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In the present paper, the parameters of Johnson - Cook (JC) constitutive model for two steels have been identified, based on the Hopkinson pressure bar test results. The experimental data has been taken from the split Hopkinson pressure bar data found in the literature. Using the measured strain pulses, the experimental stress - strain and deformation - time curves can be extracted. The experimental data have been processed using two different methods. In the first method strain rate assume to be constant during deformation and in the other one the deformation has been applied to a modeled specimen. In each method, an optimal set of material constants for JC constitutive model have been computed by minimizing the standard deviation of the numerically obtained stress - strain curve from the experimental data. Also a sensitivity analysis has been performed on JC constitutive model parameters and temperature changes during test have been investigated. The obtained results show that using constant strain rate method, leads to considerable error in results; for example in this study the minimum error is about 14%.

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Cold spray is a process which is used in coating industry and manufacturing of new parts. Experimental studies of this process are expensive and also very difficult due to high velocity of particles. Therefore, one effective method to study this process is its computer simulation. Previous works show that the Johnson-Cook hardening law has been usually used for simulation of this process. However, it is unanimously believed that this model is not able to reproduce the material behavior at extremely high strain rates commonly occurred in the cold spray process. Therefore, the simulation results are expected to improve if a suitable material model for extremely high strain rates is used. In this study, the PTW1 model was implemented in ABAQUS commercial finite element package. The cold spray process was then simulated for copper using both the PTW and Johnson-Cook hardening models. A comparison between the simulation and experimental results showed that the PTW model did improve the simulation results. The predicted flow stress by Johnson-Cook model was also shown to be not so sensitive to strain rate at extremely high strain rates.

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The Chaboche kinematic hardening model is generally used for modeling the plastic behaviour of material under quasi-static cyclic and monotonic loadings. This model is independent of strain rate and its constants are normally determined through quasi-static tests. Therefore, it cannot predict material behavior under high strain rate condition. On the other hand, the dynamic behaviour of materials even in some cyclic loadings is usually strain rate sensitive. In this investigation, the constants of Chaboche model are identified at various strain rates through quasi-static and dynamic tests and using these constants the effect of strain rate is incorporated in the Chaboche model. Moreover, the stress-strain diagrams at different strain rates are predicted using artificial neural network (ANN) and the results are compared with the experimental data. The results from the strain rate dependent Chaboche model shows reasonable agreement with the experimental data and the prediction from ANN. It is also shown in this work that the constants of Chaboche plasticity model are strain rate dependent and if the neural network is trained properly, it can be used for interpolating between the experimental data

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In This paper dynamic forming limit diagram has been investigated as fracture criteria for St13 steel. In fact, effect of various strain rates has been studied. This fracture criterion is based on the Marciniak-Kuczynski (M-K) theory and Solutions of equations have been obtained by applying the Newton -Raphson method. After solution three forming limit diagrams has been created: independent strain rate, dependent strain rate and dynamic forming limit diagram. Dynamic damage criteria investigates forming limit diagram in every strain rate. It is observed that the forming limit is increased by increasing the strain rate, Also for considering the anisotropic and the elastic-plastic behavior of material, the Hill 1948 yield criterion and the Swift hardening rule are used respectively. Also this paper is concerned with the uniaxial tensile properties and formability of sheet metal in relation to the strain rate effects. In order to verification of the results several experiments have been done with a Drop Hammer which is a high speed impact machine. For comparison between quasi static and dynamic damage criterions, all of the stages of experiment were simulated in finite element software Abaqus and results are compared together.

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Given the numerous applications of thick-walled cylinders, it is important to know the behavior of these structures. There are so many relationships for cylinders and spheres containing explosives which have been found mainly based on other experimental models. Hence derive an analytical model of the behavior of structures under internal and high-rate loading, like explosion in the cylinders, is of great importance. The main objective of this paper is to derive a mathematical model of isotropic thick-walled aluminum cylinder containing TNT in which JWL equation of state is considered for behavior of explosive expansion. The strength model the present analysis is based on the Cowper-Symonds in which strain rate at each moment is used for calculation of dynamic strength according to that. Therefore, given the instantaneous explosions pressure boundary conditions as well as instantaneous strain rate and its impact on the dynamic strength of the material, is of significant importance in this paper. With employing equations of equilibrium in thick-walled cylinders, the equations of radial and circumferential stresses and radial velocities derived. Given the instantaneous geometric and boundary conditions and correction the dynamic stress of material with respect to the strain rate, radial velocity by solving the differential equation, is calculated. After extraction of radial velocity, other stress equations will be evaluated. Furthermore, with considering the assumptions and in order to assess the overall results of the analytical modeling, computer simulation was done using Autodyn software, which shows good agreement with the analytical results.

