Taylor Impact Research Articles

An efficient and robust VUMAT implementation of elastoplastic constitutive laws in Abaqus/Explicit finite element code

This paper describes the development of an efficient and robust numerical algorithm for the implementation of elastoplastic constitutive laws in the commercial non-linear finite element software Abaqus/Explicit through a VUMAT FORTRAN subroutine. In the present paper, while the Abaqus/Explicit uses an explicit time integration scheme, the implicit radial return mapping algorithm is used to compute the plastic strain, the plastic strain rate and the temperature at the end of each increment instead of the widely used forward Euler approach. This more complex process allows us to obtain more precise results with only a slight increase of the total computational time. Corrector term of the radial return scheme is obtained through the implementation of a safe and robust Newton–Raphson algorithm able to converge even when the piecewise defined hardening curve is not derivable everywhere. The complete method of how to implement a user-defined elastoplastic material model using the radial return mapping integration scheme is presented in details with the application to the widely used Johnson–Cook constitutive law. Five benchmark tests including one element tests, necking of a circular bar and 2D and 3D Taylor impact tests show the efficiency and robustness of the proposed algorithm and confirm the improved efficiency in terms of precision, stability and solution CPU time. Finally, three alternative constitutive laws (the TANH, modified TANH and Bäker laws) are presented, implemented through our VUMAT routine and tested.

Preliminary investigation on impact resistance of additive manufactured Ti-6Al-4V

Understanding key failure mechanisms and material anomalies is one of the main challenges for an accelerated certification of additive manufactured parts. In this paper, the response to high velocity impact of Ti-6Al-4V printed by direct metal laser sintering was investigated and compared with wrought material. Taylor impact test at different impact velocities were performed with the scope to determine the velocity at onset damage development. Results show that such velocity is 57% lower than that of wrought material. Microscopy investigation on recovered samples reveals that the presence of initial voids in the microstructure, resulting from the printing process, reduces the shear resistance anticipating the formation of shear bands that is the main mechanism controlling fracture at high deformation rates.

Experimental characterization of dynamic deformation behaviour for SCM440 steel at high strain rates

The dynamic deformation behaviours of SCM 440 steel were characterized at the strain rates from 10-3 s-1 to 106 s-1. The uniaxial tensile tests at different temperature of 25 °C, 350 °C, and 700 °C were performed by a hydraulic universal testing machine equipped with a heating stage, and the compressive tests were conducted by using a spilt Hopkinson pressure bar (SHPB) at room temperature. Material coefficients of the Johnson-Cook constitutive model considering temperature effects were obtained based on the stressstrain relations from the experimental tests. In addition, Taylor impact tests on the SCM 440 steel were carried out to evaluate the accuracy of the determined material coefficients and characterize the dynamic behavior at the ultra-high strain rates and high temperature, by comparison with numerical simulations.

Constitutive Modeling of High-Strength Steel Designed for Ballistic Protection

Constitutive behaviour of a high-strength nanostructured bainitic steel NANOS-BA® was investigated in the article. A few types of mechanical tests under varying strain rates were carried out to determine the values of constants of Johnson-Cook flow and fracture models for the analysed material. In quasi-static conditions (8×10-3 s-1) the material samples were subjected to uniaxial tension and compression tests. In a high strain rates conditions (2,7×103 s-1) the Taylor impact test was carried out. On the basis of the data obtained from mechanical tests the constitutive model of the NANOS-BA® steel was built. It was then validated to determine the extent and degree of compliance between the numerical and experimental observations. The examples of combined numerical-experimental analyses of protective structures containing investigated material were shown. Small differences between the both types of results testifies that determined constants of Johnson-Cook equation may properly reproduce actual behaviour of the material, and the numerical model allows the preliminary evaluation of the effectiveness of armours containing layers of analysed grade of steel.

