D. N. Beshers

Pressure derivatives of the elastic constants of α-iron to 10 kbs

Abstract The pressure derivatives of the elastic constants of α -iron have been determined over the pressure range from 0 to 10kb, by a differential ultrasonic pulse-echo method involving pulse superposition. Measurements were made on single-crystal specimens of orientations (100), (110), and (111), thus providing several cross checks. The values found for the elastic constants and their pressure derivatives at 300°K are: B S =1664 kb C=1166kb C′=477kb d B S d P =5⋯29 d C d P =2⋯59 d C′ d P =1⋯07 using the notation B s = (C 11 +2C 12 ) 3 , C = C 44 , C′= (C 11 −C 12 ) 2 . On the basis of a continuum model, a value for the Gruneisen constant has been calculated from the pressure derivatives. This value agrees closely with that obtained from thermal expansion data. Combining the present result with data on temperature dependence, the elastic constants of α-iron are found to be explicit functions of temperature. The present value for the pressure derivative of the bulk modulus, which is in reasonable agreement with previous ultrasonic measurements, is nearly 40 per cent larger than the value calculated from Bridgmans static measurements.

Elastic Stiffness Coefficients of Iron from 77° to 673°K

The elastic stiffness coefficients of single‐crystal iron have been measured at room (300°K) and liquid‐nitrogen (77°K) temperatures using the ultrasonic pulse‐echo technique. The three coefficients were determined from a total of seven independent modes. The values at 300°K are C11=2.28±0.02, C12=1.32 ±0.04, and C44=1.165±0.01, in units of 1012 dyn/cm2; the corresponding values at 77°K are 2.36±0.02, 1.34±0.04, and 1.19±0.01.The coefficients C11, (C11+C12+2C44)/2, and (C11+2C12+4C44)/3 of iron have been measured from 77° to about 673°K. C11 and (C11+2C12+4C44)/3, as well as the polycrystalline stiffness λ+2μ, depart from a linear dependence on temperature above about 300°C. It was not possible to say whether the same effect occurred in (C11+C12+2C44)/2 because of significant scatter in the data.The Debye temperature Θ0 was found from the stiffnesses extrapolated to 0°K, to be 471.5°K.

Magnetomechanical damping in iron

We have carried out a complete, detailed study of magnetomechanical damping on a set of annealed and deformed iron specimens. The results for macroeddy‐current and microeddy‐current damping are consistent with previous data on iron. The macroeddy peak gives a good indicator of achieving saturation. The microeddy damping offers a usable method for estimating domain size. The slope of damping versus amplitude in the hysteretic Rayleigh region is inversely proportional to the square of a measure of internal stress, as predicted by Smith and Birchak (SB). At higher amplitudes, in annealed and slightly deformed specimens, the damping increases more rapidly than in the Rayleigh region, a phenomenon not previously recognized, and contrary to existing models. The very long straight line in the Rayleigh region, implying a lack of any linear scale for the hysteresis, suggests that there is a fractal nature to the process. This suggestion is consistent with the SB theory. A possible model for the elementary hysteret...

Effects of a stress field on boron ion implantation damage in silicon

The effect of stress fields on the nucleation of defects from boron ion implantation into silicon has been examined. Two different processing techniques were used to create the stress field: formation of an oxide‐filled trench and formation of windows etched into nitride films. Interstitial dislocation loops created by the boron implantation were found to be preferentially oriented with respect to the stress field. A correlation between the force resulting from the stress field and the orientation of the dislocation loops was found.

Internal friction during ultrasonic deformation of alpha‐brass

A high‐intensity ultrasonic apparatus was utilized to study the variation with strain amplitude e of internal friction Q−1 and modulus defect ΔS/S in α‐brass, as influenced by composition, grain size, and prestress. Q−1(e) manifests three regions: I, where Q−1 is independent of e; II, where Q−1 rises and then levels off; III, where Q−1 rises rapidly. Regions I and II are superficially similar to the Granato‐Lucke regions, but different mechanisms seem to be acting; region II has not been recognized before in brass. The strain at the onset of region III, eu, is found to be proportional to the flow stress and to increase with decreasing grain size. Above eu, ΔS/S varies much faster than Q−1, both quantities increasing with increasing grain size, increasing with a small prestress, but decreasing when the prestress exceeds the yield stress. The slope m′≡d logQ−1P/d loge decreases with increasing e, reaching values in the range 0–1 for e≳2eu. Between eu and 2eu, m′ is sensitive to structure, increasing with zi...

