Quantitative Analysis of Fatigue Microstructures in Copper Using Transmission Electron Microscopy for Calculation of a Material Nonlinearity Parameter and Comparison with Ultrasonic Testing

NASA Langley Research Center researchers have shown that the use of nonlinear ultrasonics to extract the material nonlinearity parameter, Beta (), is a sensitive method for determining the fatigue state of metallic materials. Beta calculations of the fatigue state of cyclically deformed, wavy-slip metals have demonstrated good to excellent agreement with experimentally obtained  values. Data for input into the  theory has, however, been compiled from various sources, as well as for different metals, due to limited data available to theorists. There has, thus, not been a comprehensive quantitative examination of model  equations using transmission electron microscopy (TEM) to measure material parameters and calculate , for comparison with  values determined using ultrasonic testing, on the same set of samples. In this thesis, fatigue data, ultrasonic testing results, optical microscopy, and dislocations measurements from TEM observations were compared, for a single set of un-fatigued and fatigued copper single-crystals, to conduct an analysis of the  theory. TEM studies of dislocations parameters, upon which the model equations are based, were measured for fatigued copper single-crystals exhibiting a variety of microstructures. The variety of microstructures included vein structure, persistent slip band (PSB) structure and cellular structure. Dislocation parameters such as the volume fractions of veins and PSBs, loop lengths, dipole heights and density of dislocations were measured from TEM images. These data and other relevant material parameters were then employed to calculate . Ultrasonic testing was performed, prior to TEM work, on the same samples, to obtain experimental  values. Ultrasonic testing  values were subsequently compared with theoretical calculations, based upon Hikata, Chick and Elbaum and Cantrell theories, to make comments on the applicability of model equations. TEM observations and  calculations suggest that harmonic generation contributing to  for fatigued copper single-crystals is predominantly from primary and secondary screw iii monopoles in the channel regions. Primary dipole heights in fatigued copper single-crystals were observed by TEM to be less than 3nm. According to  calculations from the theory, the primary edge dipole contribution,  dp , from the veins and PSB walls, is less than 10f  mp due to dipoles. The  dp term is, thus, negligible in  calculations for fatigued single-crystal copper. Primary edge dipole loop lengths were short, approximately 10nm, and primary screw monopole loop lengths were one magnitude greater, approximately 100nm. Thus, the contribution of primary edge dipoles, from within the veins and walls, to  mp was less than 10f the contribution to  mp from primary and secondary screw monopoles, in the channel regions and cell interiors, and also negligible. The current work also suggests that  calculations employing loop lengths in excess of 20nm and primary edge dipole densities between 10 15-16 m -2 in fatigued copper would be overestimated contributions to harmonic generation. Model equations by Hikata et al. and Cantrell, which are a function of loop length to the fourth power and dislocation densities to the first power, explain the non-monotonic, increasing then decreasing  trend observed experimentally, resulting from the trade-off between decreasing loop lengths and increasing densities in the channel regions, with increasing applied plastic strain. Experimental  values, which increase as the square root of cumulative plastic strain in fatigued copper single-crystals along [5-41] and [-1-11] directions, provide evidence contrary to Kim et al.'s predicted increase in  as the square of cumulative plastic strain. It has therefore been determined that there is good quantitative agreement between calculated  values, using Hikata et al. and Cantrell's model equations, with experimental  values, obtained using ultrasonic testing, according to Dace's method.

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