Johnson-Cook Model Parameters Research Articles

Oblique penetration of spherical tungsten alloy projectiles on high-strength steel plates

The uniaxial tensile and dynamic compression properties of 22SiMn2TiB high-strength steel were first investigated, which shows certain strain-rate effects and obvious temperature-softening effects. Ballistic tests were carried out on 12 mm thick 22SiMn2TiB steel using ∅11 mm tungsten projectiles at 0°∼45° obliquity and a velocity of 500∼900 m/s. The study found that the ballistic limit velocity (BLV) increased monotonously with the increase of the obliquity. Based on the De Marre equation, a BLV calculation model was calibrated, which predicted experimental results well. Corresponding numerical simulation was carried out using LS-DYNA with fitted Johnson-Cook model parameters, its results are in good agreement with the test's. Additionally, the protective mechanism of the 22SiMn2TiB steel plate at an oblique angle was revealed through microscopic morphology analysis of the high-strength steel plate. It identifies adiabatic and normal shear failure, tensile and tensile-shear mixed failure, and the formation of different cracks in two groups, ultimately leading to plugging failure. The study provides a reference for the engineering design of the defensive structures using 22SiMn2TiB high-strength steel.

Numerical simulation on dynamic compression properties of sandstone under axial static preload

In this study, through a series of static mechanical tests and split Hopkinson pressure bar (SHPB) dynamic impact tests, the static and dynamic mechanical parameters of yellow sandstone are determined, and the Holmquist–Johnson–Cook model parameters of the rock are determined by the test data and theoretical calculation. The feasibility of a numerical model is verified, based on which the SHPB impact process under different axial pressure is subjected to numerical analysis. The results show that with increasing impact load, the degree of rock breakage increases, and the dynamic compressive strength and dynamic elastic modulus increase continuously. With the application and increase of axial pressure, the dynamic compressive strength and dynamic elastic modulus of the rock decrease gradually under the same impact load, and the maximum cumulative strain keeps increasing, indicating that under the influence of axial pressure, micro-cracks in the rock have initially developed and expanded. With increasing axial pressure, the rock is more vulnerable to breakage, and its weakening degree keeps increasing. The energy utilization rate of one-dimensional dynamic and static combined loading is affected by the axial compression ratio and impact load. At low axial compression ratio, the rock has high impact resistance but high energy utilization rate; at high axial compression ratio, the rock has low impact resistance but low energy utilization rate. Therefore, the combination of axial compression ratio and impact velocity can improve the crushing effect and energy utilization rate on the premise of clear crushing form requirements.

Study of effect of loading rate on mechanical properties of SS316LN and evaluation of parameters of Johnson-Cook model using parametric FE analysis and experimental data

The objective of this work is to evaluate the parameters of strain rate dependent Johnson-Cook material model using a hybrid procedure which uses finite element analysis as well as experimental data. The large strain rate tests were conducted to using split Hopkinson pressure bar test setup, whereas the quasi-static test was carried out using conventional testing machines. Johnson-Cook material model has been used to simulate the plastic deformation behavior of material under the high strain loading. This model provides the flow stress of the material as a function of equivalent plastic strain, plastic strain rate and temperature. The parameters, i.e., A, B, n, C and m of the model have been determined using a hybrid procedure as mentioned earlier. One of the important issues in split Hopkinson pressure bar testing is the variation of strain rate during the duration of loading. Due to decrease in reflected strain magnitude, the strain rate continuously decreases (as strain rate is proportional to reflected strain signal) and it is a characteristic of the above test method. However, this creates problem in evaluation of parameters of Johnson-Cook material model using conventional procedure. In this work, a modified procedure has been developed in order to take into account of this variation in strain rate as function of applied strain. The results of the method has been validated with experimental data. The parameters have been evaluated only for room temperature data and the effect of temperature shall be studied in future.

