Hassel Ledbetter

Elastic‐constant variability in stainless‐steel 304

Variability of elastic constants in stainless‐steel 304 was determined by measuring longitudinal and transverse ultrasonic velocities in 20 samples acquired randomly. Three kinds of variations—sample to sample, directional within a sample, and repeated measurements on a single sample—are reported for four elastic constants: the bulk modulus, Young’s modulus, shear modulus, and Poisson’s ratio. Because of surprisingly small variations, 1% or less, the principal problem became measurement sensitivity and reproducibility. To overcome this problem, a high‐resolution measurement system was devised using general‐purpose equipment augmented with a very simple impedance‐transforming amplifier and an FET transmission gate. With this system the often‐reported troublesome transit‐time correction disappeared. Effects due to frequency and directionality were negligible.

Internal strain (stress) in an SiCAl particle-reinforced composite: an X-ray diffraction study

Abstract SiC and aluminum alloy 6061 posses very different thermal expansion coefficients: 3.3 × 10 −6 K −1 and 22.5 × 10 −6 K −1 respectively. Thus, we expect large internal strains and stresses in these composites because the two constituents form interfacial bonds at high temperatures and are cooled to ambient temperatures. From a simple elastic model, we expect a hydrostatic tensile stress in the aluminum matrix and a hydrostatic compressive stress in the SiC particles. Using conventional back-reflection diffraction geometry with Cu Kα radiation, we studied three surfaces of a plate speciment. For both phases, we determined the unit-cell dimensions for two situations: unmixed and mixed in the final composite. The SiC particles showed a compressive stress and the aluminum matrix a tensile stress, equal to 75% of the yield strength. Measurements and theory show that both stress tensors are approximately hydrostatic.

Contactless Mode-Selective Resonance Ultrasound Spectroscopy: Electromagnetic Acoustic Resonance

A noncontacting resonant-ultrasound-spectroscopy (RUS) method for measuring elastic constants and internal friction of conducting materials is described, and applied to monocrystalline copper. This method is called electromagnetic acoustic resonance (EMAR). Contactless acoustic coupling is achieved by energy transduction between the electromagnetic field and the ultrasonic vibrations. A solenoidal coil and static magnetic field induce Lorentz forces on specimen surfaces without using a coupling agent. By changing the field direction, a particular set of vibration modes can be selectively excited and detected, an advantage in identifying the vibration modes of the observed resonance peaks. Contactless coupling allows the measure of intrinsic internal friction free from energy loss associated with contact coupling. The elastic constants and internal friction measured by EMAR are compared with those by the usual RUS method for a rectangular-parallelepiped copper monocrystal. Both methods yielded the same ela...

Elastic constants of monocrystal iron from 3to500K

Resonant ultrasound spectroscopy was used to measure the monocrystal elastic constants of iron over a temperature range of 3–500K. All the moduli behave normally as a function of temperature and are well described by the semiempirical Einstein-oscillator model. Values at 300K are bulk modulus=166.2±0.9GPa; shear constant C′=(C11−C12)∕2=48.15±0.9GPa; shear constant C44=115.87±0.17GPa. The Poisson ratio (ν100) is 0.3679±0.0005. Representation surfaces of Young’s and torsion moduli are presented. The Debye temperature (θD) is 476.3K as calculated from 3K measured elastic constants. A thermodynamic Gruneisen parameter γth=1.65 is calculated. The temperature dependence of the internal friction associated with C′ is very different from that associated with C44. Possible reasons for this difference are suggested.

Elastic constants of natural quartz

The elastic constants of a natural-quartz sphere using resonance-ultrasound spectroscopy (RUS) are measured. The measurements of the near-traction-free vibrational frequencies of the sphere are matched with the predicted frequencies from the dynamic theory of elasticity, with optimized estimates for the elastic constants driving the differences between these sets of frequencies to a minimal value. The present computational model, although based on earlier approaches, is the first application of RUS to trigonal-symmetry spheres. Quartz shows six independent elastic constants, and our estimates of these constants are close to those computed by other means. Except for C14, after a 1% mass-density correction, natural quartz and cultured quartz show the same elastic constants. Natural quartz shows higher internal frictions.

A general elastic-anisotropy measure

We propose an elastic-anisotropy measure. Zener’s familiar anisotropy index A=2C44∕(C11−C12) applies only to cubic symmetry [Elasticity and Anelasticity of Metals (University of Chicago Press, Chicago, 1948), p. 16]. Its extension to hexagonal symmetry creates ambiguities. Extension to orthorhombic (or lower) symmetries becomes meaningless because C11−C12 loses physical meaning. We define elastic anisotropy as the squared ratio of the maximum/minimum shear-wave velocity. We compute the extrema velocities from the Christoffel equations [M. Musgrave, Crystal Acoustics (Holden-Day, San Francisco, 1970), p. 84]. The measure is unambiguous, applies to all crystal symmetries (cubic-triclinic), and reduces to Zener’s definition in the cubic-symmetry limit. The measure permits comparisons between and among different crystal symmetries, say, in allotropic transformations or in a homologous series. It gives meaning to previously unanswerable questions such as the following: is zinc (hexagonal) more or less anisotro...

Estimation of Debye temperatures by averaging elastic coefficients

Elastic Debye temperatures θ were calculated by averaging elastic stiffness coefficients. For cubic symmetry, eight averaging methods were evaluated with respect to a computationally exact θ. Reusss θ, corresponding to uniform stress, gave better agreement than Voigts θ, corresponding to uniform strain. Hills geometrical θ gave the best agreement.

Orthotropic elastic constants of a boron‐aluminum fiber‐reinforced composite: An acoustic‐resonance‐spectroscopy study

Acoustic‐resonance spectroscopy was used to determine the complete elastic constants of a uniaxial‐fiber‐reinforced metal‐matrix composite: boron‐aluminum. This material exhibits orthotropic macroscopic symmetry and, therefore, nine independent elastic stiffnesses Cij. The off‐diagonal elastic constants (C12,C13,C23), which contain large errors when measured by conventional methods, were especially focused on. Good agreement emerged among present results, a previous pulse‐echo study, and theoretical predictions using a plane‐scattered‐wave ensemble‐average model. Attempts to measure the internal‐friction ‘‘tensor’’ failed.

Stainless‐steel elastic constants at low temperatures

For stainless steels 304, 310, and 316, longitudinal and transverse ultrasonic velocities were measured by a pulse‐echo method between 295 and 4 K. From these velocities were computed five elastic constants: longitudinal modulus, shear modulus, Young’s modulus, bulk modulus, and Poisson’s ratio. All three steels show low‐temperature elastic‐constant anomalies, which arise from magnetic phase transitions.

Monocrystal elastic constants of orthotropic Y1Ba2Cu3O7 : an estimate

For Y{sub 1}Ba{sub 2}Cu{sub 3}O{sub 7}, using only reported monocrystal measurements and some analysis--theory, we estimated the complete nine-component orthotropic-symmetry elastic-stiffness matrix, the Voigt {ital C}{sub {ital ij}} matrix. Comparison with very-high-frequency tetragonal-symmetry phonon-dispersion results shows good agreement (9% on average), except for {ital C}{sub 12}.