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Instrumented Taylor anvil-on-rod impact tests for validating applicability of standard strength models to transient deformation states
Abstract and Figures
Instrumented Taylor anvil-on-rod impact tests have been conducted on oxygen-free electronic copper to validate the accuracy of current strength models for predicting transient states during dynamic deformation events. The experiments coupled the use of high-speed digital photography to record the transient deformation states and laser interferometry to monitor the sample back (free surface) velocity as a measure of the elastic/plastic wave propagation through the sample length. Numerical continuum dynamics simulations of the impact and plastic wave propagation employing the Johnson-Cook [Proceedings of the Seventh International Symposium on Ballistics, 1983, The Netherlands (Am. Def. Prep. Assoc. (ADPA)), pp. 541–547], Zerilli-Armstrong [J. Appl. Phys. C1, 1816 (1987)], and Steinberg-Guinan [J. Appl. Phys. 51, 1498 (1980)] constitutive equations were used to generate transient deformation profiles and the free surface velocity traces. While these simulations showed good correlation with the measured free surface velocity traces and the final deformed sample shape, varying degrees of deviations were observed between the photographed and calculated specimen profiles at intermediate deformation states. The results illustrate the usefulness of the instrumented Taylor anvil-on-rod impact technique for validating constitutive equations that can describe the path-dependent deformation response and can therefore predict the transient and final deformation states.
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... Symmetrical boundary condition is satisfied by restricting the horizontal displacement for central specimen axis and vertical displacement for the rear anvil surface. Mechanical properties of the specimen material and the initial velocity are taken according to data presented in [2,9]. Dynamic yield stress of von Mises model is determined by fitting the final specimen length between the simulation and experiment. ...
... A comparative numerical analysis of various approaches was carried out to determine the most applicable method for predicting the dynamic fluidity process when testing metal samples by Taylor. Modeling results are compared to experimental data of Taylor tests for oxygen-free electronic (OFE) copper [9] where specimens were 75 mm length rods with length to diameter ratio of 4 : 1. Numerical simulations using J-C model are compared to the results received utilizing the traditional von Mises approach. Experimental results [9] are giving the specimen side profile for three different time instances (figure 2). ...
... Modeling results are compared to experimental data of Taylor tests for oxygen-free electronic (OFE) copper [9] where specimens were 75 mm length rods with length to diameter ratio of 4 : 1. Numerical simulations using J-C model are compared to the results received utilizing the traditional von Mises approach. Experimental results [9] are giving the specimen side profile for three different time instances (figure 2). The utilized model parameters (as suggested in [9]) are given in table 1. ...
The finite element method is used for simulation of productivity in dynamic Taylor tests. Two different approaches for prediction of plastic deformation of finite element method is employed for numerical simulation of yielding under dynamic impact Taylor tests. Obtained results of modeling are compared with experimental ones. These are Johnson–Cook model and von Mises yielding criterion enhanced by incubation time approach. The simulation results have shown that the simplest method based on von Mises plasticity model provides good coincidence with experimental profiles of specimen shape in the course of deformation. The shortcoming is that the correct value of yield stress is depending on the loading rate and should be known beforehand. Thus, if there was a method to predict the value of dynamic yield stress to be used within von Mises criterion then this simple approach could be the optimal choice for simulation of dynamic plasticity in conditions of Taylor test.
... Initially, all the experimental analysis was based only on the comparison of initial and final lengths of the rod, providing a possibility to estimate "dynamic yield stress". Further development of experimental methods made it possible to track deformation of the sample during impact with high time resolution and also record the oscillation profile of the back surface of the rod using laser interferometry Eakins, Thadhani (2006). All this progress converted Taylor's test into an extremely very powerful method of investigation of high-speed processes inside dynamically deformed material. ...
... A "mushroom" shape of the rod end is often appearing as the result of deformation for a number of metals and alloys Borodin, Mayer (2015). The shape of the profile of the rod and its change in the process of deformation Eakins, Thadhani (2006), Borodin, Mayer (2015) provides significant information about the mechanisms of plastic deformation (ex. localization of plastic flow, etc.). ...
... Nowadays a number of models of plastic deformation and plasticity criteria have been used by various authors to describe Taylor's tests Wilkins, Guinan (1973), Eakins, Thadhani (2006), Mase (1970), Johnson, Cook (1983), Steinberg et al. (1980) but they all have their drawbacks. Many of these models are included in popular commercial FEM codes (ANSYS, LS Dyna, etc.). ...
