Tensile Wave Research Articles

Numerical simulation of tensile axial impact of stainless steel tubes and zircaloy rod

Numerical simulation was carried out using ANSYS/LS-DYNA on empty and boron carbide filled stainless steel tubes and zircaloy rod for studying their elastic wave propagation during tensile impact. While empty stainless steel tubes and zircaloy rod showed perfect one dimensional wave propagation, presence of boron carbide powder increased the stress underwent by the tube as the tensile stress wave approached the powder. Furthermore, the wave propagation time of boron carbide filled tube increased in comparison with the empty tube. Experimental results compared well for the plateau region of the strain-time history of the boron carbide powder filled tube. For the empty steel tube and zircaloy rod there was good comparison of strain amplitude.

Integrated continuum-atomistic modeling of nonthermal ablation of gold nanofilms by femtosecond lasers

Ultrafast nonthermal ablation of gold nanofilms is studied using a combined two-temperature model and molecular dynamics method. The results show that for thinner films the tensile stress is directly reversed from the initially generated compressive stress. For thicker films, on the other hand, the tensile stress wave is reflected from the irradiated surface. The key driving force for ultrafast nonthermal material ablation is conventional thermal stress, instead of the hot electron blast force.

Two approaches to study essentially nonlinear and dispersive properties of the internal structure of materials

It is shown that essentially nonlinear models for solids with complex internal structure may be studied using phenomenological and proper structural approaches. It is found that both approaches give rise to the same nonlinear equation for traveling longitudinal macrostrain waves. However, presence of the connection between macro- and microfields in the proper structural model prevents a realization of some important solutions. First, it is obtained that simultaneous existence of compression and tensile waves is impossible in contrast to the phenomenological approach. Then, it is found that correlation between macro- and internal strains gives rise to the crucial influence of the velocity of the macrostrain wave on the existence of either compression or tensile localized strain waves. Also, it is shown that similar profiles of the macrostrain solitary waves may be accompanied by distinct profiles of the microstrain waves. Finally, the dispersion curves for the waves belong to the different branches. This is important for internal structural deviations caused by the dynamical loading due to the localized macrostrain wave propagation and demonstrates a need in the development of the proper structural approaches relative to the phenomenological ones.

Modeling of concrete behavior under high strain rates with inertially retarded damage

The paper proposes a novel approach to model the influence of high strain rates on the behavior of quasi-brittle materials like concrete. It is based on gradient continuum damage, where the gradient part is extended with an inertia of damage. This causes a retardation of damage due to the fact that micro-cracks cannot spread out arbitrarily fast. The application is demonstrated with uniaxial tensile wave propagation and for a plane stress case. Increasing strain rates lead to an expansion of the linear stress–strain behavior with stresses exceeding the quasistatic material strength.

Impacts on thin elastic sheets

We study transverse impacts of rigid objects on a free elastic membrane, using thin circular sheets of natural rubber as experimental models. After impact, two distinct axisymmetric waves propagate in and on the sheet. First, a tensile wave travels at sound speed leaving behind the wavefront a stretched domain and then a transverse wave propagates on the stretched area at a lower speed. In the stretched area, geometrical confinement induces compressive circumferential stresses leading to a buckling instability, giving rise to radial wrinkles. We report on a set of experiments and theoretical remarks on the conditions of occurrence of these wrinkles, their dynamics and wavelength.

Dynamic split tensile test of Flattened Brazilian Disc of rock with SHPB setup

The Flattened Brazilian Disc (FBD) specimens were impacted diametrically by a pulse shaping split Hopkinson pressure bar to measure dynamic tensile strength of a brittle rock. With application of strain gauge technique, the stress waves traveling through the incident bar, the transmission bar as well as the FBD specimen were recorded and analyzed. The loading history was determined based on the one-dimensional stress wave theory. The dynamic equilibrium condition in the specimen was approximately satisfied, this claim was supported by the numerical simulation of dynamic stress evolution in the specimen, with the conclusion that a short time after impact the pattern of dynamic stress distribution in the specimen was symmetric and similar to that of the counterpart static loading. The validity of the test was further verified experimentally, as the waveforms acting on the two flat ends of the FBD specimen, respectively, were of nearly the same shape, and the rupture modes of the specimens were generally such that crack first initiated at the center of the disc and subsequently propagated along the loading diameter, whereas crush zones were implied to form lastly near the two flat ends of the broken specimen. The dynamic tensile strength of marble was measured at the critical point when the tensile strain wave recorded at the disc center got peak value of the strain derivative with respect to time.

