Plastic Wave Velocity Research Articles

A theoretical model and verification of soil column deformation under impact load based on the Duncan-Chang model

The dynamic compaction method has been widely adopted in foundation treatment to densify the soil fillers. However, for the complexity of the impact behavior and soil mechanical properties, the theoretical research of dynamic compaction lags behind its practice for complex soil properties and stress paths. This paper presents a theoretical model applied to describe soil column plastic deformation under impact load. The relationship among stress increment, strain increment, and plastic wave velocity was derived from the aspect of propagation characteristics of stress waves in soil first. Combined with the Duncan-Chang Model, a one-dimensional theoretical model was established then. A numerical model was developed further to check the performance of the model. It showed that the deformation at the end of the soil column was mushroom-shaped. Both the axial and lateral deformation increased with the impact velocity. While some particles located at the side of the soil column end may splash under repeated impact. The theoretical deformations of the soil column were consistent with the experimental results both in the direction of axial and lateral.

Investigation of the Propagation of Stress Wave in Nickel-Titanium Shape Memory Alloys

Based on irreversible thermodynamic theory, a new constitutive model incorporating two internal variables was proposed to investigate the phase transformation and plasticity behavior in nickel-titanium (NiTi) shape memory alloys (SMAs), by taking into account four deformation stages, namely austenite elastic phase, phase transition, martensitic elastic phase, and plastic phase. The model using the material point method (MPM) was implemented by the FORTRAN code to investigate the stress wave and its propagation in a NiTi rod. The results showed that its wave propagation exhibited martensitic and austenitic elastic wave, phase transition wave, and plastic wave. However, a double-wave structure including the martensitic and austenitic elastic wave and plastic wave occurred when the martensitic elastic wave reached the phase transformation wave. Thus, the reflection wave at a fixed boundary exhibited a different behavior compared with the elastic one, which was attributed to the phase transition during the process of reflection. It was found that the stress increment was proportional to the velocity of phase transition wave after the stress wave reflection. In addition, the influences of loading direction and strain rate on the wave propagation were examined as well. It was found that the phase transition wave velocity increased as the strain rate increased. The elastic wave velocity of martensite under compressive conditions was larger than that under tensile loading. In contrast, the plastic wave velocity under compression was less than that subjected to the tensile load.

Application of an extended Rusinek–Klepaczko constitutive model to predict the mechanical behavior of 6082-T6 aluminum under Taylor impact test conditions

The application of an extended Rusinek–Klepaczko constitutive equation to predict the mechanical response of 6082-T6 aluminum under the Taylor impact test conditions was presented in this article. The numerical results obtained in the study were verified through a comparison with the experimental data extracted from the Taylor anvil-on-rod impact experiments. It was concluded that the extended Rusinek–Klepaczko constitutive model predicts the behavior of the tested aluminum alloy under applied loading conditions with satisfactory accuracy. Moreover, it was found that the plastic wave phenomenon in this material is very limited and that there was no region of constant plastic wave velocity. Strain rates up to 1.6 × 104 s−1 were recorded during the Taylor impact experiments; therefore, this value may be set as the upper limit of the extended Rusinek–Klepaczko model for the alloy, which was validated with the anvil-on-rod experiment.

Analysis of dynamic mechanical behavior in reverse Taylor anvil-on-rod impact tests

A one-dimensional analytical model has been developed for the reverse Taylor anvil-on-rod impact experiment to provide a method of extracting quantitative information from transient deformation states obtained from high-speed camera data. An indication of the plastic wave velocity and dynamic flow stress at varying locations and time are presented for two Cu OFE specimens impacted at 83 ± 1 and 205 ± 3 m / s . The results provide supporting evidence of previously reported “non-linear” and “quasi-steady” plastic wave propagation response, as well as a region of perfectly plastic behavior, which is independent of strain rate in the higher impact velocity experiment. Additionally, the results show good agreement with the average value of dynamic yield stress calculated using Wilkins’ analysis, based on a perfectly plastic material response. Furthermore, this work demonstrates the importance of careful design of Taylor impact experiments for minimizing measurement error and capitalizing on perfectly plastic response, for investigating the dynamic mechanical behavior of materials.