Plastic deformation of samples undergoing Taylor anvil-on-rod impact test is simulated utilising finite element method (FEM).
Classical (bilinear plasticity using von Mises stress, Johnson-Cook plasticity model) plasticity models and a new plasticity model
based on notion of incubation time of plastic flow initiation are employed to model dynamic deformation of tested samples. In
order to verify the obtained solutions, the received predictions are compared available experimental measurements of deformed
sample shapes for two different materials (copper, aluminium) and various initial sample velocities. It is shown that bilinear von
Mises plasticity model is not able to provide satisfactory coincidence between the shape of the sample boundary received in
numerical simulations and in real experimental conditions. At the same time, models accounting for rate dependency of deformation
are providing much more accurate results. Substitution of the concept of "dynamic" yielding stress of a material, depending on the
rate of deformation by characteristic time of plastic stress relaxation provides a powerful tool for robust prediction of plastic
deformation for a wide range of strain rates. The parameter of the characteristic relaxation time has a clear physical interpretation
and theoretically can be evaluated from microstructural studies.
... A cylindrical slug of metal impacts a larger block at a speed fast enough to induce plastic deformation in the sample. Here we recreate an experiment from Eakins et al. [92]. In this experiment, a copper cylinder, 9.45-mm radius 75-mm long, was hit We model this problem in 3D. ...
... We ran our simulation for 300-μs, which was sufficient for the sample to reach its final form. Our results with FSISPH are compared to the experimental and AutoDyn results of Eakins et al. [92]. Qualitatively, the experimental and AutoDyn profiles match our FSISPH result. ...
We present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.
... The cylindrical projectile is experiencing complex inhomogeneous stress, and strain rate deformation. With high strain rate and large plastic deformation just beyond the strain rates imposed by the SHPB technique, the Taylor impact test has been widely employed to estimate the dynamic yield strength and validate the constitutive models, e.g., Johnson and Cook [38] , Zerilli and Armstrong [39] , Chapman et al. [40] , Sarva et al. [41] ., Eakins et al. [42] . ...
... Then the mesh is regarded to be satisfied with convergence criterion. The mesh throughout the rod is with the element size of 0.2 × 0.2 × 0.2 [mm 3 ], which is sufficient to provide accurate solutions [42] . The cylindrical rod with 20 [mm] long and 5 [mm] in diameter is meshed with 16,000 solid elements and 18,584 nodes. ...
The constitutive behaviour of a near α Ti3Al2.5V alloy, conceived for impact resistant turbine engine containment applications, is characterized at quasi-static, medium, and high strain rates ranging from 10⁻³ [s⁻¹] to 10⁶ [s⁻¹] by using the cylindrical compression specimen and shear compression specimen. Systematic tests have been conducted on a screw driven Zwick test machine, a hydraulic Instron machine, a recently designed split Hopkinson pressure bar and a nitrogen 12 [mm] bore gas gun synchronized with high-speed Kirana camera. The adiabatic heating effect from medium to high rates is evaluated experimentally. Digital image correlation technique is employed for strain measurement from simultaneously recorded images. The Ti3Al2.5V alloy presents noticeable strain rate sensitivity. The strain hardening decreases with increasing strain rate. The microstructural characterization reveals that this alloy fails by dynamic shear localization. A simple constitutive model combining the advantages of Johnson-Cook model and Kuang-Huang-Liang model is proposed for finite element simulations of the impact tests. The model predicts the deformed specimen shapes from Taylor impact experiments with good agreement, indicating the suitability of the constitutive model to predict complex strain rate and temperature dependent impact events.
... More recently, the deceleration profile measured at the rear of the projectile has be used [3], or the deformation-time history for a 2D projectile profile (e.g. [4]). Digital image correlation (DIC) techniques now allow the additional measurement of time-dependent strain and strain-rate on the surface of the deforming projectile (e.g. ...
... [5]). Rod-onanvil experiments have been used to validate constitutive models of copper [4], aluminium alloy [5], tantalum [6], and others. ...