The mechanisms for strengthening under dynamic loading for low carbon and microalloyed steel

Taylor impact experiments were conducted to examine the mechanical behavior of four grades of structural steels. The dynamic mechanical response of microalloyed (HSLA), bainitic (MnB), low carbon (LC) and interstitial free (IF) steels at high strain rate loading were investigated systemically through Taylor impact test, over the range of impact velocities: 220 m/s, 270 m/s and 300 m/s. The study was focused on understanding the effect of microstructure on dynamic behavior of investigated materials. The various metallurgical phenomena that influence the mechanical behavior of the investigated steels during Taylor testing are difficult to isolate experimentally. In the present study, the data needed to interpret mechanical tests performed to define the inhomogeneous mechanical state of the steel specimens were obtained from the results of the hardness distributions and microstructural analysis. Examination of the cross sections of the tested specimens reveals that the work hardening, represented by hardness distributions, expands non-uniformly along the length and width of the Taylor specimen. This distribution appears to be related to the chemical composition and microstructure of the investigated steels. The mechanisms of different strengthening modes were discussed based on previous analysis of the uni-axial stress and strains response of these materials.

Determination of constitutive parameters from a Taylor test using inverse analysis

AbstractIdentification of material constitutive parameters is critical for accurate representation of the mechanical behavior of materials at high strain rates. However, customary characterization procedures based on curve fitting of stress‐strain curves, in some cases, are not accurate when the mechanical response exhibits strain rate dependency. In this paper, an inverse characterization technique based on the Taylor impact test is proposed. The technique uses a data reduction operator based on line moments and genetic algorithm optimization to determine the optimum constitutive parameters. Material parameters for a low carbon steel associated with the Plastic Kinematic model were determined using the proposed method.

Effect of a viscoelastic target on the impact response of a flat-nosed projectile

Taylor impact is a widely used strategy in which a flat-nosed projectile is fired onto a rigid anvil directly to determine the dynamic strength of rod specimens. Nowadays, the rigid anvil is often replaced by an output target bar to ensure the accuracy of measurement via recording strain signals in the output bar. For testing the dynamic strength of low-density materials, a low-impedance target bar, which exhibits viscoelastic characteristics is often employed. In this paper, an extended Taylor model is proposed to improve the idealization of treating the target bar as perfectly rigid material in the classic Taylor model, and the viscoelastic effect of the target bar is incorporated. The viscoelastic target bar is depicted by two elastic springs and one dashpot. Based on the plastic shock wave theory in the flat-nosed projectile associated with the viscoelastic wave analysis in the target bar, the viscoelastic effect of the target bar on the impact response of the flat-nosed projectile is investigated. The finite element simulation is also carried out to verify the theoretical model, and good agreement is found. The present theoretical model is also called the Taylor-cylinder Hopkinson impact, which provides a more accurate way to identify the dynamic material parameters. The dynamic responses of the present model are further compared with previous elastic and rigid target bar models. It is found that the viscoelastic effect of the target bar should be taken into consideration in the Taylor-cylinder Hopkinson impact test for low-impedance materials.

Dynamic Behavior and Constitutive Model for Two Tantalum-Tungsten Alloys under Elevated Strain Rates

The quasi-static and dynamic deformation behavior of two Ta-W alloys (Ta-2.5W and Ta-10W, mass fraction) was investigated by the quasi-static and dynamic compression test and Split Hopkinson pressure bar (SHPB) and Taylor impact tests. The results show that the yield stress of Ta-W alloys exhibits sensitivity to strain rate and W content. Based on the quasi-static and high strain-rate experimental data, the material constants in Johnson-Cook (JC) model were obtained for the two Ta-W alloys. In addition, validation of the derived constitutive model was carried out through comparison of Taylor impact inhomogeneous deformations under high strain rate (103∼104 s−1), obtained from simulations with their experimental counterparts. It is shown that the simulation results agree well with post-test geometries in terms of side profiles and impact-interface footprints for Taylor impact tests. To bridge the different spatial scale involved in the process of tantalum-tungsten alloy deformation, a meso-scale research was proposed via optical microscope (OM) image analysis. The results presented in this paper, provide new insights into the mechanisms suitable for the constitutive relations determination process.