Influence of strain rate on the stress-strain curve in the range of Lüders strain

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The Crack-Arrest Properties of 9%Ni Steel and its Weldment (1st Report)

In the previous papers, the authors proposed a realistic crack arrest concept to assess the structural integrity of LNG storage tank and the surface-notched double tension test to evaluate the crack arrest properties of 9% Ni steels and their weldments. This paper deals with dynamic analysis of the run/arrest events confirmed in the surface-notched double tension tests conducted on 9% Ni steels by three-dimensional linear elastic finite element method.Prior to the analysis, dynamic deformation behaviors of the specimen and crack velocities were measured under the potentially extensive propagation and arrest of brittle crack during testing. These experiments verified that a brittle crack propagated through the specimen and/ or was arrested at the notch tip under the fixed grip conditions. These experimental data were used as input data in the analysis by general purpose program ADINA. Crack propagation was simulated in such manners that the nodal points on crack propagation line were constrained by truss elements which were eliminated at the time interval corresponding to crack velocity. Excellent agreement was obtained between experimental and FEM results as to the dynamic deformation behavior of specimen. Variation of dynamic stress intensity factor with crack propagation was obtained by energy balance theory.Dynamic analysis shows that KD decreases as the notch depth becomes shallow and that KD indicates minimum value at the notch end. In linear elastic fracture mechanics, the arrest of propagating crack is to occur when dynamic stress intensity factor KD of the crack becomes lower than crack arrest toughness Ka of the material. Present results of experiments and analyses do not necessarily support the Ka concept stated above because it happened that KD of the propagationg crack showed lower value than that of the arrested crack.Crack arrest at the notch end occurs if sufficient plastic deformation is allowed there when triaxiality at the crack tip is low and crack velocity is slower than plastic wave velocity. Since the surface defects existed in the welded structure are generally small, there hardly exists the possibility of crack propagation failure of 9% Ni steel and its weldment in LNG storage tank.

Propagation of a Plastic Wave in Snow

AbstractWhen snow is pushed very fast by a moving body a plastic wave is generated at the head of the body. If the velocity of the moving body becomes close to that of the plastic wave, the snow may exert a great resistive force against the body as predicted by Yosida. It is, therefore, very important to study the dynamic behaviour of snow at a high rate of deformation, such as takes place when a snow plough is used on the highway, a train runs on a railroad covered with snow, or an avalanche occurs. Hence, this study is concerned with the safety and maintenance of winter traffic and transportation, and also with the generation and propagation of an avalanche. In order to clarify the detailed processes of the deformation of snow at high rates, laboratory experiments were made by compressing snow at high speed. The propagation of a plastic wave through snow was observed by using a high-speed camera and a pressure-detecting device. Analyses of the data obtained gave the velocity of the plastic wave for various kinds of snow whose density ranged from 0.17 to 0.46 Mg m-3and free-water content from o to 17%, whereby studies were made into the dependences on the density and free-water content of the velocity of the plastic wave. When the impact velocity was 4.3 ± 0.2 m s-1, the wave velocity ranged from 5 m s-1for a new snow to 12 m s-1for a fine-grained, well-settled snow. The plastic-wave velocity in wet snow was, in general, smaller than that in dry snow of the same density. Changes in density and structure of snow associated with the passage of a plastic wave were studied and discussed. The pressure at the wave front was measured; values of 0.1-0.3 bar were obtained, these are of the same order as the value estimated from theoretical formulae. The plastic-wave velocity was also observed for a confined snow, which showed a larger velocity and plastic strain than an unconfined snow.

Propagation of a Plastic Wave in Snow

AbstractWhen snow is pushed very fast by a moving body a plastic wave is generated at the head of the body. If the velocity of the moving body becomes close to that of the plastic wave, the snow may exert a great resistive force against the body as predicted by Yosida. It is, therefore, very important to study the dynamic behaviour of snow at a high rate of deformation, such as takes place when a snow plough is used on the highway, a train runs on a railroad covered with snow, or an avalanche occurs. Hence, this study is concerned with the safety and maintenance of winter traffic and transportation, and also with the generation and propagation of an avalanche. In order to clarify the detailed processes of the deformation of snow at high rates, laboratory experiments were made by compressing snow at high speed. The propagation of a plastic wave through snow was observed by using a high-speed camera and a pressure-detecting device. Analyses of the data obtained gave the velocity of the plastic wave for various kinds of snow whose density ranged from 0.17 to 0.46 Mg m-3 and free-water content from o to 17%, whereby studies were made into the dependences on the density and free-water content of the velocity of the plastic wave. When the impact velocity was 4.3 ± 0.2 m s-1, the wave velocity ranged from 5 m s-1 for a new snow to 12 m s-1 for a fine-grained, well-settled snow. The plastic-wave velocity in wet snow was, in general, smaller than that in dry snow of the same density. Changes in density and structure of snow associated with the passage of a plastic wave were studied and discussed. The pressure at the wave front was measured; values of 0.1-0.3 bar were obtained, these are of the same order as the value estimated from theoretical formulae. The plastic-wave velocity was also observed for a confined snow, which showed a larger velocity and plastic strain than an unconfined snow.

