Elastic-plastic Wave Propagation Research Articles

Effects of underground explosions on soil and structures

Much effort has been dedicated to the study of underground explosions because they pose a major threat to people and structures below or above the ground. In this regard, it is especially important to model the propagation of blast waves in soil and their effects on structures. The main phenomena caused by underground explosive detonation that must be addressed are crater or camouflet formation, shock wave and elastic–plastic wave propagation in soil, and soil-structure interaction. These phenomena can be numerically simulated using hydrocodes, but much care must be taken to obtain reliable results. The objective of this study is to analyze the ability of a hydrocode and simple soil models that do not require much calibration to approximately reproduce experimental and empirical results related to different buried blast events and to provide general guidelines for the simulation of this type of phenomena. In this regard, crater formation, soil ejecta, blast wave propagation in soil, and their effects on structures below and above the ground are numerically simulated using different soil models and parameters; the results are analyzed. The properties of soil have a significant effect on structures, the ejecta, and the propagation of shock waves in soil. Thus, the model of the soil to study these phenomena must be carefully selected. However their effect on the diameter of a crater is insignificant.

A coupled DISC – 1D variational-difference approach to simulate the rigid projectile penetration into a concrete medium

A new effective approach to analyze penetration of a rigid projectile into a concrete medium is presented. The penetration analysis is based on the previously developed DISCS model approach in which the concrete medium is subdivided into discs, responding in the radial direction under plain strain conditions. The major new feature of this paper lies in the developed approach, which is a hybrid of the above DISCS model approach and of the 1D solution of cylindrical elastic-plastic wave propagation through the concrete medium in the radial direction. The 1D cylindrical problem in each of the discs planes is solved by the variational-difference method. The present approach uncouples the two-dimensional penetration problem into two connected one-dimensional problems and enables fast calculations of the projectile motion time history (i.e. deceleration, velocity and depth) as well as the displacement, velocity, strain and stress fields in the discs. The present approach is significantly faster and much simpler compared to a common 2-D axisymmetric analysis in which calculations in both radial and vertical directions are simultaneously performed and this requires much more computational time. An added efficiency is provided by the DISCS approach, which allows to perform analysis only in discs that are in contact with the projectile nose. This reduces considerably the volume of calculations, yet considers all discs that contribute to the instantaneous resistance and enables precise analysis of the penetration problem. The advanced modeling of a typical disc response yields a realistic acceleration time history that is very similar to test measured signals. Comparisons of the present approach analysis results with projectile decelerations and penetration depths as well as with available measured in-target radial stress time histories demonstrate the high fidelity of the proposed approach. The present approach predictions are in considerably closer agreement with test data compared with other simplified methods as well as with 2-D computational analysis results.

Work Hardening and Microstructural Effect during Dynamic Deformation of Polycrystalline Copper

Dynamic deformation of metals in the elevated strain rate interval of elastic-plastic wave propagation is relevant to technological conditions, such as structural response to impact, ballistic effects, and metal forming processes. In the present work, the work hardening of quasi-static and dynamically deformed copper using a split pressure bar was evaluated for two different grain sizes. From slip lines observations in conditions of both dynamic and quasi-static strain rates, as well as an insensitivity to grain size of the yield stress, it is suggested that copper behave like a single crystal under dynamic deformation. It is shown, for the first time, that the work hardening rate during dynamic deformation of polycrystalline copper remains higher up to the fracture.

Elastic–Plastic Wave Propagation in Uniform and Periodic Granular Chains

We investigate the properties of high-amplitude stress waves propagating through chains of elastic–plastic particles using experiments and simulations. We model the system after impact using discrete element method (DEM) with strain-rate dependent contact interactions. Experiments are performed on a Hopkinson bar coupled with a laser vibrometer. The bar excites chains of 50 identical particles and dimer chains of two alternating materials. After investigating how the speed of the initial stress wave varies with particle properties and loading amplitude, we provide an upper bound for the leading pulse velocity that can be used to design materials with tailored wave propagation.

