Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 106 STRESS ANALYSIS USING BREMSSTRAHLUNG RADIATION F. A. Selim 1, D.P. Wells 1, J. F. Harmon 1, J. Kwofie 1, A. K. Roy 2, T. White 3 and T. Roney 3 1 Idaho State University, Idaho Accelerator Center, Campus Box 8263, Pocatello, ID 83209 2 University of Nevada, Box 454027, Las Vegas, NV 89154 3 Idaho National Engineering and Environmental Laboratory, P.O. Box1625-2802, Idaho Falls, ID 83415 ABSTRACT Diffraction methods are the most reliable nondestructive methods of measuring residual stress. X-ray diffraction is restricted to penetration depths of some 10 µm, whereas neutron diffraction can provide information at significantly higher depths, but the cost is very high and the availability of facilities is much lower. A sensitive nondestructive probe for detecting defects and measuring stresses in thick materials (tens of cm) does not exist. The first highly penetrating system to measure stress/strain in thick materials based on using bremsstrahlung beams from small electron accelerators (3-6 MeV Linacs), is presented in this paper. These bremsstrahlung beams, which exhibit excellent penetration, create positrons inside the materials via pair production. The positrons annihilate with the material electrons emitting 511 kev radiation, which is influenced by the momentum distributions of the atomic electrons. Because of the fact of positron trapping at defects, positron annihilation is very sensitive to any change in the microstructure and can probe nano-void defects. Open volume defects, voids or dislocations are reflected in the line width of the 511 kev peak. Tensile stresses and resultant strains have been measured in an engineering alloy using this technique. This technique can be used to infer residual stress and to detect defects in crystals, polymers, metals and alloys up to tens of gm/cm 2 for material science and engineering applications. The low cost and compact size of small electron accelerators, and the high penetrability of MeV bremsstrahlung beams allow the development of portable systems for industrial applications. INTRODUCTION Sensitive nondestructive probes for stress analysis in thick materials are important in a wide range of applications. Diffraction methods offer the most sensitive nondestructive probes for stress analysis. X-ray diffraction [1] is widely used to measure stress, but it is restricted to small penetration depths (about 10 µm maximum). Synchrotron radiation [2] can provide information at depths up to 100 µm. Neutron diffraction [3] can provide information at much higher depths but the number of neutron diffraction facilities is very limited and the cost is very high. Other nondestructive methods [4] are also limited by their small penetration depth or their poor sensitivity. Raman spectroscopy represents another nondestructive method for stress analysis, but it is also limited to surface regions. Ultrasound technique is useful for high penetration depths, but it is only sensitive to macroscopic effects. Magnetic methods have also poor sensitivity and are limited to magnetic materials.
This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website www.dxcicdd.com ICDD Website - www.icdd.com
Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 107 Positron annihilation spectroscopy has been established as a sensitive nondestructive tool to study open volume defects [5], and is considered to be a unique technique to probe atomic scale defects. However it is also limited to thin materials because of the limited range of positrons in matter. The purpose of this study is to develop a highly penetrating sensitive probe for stress analysis in thick materials based on γ-ray induced positron annihilation spectroscopy. We have showed very recently [6] that positron annihilation spectroscopy can be extended to thick materials up to tens of gm/cm 2 by using MeV γ- rays as the primary beam instead of a positron beam. The high-energy photons penetrate deeply inside the material creating positrons via pair production. The positrons thermalize and annihilate with the material electrons emitting annihilation radiation, which carry information about the electron momentum distributions. This paper shows that γ-ray induced positron annihilation spectroscopy can be used to analyze stress and strain in engineering materials such as Zircaloy-4 (Zr-4). The basis of positron annihilation spectroscopy of defects will be explained below. Further, the experimental setup of the proposed technique and some initial measurements will be presented. POSITRON SPECTROSCOPY OF DEFECTS Positron thermalizes in material and then annihilates with an electron emitting two 511 kev annihilation photons. Spectroscopic studies [7] of annihilation radiation are classified into two categories, which are distinguished by the sensitivity of positron annihilation to the electron density (positron lifetime measurements) and the sensitivity of positron annihilation to the electron momentum distributions (Doppler broadening and angular correlation of