A numerical ballistic performance investigation of Armox 500T steel through ductile damage models

In this work, the ballistic response of an armor steel, Armox 500T, is numerically investigated through finite element (FE) analysis by utilizing the Johnson–Cook (JC) and modified Mohr–Coulomb (MMC) damage models, with a focus on emphasizing the consequences of different modeling approaches. Although Lode-dependent failure models are considered to increase the accuracy of numerical predictions for ductile failure, there remains a complete lack of clarity as to whether all conditions and materials necessitate the adoption of such models for ballistic impact simulations. In this context, MMC and JC model parameters are calibrated through tensile test data available in the literature enabling direct comparison between them. Damage models are then validated using ballistic impact tests of Armox 500T performed with 7.62 API projectiles. The results indicate that the MMC model outperforms the JC model at predicting the failure modes while both models demonstrate strong performance in anticipating the residual velocity. The influence of projectile nose shape, target plate thickness, and impact angle are further investigated, and the effect of incorporating the Lode parameter is discussed in detail. Impact simulations with the blunt projectile nose shape is found to be highly sensitive to the effect of Lode angle on failure, with differences of up to 20% between models, while 7.62 API shows the lowest sensitivity. The difference between the models’ predictions is observed to increase at lower impact velocities and higher impact angles demonstrating the necessity of a Lode-dependent failure model for such cases. The JC model consistently yields smaller residual velocities compared to the MMC model in all cases indicating that the MMC is more conservative in terms of predicting protective performance of Armox 500T.

Optimization of Johnson-Cook Constitutive Model Parameters Using the Nesterov Gradient-Descent Method.

Numerical simulation of impact and shock-wave interactions of deformable solids is an urgent problem. The key to the adequacy and accuracy of simulation is the material model that links the yield strength with accumulated plastic strain, strain rate, and temperature. A material model often used in engineering applications is the empirical Johnson-Cook (JC) model. However, an increase in the impact velocity complicates the choice of the model constants to reach agreement between numerical and experimental data. This paper presents a method for the selection of the JC model constants using an optimization algorithm based on the Nesterov gradient-descent method. A solution quality function is proposed to estimate the deviation of calculations from experimental data and to determine the optimum JC model parameters. Numerical calculations of the Taylor rod-on-anvil impact test were performed for cylindrical copper specimens. The numerical simulation performed with the optimized JC model parameters was in good agreement with the experimental data received by the authors of this paper and with the literature data. The accuracy of simulation depends on the experimental data used. For all considered experiments, the calculation accuracy (solution quality) increased by 10%. This method, developed for selecting optimized material model constants, may be useful for other models, regardless of the numerical code used for high-velocity impact simulations.

A novel calibration procedure of Johnson-Cook damage model parameters for simulation of scratch abrasion

Numerical simulation of scratch abrasion requires the use of a material damage model to simulate material degradation and removal. From our previous research, the stress state during scratch was found to show negative values of stress triaxiality and Lode angle parameter. However, models are “classically” calibrated using experiments with positive triaxiality and Lode angle parameter. In this work, a novel “scratch-based” calibration procedure is developed to acquire Johnson-Cook (JC) damage model parameters, using experimental scratch tests showing negative stress triaxiality and Lode angle parameter. An optimization procedure is used to obtain the parameters by minimizing the error between the experimental and numerical wear rates. Fracture loci obtained from both calibration procedures vary significantly, thus estimating different material losses. This highlights the importance of the calibration process of the damage model. The validity of the exponential Johnson-Cook fracture locus is questioned since it cannot account for accurate predictions under the entire range of stress triaxiality values covered in the paper. Hence, it may not be feasible for any calibration approach to obtain a single set of JC model parameters to accurately estimate the material loss for different cases of abrasion.

Determination of Johnson-Cook Constitutive of 15-5 PH Steel Processed by Selective Laser Melting.

To obtain a Johnson-Cook model of 15-5 PH steel formed by selective laser melting (SLM), and to determine the difference between the forging process, in this work, mechanical testing, penetration testing and numerical simulations were used to study 15-5 PH steel formed by SLM and forging. Finally, the Johnson-Cook model parameters and failure parameters of the 15-5 PH steel formed by SLM and forging were obtained. We found that the SLM process was beneficial for refining the grain size of 15-5 PH steel and for improving the mechanical properties of 15-5 PH steel, where the yield strength of its specimens increased by 13.1% compared with the forged specimens. The error between the numerical simulations and penetration tests was less than 10%, which verified the validity of the numerical model parameters. It was also found that the penetration ability and abrasion resistance of the SLM-shaped projectiles were slightly superior to those of the forged projectiles.