A high hardness armour steel (HHA) has been subjected to mechanical characterization under tension, compression, and shear loading at quasi-static and dynamic rates incorporating ambient and elevated temperatures. The resulting data has been used to derive constants for four plasticity constitutive models: Johnson-Cook (JC), Zerilli-Armstrong (ZA), modified Johnson-Cook (MJC), and a generalized J2-J3 yield surface (GYS). The resulting models have been used to predict the response of the HHA material during Taylor rod-on-anvil experiments. High speed photography and digital image correlation was used during the rod-on-anvil experiments to capture both transient deformation profiles and maximum principal strain along the surface of the rod (i.e. compression along the length of the rod). The JC, MJC, and GYS models were found to provide the best prediction of the shape of the rod (nose diameter and length), within 2% of the experimental measurement in all four rod-on-anvil experiments which did not result in fracture. The JC and GYS models, furthermore, were found to provide the best agreement with the measured transient surface strain profiles, predicting the experimental measurement to within 10% at all measurement locations and time steps for the experiment resulting in maximum deformation (impact velocity = 208 m/s). The results suggest that the added complexity of models such as the MJC and GYS, which incorporate strain hardening saturation, two-part strain rate dependency, and J3 plasticity effects, are unnecessary for HHA under the loading conditions experienced during rod-on-anvil experiments.
... Lidén [15] studied the geometry and motion of long rod-shaped projectiles after they penetrated thin, obliquely oriented, moving armor plates; he showed that the velocity, direction, and thickness of the target have a major influence on the failure or fracture of the projectile. Eakins [16,17] carried out reverse ballistic Taylor impact experiments using oxygen-free copper material and at velocities of 83 m/s and 205 m/s. Outline data for the specimen at different instants was captured by a highspeed camera, and the position and velocity of the plastic wave were measured using an optical method with highspeed photographs. ...
Reverse ballistic impact tests are widely used for studying dynamic responses because they provide more comprehensive and quantitative projectile/rod response results than forward impact tests. To examine equivalent forward and reverse conditions, a series of 8-cm length oxygen-free copper rods with varying length–diameter ratios was used in forward and reverse ballistic Taylor impact experiments with velocities and strain ratios of 104–215 m/s and 1.25 × 10³–2.5 × 10³ s⁻¹, respectively. Digital image correlation (DIC) and traditional optical measurements were used to determine instantaneous responses at the μs level. Based on DIC, transient structural deformation, and plastic wave propagation, the forward and reverse length difference at similar velocities ranges from 2 to 6.95 %. Rules governing deformation from the perspective of energy, along with rules for changes in energy and plastic wave propagation were determined. The relative deformation energy error was below 5 % for target projectile mass ratios above 20.
... It allows one to investigate the influence of the internal defect structure on the macroscopic strength and ductility of metals. Simulation results could be verified by means of comparison with the experimental data for the shock wave propagation [26,27] and Taylor tests on rod compaction experiments [28,29]. This way allows one to calculate the change of defect structure [30,31] and its influence on the strength parameters of metals as well [32]. ...
Some recent experiments with ultrafine-grained metal samples reveal that it has an abnormal mechanical response on the intensive dynamical loading caused by its impact or electron beam irradiations. On the basis of the original plasticity model, which takes into account dislocation slip and grain boundary sliding, we show that this response is usual for such structure. Moreover, our calculations predict an inverse Hall-Petch relation for ultrafine grained metals at extremely high strain rates (above 107 s-1), while the classical low strain rate experiments and molecular dynamic simulations detects such inverse Hall-Petch relation only for nanocrystalline materials. The main outcomes of present work are the described plasticity model and the conclusions that the ultrafine-grained metals (with grains of about 100-200 nm in diameter) has to have maximal dynamic shear strength and it is the most persistent to dynamic spall fracture because of maximal energy dissipation in it.
... More details describing the experimental setup can be found elsewhere. [17][18][19][20][21] ...
The high-strain-rate dynamic mechanical properties of a zirconium-based (Vitreloy106) bulk metallic glass reinforced with tungsten particles are evaluated using anvil-on-rod impact experiments. The experiments employ a reverse Taylor impact configuration in which a rigid anvil plate mounted on an aluminum sabot is launched to impact the flat surface of a stationary rod-shaped target sample at velocities up to 250 m/s. The impact-generated deformation propagates as a wave through the length of the rod. A high-speed digital framing camera is used to capture the transient deformation patterns of the sample, and velocity interferometry is used to monitor the free-surface velocity at the back of the sample. Constitutive equations based on the von Mises or Stassi Drucker-Prager yield criterion are then used to generate simulated transient deformation profiles and free surface velocity traces, and these are correlated with experimental measurements to validate the constitutive equation. The deformation and failure responses of the recovered impacted specimens are also characterized using microstructural analysis of the matrix and tungsten phases. In this paper we will describe the results of the work performed to date highlighting the deformation and failure responses as revealed by microstructural analysis and the validation of constitutive equations.