Wave velocities in shock-compressed cubic and hexagonal single crystals above the elastic limit

When solids are subjected to high-pressure shock-wave loading, multiple stress waves propagate with velocities dependent upon the elastic and inelastic compressibilities of the solid. The present paper shows that the inelastic or plastic waves in cubic and hexagonal single crystals do not necessarily propagate with the bulk sound speed as they do in isotropic elastic-plastic solids. This result is a consequence of anisotropy in the plastic deformation which depends on the slip plane orientation in the crystal and has important consequences with regard to the determination of compressibilities from shock-wave data. In particular, for wave propagation in the <110> directions of cubic crystals the departure from the bulk velocity can be significant (5–25 per cent). For wave propagation normal to the c-axis in hexagonal crystals, the plastic wave velocity also differs from the bulk sound speed (10–25 per cent). Plastic wave velocities are tabulated for a number of cubic crystals on the basis of the various slip systems common to these materials. The calculated velocities are then compared with experimental data on shock-loaded single-crystal aluminum and sodium chloride.

Experimental Determination of Ultrasonic Wave Velocities in Plastics, Elastomers, and Syntactic Foam as a Function of Temperature

The sound velocity of 16 plastics, two low-sound-velocity elastomers, and three types of syntactic foam have been measured at a frequency of 500 kHz in the temperature range 0°–30°C. Sound velocity values in the range 872–2836 m/sec and thermal coefficient of sound velocity in the range −0.93 to −9.55 m/sec°C are reported.

Propagation of one-dimensional unloading waves in materials exhibiting yielding delay phenomena

The nature of possible unloading waves in materials exhibiting yielding delay phenom ena has been discussed in this paper. The differential equation governing the propagation of the waves, has been solved by this method of characteristics. In this case also as in materials not exhibiting yielding delay phenomena, the unloading wave propagates with the velocity of elastic waves, if it is a wave of discontinuity, and if the load is suddenly increased the unloading wave travels with plastic wave velocity.

Experimental determination of ultrasonic wave velocities in plastics as functions of temperature. IV. Shear velocities in common plastics

AbstractThe temperature dependence of acoustic shear velocities are reported for Poly‐Penco nylon, type G Plexiglass [poly(methyl methacrylate)], TFE Teflon (tetrafluoroethylene), low‐ and high‐density polyethylene, Lexan (polycarbonate), and Delrin Acetal (nylon). Most of the data were obtained at a frequency of 1 Mc./sec. over the temperature range of 25–100°C. In addition, previously unreported longitudinal velocities to ∼125°C. are reported for Lexan and Delrin Acetal.

Experimental determination of ultrasonic wave velocities in plastics as functions of temperature. I. Common plastics and selected nose‐cone materials

AbstractAn experimental study was conducted to determine previously unavailable data showing the relationship between temperature and the velocity of longitudinal ultrasonic waves through several plastics. The ultrasonic frequencies used were between 1 and 10 Mc./sec., and the temperature range covered was between room temperature and 100°C. Velocity–temperature curves were determined for nylon, a high‐ and a low‐density polyethylene, Plexiglas, Teflon, and for several reentry vehicle nose‐cone materials, including chopped nylon phenolic, tape‐wound nylon phenolic, Castable 124, Avcoat I, and Avcoat 19. Less complete data were obtained for Avco phenolic fiber glass, General Electric phenolic fiber glass, and oblique tape‐wound refrasil. These layered materials are difficult to measure, and the velocity of acoustic waves is very dependent on the direction of propagation with respect to the laminations. For most of the materials studied the velocity was found to decrease more or less linearly with increasing temperature. Typically, the velocities at 100°C. were 9–31% less than at room temperature.