Modeling of Shock Wave Resistance in Composite Solids

The paper describes briefly the problem of elastic-plastic shock wave propagation in solids. Such waves originate by acting of explosion waves or by high velocity impact of solid parts on the structure. Computational simulations are applied to the elastic problem of propagation of waves in composite material reinforced by fibres. The fibres are supposed to be much stiffer than the matrix. The wave in such material is influenced by reflexion and refraction on the interface between fibres and the matrix and by the interaction of then waves. The wave is strongly damped in such composites in this way. The aim of this paper is to contribute better understanding and modelling of waves propagation using commercial software ABAQUS.

An Analysis of Propagation of Elastic-Plastic Spherical Waves in a Thick-Walled Sphere

An analysis of dynamic behavior is carried out in the case when dynamic load with central symmetry is applied on the inner surface of the cavity with central symmetry of a thick-walled elastic-work hardening plastic sphere. The static stress-strain curve for the material in simple tension is assumed to be a smooth curve, concave toward the strain axis. Formulas are derived of the propagation speeds of spherical waves in an isotropic elastic-work hardening plastic body. Ordinary differential equations are derived among physical quantities along characteristic curves. Formulas of propagation speeds of the spherical waves in approximate bodies such as the elastic-linear hardening plastic, the elastic-perfectly plastic, the rigid-work hardening plastic, the rigid-linear hardening and the rigid-perfect plastic bodies are derived from one in the elastic-work hardening plastic body. Calculated results are also presented on the basis of the propagation theory of the spherical waves in the elastic-work hardening plastic body.

An Analysis of Propagation of Elastic-Plastic Spherical Waves in a Thick-Walled Sphere

An analysis of dynamic behavior is carried out in the case when dynamic load with central symmetry is applied on the inner surface of the cavity with central symmetry of a thick-walled elastic-work hardening plastic sphere. The static stress-strain curve for the material in simple tension is assumed to be a smooth curve, concave toward the strain axis. Formulas are derived of the propagation speeds of spherical waves in an isotropic elastic-work hardening plastic body. Ordinary differential equations are derived among physical quantities along characteristic curves. Formulas of propagation speeds of the spherical waves in approximate bodies such as the elastic-linear hardening plastic, the elastic-perfectly plastic, the rigid-work hardening plastic, the rigid-linear hardening and the rigid-perfect plastic bodies are derived from those in the elastic-work hardening plastic body. Calculated results are also presented on the basis of the propagation theory of the spherical waves in the elastic-work hardening plastic body.

High-strain-rate dynamic mechanical behavior of a bulk metallic glass composite

The high-strain-rate mechanical properties, deformation mechanisms, and fracture characteristics of a bulk metallic glass (BMG)-matrix composite, consisting of an amorphous Zr57Nb5Cu15.4Ni12.6Al10 (LM106) matrix with crystalline tungsten reinforcement particles, were investigated using gas gun anvil-on-rod impact experiments instrumented with velocity interferometry (VISAR) and high-speed digital photography. The time-resolved elastic-plastic wave propagation response obtained through VISAR and the transient deformation states captured with the camera provided information about dynamic strength and deformation modes of the composite. Comparison of experimental measurements with AUTODYN-simulated transient deformation profiles and free surface velocity traces allowed for validation of the pressure-hardening Drucker–Prager model, which was used to describe the deformation response of the composite. The impacted specimens recovered for post-impact microstructural analysis provided further information about the mechanisms of dynamic deformation and fracture characteristics. The overall results from experiments and modeling revealed a strain to failure of ∼45% along the length and ∼7% in area, and the fracture initiation stress was found to decrease with increasing impact velocity because of the negative strain-rate sensitivity of the BMG.

