Transient Stress Waves Research Articles

Detecting Delaminations in Concrete Slabs With and Without Overlays Using the Impact-Echo Method

The paper demonstrates the feasibility of detecting delaminations in reinforced concrete slabs using the impact-echo method, a nondestructive testing technique based on transient stress wave propagation. The results of two laboratory studies are discussed. One study involved detecting artificial delaminations embedded at unknown locations in a reinforced concrete slab. All the artificial delaminations in the slab were located. The second study was aimed at showing the feasibility of detecting delaminations in reinforced concrete slabs with asphalt concrete overlays. Two reinforced concrete slab specimens with corrosion-induced delaminations were tested. Prior to overlaying the slabs with asphalt concrete, the depths of delaminations as determined by impact-echo testing were verified by drilling at selected points. After the asphalt concrete overlays were applied, the slabs were retested. It was found that the impact-echo method could successfully locate the delaminations in the slabs through the asphalt concrete overlays.

Transient stress waves interaction with planar flaws

The NBS Center for Building Technology in the United States is developing sonar impact‐echo techniques for non‐destructive testing, notably to trace flaws in concrete, in which flaws reflect the sound waves generated by an impact on the surface. This paper deals with a fundamental aspect of the concept, namely the propagation of the waves within the mass and their interaction with the flaws. The results have validated the use of finite element analysis for studying transient wave propagation in elastic solids.

A finite element study of the interaction of transient stress waves with planar flaws

This paper presents a finite element study of transient wave propagation in plates containing planar flaws. The effects on displacement waveforms caused by waves diffracted from the sharp edges of a flaw are determined. Displacement fields within a plate containing a flat-bottom hole show the interaction of transient stress waves with a planar flaw. Waveforms obtained from the finite element analysis were compared with experimentally obtained waveforms.

TRANSIENT STRESS WAVES IN AN INFINITE VOIGT-VISCOELASTIC SLAB

The transient stress waves in an infinite viscoelastic slab subjected to plane strain are investigated. The solution based upon displacements which satisfy directly the equations of motion for a Voigt solid and the initial and boundary conditions is given by the method using Stokes theorem for the case of arbitrary shock loads. The shock loads are assumed to be applied on the face or in the interior of the slab. The displacements are represented in terms of Fourier transforms and eigenfunctions. The eigenfunctions are derived from the equations of motion for an elastic solid and satisfy the orthogonality relation induced by the corresponding boundary conditions.

Fundamental considerations in dynamic fracture

Recently posed questions regarding crack propagation under dynamic transient loads in the form of stress waves are reviewed. Particular attention is devoted to limitations in the accuracies of currently employed experimental methods, notably those based on photoelasticity and on the method of caustics. These limitations are discussed in light of highly transient stress wave conditions at the running crack tip and address also the certainty with which crack tip locations and crack tip speeds can be determined. The problem of representing crack speed behavior in terms of a K- ν relation is discussed and the belief that instantaneous crack speed depends on the past history of the crack tip stress field is supported. A rational view is presented as to why the limiting crack speed is less than the theoretically predicted value.

Computations and measurements of transient stress waves and electrical voltages generated by transmitting ultrasonic piezoelectric transducers

the Mason model is used to compute the transient stress generated by a thickness mode piezoelectric transducer excited by a step voltage for various backings or loadings. The predicted stress pulse is experimentally shown to conform with the plane wave component of the radiation field. Verification is effected after visualizing the real radiation field and isolating its plane wave component and after applying surface transduction for detection. From the transmitting transducer a generated voltage is brought to attention. This quantity is closely related to the width of the initial pulse in the received ultrasonic signal display. The theoretical induced voltages are verified experimentally.

Shock deformation of brittle solids

In terms of shock‐compression characteristics, minerals of geophysical interest are placed in a class of materials which, because of some rather unique Hugoniot and shock‐compression properties, are classified as brittle solids. The physical processes responsible for these shock‐wave properties are not yet well established. However, recent experimental observations and theories based on localized, nonhomogeneous shear deformation and a transient nonuniform thermal state appear to provide a reasonable qualitative picture. In the present work, some of the terminal and transient shock‐compression features observed in brittle solids are reviewed with particular emphasis on Hugoniot release‐wave measurements. The possibility of instabilities in the laws governing shear deformation leading to observed heterogeneous deformation is considered, and although an elementary model is treated, the method shows promise of predicting the material and kinematic properties governing occurrence, growth, and frequency of localized deformation features. Transient stress wave calculations in crystalline quartz demonstrate how the kinematic environment governing instability growth is established under shock‐wave compression. In addition, the transient nonuniform thermal state resulting from heterogeneous deformation is shown to provide a possible explanation for the observation of both ‘fluidlike’ and ‘solidlike’ shock release waves depending on the competing properties of thermal diffusion, melting temperature, and degree of thermal localization. The analysis shows a striking difference between those minerals which do, and do not, undergo a shock‐induced phase transition and leads to speculated similarities between the kinetics of shock‐induced phase transformation in brittle solids and the kinetics of thermal detonation in explosives.