Experimental determination of ultrasonic wave velocities in plastics as functions of temperature. II. Effect of lamination angle for layered materials

AbstractUltrasonic longitudinal wave velocities in layered materials were measured as a function of the lamination angle at several temperatures. It was found that the longitudinal wave velocity versus lamination angle curve maintains the same shape (for a given material) for temperatures between 25 and 125°C. Furthermore, it was found that the wave velocity versus lamination angle curve can be predicted to within 2% by a theoretical equation involving only the lamination angle, &amp; thetas; (taken as the angle between the grain of the sample and the direction of sound propagation); c (0°), the measured wave velocity at an angle of 0°; and c (90°) the measured wave velocity at an angle of 90°. Finally, it was found that the longitudinal wave velocity of certain materials varies as much as 25% between lamination angles of 0° and 90°, while other materials show less variation, and some none at all.

Experimental determination of ultrasonic wave velocities in plastics as functions of temperature. III. Rigid epoxy foam

AbstractThe velocity and attenuation of longitudinal bulk waves in a solid epoxy foam were measured by an acoustic pulse technique in the frequency range of 0.667–4.0 Mc./sec. and in the temperature range from ambient to 150°C. The measurements are reported with the density of the solid epoxy and with aluminum impurity loading as parameters. Over the indicated temperature and frequency ranges, complete attenuation and velocity measurements are reported for one foam corresponding to a density of 0.325 g./cc. In the density range of 0.088–0.325 g./cc. for the unloaded foams, attenuation is reported at room temperature. It is observed that the longitudinal velocities for all the densities decrease with temperature by about 40% in a span of 100°C. and that an approximately linear relation exists with temperature. The velocities in the foams loaded with small percentages of aluminum and heat‐treated at 250°C. exhibit temperature behavior which is dependent upon the combined effects of loading, density change, and epoxy properties. For the loaded foam with the highest density (1.068 g./cc.), velocity is reported to a temperature of about 250°C. The velocities of all the various density samples with the exception of the loaded foams exhibit inflections at a temperature of about 110°C. The attenuation–temperature measurements on the 0.325 g./cc. sample show similar behavior at this temperature except that the effect is much more pronounced than the velocity inflection, hence a better indication of the transition. The precision of the measurement is about 2% for the relative longitudinal velocities and about 20% for the attenuation.

The propagation of plane irrotational waves through an elastoplastic medium

This paper is an attempt at a systematic investigation of wave propagation in a metal, treating interactions between elastic and plastic waves, and the formation and propagation of shock waves, in the general case of motions with unidirectional strain arising from an initial smooth loading­ unloading pulse. A stress-strain relation with linear elastic paths and concave-upward plastic paths (where compression is measured as positive) is derived and used so that the elastic wave velocity is uniform, and the plastic wave velocity an increasing function of stress. The analysis is in terms of engineering stress and strain with a Lagrangian co-ordinate system. Analytic solutions to the interactions between different types of continuous waves are developed incorporating an expression for the motion of the elastic-plastic boundary. An analysis of the breakdown of a smooth plastic compression wave into a shock wave is presented, and the propaga­ tion conditions derived. It is shown that the heat dissipated is proportional to the cube of the strain jump, its low value for moderate shock strength suggests that the shock does not appreciably affect the stress-strain relation, an assumption from which a solution for the unloading of a plastic compression front by an overtaking elastic wave, while shock formation is taking place, is derived. A numerical illustration of this solution for a particular pulse in aluminum is given

Properties of Elastic and Plastic Waves Determined by Pin Contactors and Crystals

Experimental techniques are described by which one can observe the separation of a shock wave in a metal into an elastic wave and a slower plastic wave. The plastic-wave velocity was about 15 percent less in steel and 10 percent less in tungsten than the elastic-wave velocity, at pressures imparted by Composition B explosive. Elastic-wave velocities were the same, within experimental error, as the measured sound velocities. The pressure in the elastic wave in SAE 1020 steel, deduced from the material and wave velocities, is independent of the plastic-wave pressure within experimental accuracy, and is about 12 kilobars. SAE 1040 steel, however, does not exhibit a single characteristic elastic-wave pressure. The pressure initially is about 6 kilobars, and increases to about 12 kilobars before the arrival of the plastic wave.