Characterization of hardening behaviors of 4130 Steel, OFHC Copper, Ti6Al4V alloy considering ultra-high strain rates and high temperatures

This paper is concerned with the characterization of dynamic hardening behaviors of metallic materials at ultra-high strain rates ranging from 104 s−1 to 106 s−1. As typical metallic materials, three kinds of materials are selected for body centered cubic (BCC), face centered cubic (FCC), and hexagonal close packed (HCP) structures: 4130 steel; OFHC copper; and Ti6Al4V alloy, respectively. In order to investigate the hardening behaviors for the three materials, uniaxial tensile tests are conducted at room temperature of 25 °C and a wide range of strain rates from 10−3 s−1 to 103 s−1 with the Instron 5583, a high speed material testing machine (HSMTM), and a tension split Hopkinson pressure bar (TSHB). To consider the thermal softening effect at different strain rates, tensile tests are additionally performed at an elevated temperature up to 200 °C and strain rates of 10−3 s−1, 10−1 s−1, and 102 s−1. Hardening curves obtained from several experiments are expressed with a constitutive model by multiplying a strain hardening term, a strain rate hardening term, and a thermal softening term to describe material behaviors at large plastic strain, high strain rate, and elevated temperature, respectively. A well fitted constitutive model is utilized to interpolate and extrapolate stress–strain relation from low to ultra-high strain rates. The experimental and extrapolated data are implemented into finite element simulations as the preliminary material properties before calibration. A hybrid experimental-numerical approach is applied to precisely calibrate the extrapolated hardening behaviors at ultra-high strain rates by utilizing the Taylor impact test results. During the Taylor impact tests, images of several sequentially deformed shapes of projectiles are acquired by a high speed camera to compare with numerical simulation results. The stress–strain curves after calibration give notable improvements in the accuracy of numerical estimation of the deforming shapes of projectiles at ultra-high strain rates.

Experimental Study and Numerical Modelling of Low Velocity Impact on Laminated Composite Reinforced with Thin Film Made of Carbon Nanotubes

In this work, polymer laminated composites based on Epon 862 Epoxy resin, T300 6 k carbon fibers and carbon nanotubes (CNTs) were tested with the aim to elucidate the effect of CNTs on impact properties including impact force and capacity to absorb impact energy. The polymer matrix was reinforced by a random distribution of CNTs with fraction ranging from 0.5 to 4.wt%. Composite panels were manufactured by using the infusion process. Taylor impact test was used to obtain the impact response of specimens. Projectile manufactured from a high strength and hardened steel with a diameter of 20 mm and 1.5 kg of mass was launched by a compressed gas gun within the velocity of 3 m/s. Impact force histories and absorbed energy of specimens were recorded. A numerical model was employed to simulate the impact performance. This model has been accomplished by forming a user established subroutine (VUMAT) and executing it in ABAQUS software. Finally, the effect of CNTs amount on dynamic properties of laminated composites was discussed.

Dynamic properties of hybrid composite structures based multiwalled carbon nanotubes

The present paper investigates an experimental approach concerning the determination of dynamic behavior and damage kinetics of composite materials based on multiwalled carbon nanotubes (MWCNTs), embedded in electrospun reactive nanofibers in the Taylor impact test. Different impact energies have been considered namely; 21J and 39J to investigate the composite response. Projectiles are manufactured from a commercial steel 2071 with a nominal diameter of 50 mm and 1600 g of weight. The projectile was fired against a composite specimen initially hooked on a cell effort by a compressed gas gun within the velocity of 5 m/s and 7 m/s. Three types of specimens are considered: (1) MAT1 (carbon fiber reinforced epoxy polymer composite), MAT2 (consists of MAT1 and electrospun Polybenzmideazole-Bismaleimide (PBI-BMI) nanofibermats between carbon fiber layers) and MAT3 (consists of MAT2, where PBI-BMI nanofibermats are reinforced with multiwalled carbon nanotubes (MWCNTs)). The effect of the MWCNTs on the dynamic properties of the composite structures was studied. Microscope observations reveal damage progressive, buckling and crush-front propagation during tests. Application of the PBI-BMI reactive nanofibermats reinforced with MWCNTs leads to damage prevention, reducing damage area in composite samples.