Cubic non-linearity and longitudinal surface solitary waves

It is shown that for some seismic media both quadratic and cubic non-linearities should be taken into account in the governing equation for longitudinal waves. The new equation is obtained to account for non-linear surface waves in a medium surrounding a non-linearly elastic rod. Exact solutions of the equation allow us to describe simultaneous propagation of tensile and compressive localized strain waves. Various interactions between these waves give rise to both the multi-bump and “Mexican hat” localized wave structures closer to the surface waves recently observed in experiments.

The acceleration of solid particles subjected to cavitation nucleation

The cavity–particle dynamics at cavitation inception on the surface of spherical particles suspended in water and exposed to a strong tensile stress wave is experimentally studied with high-speed photography. Particles, which serve as nucleation sites for cavitation bubbles, are set into a fast translatory motion during the explosive growth of the cavity. They reach velocities of ~40 ms−1and even higher. When the volume growth of the cavity slows down, the particle detaches from the cavity through a process of neck-breaking, and the particle is shot away. The experimental observations are simulated with (i) a spherical cavity model and (ii) with an axisymmetric boundary element method (BEM). The input for both models is a pressure pulse, which is obtained from the observed radial cavity dynamics during an individual experiment. The model then allows us to calculate the resulting particle trajectory. The cavity shapes obtained from the BEM calculations compare well with the photographs until neck formation occurs. In several cases we observed inception at two or more locations on a single particle. Moreover, after collapse of the primary cavity, a second inception was often observed. Finally, an example is presented to demonstrate the potential application of the cavity–particle system as a particle cannon, e.g. in the context of drug delivery into tissue.

Elucidating the Thermal, Chemical, and Mechanical Mechanisms of Ultraviolet Ablation in Poly(methyl methacrylate) via Molecular Dynamics Simulations

[Figure: see text]. Laser ablation harnesses photon energy to remove material from a surface. Although applications such as laser-assisted in situ keratomileusis (LASIK) surgery, lithography, and nanoscale device fabrication take advantage of this process, a better understanding the underlying mechanism of ablation in polymeric materials remains much sought after. Molecular simulation is a particularly attractive technique to study the basic aspects of ablation because it allows control over specific process parameters and enables observation of microscopic mechanistic details. This Account describes a hybrid molecular dynamics-Monte Carlo technique to simulate laser ablation in poly(methyl methacrylate) (PMMA). It also discusses the impact of thermal and chemical excitation on the ensuing ejection processes. We used molecular dynamics simulation to study the molecular interactions in a coarse-grained PMMA substrate following photon absorption. To ascertain the role of chemistry in initiating ablation, we embedded a Monte Carlo protocol within the simulation framework. These calculations permit chemical reactions to occur probabilistically during the molecular dynamics calculation using predetermined reaction pathways and Arrhenius rates. With this hybrid scheme, we can examine thermal and chemical pathways of decomposition separately. In the simulations, we observed distinct mechanisms of ablation for each type of photoexcitation pathway. Ablation via thermal processes is governed by a critical number of bond breaks following the deposition of energy. For the case in which an absorbed photon directly causes a bond scission, ablation occurs following the rapid chemical decomposition of material. A detailed analysis of the processes shows that a critical energy for ablation can describe this complex series of events. The simulations show a decrease in the critical energy with a greater amount of photochemistry. Additionally, the simulations demonstrate the effects of the energy deposition rate on the ejection mechanism. When the energy is deposited rapidly, not allowing for mechanical relaxation of the sample, the formation of a pressure wave and subsequent tensile wave dominates the ejection process. This study provides insight into the influence of thermal, chemical, and mechanical processes in PMMA and facilitates greater understanding of the complex nature of polymer ablation. These simulations complement experiments that have used chemical design to harness the photochemical properties of materials to enhance laser ablation. We successfully fit the results of the simulations to established analytical models of both photothermal and photochemical ablation and demonstrate their relevance. Although the simulations are for PMMA, the mechanistic concepts are applicable to a large range of systems and provide a conceptual foundation for interpretation of experimental data.