Internal friction in rocks

This paper intends to show that the low‐amplitude effects, in particular the attenuation proportional to the frequency from very low frequencies up to the kilohertz range, are connected with the motion of dislocations in cracks. The measurements have been made of the resonant frequencies and the internal friction of spherical rock speciments, including Solenhofen limestone, Indiana limestone, Westerley Granite, Friedensville sphalerite, galena, magnetite, and olivine of small grain sizes. The different types of stresses are thus easily determined through the various modes of motion. On the basis of dislocation motion in cracks, it is shown that the ratio of the radial Q to the torsional Q is about 0.8 and is nearly independent of the crystal structure. This result is in agreement with the measurements, which vary from about 0.6 to 0.9. From longitudinal and torsional measurements of cylinders, the torsional Q’s are nearly twice those for the longitudinal mode. The model used also agrees with the variation...

Damping Peaks in Deformed Nickel

The internal‐friction spectrum of zone‐refined nickel [R(273°K)/R(4.2°K)=600] has been examined at 30 kc/sec, in the temperature range 77°‐350°K. Plastic deformation produces two prominent relaxation peaks, each the sum of several simple peaks. At 30 kc/sec, one peak, which occurs at 138°±7°K, has been identified as the Niblett and Wilks peak, and the other, which has its maximum at 248°±40°K, has been shown to be the Bordoni peak. Both peaks have been studied as a function of cold work, grain size, state of annealing, and strain amplitude.One major result of these studies is a demonstration that the Bordoni peak is only large at low‐to‐moderate flow stresses and vanishes at high flow stress (greater than 50 000 psi) with the Niblett and Wilks peak being the predominant feature of the damping spectrum at the higher‐flow stresses (greater than 30 000 psi). Moreover, the present results in Ni show such similarity to results obtained on deformation‐induced peaks in bcc metals that, if the definition of the B...

Apparatus for examining structures using stimulated acoustic emission

Abstract : A vibrator is held in contact with a structure undergoing testing, such as an airplane wing. Vibrations are distributed through the structure and structural defects such as fissures will respond by emitting an acoustical signal. The acoustic signal may occur over a wide frequency range. A pick-up having a crystal transducer also makes contact with the surface of the structure to detect acoustic emissions. The crystal has a wide band response capable of detecting structural defect acoustic emissions. The pick-up has electrical leads connected thereto so that the acoustic emissions are converted to electrical signals which may be recorded or viewed on an oscilloscope. Movement of the pick-up across the surface of the structure will help determine the location of the structural defect. (Author)

Damping Spectrum of Iron

The internal friction of iron was measured from 0° to 400°C at 1 cps. The results were analyzed in terms of the magnetomechanical contributions to the damping, discernible peaks, and the remaining background. Three new features of the damping spectrum are reported: a magnetomechanical rise above 200°C which corresponds to the ΔE effect; a sharp, but unstable, rise in the background damping above 150°C with an apparent activation energy of approximately 16 kcal/mole; and a dislocation dragging peak in the vicinity of 125°C. The variation of each feature with nitrogen concentration, amount of cold work, and some other variables is reported. Changes in the magnetomechanical and background damping at high nitrogen concentrations are associated with a change in the mode of precipitation. Maringers magnetomechanical peak is confirmed.

Internal Friction in Westerley Granite: Relation to Dislocation Theory

Compressional wave‐velocity and attenuation measurements have been made for fine‐grained Westerley granite over a frequency range from 25 kHz to 2.5 MHz. The internal friction Q−1 varies by a factor of 10 over this frequency range, increasing from 0.80×10−2 around 25 kHz to 6.5×10−2 at 2.5 MHz. The measurements are consistent with the low‐ and high‐frequency components associated with kink motion of dislocations. The constants evaluated from the measurements are consistent with values obtained for polycrystalline metals.