Notch X mm Fig. 8 Strain εz distribution of α-fe321 plane superimposed upon the CT image in the X- section at = Notch Measurement position X mm Crack tip mm Gauge volume Fig. 9 Strain εz distribution of α-fe321 plane superimposed upon the CT image in the X- section at =

7 Copyright JCPDS-International Centre for Diffraction Data 29 ISSN the crack propagation was distributed near the crack face estimated by CT. Fig. 9 shows that the strain ε z was circularly distributed exactly toward the front of the crack. These results express well the feature of the strain distribution in the vicinity of the crack tip. However, the tensile strain value at the position of X=.9mm and =-1.5mm near the surface area of the specimen was relatively low compared with it at the position of X=.4mm and = mm. Because the length of gauge volume is long in this experiment, the measurement strain may become the mean value when the measurement position is on the crack tip. Figures 1 and 11 show the strain ε z distributions of four lattice planes of α-fe211, 31, 321 and 42 planes in the X- section (at = ) and the X- section (at = ), respectively. It was shown that the size of tensile strain distribution area has a dependence on the lattice plane, although the trends for difference lattice planes are similar. It can be expected that a leading cause of the differences will be an intergranular strain, but it is not clear yet. Therefore, we need further studies to unravel this problem. CONCLUSION A computerized tomography and a strain mapping in the vicinity of a crack tip in steel specimen were investigated using a high energy white X-ray obtained from BL28B2 beam line at SPring-8 in Japan. Main conclusions are as follows. 1) The computerized tomography of the crack in the specimen under the tensile loading was practicable by using the synchrotron white X-ray. 2) The contour map of the internal strain near the crack tip of the steel of 5mm diameter could be obtained using the white X-ray with energy ranging from 5keV to 15keV. Distance from notch center, mm Distance from notch center, mm.6 Strain (a) α-fe211 plane.6 Strain (c) α-fe321 plane Distance from notch center, mm Distance from notch center, mm.6 Strain (b) α-fe31 plane.6 Strain (d) α-fe42 plane Fig. 1 Strain ε z distributions of α-fe211, 31, 321 and 42 planes in the X- section at =

8 Copyright JCPDS-International Centre for Diffraction Data 29 ISSN ) It was confirmed that the synchrotron white X-ray is useful for the computerized tomography of the internal crack and the strain mapping near it. 4) It would be useful to compare (hkl-averaged) strains from this experiment with theoretical distributions from fracture mechanics (extensions of Eqs. 3-6). ACKNOWLEDGEMENT The synchrotron radiation experiments were performed at the BL28B2 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No.27B1543). The authors would like to acknowledge Dr. asuhiko Imai (JASRI) for his help during the experiment. REFERENCES [1] M. Croft,. hong, N. Jisrawi, I. akharchenko, R.L. Holtz, J. Skaritka, T. Fast, K. Sadananda, M. Lakshmipathy and T. Tsakalakos, Int..J. Fatigue, 25, 27, [2] M. Rahman, M. E. Fitzpatrick, L. Edwards, S. Pratihar, M. Peel, A. Steuwer and T. Buslaps, Mater. Sci. Forum, 28, , [3] J. Shibano, T. Shobu, K. Suzuki, K. Kiriyama, K. Kajiwara, H. Kaneko and M. Kobayashi, Mater. Sci. Forum, 28, , [4] J. Shibano, K. Kajiwara, K. Kiriyama, T. Shobu, K. Suzuki, S. Nishimura, S. Miura and M. Kobayashi, J. the Society of Materials Science, Japan, 28, 57, [5] H. Tada, P. C. Paris and G. R. Irwin, The stress analysis of cracks handbook 3rd ed., The American Society of Mechanical Engineers: New ork, 2, Strain Distance from axis of specimen, mm (a) α-fe211 plane 2. Strain Distance from axis of specimen, mm (c) α-fe321 plane Strain Distance from axis of specimen, mm (b) α-fe31 plane 2. Strain Distance from axis of specimen, mm (d) α-fe42 plane Fig. 11 Strain ε z distributions of α-fe211, 31, 321 and 42 planes in the X- section at =