Computational study of the generation of crystal defects in a bcc metal target irradiated by short laser pulses

The generation of crystal defects in a Cr target irradiated by a short, 200 fs, laser pulse is investigated in computer simulations performed with a computational model that combines the classical molecular dynamics method with a continuum description of the laser excitation of conduction band electrons, electron-phonon coupling, and electron heat conduction. Interatomic interactions are described by the embedded atom method (EAM) potential with a parametrization designed for Cr. The potential is tested by comparing the properties of the EAM Cr material with experimental data and predictions of density functional theory calculations. The simulations are performed at laser fluences close to the threshold for surface melting. Fast temperature variation and strong thermoelastic stresses produced by the laser pulse are causing surface melting and epitaxial resolidification, transient appearance of a high density of stacking faults along the {110} planes, and generation of a large number of point defects (vacancies and self-interstitials). The stacking faults appear as a result of internal shifts in the crystal undergoing a rapid uniaxial expansion in the direction normal to the irradiated surface. The stacking faults are unstable and disappear shortly after the laser-induced tensile stress wave leaves the surface region of the target. Thermally activated generation of vacancy-interstitial pairs during the initial temperature spike and quick escape of highly mobile self-interstitials to the melting front or the free surface of the target, along with the formation of vacancies at the solid-liquid interface during the fast resolidification process, result in a high density of vacancies, on the order of ${10}^{\ensuremath{-}3}$ per lattice site, created in the surface region of the target. The strong supersaturation of vacancies can be related to the incubation effect in multipulse laser ablation/damage and should play an important role in mixing/alloying of multicomponent or composite targets.

Focusing of shock waves induced by optical breakdown in water

The focusing of laser-generated shock waves by a truncated ellipsoidal reflector was experimentally and numerically investigated. Pressure waveform and distribution around the first (F(1)) and second foci (F(2)) of the ellipsoidal reflector were measured. A neodymium doped yttrium aluminum garnet laser of 1046 nm wavelength and 5 ns pulse duration was used to create an optical breakdown at F(1), which generates a spherically diverging shock wave with a peak pressure of 2.1-5.9 MPa at 1.1 mm stand-off distance and a pulse width at half maximum of 36-65 ns. Upon reflection, a converging shock wave is produced which, upon arriving at F(2), has a leading compressive wave with a peak pressure of 26 MPa and a zero-crossing pulse duration of 0.1 mus, followed by a trailing tensile wave of -3.3 MPa peak pressure and 0.2 mus pulse duration. The -6 dB beam size of the focused shock wave field is 1.6 x 0.2 mm(2) along and transverse to the shock wave propagation direction. Formation of elongated plasmas at high laser energy levels limits the increase in the peak pressure at F(2). General features in the waveform profile of the converging shock wave are in qualitative agreement with numerical simulations based on the Hamilton model.

An effective medium model for elastic waves in microcrack damaged media

Direct numerical simulations of waves traveling through microcrack-damaged media are conducted and the results are compared to effective medium calculations to determine the applicability of the latter for studying wave propagation. Both tensile and compressive waves and various angular distributions of randomly-located cracks are considered. The relationships between the input wavelength and the output wave speed and output signal strength are studied. The numerical simulations show that the wave speed is nearly constant when 1/ ka > 60 for tensile waves and 1/ ka > 10 for compressive waves, where k is the wave number and a is the average half-crack length. The direct simulations also show that when the input wavelength is much longer than the crack length, 1/ ka > 60, the wave can pass through the damaged medium relatively unattenuated. On the other hand, when the input wavelength is shorter than a “cut off” wave length, the output wave magnitude decreases linearly with the input wavelength. The effective medium wave speed and magnitude calculations are not dependent on the input wavelength and therefore the results correspond well with the numerical simulations for large 1/ ka. This suggests a minimum wavelength for which the homogenized methods can be used for studying these problems.