Experimental efforts for Taylor-anvil impact tests have often been limited to near room temperature. The ‘Reverse Gun’ method proposed by Gust in 1982 allows for the Taylor impact specimen to be uniformly heated without temperature losses before impact. Through the use of finite element analysis, we explore two topics in this work. First, we examine whether the reverse gun experimental configuration is comparable to the traditional Taylor-anvil setup. Second, we assess the accuracy of several commonly employed flow strength models in terms of their ability to predict the reverse gun experimental results which involve dynamic loading conditions and complex thermo-mechanical coupling. The reverse gun simulations are performed for tantalum targets at initial temperatures in the range 295 K to 1295 K and velocities from 135 m/s to 242 m/s. We show that with suitable care in the modeling of the preheated reverse gun experiments one can make valuable assessments of flow strength models. Given the conditions explored, these observations probe the thermal softening, strain hardening, and strain rate sensitivity of the material.
The Chapter “Low-Pressure Cold Spray” presents a description of basics of LPCS technology, bonding mechanisms, temperature effects and LPCS localization processes. To illustrate the main aspects of LPCS system parameters determination, the numerical simulation and experimental data are presented. The emphasis is placed on the proper development of the cold-sprayed metal matrix composite coatings and their structure and properties, which are of paramount importance to the success of LPCS. Processes such as bonding, hardening and softening of the coating materials during cold spraying and coating structure formation at following heat treatment (sintering) are dealt with from the theoretical as well as practical aspect.
Quasi-static, quasi-dynamic and dynamic compression tests have been performed on a nitrogen alloyed austenitic stainless steel. For all strain rates, a high strain hardening rate and a good ductility have been achieved. In addition, this steel owns a great strain rate sensitivity. The temperature sensitivity bas been determined between 20°C and 400°C. Microstructural analysis has been performed after different loading conditions in relation to the behaviour of the material. Johnson-Cook and Zerilli-Armstrong models have been selected to fit the experimental data into constitutive equations. These models do not reproduce properly the behaviour of this type of steel over the complete range. A new constitutive model that fits very well all the experimental data at different strain, strain rate and temperature has been determined. The model is based on empirical considerations on the separated influence of the main parameters. Single Taylor tests have been realized to validate the models. Live observations of the specimen during impact have been achieved using a special CCD camera set-up. The overall profile at different times are compared to numerical predictions using LS-DYNA code.
The well-known theory of Taylor1 for the mushrooming of flat-ended projectiles uses a momentum equilibrium equation across the plastic wave front, as a basis for the analysis of the strain distribution. An analysis is now presented which employs basically the same approach as Taylor's in the general simplifying concepts of the process, but applies instead an energy equilibrium equation across the plastic wave. The resultant equations defining the final geometry are of simple form and the profiles predicted appear to be in closer agreement with experiment than are given by Taylor's theory. The present theory is developed to take some account of strain hardening, which appears to affect considerably the final profile. Essential differences between the present energy-based theory and Taylor's momentum-based theory are discussed.
It has long been known that metals may be subjected momentarily to stresses far exceeding their static yield stress without suffering plastic strain. One of the simplest methods for subjecting a metal to a high stress for a short time is to form it into a cylindrical specimen and fire this at a steel target. The front part of this projectile crumples up, but the rear part is left undeformed. If the target is rigid the distance which this portion travels while it is being brought to rest may be taken as the difference between the initial length and the length of the deformed specimen after impact. Knowing the velocity of impact, a minimum possible value can be assigned to the maximum acceleration of the material, and from this a minimum value for the yield stress can be calculated. The actual yield stress is considerably greater than this minimum, and methods are given for calculating a more probable value.