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In this article constitutive equations on dynamic behavior of off- axis polymer matrix composites in different strain rates were investigated. Using the Hill Anisotropy and assumptions governing in fiber composites, a model was developed to express the dynamic behavior of polymer matrix composites. Using the flow rules and effective stress and assumptions in fiber composites like non plastic behavior of composites in fiber direction, the Hill parameters were omitted and reduced to one namely a_66 parameter. This model was called2D one- Parameter Plastic Model (also it can be developed for 3D composite layers). This model was developed for off axis composites as well. For each composite with different fiber directions, effective stress- effective strain was introduced. With choosing the right value for parameter a_66 by try and error, all the stress- strain curves were collapsed in to one single curve. Using this model and the experimental static and quasi- static results gathered from different authors (in range of〖 0.01s〗^(-1)), a viscoplastic model was obtained which can predict the polymer composite respond both in static and high strain rate tests (between 400 s^(-1) and 700s^(-1)). Constant parameters in high strain rates in this model were calculated through extrapolating the data in the static test rang. The accuracy of this model was investigated and approved by Split Hopkinson Pressure Bar test. The results showed that the visco plastic model can predict the dynamic respond of composite fibers in high strain rates very well.

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Mechanical properties of polymeric materials are significantly sensitive to the loading rate. Therefore, it is necessary to develop a dynamic constitutive model to investigate their strain rate dependent mechanical behavior. In this study, first by conducting torsion experiments the shear behavior of neat and reinforced epoxy with carbon nano-fibers (CNFs) was studied experimentally. Then, the Johnson-Cook (J-C) model has been modified to be able to model the shear behavior of neat polymers. The strain rate effects on elastic behavior of polymers were considered by introducing a material equation. Then, by combining the modified Johnson-Cook (MJ-C) model with a micromechanical model (Halpin-Tsai model) and using pure polymer experimental tesults and mechanical properties of carbon nano fiber, the strain rate dependent mechanical behavior of polymers reinforced with CNFs at arbitrary strain rates and volume farction of carbon nanofiber has been predicted. The new model presented in this research is called as the dynamic-micromechanical constitutive model. The predicted results for the neat and nano-phased polymers were compared with conducted and available experimental results. It has been shown that the present dynamic constitutive model can predict the strain rate dependent mechanical behavior of polymeric materials with a good accuracy.

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In this paper, the mechanical behavior of the Graphene Oxide (GO)/ epoxy nanocomposites has been investigated under different strain rates. To reach this goal, GO nano sheets were synthesized through Hummers method (a chemical method) and then GO/epoxy nanocomposite was prepared using the solution-based method. Standard specimens test were made from nanocomposite. In order to study the static and dynamic behavior of material, the static pressure test and the split pressure hopkinson bar test were performed on the specimens, respectively. The results showed that the stiffness and the strength of epoxy increase with adding GO to it. It was found that the behavior of epoxy is dependent on the strain rate so intense that its dynamic strength is more than static one about 50%. Furthermore, the effect of GO in low strain rates is more than high strain rates such that adding 0.3% weight ratio of GO increase the strength of epoxy by nearly 20% and 5% in 0.01 s^(-1) and 1100 s^(-1) of strain rates, respectively. In addition, the comparison of Scanning Electron Microscopy (SEM) images from the fracture surfaces of neat epoxy and its composite showed that the surface toughness of nanocomposite is more than epoxy’s.

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FLDs, in fact are the range of strain combinations which identify the beginning of local necking. Different parameters such as sheet thickness, structural defects, temperature, loading direction, forming speed and etc. have influence on these diagrams and one of the most effective parameters is forming speed and it has a direct connection with press speed in sheet forming. In this research FLD are calculated for aluminum 6061 sheets with 3mm thickness in rates of 20, 100 and 200 mm/min experimentally and simulated in the rates of 20, 100, 200, 500 and 800mm/min. In order to do the experimental tests, bulge test is conducted in sheets in six different sizes according to standard by hydraulic press and built steel die. Also numerical modeling was done using the Abaqus finite element software and the maximum strain gauge criterion by entering the Johnson Cook data. Experimental and modelling results verify is studied by surveying the tearing location and errors between FLDs and result showed that experimental and numerical data are compatible with acceptable errors. It was observed that by increasing forming speed FLD increases, in a way that by increasing the press speed from 20 mm/min to 200 mm/min, FLD increases for 30 percentage. This variation can have different reasons such as friction effect and interaction effects between die and sheets, because at the low forming speed (of less than 100 1/s for strain rate) and at the room temperature, the effect of strain rate and mass inertia are minimal.