Research on the Dynamic Damage Properties and Determination of the Holmquist–Johnson–Cook Model Parameters for Sandstone

During blasting in engineering construction, the surrounding rock becomes unstable and is damaged under the impacts of multiple low-amplitude stress waves. It is of great practical significance to understand the damage evolution characteristics and the attenuation of the mechanical properties of rocks subjected to multiple stress waves. Single impact and repeated impact tests for sandstone were carried out using a split Hopkinson pressure bar (SHPB) loading system. The single impact test results showed that the sandstone materials were strain-rate-dependent, and the dynamic constitutive curve could be divided into four stages, namely the linear elastic stage, the new crack formation stage, the plastic strengthening stage and the unloading stage. The failure pattern mostly indicated splitting tensile failure, and the impact damage threshold was 45 J. The relationship between the damage and stress wave amplitude was D = 0.0029·exp\({\boxed{f_{()}}}\)(5.4127•σ/76.13) − 0.0504. The repeated impact test results showed that the dynamic compressive strength and the dynamic elastic modulus decreased, while the failure strain increased gradually as the number of impacts (n) increased. The sandstone specimen under repeated impacts had only one fracture surface compared with the single impact failure pattern. The cumulative damage presented the development form of ‘rapid rise–steady development–rapid rise’, and the damage evolution law could be expressed by D = 0.265 − 0.328·ln⁡⁡⁡\({\boxed{f_{()}}}\)(ln13.989/n). Finally, a set of methods to determine the Holmquist–Johnson–Cook (HJC) model parameters for sandstone was proposed based on a single impact test, repeated impact test, uniaxial compression test and triaxial compression test. The numerical simulation results of the SHPB test showed that the dynamic constitutive curves of sandstone were in good agreement with the experimental results.

Statistical Determination of Johnson-Cook Model Parameters for Porous Materials by Machine Learning and Particle Swarm Optimization Algorithm

Statistical Determination of Johnson-Cook Model Parameters for Porous Materials by Machine Learning and Particle Swarm Optimization Algorithm

Experimental and numerical investigation of sheet metal failure based on Johnson-Cook model and Erichsen test over a wide range of temperatures

The identification of Johnson-Cook parameters and the effect of different temperature gradients on A1050 sheet metal formability were performed. Tensile tests and modified Erichsen were carried out at different temperatures and also combined with numerical simulation to identify Johnson-Cook model parameters and the failure criterion. The obtained parameters were validated using the steam bulge test. A good correlation between numerical and experimental results was obtained in terms of failure behavior during the hot forming process. It was observed that hot forming improves the Erichsen index, and the thermal gradient strongly affects the failure zone position in the deformed specimens.

Corrigendum to “Identification of plastic constitutive Johnson–Cook model parameters by optimization-based inverse method” [J. Comput. Des. Eng., 2021; 8(4) 1082–97

Corrigendum to “Identification of plastic constitutive Johnson–Cook model parameters by optimization-based inverse method” [J. Comput. Des. Eng., 2021; 8(4) 1082–97

Identification of plastic constitutive Johnson–Cook model parameters by optimization-based inverse method

Abstract Because the design of most products incorporates numerical analysis such as the finite element method, these days, accurate determination of dynamic material model parameters is significant. Usually, the dynamic constitutive model parameters such as those in the Johnson–Cook (JC) model are determined by fitting stress–strain curves obtained by split Hopkins pressure bar (SHPB) tests at various strain rates and temperatures. However, the determination of model parameters by fitting cannot consider potential three-dimensional heterogeneities of stress propagation because the stress and strain are calculated with the assumption of one-dimensional wave propagation. In this study, to accurately determine plastic constitutive model parameters considering all of the potential heterogeneities of stress propagation, an optimization-based inverse method was proposed. Multiple objectives were defined with multiple experimental data that were obtained by SHPB tests at different conditions. The error was defined using transmitted and reflected bar signals obtained in experiments and finite element analysis with candidate model parameters. JC model parameters were set as design variables and determined to minimize the error. To show the reliability of the proposed method, experimental data were generated numerically by FE analysis with known model parameters. The parameters determined by the proposed method were compared with the known exact values. Model coefficients were also determined by fitting the stress–strain relations to show the superiority of the proposed method. Though the fitting of stress–strain curves can also reasonably determine the model coefficients, it was shown that the model parameters could be determined accurately by the proposed optimization-based inverse method.