Design and application of an instrumented projectile for load measurements during impact

No standardised device is available yet to measure contact forces continuously during transverse impacts caused by a projectile on a metal plate or a thin-walled structure. This study describes the design and validation phases of an instrumented projectile (mass = 1 kg) that can be used to achieve such measurements. The impact force, indeed, is computed from the strain data collected by some strain gauges glued on to a projectile part, which remains elastic during shock. Under numerically defined conditions, the projectile geometry makes it possible to record signals that are not disturbed by the reflections of the compressive and tensile strength waves appearing inside the projectile during and after shock. Gauge signal post-filtering is then virtually useless. The strain gauge-instrumented projectile sensitivity is used to study the effects of small clamping pressure variations during the transverse impact study on shipbuilding steel plates. A second application deals with the impact of an automotive steel dome initially drawn with a bulge test apparatus.

Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water

A free-Lagrange numerical method is implemented to simulate the axisymmetric jetting collapse of air bubbles in water. This is performed for both lithotripter shock-induced collapses of initially stable bubbles, and for free-running cases where the bubble initially contains an overpressure. The code is validated using two test problems (shock-induced bubble collapse using a step shock, and shock–water column interaction) and the results are compared to numerical and experimental results. For the free-running cases, simulations are conducted for a bubble of initial radius 0.3 mm located near a rigid boundary and near an aluminium layer (planar and notched surfaces). The simulations suggest that the boundary and its distance from the bubble influence the flow dynamics, inducing bubble elongation and jetting. They also indicate stress concentration in the aluminium and the likelihood of aluminium deformation associated with bubble collapse events. For the shock-induced collapse, a lithotripter shock, consisting of 56 MPa compressive and −10 MPa tensile waves, interacts with a bubble of initial radius 0.04 mm located in a free field (case 1) and near a rigid boundary (case 2). The interaction of the shock with the bubble causes it to involute and a liquid jet is formed that achieves a velocity exceeding 1.2 km s−1 for case 1 and 2.6 km s−1 for case 2. The impact of the jet on the downstream wall of the bubble generates a blast wave with peak overpressure exceeding 1 GPa and 1.75 GPa for cases 1 and 2, respectively. The results show that the simulation technique retains sharply resolved gas/liquid interfaces regardless of the degree of geometric deformation, and reveal details of the dynamics of bubble collapse. The effects of compressibility are included for both liquid and gas phases, whereas stress distributions can be predicted within elastic–plastic solid surfaces (both planar and notched) in proximity to cavitation events. There is a movie with the online version of the paper.

Reloading effects on plane plates subjected to non-contact underwater explosion

Underwater explosion damage of a plane plate restrained at its edges occurs in more than one phase. While the initial plate kick-off velocity is due to the primary shock pulse, the secondary, tertiary and the following responses are clearly due to the reloading effects. The tensile wave during reflection creates water breaking which causes bulk or midmass cavitation whereas the rarefaction produced by the moving plate at its front causes surface cavitation. Multiple reflection of the tensile wave between the cavitated zone and the plate surface causes multiple pressure peaks. Closure of the cavitated space by the interaction of the expanding gas bubble causes major reloading on the plate. After a long gap, the secondary pulse emitted by the gas bubble is felt by the plate. This paper brings out a detailed insight into the reloading phenomenon by comparing the total damage measured during experiments against the theoretical primary pulse damage.

Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation

AbstractThis paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method. More precisely, we are interested in explicit algorithms. We prove that by using a specific lumping technique, the critical time step is exactly the same as if no crack were present. This somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack. The new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids. To be precise, the results obtained are valid only when the crack is modelled by the Heaviside enrichment. Note also that the resulting lumped matrix is block diagonal (blocks of size 2 × 2). For constant strain elements (linear simplex elements) the critical time step is not modified when the element is cut. Thanks to the lumped mass matrix, the critical time step never tends to zero. Moreover, the lumping techniques conserve kinetic energy for rigid motions. In addition, tensile stress waves do not propagate through the discontinuity. Hence, the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack. Both these techniques will be used in a numerical experiment. Copyright © 2007 John Wiley & Sons, Ltd.

