Investigation of Nuclear Acoustic Resonance for the Nondestructive Determination of Residual Stress
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INVESTIGATION OF NUCLEAR ACOUSTIC RESONANCE FOR THE NONDESTRUCTIVE DETERMINATION OF RESIDUAL STRESS G. A. Matzkanin Southwest Research Institute San Antonio, Texas and R. G. Leisure and D. K. Hsu Colorado State University Fort Collins, Colorado ABSTRACT Nuclear acoustic resonance has been studied in cylindrical specimens of polycrystalline aluminum deformed in compression and tension. The acoustic absorption lineshape is found' to be asymmetric and dependent on the amount of deformation. Analysis of the signals in terms of an admixture of the real and imaginary parts of the nuclear susceptibility has been performed. The linewidth measured from the experimental signals varies with deformation exhibiting a minimum between twelve and fifteen percent strain. INTRODUCTION attenuation as the applied magnetic field was slowly swept through the resonance condition were measured As is well known, residual stresses and inter by means of a second transducer bonded to the other nal strains play important roles in determining the end of the specimen. To enhance the signal-to-noise service behavior of many materials, components and ratio, synchronous detection and signal averaging structures. As such, the detection and quantita were used. Experimental conditions are d'tailed in tive characterization of residual stresses and Table I. internal strains are crucial factors in the ratio nal assessment of the serviceability of structural RESULTS materials. The present program was initiated in response to the important need for a practical Typical NAR signals obtained from aluminum method of making residual stress measurements in specimens subjected to various amounts of compres nonferromagnetic materials. One of the methods sive deformation are shown in Fig. 4. The indicated under investigation is nuclear acoustic resonance strain values were determined from the changes in (NAR) in which changes in acoustic absorption due specimen length after deformation. The displayed to nuclear magnetic resonance (NMR) are measured. NAR signals are the first derivatives of the acous The advantage of this approach for NDE over the tic absorption. The amplitudes of these signals conventional inductive NMR method is that the cannot be directly compared since this parameter is acoustic approach is sensitive to the interior of affected by the bonding characteristics of the bulk metal specimens whereas the inductive approach transducers among other factors. However, all of is limited to the electromagnetic skin depth which the detected NAR signals were found to be asymmetric is typically only 10 to 100 microns at the radio in agreement with previously reported results for frequencies usually employed. single crystai aluminum. (2) This asymmetry has been shown both experimentally(3) and theoretically(4) to The effect of residual stress and internal be associated with an admixture of x' and x" (the strain on the nuclear resonance signal (either real and imaginary parts,. respectively, of the com inductive or acoustic) is associated with the plex nuclear susceptibility) according to the fol interaction between the nuclear quadrupole moment lowing expression for the resonant acoustic absorp and the electric field gradient (EFG) determined tion by other ions and electrons. For cubic symmetry the EFG normally vanishes, however, lattice distor (1) tion associated with stress-strain. fields can pro duce EFG's in nominally cubic materials {Figs. 1 where B is a factor depending on the acoustic veloc and 2). The resulting quadrupole interaction per ity and electrical conductivity. turbs the magnetic energy levels thus modifying the detected nuclear resonance signal. The relative amplitudes of the peaks of the NAR first derivatives are a measure of the asyrnrnet~y of EXPERIMENTAL the acoustic absorption lineshape and can be used to determine the percentages of x' and x" based on the The NAR approach, illustrated in Fig. 3, assumption of a Gaussian lineshape. The amounts of involves coupling ultrasonically to a specimen x" determined in this way are listed in the second \~hich is subjected to a static magnetic field. In column of Table II, while similar reisults obtained the experiments reported here, a continuous wave by analyzing the experimental acoustic absorption (cw) transmission method was used. (1) Acoustic second derivatives ar~ listed in the third column. standing waves of approximately 60 MHz were estab No consistent variation of x" with strain was found lished by means of a transducer bonded to one end and except for the undeforrned specimen, the x" com of a cylindrical specimen. Changes in acoustic ponents computed from the two derivatives are quite 92 different. The