Dynamic Mechanical Behavior Characterization of Epoxy-Cast Al + Fe2O3 Thermite Mixture Composites

The dynamic mechanical behavior characterization of epoxy-cast stoichiometric mixtures of nano- or micron-scale aluminum and hematite (Fe2O3) powders is investigated in this work. Experiments conducted on rod-shaped samples, using instrumented reverse Taylor impact tests employing high-speed imaging and velocity interferometry, show that these composites exhibit viscoelastic deformation and brittle fracture behaviors. Upon impact, the samples display significant elastic and plastic deformation during both the loading and unloading stages, as determined from quantitative high-speed camera measurements of the transient deformation states. Approximately 50 pct elastic recovery of total axial strain was observed to occur rapidly (within tens of microseconds) after impact. A one-dimensional elastic-plastic wave propagation analysis was used for estimating the composite’s dynamic average yield stress and total plastic strain. The results reveal that the nano-Al + Fe2O3-containing epoxy composite is most resilient, has the highest strength, and is more capable of absorbing impact energy. The analysis additionally provides detailed information about elastic and plastic wave interactions for discrete times, up to the final state of the material. Calculations and observations through the coupling of high-speed camera images and velocity interferometry (VISAR) measurements show that the elastic recovery coincides with peak axial strain and the interaction of elastic and plastic waves propagating within the rod-shaped specimen. Hence, such an instrumented Taylor test provides a detailed view of the general wave structure within the material upon impact and, at the same time, enables a complete description of the stress-strain response.

Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

It is well known that a specimen for impact testing must be optimized in terms of its dimensions. The main reason is to reduce strain gradients due to the effects of elastic–plastic wave propagation. On the other hand, when a split Hopkinson bar in tension is applied, the net displacement of the specimen ends is very limited, usually from 2.0 to 3.0 mm. Thus, to reach a maximum strain of 0.5 the specimen length must be reduced in dimensions from 4.0 to 6.0 mm. Consequently, small diameters or lateral dimensions and lengths must be applied to assure one-dimensional deformation. Such small lengths substantially perturb the determination of real material behavior. So the main motivation of this study was to perform a systematic analysis, numerical and analytical, to find differences in the behavior of short and long specimens loaded in impact tension. The finite element code ABAQUS/Explicit has been used to simulate several specimen lengths from 10 to 40 mm submitted to impact velocities ranging from 10 to 100 m/s.

Laser shock processing of Ti-6Al-4V alloy

Laser shock processing of Ti-6Al-4V alloy is considered. A mathematical model governing the laser non-conduction-limited heating is introduced and a numerical solution for the temperature distribution is presented. The pressure (recoil pressure) generated across the solid-vapour interface is determined and it is considered as an impact load for the elastic-plastic wave generation in the surface region of the substrate material. The depth of the plastic region is predicted from the elastic-plastic wave propagation analysis. An experiment is carried out to ablate the surface using a neodymium-doped yttrium aluminium garnet laser with 8 ns pulse length and 0.5 J energy content. Scanning electron microscopy is carried out to examine the surface morphology of the irradiated region. It is found that microhardness increases by 1.5 times the base hardness of the substrate material. The depth of the plastic region predicted extends 0.195 mm from the surface, which agrees well with the experimental findings. In addition, some localized microcracks are observed at the surface of the workpiece.

Investigation Into Laser Shock Processing

Laser shock processing is a good candidate for surface industry due to its rapid processing, localized ablation, and precision of operation. In the current study, laser shock processing of steel was considered. The numerical solutions for temperature rise and recoil pressure development across the interface of the ablating front and solid are presented. The propagation of elastic-plastic waves in the solid due to recoil pressure loading at the surface is analyzed and numerical solution for the wave propagation was obtained. An experiment was conducted to ablate the steel surfaces for shock processing. Scanning electron microscopy was carried out to examine the ablated surfaces shock processing while transmission electron microscopy was conducted to obtain dislocation densities after the shock processing. It was found that surface hardness of the workpiece increased in the order of 1.8 times of the base material hardness, and the dislocation was the main source of the shock hardening in the region affected by laser shock processing.