Compression wave studies on calcite rock

Dynamic compression wave studies have been conducted on three calcite rocks, Solenhofen limestone, Oakhall limestone, and Vermont marble, in the stress range of 0–5 GPa. Plate impact techniques provided transient stress wave input, and diffuse laser interferometry was used to study the evolution of these pulses through various thicknesses of rock. Both loading response and release wave response were determined from the time‐resolved particle velocity profiles. The calcite I–II and II–III phase transitions dramatically influence wave propagation in this stress region. The I–II transition begins between 0.6 and 1.2 GPa depending on rock type and is found to be consistent with a reversible, displacive polymorphic phase change. A constitutive model based on stress heterogeneity describes most of the features associated with the I–II transition. The calcite II–III transition proceeds above 2.4 GPa, and peak stress values traverse a metastable Hugoniot. This wave feature and others are more characteristic of a slower, reconstructive phase change. We conclude that stress wave features reveal striking differences in the nature of the shock‐induced calcite transitions and that these transitions strongly influence the dynamic constitutive behavior of calcite rock.

Amplitude and frequency response of copper single crystals to one-dimensional transient stress waves

Several annealed copper single crystals of various lengths are loaded dynamically in compression along the crystallographic orientation [100] by means of the split Hopkinson bar. The tests are run at room temperature with a strain rate of approximately 5 × 103 s−1. These dynamic results are used to study the amplitude and frequency response which is then related to the permanent deformation. It is found that the change of the incident stress wave profile is controlled by dissipation and dispersion as well. The nucleation of plastic deformation causes an effective damping of high frequency components in the Fourier components of the incident stress wave σI(t). In difference to previous papers where the amplitude changes of σI(t) are currently investigated, significant attention is paid to the frequency changes of σI(t). This approach extends considerably the knowledge obtainable from the Hopkinson split bar testing, namely the new way of acoustic signal detection in plastically deformed materials seems to be possible. Kupfereinkristalle werden entlang der kristallographischen [100]-Achse mittels der Methode des geteilten Hopkinsonschen Meßstabes dynamisch durckbelastet. Es werden die Amplituden- und Frequenzcharakteristiken der Reaktion dieser Einkristalle auf die Wirkung der eindimensionalen Spannungswelle untersucht. Es zeigt sich, daß die Bildung der plastischen Verformung den Hochfrequenzteil des Fourier-Spektrums der belastenden Spannungswelle merklich beeinflußt. Es wird gezeigt, wie man diese Änderungen für die Beschreibung der dynamischen Werkstofftragfähigkeit und für die Lösung einiger, mit dem Nachweis der Signale der akustischen Emission zusammenhängender Probleme benutzen kann.

Non-linear mechanical response of various metals. I. Dynamic and static response to simple compression, tension and torsion in the as-received and annealed states

The mechanical behaviour of some metals has been investigated experimentally for compressive, tensile and torsional loading cycles of about 120 and 370 mu s duration and for steady-state loading in each of the three modes of deformation. For the dynamic measurements the split Hopkinson bar technique has been used in the three modes between two rods and deformed under the action of a transient stress wave induced by dynamically loading the free end of one of the rods. The experimental results show that for the range of high strain rates investigated, the dynamic stress-strain curve is independent of strain rate in all three modes of deformation. For compression and tension, the dynamic stress levels for a given value of the strain exceed the corresponding effectively static stress levels. In marked contrast, only a comparatively small difference has been detected between the corresponding dynamic and static stress levels in torsion over a range of strain rates from approximately 10-3 to approximately 103 s-1.

Analysis of stress wave in layered structures

Numerical procedures of the method of characteristics is presented to treat the problems of multilayered structures under impulsive load. A set of eight algebraic equations which are readily to be programmed into computer are derived. Stress analysis of a typical dynamic layered structure is given to illustrate the effectiveness of the method. Results of the example problem reveal the fact that pulse shape is very sensitive to transient stress wave propagation.

Skew crack propagation at the diffraction of a transient stress wave

Skew crack propagation at the diffraction of a transient stress wave

Nonlinear transient stress-waves in cylindrical and conical shells

In this paper a nonlinear Timoshenko-type theory of shells is used to analyze the transient axisymmetric stress waves produced in elastic cylindrical and truncated conical shells by an input at one edge. The analysis utilizes the method of characteristics and an asymptotic method. Prior work in this area has been based on linear shell theories and on the exact equations of linear elasticity. The methods suggested here allow one to establish how in the course of time the nonlinearities affect the linear solutions.

Strongly Coupled Stress Waves in Heterogeneous Plates

Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.