Determination of Johnson Cook parameters for Ti-6Al-4 V Grade 5 experimentally by using three different methods

Accurate results can be obtained from numerical simulation only when it replicates or rather simulates the actual machining process as precisely as possible. To achieve the closest precision; boundary conditions, material model and mechanical material properties should be provided properly to the simulation file. Among all the material models, Johnson Cook material model is relatively simple to use. Every process operates under several loading condition with different deformation temperature and these values are different for different materials. For the successful simulation it is essential to have knowledge of exact Johnson Cook model parameters used for respective process and material at its operating temperature and strain rate. In this paper, Johnson Cook model parameters for Ti-6Al-4 V Grade 5 are found experimentally with strain rates as 1 × 10 −4 s −1 , 1.5 × 10 −4 s −1 , 1 × 10 −3 s −1 and 1.5 × 10 −3 s −1 and elevated temperature variations of 200 °C, 300 °C, 400 °C, 800 °C, 1000 °C, 1200 °C and at room temperature. Tensile test is conducted as it is the most suitable and cost effective among all to find properties, properties found are further used to find JC parameters by using three different methods: regression analysis method, least square method and logarithmic plot graph method. Values obtained after using all three methods are compared with each other and it is found that the deviation in values is not wide enough to hinder the results. This ensures that the researcher can practice whichever method is convenient to them according to their expertise.

Inverse Determination Method of Johnson-Cook Model Parameters Based on the Stress State Test of Notched Specimens

Inverse Determination Method of Johnson-Cook Model Parameters Based on the Stress State Test of Notched Specimens

Confirmation of Johnson-Cook Model Parameters for Nimonic 80A alloy by Finite Element Method

Nimonic 80A superalloy is frequently used due to its high creep resistance, oxidation resistance and high resistance to high temperature corrosion. On the other hand, due to compatibility of simulation of plastic deformation processes, Johnson-Cook model is chosen among the materials models such as Zerille Armstrong, Bordner Partom, Steinberg-Guinan etc. In this study, primarily, quasi-static compression tests were performed for 10-3, 10-2 and 10-1 s-1 strain rates at room temperature. Secondly, dynamic compression tests were secondly conducted at high strain rates ranging from 370 to 954 s-1 using the Split Hopkinson Pressure Bar (SHPB) apparatus. Then, the compression tests were conducted at a temperature level from 24~200 °C at the reference strain rate. Johnson-Cook model parameters of Nimonic 80A were determined by analyzing the data obtained from the tests. Lastly, the compression simulations with finite element method (FEM) were performed in ANSYS Workbench to confirm the accuracy of the parameters. In the light of the results, it was determined that there is an average of %3.23 deviation between the experimental and the simulation values. The result showed that accuracy of the Johnson-Cook parameters for Nimonic 80A superalloy was verified with FEM.

Influence of SD effect on Johnson–Cook hardening constitutive material model: Numerical and experimental investigation for armor steel

The influence of strength–differential (SD) effect has been investigated on Johnson–Cook (JC) material model parameters for armor grade RHA steel. Two set of JC model parameters has been developed with the help of compressive and tensile flow curve. Further, a finite element analysis (FEA) of static (at 10−3 s−1) and dynamic indentation (at 104 s−1) has been performed to validate the effect of tensile and compressive JC material model parameters. In addition, static and dynamic indentation FEA results has been compared with the expanding cavity model (ECM) and experimental Split–Hopkinson pressure bar results, respectively. FEA simulation with compressive data has been shown good agreement with experimental results and analytical models. %SD effect is increased with an increase in plastic strain in armor grade RHA steel.