Dynamic properties of carbon nanotubes reinforced carbon fibers/epoxy textile composites under low velocity impact

Abstract In this study, the impact response of polymer composites containing a random distribution of carbon nanotubes (CNTs) has been investigated by considering energy profile diagrams and associated force-time curves. The composite consists of CNTs initially filled Epon 862 Epoxy resin and implanted between plies of T300 6k Carbon fiber with 5HS (satin) weave. Different mass fractions of CNTs were used: 0% as reference, 0.5%, 1%, 2% and 4%. Taylor impact test was used to obtain the impact response of specimens. Projectile manufactured from a high strength and hardened steel with a diameter of 20 mm and 1.5 kg of mass was launched by a compressed gas gun within the velocity of 7 m/s. Deformation histories and damage modes of specimens were recorded during impact using high-speed camera. The effect of CNTs amount on dynamic properties and damage process was discussed.

Parameter Estimation of Metal Plasticity from Time History Data of Taylor Impact Test

Characterisation of material response under intensive dynamic loading due to explosion or projectile impact bears great importance as material properties are significantly influenced by strain rate. Among the several available methods, Taylor impact test is the simplest experimental approach for characterizing plastic behaviour of metals under high strain rate (up to 105 s-1). Here in, a cylindrical rod is impacted upon a rigid stationary anvil and the dynamic yield strength is estimated from the final deformed dimensions of the rod. Development of high speed photography enables the capturing of the time evolution of these dimensions experimentally. These time histories are rich with information about the material plastic behaviour and thus using them in estimating metal plasticity would be an important development. In the present study, an attempt is made to formulate an inverse problem and estimate parameters of metal plasticity using the time history data obtained from the Taylor impact test.

Characterization of Hardening Behavior at Ultra-High Strain Rate, Large Strain, and High Temperature

This paper is concerned with the characterization of the OFHC copper flow stress at strain rates ranging from 10−3 s−1 to 106 s−1 considering the large strain and high temperature effects. Several uniaxial material tests with OFHC copper are performed at a wide range of strain rates from 10−3 s−1 to 103 s−1 by using a INSTRON 5583, a High Speed Material Testing Machine (HSMTM), and a tension split Hopkinson pressure bar. In order to consider the thermal softening effect, tensile tests at 25°C and 200°C are performed at strain rates of 10−3 s−1,101 s−1, and 102 s−1. A modified thermal softening model is considered for the accurate application of the thermal softening effect at high strain rates. The large strain behavior is challenged by using the swift power law model. The high strain rates behavior is fitted with the Lim–Huh model. The hardening curves are evaluated by comparing the final shape of the projectile from numerical simulation results with the Taylor impact tests.

Influence of Mass Ratio on Forward and Reverse Ballistic Impact Equivalence: Experiments, Simulations, and Mechanism Analysis

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.

Validation of the Hardening Behaviors for Metallic Materials at High Strain Rate and Temperature by Using the Taylor Impact Test

This paper is concerned with the validation of the dynamic hardening behaviors of metallic materials by comparing numerical and experimental results of the Taylor impact tests. Several uniaxial tensile tests are performed at different strain rates and temperatures by using three kinds of materials: 4130 steel (BCC); OFHC copper (FCC); and Ti6Al4V alloy (HCP). Uniaxial material tests are performed at a wide range of strain rates from 10−3 s−1 to 103 s−1. Moreover, tensile tests are performed at temperature of 25 °C and 200 °C at strain rates of 10−3 s−1, 10−1 s−1, and 102 s−1, respectively. A modified Johnson–Cook type thermal softening model is utilized for the accurate application of the thermal softening effect at different strain rates. The hardening behaviors of the three materials are characterized by comparing the seven sequentially deformed shapes of the projectile from numerical and experimental results of Taylor impact tests.