Impact shear-numerical analyses of ASB evolution and failure for Ti-6AI-4V alloy

In this contribution a study is reported on a shear zone evolution at high strain rates for Ti-6Al-4V-alloy. Such process of deformation, leading to development of Adiabatic Shear Band (ASB), is typical for fast and impact shearing. A very special experimental technique developed at LPMM-Metz has permitted for shear tests at a wide range of strain rates and also for development of an advanced constitutive relation valid for that range of strain rates and also for a range of temperatures (range of strain rates from 10 -4 l/s to about 10 5 l/s). This experimental technique called the Modified Double Shear has been applied to test Ti-6Al-4V alloy. In order to estimate the effect of stress concentration on the sensitivity to ASB triggering four different specimen geometries with different stress concentrators were tested and analyzed. After identification of all material constants for Ti-6Al-4V alloy in the advanced constitutive relation, this relation has been introduced into the finite element code ABAQUS Explicit. The constitutive relation accounts for the effects of strain hardening, rate sensitivity and thermal softening. In this way a complete dynamic approach with elastic-plastic wave propagation, adiabatic shear band development and failure could be studied numerically for all four geometries with different stress concentrators. In addition, the Critical Impact Velocity (CIV) in shear has been estimated analytically and numerically for Ti-6Al-4V. A very good agreement between experiments and numerical simulations are achieved.

Impact tension of sheet metals - Effect of initial specimen length

It is well known that a Specimen for impact testing of materials must be optimized concerning its dimensions. The main reason is to reduce strain gradients due to the effects of elastic-plastic wave propagation. On the other hand, when Split Hopkinson Bar (SHB) is applied for tension test, the net displacement of the specimen ends is very limited, usually from 2.0 to 3.0 mm. Thus, to reach maximum strain 0.5 the specimen length must be reduced to dimensions from 4.0 mm to 6.0 mm. Consequently small diameter, or lateral dimensions in case of flat specimen, must be applied to assure one-dimensional deformation. Such small lengths substantially perturb the real material behavior to be determined. So the main motivation of this study was to perform a systematic analysis, numerical and analytical, to find differences in behavior of short and long specimens loaded in impact tension. The FE code Abaqus/Explicit has been used to simulate several specimen lengths from 10 mm to 40 mm, and several velocities from 10 m/s to 100 m/s.

Laser Short Pulse Heating and Elastic-Plastic Wave Generation

Laser induced shock processing improves the mechanical and tribological properties of metallic surfaces. During the high power intensity laser beam interaction with the solid substrate ablation of the surface occurs, which in turn results in a recoil pressure developing in the interaction zone. This triggers the generation of elastic-plastic waves that propagate in the solid substrate and as a consequence a plastic region is developed in the vicinity of the substrate surface. In the present study, short pulse laser heating of steel is considered, and the Fourier and the electron kinetic theory models pertinent to laser heating are introduced. The governing equations of heating are solved numerically with the appropriate boundary conditions considered. The recession and vapor front velocities, and vapor pressure and recoil pressures are determined for different laser power intensities. The elastic-plastic wave propagation in the solid substrate is modelled and findings are compared with the results of the previous studies. It is found that the rapid rise of the surface temperature occurs at high laser power intensities and the recoil pressure generated at the interface substantiates, which in turn results in elastic-plastic wave propagation in the solid substrate. This develops a plastic region in the order of 0.9 µm in the surface vicinity of the solid substrate and the time required for this deformation is in the order of 25 ns. In addition, the depth of the plastic region developed in the present study agrees well with the previous results.

The bifurcation problem of columns caused by elastic-plastic stress wave propagation

In this paper, the dynamic buckling of an elastic-plastic column is studied. Let its dynamic buckling under step load be reduced to a bifurcation problem caused by the propagation of axial elastic-plastic stress wave. The critical buckling condition is given and the reflection of the elastic-plastic stress wave is taken into consideration. In the end, numerical computation and conclusions are presented and obtained.