Experiments On Transient Waves In A Periodic Stack

Transient waves were initiated by allowing a thick PMMA disk to strike a periodic stack of ceramic layers bonded by thin weak silicone rubber layers. Pressure at interfaces of ceramic and bond layers was measured by carbon gauges along the centerline of the stack. Comparison of experimental histories with those from a 1-D analysis (JASA 94(1), 1993) and a 2-D axisymmetric analysis reveals that the waves propagate two-dimensionally and that flexure of the ceramic layers controls attenuation and shape of compressive wave of first arrival. Visco-elasticity of the bond material sharply reduces tensile stresses. 1 Experiment Transient stress waves were initiated in a weakly coupled periodic stack of square Aluminum Nitride (A1N) ceramic tiles 10.16 cm in size, bonded by a thin weak silicone rubber, ME625, Tham[l]. In one case, tile and bond thicknesses were 1.27 cm and 0.3 mm; and in the second case, 2.54 cm and 0.6 mm. Piezo-resistive carbon gauges 0.08 mm thick of the type C300-50EKRTE from Dynasen Inc. were inserted at the bottom of the first four tiles along the center line of a stack with 10 tiles. Each gauge served as the active resistor of a Wheatstone quarter-bridge circuit. Just before the passage of the wave, the bridge was supplied by a 45 V pulse with a 300 ps duration. The initially balanced bridge was unbalanced by the change in resistance of the gauge from applied pressure. The output voltage was recorded by a 200 Mhz transient recorder. Given the specific gauge calibration and non-linearity of the bridge, pressure histories are valid up to 300 |is from impact. The high electric current in the system produced an inevitable temperature drift of the gauges Transactions on the Built Environment vol 22, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509 544 Structures Under Shock And Impact yielding a fictitious pressure rise of the order of 1.75 MPa per 100 ps. The stack was placed in a metal casing facing the muzzle of a 7 cm diameter compressed air gun at the Ernst Mach Institute, Freiburg, Germany. The stack was struck in its centre by a PMMA disk 5.75 cm in diameter and 2 cm thick, launched by a compressed air accelerator. Velocity of the disk at impact ranged from 14 m/sec to 58 m/sec. Velocities were kept low to avoid damaging the struck ceramic tile. A laser beam in the axis of the launch tube reflecting from the top surface of the first ceramic tile allowed the alignment of stack and disk axes. This procedure resulted in a tilt smaller than 2 mrad. The experimental set up of the stack is shown in Figure 1. A typical digitized output of normal stress o^ in a stack of 10 (10.16 x 10.16 x 1.27 cm) ceramic tiles is shown in Figure 2. The broken horizontal line labeled p^ defines the computed 1-D pressure exerted by the PMMA disk upon the ceramic tile according to

Dispersive Pulse Propagation Parallel to the Interfaces of a Laminated Composite

This paper presents a theoretical analysis of the geometric dispersion of transient stress waves in a linearly elastic laminated composite. The loading is a uniform pressure of step-function time-dependence, applied to a half space. The laminates are perpendicular to the half-space boundary. The mathematical treatment is borrowed from the theory of wave propagation in rods. Fourier transforms are applied to time and the coordinate in the propagation direction. Inversion of the spatial transform by residues yields a formal solution in the form of an infinite series of integrals. Each of these integrals is the contribution to the transient response from a mode of sinusoidal wave propagation. Application of the saddle-point technique for long-time asymptotic approximation indicates that the low-frequency portion of the integral from the first mode gives the dominant contribution, called the head-of-the-pulse approximation. The form of the expression for the head-of-the-pulse approximation leads to the definition of a characteristic dispersion time τ. Since τ is a single quantity which describes the dispersion of the wave, it simplifies parametric studies. A closed-form algebraic expression for τ is presented, which has a simple dependence on the propagation distance and spacing of the laminates. Numerical examples for boron-epoxy and glass-epoxy laminates are given.

Regions of effective application of the methods of three-dimensional and two-dimensional analysis of transient stress waves in shells and plates

Transient stress waves caused by inputs (applied load, constrained displacements or constrained velocities) acting or increasing to their maximum values during a short time interval are investigated in shells of revolution and in plates within the framework of the linear theory of elasticity. The conclusions on space-time regions of valid and effective application of approximate methods of integration of the equations of the theory of elasticity, approximate equations, and methods of integration of approximate equations are presented.

On results of comparison of a finite-difference method and the method of steepest descents for the analysis of transient stress waves in plates

On results of comparison of a finite-difference method and the method of steepest descents for the analysis of transient stress waves in plates

Hardness Plateaus and Twinning in Steel by Explosives with Lined Cavities

This paper describes the changes in hardness and microstructure in annealed low carbon steel by jets squirted from high explosives with steel-lined conical cavities. Hardness measurements and photomicrographs were taken along different radii in a plane normal to the axis of the crater in the steel. Each hardness versus distance curve exhibited a series of plateaus along which the hardness remained constant. The plateaus appear to be related to Neumann bands which are present in the steel. It appears that the impact of an element of the jet on the steel initiates a transient compressional stress wave in the body of the steel which results in the hardness plateaus and the increase in the number of twin directions with hardness.

Conical Surfaces of Fracture Produced by Asymmetrical Impulsive Loading

Conical surfaces of fracture generated in thick-walled cylinders that were asymmetrically and impulsively loaded through the use of internal explosive charges are presented. It is deduced from qualitative considerations that the conical fractures result from the interaction between transient tensile stress waves. The two tensile stress waves that are responsible for the fracture arise from a single compressional stress wave that is reflected from two inclined free surfaces. The angle of fracture associated with these conical surfaces has been used to measure the velocity of propagation of the stress waves in low-carbon steel, brass, copper, lead, and 24ST aluminum alloy.