implication of these results is that ACKNOWLEDGEMENTS the assumption of a Gaussian lineshape for acoustic absorption from deformed aluminum may not be valid. The assistance of Don Allred and Gary Ashton at Indeed, comparisons between the experimental signals Colorado State University in performing the experi and Gaussian lineshapes (shown by open circles in mental measurements is gratefully acknowledged. The Fig. 4} show that the deviation from a Gaussian research was supported by the Air Force Office of lineshape increases with increasing deformation. Scientific Research (AFSC} under Contract #F44G20- 76-C-0114. In addition to determining x", theNAR signals from deformed aluminum were analyzed to obtain REFERENCES information on the acoustic absorption linewidth. The linewidths determined by measuring the peak-to 1. Leisure, R. G. and Btflef, D. I., "CI'I Microwave peak separations of the experimentally recorded Spectrometer for Ultrasonic Paramagnetic signals are tabulated in columns 2 and 3 of Table Resonance," Rev. Sci. Instrum. 12_, 199 (1968}. III for the first and second derivatives, respec 2. Buttet, J., Gregory, E. H., and Bailey, D. K., tively. Determined in this way, the experimental "Nuclear Acoustic Resonance in Aluminum Via linewidth initially decreases with plastic deforma Coupling to the Magnetic Dipole Moment," Phys. tion and then increases for strains greater than Rev. Lett.~. 1030 (1969}. approximately 15 percent. Although a change in resonance linewidth is expected for quadrupole per 3. Leisure, R. G., Hsu, D. K., and Seiber, B. A., turbed energy levels, the results presented here "Nuclear-Acoustic-Resonance Absorption and are difficult to interpret analytically since the Dispersion in Aluminum," Phys. Rev. Lett. 30, variation of the admixture of x' and x" with strain 1326 (1973}. also affects the linewidth. Thus for comparison with theory, the linewidth in terms of the x" com 4. Fedders, P. A., "Acoustic Magnetic Resonance in ponent must be extracted from the experimental NAR Metals via the Alpher-Rubin Mechanism," Phys. signals. Rev. BB 5156 (1973}. Interesting results have been obtained indi Table I. cating that the acoustic absorption lineshape for Experimental Conditions the deformed aluminum specimens is dependent on the frequency used to modulate the static magnetic field SPECIMENS: 99.999-% PURE POLYCRYSTALLINE for synchronous detection. As shown in Fig. 5, for ALUMINUM a lightly deformed specimen (5% tensile strain}, the NAR lineshape is essentially independent of modula CYLINDERS: 1/2-IN. LONG BY 1/2-IN. DIAMETER tion frequency (results were obtained in the 25-100 FREQUENCY: 60 MHz Hz range} whereas for a highly deformed specimen (25% tensile strain} the lineshape changes substan MAGNETIC FIELD: 54 kG tially with modulation frequency·. In fact, as the modulation frequency is decreased from 100 Hz to TEMPERATURE: 4.2°K & 65•K 35 Hz, the lineshape for the 25% tensile strain specimen changes from approximately 50% or 60% x" ACOUSTIC MODE: SHEAR to approximately 20% x". Since the modulation fre Table II. quency determines the depth of penetration of the The Imaginary Component, x", of the Complex Nuclear magnetic field into the specimen, a possible inter Susceptibility for Plastically Deformed pretation of these results is that the change in Aluminum Based on Measurements of lineshape observed for the 25% deformed specimen Experimental Curves and Gaussian may be associated with inhomogeneous deformation Lineshape Assumption existing in this specimen. Strain x"!%1 CONCLUSIONS (%) First Derivative Second Derivative As a consequence of the results obtained to 0 84 89 date, the following conclusions are reached: 4.8 49 88 9.8 82 63 (1} Nuclear acous~ic resonance signals observed in polycrystalline aluminum 14.9 53 71 are quantitavely similar to NAR signals 19.8 48 77 in single crystal aluminum. 25.0 66 51 (2} The NAR signals are asymmetric due to Table III. an admixture of X' and X"· The Acoustic Absorption Linewidth for Plastically Deformed Aluminum Measured from Experimental Curves (3} The"NAR linewidth and admixture of x' Strain Linewidth (Gauss) and x" vary with plastic deformation. (%) First Derivative Second Derivative (4} The NAR lineshape for plastically deformed aluminum does not fit a 0 9.3 10.5 Gaussian function. 4.8 8.0 11.3 9.8 7.3 9.7 (5} The effect of modulation frequency 14.9 7.2 8.5 on lineshape depends on the amount of plastic deformation. 19.8 8.9 9.3 ,, 25.0 8.0 10.5 I STRAIN I ELECTRIC FIELD lOTHER IONS;· ~ GRADIENT ELECTRONS GRADIENT ELASTIC TENSOR EFG IN CUBIC CRYSTAlS CAUSED BY: lr 1. Stress-Strain Fields Produced by External Loads or Lattice Defects I ELECTRIC FIELD GRADIENT l 2. Charge Difference Between Point Defects and Host Ions I' 3. Redistribution of Conduction Electrons Around a Defect in the Case of Metals QUADRUPOLE