A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A linear model for attenuation of waves is presented, with Q, or the portion of energy lost during each cycle or wavelength, exactly independent of frequency. The wave propagation is completely specified by two parameters, e.g., Q and c0, a phase velocity at an arbitrary reference frequency ω0. A simple exact derivation leads to an expression for the phase velocity c as a function of frequency: c/c0 = (ω/ω0)γ, where γ = (1/π) tan−1 (1/Q). Scaling relationships for pulse propagation are derived and it is shown that for a material with a given value of Q, the risetime or the width of the pulse is exactly proportional to travel time. The travel time for a pulse resulting from a delta function source at x = 0 is proportional to xβ, where β = 1/(1 - γ). On the basis of this relation it is suggested that the velocity dispersion associated with anelasticity may be less ambiguously observed in the time domain than in the frequency domain. A steepest descent approximation derived by Strick gives a good time domain representation for the impulse response. The scaling relations are applied to field observations from the Pierre shale formation in Colorado, published by Ricker, who interpreted his data in terms of a Voigt solid with Q inversely proportional to frequency, and McDonal et al., who interpreted their data in terms of nonlinear friction. The constant Q theory fits both sets of data.

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Constant Q-wave propagation and attenuation

The purpose of this review is to discuss the development and the state of the art in dynamic testing techniques and dynamic mechanical behaviour of rock materials. The review begins by briefly introducing the history of rock dynamics and explaining the significance of studying these issues. Loading techniques commonly used for both intermediate and high strain rate tests and measurement techniques for dynamic stress and deformation are critically assessed in Sects. 2 and 3. In Sect. 4, methods of dynamic testing and estimation to obtain stress–strain curves at high strain rate are summarized, followed by an in-depth description of various dynamic mechanical properties (e.g. uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness) and corresponding fracture behaviour. Some influencing rock structural features (i.e. microstructure, size and shape) and testing conditions (i.e. confining pressure, temperature and water saturation) are considered, ending with some popular semi-empirical rate-dependent equations for the enhancement of dynamic mechanical properties. Section 5 discusses physical mechanisms of strain rate effects. Section 6 describes phenomenological and mechanically based rate-dependent constitutive models established from the knowledge of the stress–strain behaviour and physical mechanisms. Section 7 presents dynamic fracture criteria for quasi-brittle materials. Finally, a brief summary and some aspects of prospective research are presented.

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A Review of Dynamic Experimental Techniques and Mechanical Behaviour of Rock Materials

Review of experimental techniques for high rate deformation and shock studies

Enhancement of barrier and corrosion protection performance of an epoxy coating through wet transfer of amino functionalized graphene oxide

Stress-strain behavior of sand at high strain rates

Response of granular media to rapid penetration

Glass bars and plates were subjected to impact loading. Failure waves were observed to propagate behind the compression waves. Material traversed by the failure wave suffers total loss of tensile strength and substantial drop in shear strength. Failure wave propagation velocities exceed the maximum crack propagation speed, but are not constant. In bars, failure wave speed range from 2.3 to 5.2 mm/μs, increasing with increasing impact velocity; in plates, the wave speed is about 2 mm/μs. The failure is ‘‘explosive’’ in nature, leading to radial expansion in bars and an increase in mean stress in plates.

Impact‐induced failure waves in glass bars and plates

Failure waves have been recently observed in glass plates and rods struck by high-speed projectiles. These waves propagate into material that has been prestressed by a compressive shock. The wave propagation speed exceeds the maximum crack speed and is not constant. Behind the failure wave there is a total loss of tensile strength and a substantial drop in shear strength. The failure is explosive, leading to radial expansion in unconfined targets and presurization in confined targets.

Failure Waves in Glass

The spall strength of soda lime glass was measured with Manganin stress gauges, in planar impact experiments, below and above the Hugoniot elastic limit of the glass. It was found that while in its elastic range the glass can withstand very large tensions (over 30 kbars), its spall strength reduced to zero when shocked just above the HEL. This confirms the assumption that the elastic limit marks the onset of fracture in glass upon shock loading.

Stephan Bless

Papers

Stress-strain behavior of sand at high strain rates

Response of granular media to rapid penetration

Impact‐induced failure waves in glass bars and plates

Failure Waves in Glass

Spall strength of shock‐loaded glass