Laser induced foaming and chemical modifications of gelatine films

This paper reports on the investigation of the microfoaming and chemical modifications following single-pulse laser irradiation conducted at 248 nm (KrF excimer laser, 20 ns fwhm) and at 266 and 355 nm (Nd:YAG laser 4th and 3rd harmonic, 6 ns fwhm) of gelatine films. Fluorescence emissions of the films were studied by laser induced fluorescence and spectrofluorimetry and the emission lifetimes were measured by time-correlated single photon counting. The main fluorophores responsible of the observed emissions are due to aromatic amino acids like tyrosine and derived crosslinked products, possibly formed during the laser foaming. It is observed that laser irradiation with a single ns UV pulse induces modifications on the relative intensity of emissions depending on the irradiation wavelength and type of film. It was earlier anticipated that the foaming mechanism can be viewed as a cavitation phenomenon mainly induced by the laser launched tensile wave at the film surface. Spectroscopic investigations confirm that the major accompanying chemical modifications are related with the relative increase of the fluorescence of dityrosine moieties and other products derived of the photoxidation of tyrosine. These modifications are related to the structural disruption induced by foaming and to the increase of temperature in the irradiated region. This approach opens up the possibility to gain information on the molecular structure of the new nanofoamy material, as well as on its microscopic distribution with emerging fluorescence-based confocal systems allowing high spatial resolution. The results shown have important consequences for the laser processing of biopolymers of interest in biomedical applications since the resulting laser foam exhibits properties close to those of the natural extracellular matrix.

Damage evolution in adhesive joints subjected to impact fatigue

There is increasing interest in the effects of low-velocity impacts produced in components and structures by vibrating loads. This type of loading is known as impact-fatigue. The main aim of this paper is to investigate the behaviour of adhesive joints exposed to low-velocity impacting, to study the impact-fatigue life and to compare this loading regime with standard fatigue (i.e. non-impacting, constant amplitude, sinusoidal fatigue). To this effect, bonded aluminium single lap joints have been subjected to multiple impacting tensile loads and it has been shown that this is an extremely damaging load regime compared to standard fatigue. Two modifications of the accumulated time-stress model have been proposed to characterise the impact-fatigue results presented in this paper. The first model has been termed the modified load-time model and relates the total cumulative loading time of the primary tensile load wave to the mean maximum force. The second model attempts to characterise sample damage under impact-fatigue by relating the maximum force normalised with respect to initial maximum force to the accumulated loading time normalised with respect to the total accumulated loading time. This model has been termed the normalised load-time model. It is shown that both models provide a suitable characterisation of impact-fatigue in bonded joints.

Improved description of longitudinal strain solitary waves

It is found that simultaneous existence of compressive and tensile localized strain solitary waves in a rod can be described by the model equation containing both quadratic and cubic nonlinear terms. Only propagation of these waves is described by exact travelling wave solutions. However, numerical solution demonstrates that both kinds of these waves may be generated from an arbitrary input and interact each other keeping their shape and velocity. Moreover, one and the same input gives rise to a different number of these kinds of waves, and it is quadratic nonlinearity that determines it.

ポリエチレン繊維補強コンクリートの接触爆発に対する耐爆性能

When designing explosive-resistant concrete structures, reducing brittle spall due to reflected tensile stress wave is the most important problem. In order to apply high-toughness fiber-reinforced concrete to explosive-resistant structures, experimental investigations were conducted regarding evaluation of the damages in polyethylene fiber-reinforced concrete (PEFRC) slabs subjected to contact detonation. As a result, it was shown that the PEFRC was very effective in reducing spall due to detonation as compared with normal concrete. Moreover, the formulation estimating the damage depth in the PEFRC slab subjected to contact detonation was derived based on the test results.