Warren P. Mason

Fatigue Mechanism in fcc Metals at Ultrasonic Frequencies

A comparison is made of microstructural changes leading to fatigue of copper and alpha‐brass at small strain amplitudes imposed at the normal test frequency of 1700 cpm and at the ultrasonic frequency of 17 000 Hz. A striking difference appears in the distribution of slip. At normal frequency the slip spreads densely over a grain, with no slip‐band cracking (stage S of the S‐N curve). At ultrasonic frequency the slip concentrates in single isolated bands in only occasional grains and reduces these to microcracks before any general spread of slip can be observed. However, as might be expected, the ultrasonic slip did spread in specimens tested at elevated temperatures, which expedited dislocation climb and diffusion processes; then this spreading of slip prevented the slip‐band microcracking at ultrasonic frequency also. The internal friction for the copper was so high that fatigue cracks could not be generated even at room temperature.

Fatigue Mechanism in Iron at Ultrasonic Frequency

A metallographic study compares the fatigue mechanism in low‐carbon iron subjected on the one hand to cycles of strain at an ultrasonic frequency of 17 000 Hz and on the other to 1700 cpm, the relative low order employed in usual engineering tests. It is found that the ultrasonic frequency can produce fatigue cracks at strain amplitudes much smaller than those which up to now have been regarded as safe at low frequency. Further, whereas small amplitudes at low frequency spread abnormal deformation primarily in grain boundaries, those at ultrasonic frequency concentrate it in a relatively few isolated slip bands thereby, it is suggested, heightening their damaging effects.

Equivalent electromechanical representation of trapped energy transducers

Trapped energy resonators and transducers have attained a considerable importance in quartz crystal technology both as single-frequency resonators for the control of crystal oscillators and as drivers for the monolithic crystal filter which appears likely to have a wide use as a channel filter for the separation of voice frequency channels for long-distance carrier systems, microwave radio, and submarine cable systems. It is the purpose of this paper to derive the equations for trapped energy resonators of the thickness-shear and thickness-twist types and to calculate the ratios of capacitances for straight crested waves. It turns out that the ratios are lower (coupling higher) than are observed in practice. It appears that this difference is connected with the finite width of the plate which causes the motion at the edge of the plate to be somewhat smaller than the motion in the center of the plate. While no exact solution has been obtained for the finite plate, an approximation is made which is in good agreement with the experiment. The resonator on a plate is a symmetrical device, whereas a transducer for driving a monolithic filter is a dissymmetrical device since it is driving different impedances on its two boundaries. To represent this dissymmetry requires a distributed network representation which is somewhat similar to that found for a plane longitudinal or shear wave except that the propagation constant for a trapped wave replaces that of the plane wave. The representation also requires a transformer whose transformation ratio is a function of the frequency and two negative element terms. By transformations the negative elements can be made to disappear. These together produce an equivalent circuit whose values depend on the ratio of the electrode length to the crystal thickness.

Internal friction and ultrasonic yield stress of the alloy 90 Ti 6 Al 4 V

Abstract The alloy 90 Ti 6 Al 4 V is used as a mechanical transformer to produce high strains in metal samples. The internal friction, modulus defect and limiting stable strain amplitudes have been studied over wide frequency and temperature ranges. The internal friction Q−1 of annealed samples has the low value of 5 × 10−5 which is independent of the frequency and decreases only slightly at high temperature. The result is consistent with a model in which the energy loss is produced by a non-linear motion across the Peierls kink barrier. The value found for the ratio of the internal friction to the modulus change is 0.03 which is intermediate between two theoretical calculations. This material becomes unstable at strains from 3 to 5 × 10−3. Evidence is presented which shows that this is a material with a Cottrell type pinning with pinning points on the average about 3 Burgers distances apart. Assuming that on the average one kink occurs between each pinning point, the modulus defect is consistent with about 1010 dislocations per cm2. The frequency and temperature variations are consistent with this model.

Damping of Dislocations in Lead Single Crystals

Measurements have been made of the attenuation of longitudinal waves along the 〈110〉 direction in a lead single crystal over a frequency range from 30 to 150 Mc/sec and in a temperature range from 60° to 300°K. The attenuation can be divided into a square‐law frequency term and a term consistent with the theoretical form of dislocation attenuation at high frequencies. By determining the high‐frequency asymptote of the dislocation internal friction and by assuming a reasonable dislocation density, the drag coefficient for the dislocations can be evaluated. The measurements are consistent with the sum of a phonon scattering term and a phonon viscosity term. The square‐law attenuation is about twice as large as the thermoelastic loss and over a temperature range is in agreement with the sum of a thermoelastic loss plus a phonon viscosity loss.

Internal friction, acoustic emission and fatigue in metals for high amplitude ultrasonic frequencies

Abstract High amplitudes (strains up to 3 × 10−3) have been used in studying internal friction, acoustic emission and fatigue in metals. The internal friction in the high amplitude range is due to breakaway of dislocations from pinning points and by the generation of Frank-Read loops which results in plastic strain. There are two plastic regions, one when the added loops are held up by the grain boundaries, and the second when the loops break through the grain boundaries. In the second region, slip bands are produced in the metal. As the amplitude increases slip bands can join up and fatigue in the metal occurs. Ultrasonic frequencies are useful for studying fatigue since a large number of cycles can occur in a reasonable time. Acoustic emission—that is, a noise in the sample associated with the dislocation motion—can be studied by putting transducers on the sample. It is shown that the emission is closely associated with the internal friction since it goes through two regions in the plastic range.

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.

Second‐Order Strain Accumulation at Ultrasonic Frequency

Permanent axial extension is produced by reversed cyclic straining in tension‐compression at ultrasonic frequency and in torsion at mechanically induced (low) frequency. It is shown that in both ranges the axial extension is a quadratic function of the cyclic strain amplitude, which is characteristic of second‐order effects that exist independently of the frequency of the cyclic strain.