Mechanical Properties of Low Density Polyethylene

The mechanical properties of polymers, particularly as a function of temperature and strain rate, are key for implementation of these materials in design. In this paper, the compressive response of low density polyethylene (LDPE) was investigated across a range of strain rates and temperatures. The mechanical response was found to be temperature and strain rate dependent, showing an increase in stress with increasing strain rate or decreasing temperature. A single linear dependence was observed for flow stress on temperature and log strain rate over the full range of conditions investigated. The temperature and strain rate data were mapped using the method developed by Siviour et al. based on time–temperature superposition using a single mapping parameter indicating that there are no phase transitions over the rates and temperatures investigated. Taylor impact experiments were conducted showing a double deformation zone and yield strength measurements in agreement with compression experiments.

Validation of material constitutive parameters for the AISI 1010 steel from Taylor impact tests

Numerical simulations of high strain-rate events require robust characterization of constitutive material parameters in order to predict accurately the deformation process. Historically, this characterization has been performed using non-standardized techniques such as the Taylor impact test, where specimen's final deformed geometry is used to determine the material constitutive parameters by inverse analysis. However, validation of material parameters found in this way, in terms of internal plastic strains, is an open research problem. In this work, material constitutive parameters of steel AISI 1010 found by inverse analysis from Taylor tests at ~5×103s−1 were validated. This was done by comparing the Vickers hardness profile along the axis of a deformed specimen against the numerically calculated hardness from a finite element model of the Taylor impact, which used the constitutive parameters found by inverse analysis. To map the simulated effective plastic strains found in the model into Vickers hardness, an experimentally-derived analytical relation between compressive quasi-static plastic strains and Vickers hardness on cylinders of the same material was used. It was found that the material constitutive parameters of steel AISI 1010 characterized by inverse analysis, from silhouettes of deformed Taylor tests, are capable to predict the plastic-strain distribution inside the deformed material.

Plastic deformation of high-purity a-titanium: model development and validation using the Taylor cylinder impact test

Results of an experimental study on the quasi-static and high-rate plastic deformation due to impact of a high-purity, polycrystalline, a-titanium material are presented. To quantify the plastic anisotropy and tension-compression asymmetry of the material, first monotonic uniaxial compression and tension tests were carried out at room temperature under quasi-static conditions. It was found that the material is transversely isotropic and displays strong strength differential effects. To characterize the material's strain rate sensitivity, Split Hopkinson Pressure Bar tests in tension and compression were also conducted. Taylor impact tests were performed for impact velocity of 196 m/s. Plastic deformation extended to 64% of the length of the deformed specimen, with little radial spreading. To model simultaneously the observed anisotropy, strain-rate sensitivity, and tension-compression asymmetry of the material, a three-dimensional constitutive model was developed. Key in the formulation is a macroscopic yield function [1] that incorporates the specificities of the plastic flow, namely the combined effects of anisotropy and tension-compression asymmetry. Comparison between model predictions and data show the capabilities of the model to describe with accuracy the plastic behavior of the a-Ti material for both quasi-static and dynamic loadings, in particular, a very good agreement was obtained between the simulated and experimental post-test Taylor specimen geometries.

High strain-rate plastic deformation of molybdenum: Experimental investigation, constitutive modeling and validation using impact tests

In this paper, an experimental study on the quasi-static behavior and dynamic behavior of a polycrystalline molybdenum material is presented. Due to the material's limited tensile ductility, successfully acquiring data for impact conditions is very challenging. For the first time, Taylor impact tests were successfully conducted on this material for impact velocities in the range of 140–165 m/s. For impact velocities beyond this range, the very high tensile pressures generated in the specimen immediately after impact lead to failure. A constitutive model accounting for the key features of the Mo plastic behavior, i.e. its tension–compression asymmetry and plastic anisotropy was developed. An implicit solver was used to simulate the impact deformation. A good agreement was obtained between predictions and experimental outlines of the specimens. Furthermore, it was shown that the model can be used to gain understanding of the dynamic deformation process in terms of time evolution of the pressure, the extent of the plastically deformed zone, distribution of the local plastic strain rates, and when the transition to quasi-stable deformation occurs.