annihilation radiation measurements). Positron lifetime spectroscopy is based on the fact that positron annihilation is proportional to the electronic density at the annihilation site and so it can provide information about the electronic densities in materials. The other Positron annihilation spectroscopy techniques are based on the fact that in the annihilation process, the positron does not contribute extra momentum to the center of mass of the annihilating pair. This is because positron rapidly thermalizes in a solid and remains as delocalized particle until it annihilates. On the contrary, the electron in atom has a significant momentum. Because of conservation of momentum, the two annihilation photons are nearly collinear. The electron momentum causes them to be emitted at a slight angle relative to each other. This is the basis of angular correlation of annihilation radiation measurements. The electron momentum is also reflected in the Doppler broadening of the 511 kev annihilation line in energy dispersive measurements. Hence both Doppler broadening and angular correlation of annihilation radiation measurements can provide information about the electron momentum distributions in atoms. Positron trapping at defects( i.e. localization of positron wave function at the defect site until annihilation) was discovered in 1960 [8]. It can be understood as follows: the positive charge of nuclei creates repulsive coulomb potentials for the thermalized positron in material. The lack of a positive charge at open-volume defects, such as vacancies and dislocations, provides an attractive potential that traps positrons at these sites. Positron diffusion lengths through the lattice are sufficiently long ( 100 nm) that they can probe a high number of atoms before annihilation. This creates a very high sensitivity to defects of approximately one vacancy per 10 7 atoms. The trapping of
Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 108 positrons at defects leads to characteristic changes in the measured parameters of positron annihilation spectroscopy. In lifetime measurements, the positron lifetime is increased in regions containing defects due to the lower electron density in such regions relative to regions without defects. On the other hand, when the positron wave function is localized at a defect site, its overlap with the core electrons will be decreased compared to its overlap with the less tightly bounded valence electrons and so, it will annihilate more with valence electrons. This is reflected in Doppler broadening measurements by a noticeable reduction in the broadening of the annihilation peak (i.e. a narrower 511 kev peak). Two parameters (S&W) have been often used to characterize the annihilation peak in Doppler broadening spectroscopy [9]. The S-parameter is sensitive to the annihilation with valence electrons and is defined as the ratio of the counts in the central region of the peak to the total counts in the peak. The W-parameter is more sensitive to the annihilation with high momentum core electrons and is defined as the ratio of the counts in the wing regions of the peak to the total counts in the peak. It is important to note that these peaks are a superposition of peaks associated with each atomic or molecular shell. The resulting peak is not gaussion and hence the non-standard spectroscopic functions S and W are used instead of gaussion peak fitting. EXPERIMENTAL SETUP AND SPECIMEN PREPARATION Doppler broadening spectroscopy was performed using bremsstrahlung beam-induced positrons to investigate the dependence of Doppler broadening on the tensile stress in thick materials. 6 MeV electron beams from a small-pulsed electron Linac were converted into bremsstrahlung beams by using a thick tungsten converter. Figure 1 shows the experimental setup. The bremsstrahlung beams were doubly collimated, with a stainless steel primary collimator followed by a lead collimator. The collimated beam with 2.5cm diameter was incident upon the specimen resulting in pair production and other electromagnetic processes. Positrons induced from pair production annihilate with the material electrons emitting 511 kev radiation. A high-energy resolution HPGe detector, shielded with 10 cm lead, was used to record the 511 kev radiation. The energy resolution of the detector was 1.1 kev at the 356 kev Ba-133 line and 1.3 kev at the 662 kev Cs-137 line. A detailed description of this experimental setup can be found elsewhere [6,10]. Measurements were made on cylindrical tensile specimens (10.16cm long, 2.54cm gauge length and 0.64cm gauge diameter) of Zr-4, which were previously subjected to varied amounts of tensile loading using a material-testing system machine. These tensile specimens were machined from annealed Zr-4 alloys in the longitudinal rolling direction. After the tensile stress test, each specimen has been exposed to the bremsstrahlung beam and the spectrum has been recorded during the pulse. Figure1: The experimental set-up of Doppler broadening spectroscopy using 6 MeV electron Linac.
Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 109 DATA TREATMENT& RESULTS For each specimen, the 511 kev peak was analyzed in terms of S&W parameters after subtracting background. Figure 2 shows the peak profile of the 511 kev line for one of the recorded spectrum. S is obtained by summing the counts in the central region of the peak with width of 1.2 kev, from 510.4 to 511.6 kev (1.2 kev represents the Doppler shift due to annihilation with valence electrons [9]) and dividing it by the total counts in the peak. W is obtained by summing the counts in the wing regions (from 508 to 509.2 and from 512.8 to 514 kev) and dividing it by the total counts in the peak. t-parameter is defined as the ratio between W and S. Figures 3 and 4 show the dependence of relative t parameter on the tensile stress and resultant strain respectively. The relative t represents the measured t-parameter for each specimen divided by t reference (the unstressed specimen). Uncertainties are dominated by statistical counting errors. Systematic errors in relative t- parameter values tend to cancel each other since the set up for each data point is exactly the same and we take ratio. The statistical error in the counts in each region was evaluated including the error from background subtraction. The statistical error in t- parameter was obtained by adding the errors in S & W quadratically, while neglecting the covariance term { eq.1}. 2 2 ( σ s) + ( w) 2cov( s, w sw σ t t = s σ w ) (1) Where σ s & σ w were also obtained by propagating the errors associated with the counts of each region. Notice that the covariance term has a negative sign and, if included, would reduce the uncertainty in the given numbers. 1000 800 Counts 600 400 502 504 506 508 510 512 514 516 518 520 Energy (kev) Figure 2: Peak profile of the 511 kev line
Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 110 Figure 3: Relative t as a function of stress in Zr-4, note that the large gap in stress is necessary to move past the elastic regime of the Zr-4 samples Figure 4: Relative t as a function of strain in Zr-4 Dislocation lines or any change in the spacing of the lattice planes due to residual stress act as vacancies and open volume defects. They form an attractive potential that trap positrons at these sites. This leads to more contribution from annihilation with valence electrons and consequently a decrease in the line width of the 511 peak, an increase in S parameter and a decrease in W and t parameters. This effect is clearly apparent in the reduction of t parameter with increased stress and strain values up to the maximum stress, as shown in Figures 3 and 4. The first point on each curve represents the reference specimen, which was not subjected to any stress. The second point represent the specimen subjected to 51.9 Kpsi (induced 0.013 strain), which is slightly above the stress yield point (the minimum stress required to induce plastic deformation). Measurements have not performed below this point, since there is no plastic deformation or permanent change in the microstructure. The last points on the two curves represent a specimen, which was stressed to total failure. Most of the range of strain occurs at the last point (the jump from 0.05 to 0.28 in Figure 4), equivalent to a change in stress of only 72 to 78 Kpsi. This is because most of the plastic deformation occurs just before the complete failure. The high statistical errors in the data are due to the low counting rate associated with the pulsed beam, since the repetition rate of the electron Linac is only 200 Hz. This can be addressed by raising the repetition rate of the Linac or using continuous wave electron (CW) Linacs, which would increase the counting rate by approximately 10 4. The photon beam size in the above measurements was about 2.5 cm and hence no spatial information about the stress distribution was available. However the fact that positron interacts with atomic scale defects raises the possibility that a high spatial resolution positron probe for stress analysis could be achieved if the photon beam size is greatly reduced. This may allow studying multi-axial stress fields by bremstrahlung-based positron annihilation. However this is still beyond the current capabilities of the technique.
Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 111 CONCLUSION: The feasibility of a new technique to measure stress in thick materials has been demonstrated. This technique employs bremsstrahlung beams from small electron accelerators to perform positron spectroscopy of defects. The high-energy γ-rays can penetrate deeply inside the materials probing very high depths up to tens of g/cm 2 (5-10cm in steel). By combining the high penetrability of γ-rays with the great sensitivity of positron spectroscopy to defects, a unique sensitive probe has been demonstrated, with the capability of analyzing defects and stresses in thick materials used in engineering applications. The presented measurements demonstrate the ability to measure tensile stresses. However this technique can be used to measure macroscopic or microscopic residual stresses. Because of the high sensitivity of positrons to defects, this technique can probe microscopic residual stresses, which operate over the grain or atomic scale of the material. ACKNOWLEDGEMENTS This work has been supported by Inland Northwest Research Alliance under contract ISU001. REFERENCES [1] I. C. Noyan and R. B. Cohen, Residual Stress Measurements By Diffraction and Interpretation, Springer-Verlag, New York 1987 [2] R. A. Owen, P. J. Withers and P. J. Webster, ICRS-6 Conf. Proc., Oxford, United Kingdom, July 2000., vol. 1, p.82 [3] A. Allen, M. T. Hutchings and C. G. Windsor, Adv. Phys. 34 (1985), p. 445 [4] F. A. Kandil, J.D. Lord, A. T. Fry and P. V. Grant, NPL Report MAT(A)04, NPL Materials Center, 2001. [5] P. Hautojarvi and A. Vehanen, in: Positrons in Solids, Ed: P.Hautojarvi, 1979, p.1 [6] F.A. Selim et al., Nucl. Inst. & Meth. B 192 (2002), p. 197 [7] P. J. Schultz and K. G. Lynn, Rev. Mod. Phys. 60(1988), p.701 [8] I.K. MacKenzie, T.L. Khoo, A.D. McDonald and B.T. A. Mckee, Phys. Lett. 19 (1967), p. 946 [9] P. Asoka-Kumar, K. G. Lynn and D. O. Welch, J. Appl. Phys. 76 (1994), p. 4935 [10] F.A. Selim, D.P. Wells, J.F. Harmon, J. Kwofie, G. Erickson and T. Roney, Nucl. Inst. & Meth. A 495 (2002), p. 154