A computational investigation of adiabatic shear plugging based on thermo-viscoplastic instability

The adiabatic shear plugging of a titanium alloy target impacted by a steel projectile is numerically studied by a recently developed dynamic Lagrangian finite element code ETVP. The elastic-plastic wave propagation effect in the long projectile is taken into account. The rate-dependent behaviour of the titanium alloy target is also taken into consideration by using a thermo-viscoplastic constitutive equation. Moreover, the adiabatic shear failure criterion with two control variables (both strain and strain rate) based on thermo-viscoplastic constitutive instability of materials is generalized to three-dimensional stress states and incorporated into the code. The results clearly show the developing process of adiabatic shear plugging of the target including the initiation of the localization, the widening and deepening of adiabatic shearing zone, and finally the forming of a plug. The numerical results for the residual velocities are found to be in good agreement with those measured experimentally. The corresponding energy relation in the plugging process is then analyzed from this new plugging model.

One-Dimensional Theory of Elastic-Plastic-Viscoplastic Stress Waves of Solids in Uniaxial Stress State at Eulerian Coordinate.

An elastic-plastic-viscoplastic constitutive equation has been proposed in which the understress is introduced to the plastic strain and the overstress is employed for the viscoplastic strain. The constitutive equation has a form in which the inelastic strain component is consists of steady and unsteady component. Using the equation, an analysis on the one-dimensional wave propagation in the uniaxial stress state at the spacial coordinate is done by the characteristic method. As the results, equations describing the wave propagation speed and the relation of the every physical quantities in Eulerian coordinate. Also, it is shown that the theories are derived of an elastic-plastic, elastic-viscoplastic and longitudinal elastic wave propagation in Eulerian coordinate from that of the developped elastic-plastic-viscoplastic wave propagation.

One-Dimensional Theory of Uni-Axial Shear Elastic-Plastic-Viscoplastic Stress Waves of Solids.

An uni-axial shear elastic-plastic-viscoplastic constitutive equation has been derived from the generalized constitutive equation. The constitutive equation is in which the understress in introduced to the shear strain and the overstress is employed in the shear viscoplastic strain rate. Using the constitutive equation, an analysis is done on the one-dimensional uni-axial shear elastic-plastic-viscoplastic stress wave propagation. And the equations describing the wave propagation speed and the relation of any physical quantities are derived. The derived equation for describing the shear wave propagation speed expresses the experimental results qualitatively. Also, from the developped theory of the shear elastic-plastic-viscoplastic wave propagation, the theories of a shear elastic-plastic, elastic-viscoplastic and elastic wave propagation are derived. The wave propagation speed of the elastic-viscoplastic theory can't express that of the experimental results at all except the precursor.

Dynamic elastic-plastic buckling phenomena in a rod due to axial impact

Dynamic elastic-plastic buckling phenomena which might develop in a rod from an axial impact loading are studied in order to identify the conditions for quasi-static behaviour. A discrete model for dynamic elastic-plastic buckling, which retains the axial and the lateral inertia forces, is proposed, and the relationship between the model parameters and the characteristics of an actual structure is given. Examples of different external loadings and boundary conditions are considered in order to clarify the influence of elastic-plastic axial wave propagation on the buckling process. The critical time for the initiation of buckling is obtained and the post-buckling behaviour of the model is analysed. Particular attention is paid to the role of the striking mass on the characteristics of the buckling process and on the development of the buckling shape. The numerical study reveals that the inertia of the striking mass affects considerably the development of the buckling shape causing different patterns of axial strain distributions at the initiation of buckling. The comparisons which are made between the model predictions and some previously published experimental data show that the buckling process is governed by the impact velocity as well as by the external loading history provided by the experimental technique.