Experimental Development of Johnson–Cook Strength Model for Different Carbon Steel Grades and Application for Single‐Pass Hot Rolling

Johnson–Cook (JC) high‐temperature strength material models have been widely used in finite‐element analysis (FEA) to solve variety of hot rolling problems. Herein, the temperature‐ and strain rate‐related parameters of JC model are experimentally calibrated for eight different steel grades including SAE 1018 and SAE 1045, structural steels (ASTM A572‐60, ASTM A690, and ASTM A992), two V‐modified 1535/45 grades, and one automotive advanced high‐strength steel grade. Experimental data are obtained from tensile tests performed at strain rates from 0.001 to 20 s−1 and at temperatures between 900 and 1200 °C. A genetic algorithm approach is used to determine JC model parameters for different steel chemistries and to calculate the rolling pressure for a simple flat rolling process using both a common analytical formulation and a finite‐element model (FEM). A model for the effects of steel chemistry on the JC model parameters is also discussed.

Numerical Simulation of Damage on Warm Deep Drawing of Al 6061-T6 Aluminium Alloy

This work focuses on the numerical simulation of warm deep drawing operation of car sump oil made with Al 6061-T6 aluminum alloy for the purpose of process optimization. The thermo visco-plastic behavior with damage effect of the material is described by the Johnson-Cook (JC) model. The JC model parameters for the Al 6061-T6 Aluminum alloy were exploited. Numerical simulation of the deep drawing operation was performed with the use of the ABAQUS FE software thanks to the dynamic Explicit Temperature-Displacement algorithm. The design of the different tools is obtained on the basis of the geometry of the finished product. Designing of punch, die and blank holder is performed using CATIA 3D CAD software. The warm forming method involves the heating of the blank holder and the die to a certain temperature, whereas, the punch is kept at room temperature. In this study, predefined temperatures of the die and blank holder and punch speed will be investigated among other stamping parameters. The computed damage evolution curves for a given set of the process parameters are retrieved at the end of the simulation to determine suitable forming conditions. It can be noted that the slower the damage evolution achieved within the blank, the more appropriate the process parameters. Thus, by increasing strain rate, main cracks change location.

Identification of Constitutive Model Parameters for Nimonic 80A Superalloy

Nimonic 80A is a nickel-chrome superalloy, commonly used due to its high resistance against creep, oxidation, and temperature corrosion. This paper presents the material constitutive models of Nimonic 80A superalloy. Johnson-Cook (JC) and modified JC model is preferred among the different material constitutive equations (Zerill Armstrong, Bodner Partom, Arrhenius type) due to its accuracy in the literature. Three different types of compression tests were applied to determine the equation parameters. Firstly, quasi-static tests were performed at room temperature. These tests were conducted at 10(-3), 10(-2), and 10(-1) s(-1) strain rates. Secondly, compression tests were performed at room temperature at high strain rates (370-954 s(-1)) using the Split-Hopkinson pressure bar. Finally, compression tests were performed at a temperature level from 24 to 200 degrees C at the reference strain rate (10(-3) s(-1)). Johnson-Cook and modified JC model parameters of Nimonic 80A were determined with the data obtained from these tests, and they were finally verified statistically.

Parameters of Holmquist–Johnson–Cook model for high-strength concrete-like materials under projectile impact

Holmquist–Johnson–Cook constitutive model has been widely used in analyzing the dynamic responses of concrete-like materials under projectile impact and explosive loadings, the constitutive parameters of which were always referred from the original documents and only applied to the normal strength concrete with the compressive strength of 48 MPa. Aiming to confirm the Holmquist–Johnson–Cook model parameters for high-strength concrete-like materials (compressive strength ≥60 MPa), based on the available test data from the quasi-static uniaxial compression, triaxial compression, Split-Hopkinson pressure bar, as well as the Hugoniot experiments, the strength parameters, the strain rate parameter, and the equation of state parameters of Holmquist–Johnson–Cook model for high-strength concrete-like materials are determined. Using the finite element program LS-DYNA, total eight sets of projectile penetration and perforation tests on high-strength concrete (uniaxial compressive strengths of 67.5–157 MPa) and high-strength rock targets (uniaxial compressive strengths of 60 and 154 MPa) are numerically simulated, respectively. By comparisons with the test data of penetration depths and residual velocities of the projectiles, the verifications of the proposed parameters are validated, which provides the reference for the design of protective structures.