We have used a ’’reverse gun’’ that fires a ceramic plate at a preheated metal target to study the dependence of flow stress on temperature. Impact velocity versus L f /L 0 isotherms have been determined for Al, two types of Cu, 4340 steel, and Ta at 295, 730, and 1235 K, and for U at 295 and 725 K. A modified Steinberg–Guinan constitutive model and a Grüneisen equation of state were used to obtain hydrodynamic code simulations of the deformation process. A strong temperature dependence of the length ratio was clearly evident for all materials.
A model, applicable at high‐strain rate, is presented for the shear modulus and yield strength as functions of equivalent plastic strain, pressure, and internal energy (temperature). The parameters needed to implement the model have been determined for 14 metals. Using this model, hydrodynamic computer simulations have been successful in reproducing measured stress and free‐surface‐velocity–vs–time data for a number of shock‐wave experiments.
An experimental procedure originally proposed by G. I. Taylor to determine the dynamic yield point of metals is studied, using high‐speed computer simulations. A simple method is outlined for determining the yield strength of materials that can be described by elastic‐plastic theory. Results for several metals are presented.
A laser velocity interferometer instrumentation system has been developed which can measure the velocity history of either spectrally or diffusely reflecting surfaces. The system provides two interferometer fringe signals in quadrature to improve resolution and to distinguish between acceleration and deceleration. Accuracies of 2% or better are attainable for peak surface velocities of 0.2 mm/μsec or more. The system has been applied to the measurement of free surface motion in plate‐impact experiments, and to the measurement of the velocity history of a projectile during its acceleration down a long gun barrel.
An improved description of copper‐ and iron‐cylinder impact (Taylor) test results has been obtained through the use of dislocation‐mechanics‐based constitutive relations in the Lagrangian material dynamics computer program EPIC‐2. The effects of strain hardening, strain‐rate hardening, and thermal softening based on thermal activation analysis have been incorporated into a reasonably accurate constitutive relation for copper. The relation has a relatively simple expression and should be applicable to a wide range of fcc materials. The effect of grain size is included. A relation for iron is also presented. It also has a simple expression and is applicable to other bcc materials but is presently incomplete, since the important effect of deformation twinning in bcc materials is not included. A possible method of acounting for twinning is discussed and will be reported on more fully in future work. A main point made here is that each material structure type (fcc, bcc, hcp) will have its own constitutive behavior, dependent on the dislocation characteristics for that particular structure.
The axisymmetric deformation behavior of 0.9999 Cu is investigated at strain rates from 10-4 to 104 s-1. The variations of the flow stress and of the mechanical threshold stress (the flow stress at 0 K), which is used as an internal state variable, with strain rate and strain are measured. The experimental results are analyzed using a model proposed by Kocks and Mecking: results at constant structure are described with thermal activation theory; structure evolution (strain and strain rate evolution of the mechanical threshold stress) is treated by the sum of dislocation generation and dynamic recovery processes. A significant result is that the athermal dislocation accumulation rate, or Stage II hardening rate, becomes a strong function of strain rate at strain rates exceeding 103 s-1. This leads to the apparent increased strain rate sensitivity seen in a plot of flow stress at a given strain vs the logarithm of strain rate. An explanation is proposed for the strain rate dependence of this initial strain hardening rate based on the limiting dislocation velocity and average distance between obstacles.
This paper presents results of a research program in progress to describe the behaviour of 35NiCrMoV109 high strength steel over a wide range of strain rates for numerical simulations of dynamic events. In the low strain rate regime tensile tests in combination with a numerical stress state correction in terms of necking have been carried out. In comparison to the common Bridgeman-analysis this procedure allows to determine reliable necking-corrected stress–strain curves in a shorter time with a high accuracy as well. These data have been linked to high strain rate data from a novel modified Taylor-impact test using VISAR technique and data from planar-plate-impact-tests. The yield-stress strain-rate dependency covering a strain rate range of 11 orders of magnitude (5×10−5–1.78×106 s−1) have been measured. A bcc→hcp phase transition could be observed at pressures exceeding 13 GPa. A phenomenological material model including a strength model and an equation of state has been developed. The validation of the material model has been performed by numerical simulations of the modified Taylor-impact tests and the planar-impact-tests. In addition to common analysis by comparison of sample deformation, an enhanced model validation has been made by comparing the measured and calculated VISAR-signals while this technique is normally used for plate impact-test only. Agreement between the numerical simulations and the experimental results is found for the comparison of the deformation and the characteristic profile of the VISAR-curves.