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Forming limit diagrams (FLDs) are useful tools for prediction of the instability of sheet in metal forming. The goal of this study is to evaluate the formability of 260 brass alloy sheets under various strain rates (particularly at high strain rate). Three types of experimental procedure were developed: Nakazima test (for determination of the FLD at quasi-static condition), hydrodynamic forming (for determination of the FLD at intermediate strain rate) and Electrohydraulic forming (for determination of high strain rate FLD). Electrohydraulic forming (EHF) is a high velocity sheet metal forming process in which two or more electrodes are positioned in a water filled chamber and a high-voltage discharge between the electrodes generates a high pressure to form the sheet. Arbitrary Lagrangian Eulerian (ALE) formulations coupled with fluid–structure interaction (FSI) algorithms (that are available in the advanced finite element code LS-DYNA) were used to the numerical simulation of process and design of sheet metal specimen geometries. It was found that the forming limits of brass 260 in EHF increased more than 11% relative to the quasi-static. In addition, the formability of this material under the hydrodynamic loading is 4% higher than quasi-static values.

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Elastomers are a group of polymeric materials that have unique properties, including time-dependent behavior and time-independent, the mechanical behavior of this material is affected by various factors. In this study, the effect of increasing the silica nanoparticles and strain rates in two quasi-static and dynamic states on the tensile behavior of HDPE / POE has been investigated. For this purpose, an elastomeric material was first created with 40% HDPE and 60% POE mixing ratio. Then with increasing Nano silica particles, 4 sample types including 3 samples 0.7%, 1% and 1.4%, and one sample of HDPE/POE was fabricated. The samples were loaded at strain rate of 0.04 1⁄s, 0.07 1⁄s , 0.1 1⁄s , 0.14 1⁄s , 0.17 1⁄s in a quasi-static tensile state. In dynamic mode, tensile load with a strain rate of 160 1⁄s and 100 1⁄s was applied to the specimens using a new fixture designed on the low velocity impact test machine (Drop weight impact test machine). In the dynamic loading, the behavior of the elastomeric material is extremely dependent on the strain rate, with increasing the strain rate the level of stress and forces in both quasi-static and dynamic loads will be increase. The increase in force levels in dynamic loading is much more than static. Also, the new designed mechanism provides access to dynamic tensile data at different strain rates in a low velocity impact machine. On the other hand, with increasing Nano silica percentage, the tensile strength of the samples is noticeably increased.

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At present paper, an equivalent model with different dimensions and also with different dimensions and material in comparison with main body for strain rate sensitive structures subjected to high rate loading is presented by using the novel finite similitude method. The finite similitude method provides performing a test on the model instead of the original sample. This method is used to obtain the properties of model and to reverse the obtained results for model to main body by using the principles of nature (the law of conservation of mass, the law of conservation of momentum, the law of conservation of energy and the law of conservation of entropy) which is always true for any system. The relationships for both pure dimensional and simultaneously dimensional/material scaling of strain rate sensitive structures are presented. To evaluate the efficiency of the proposed relationships, the numerical results are obtained for impacted circular plates. It should be mentioned that the numerical results are obtained by using the finite element software LS-Dyna in which the strain rate effects are considered into account by using the Cowper-Symonds and Johnson-Cook constitutive equations. The results indicate that the scaled plate to one tenth of its original dimensions and also made of different material in comparison with original plate predicts the response characteristics of the original plate with a very good accuracy.

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In this study investigated the effects of momentum variations on fracture energy in Charpy impact testing of API X65 steel by experimental and numerical methods. Experimental analysis was conducted in the various speed of impact about 3.50 to 5.72 m/s and impact energy varied about 450 to 1200 J. The experimental results showed that increase of about 63% in impact speed increased the fracture energy about 15%, because of material properties dependence on loading rate. Numeral studies were performed in two categories with ABAQUS software. First mass variation in constant velocity assumed standard quantity about 5.5 m/s in which impact energy varied about 300 to 1200 J and the second, velocity variation with constant mass assumed 50 kg that impact energy varied about 625 to 1600 J. The simulation results showed the variations in mass had not any effect in fracture energy and in all analyses, it was about 265 J. However, increasing the velocity variations with constant mass, caused a slight reduction of about 5% in the fracture energy. The reason for the difference between experimental and numerical results is the lack of consideration of the effect of strain rate on mechanical properties of tested steel in numerical analysis.

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Polymers are used in a wide range of industries. In this research, the mechanical behavior of polymers used in the glass industry has been studied. The investigated polymers included thermoplastic polyurethane (TPU), polyvinyl butyral (PVB) and sentry glas (SG). These polymers were subjected to tension and compression tests at different strain rates from 0.001 to 0.25 s^-1. Also, the mechanical dynamic properties of the polymers were extracted using the mechanical dynamic analysis test at a constant frequency. The tensile test results showed that the mechanical behavior of polyurethane is not dependent on strain rate, but SG is highly sensitive to strain rate. Also, with increasing strain rate, the fracture stress of SG decreased drastically. The pressure test results showed that TPU can withstand more stress. The glass transition temperature of TPU was lower than the other two polymers. Overall, it can be concluded that among the polymers studied in this research, TPU had better mechanical behavior.