Johnson-Cook Constitutive Equation Research Articles

Determination of Chip Compression Ratio for the Orthogonal Cutting Process

The chip compression ratio is the most important characteristic of various machining processes with chip generation. This characteristic enables the determination of kinetic and other energy loads on the tool and the machined material. This provides an overall evaluation of the machining process and the possibility of its subsequent optimization. This paper presents the results of determining this cutting characteristic by experimental method, analytical calculation, and numerical modeling. For the analytical calculation of the chip compression ratio, an analytical cutting model developed based on the variational principle of the minimum potential energy was used. A finite element model of orthogonal cutting was used for the numerical simulation of the above process characteristic. Experimentally, the chip compression ratio was determined by the ratio of the chip thickness to the cutting depth (undeformed cutting thickness). The chip thickness was determined by direct measurement using chip slices obtained during the cutting process. The Johnson–Cook constitutive equation was used as the machined material model and the Coulomb model was used as the friction model. The generalized parameters’ determination of the constitutive equation was performed through a DOE (Design of Experiment) sensitivity analysis. The variation range of these parameters was chosen based on the analysis of the effect of individual parameters of the constitutive equation on the chip compression ratio value. The largest deviations between the experimental and analytically calculated values of the chip compression ratio did not exceed 21%. At the same time, the largest deviations of simulated values of the indicated cutting characteristic and its experimental values did not exceed 20%. When comparing the experimental values of the chip compression ratio with the corresponding calculated and simulated values, the deviations were within 22%.

A Study of Drilling Parameter Optimization of Functionally Graded Material Steel–Aluminum Alloy Using 3D Finite Element Analysis

Composite materials, such as aluminum alloy FGMs, provide advantageous weight reduction properties compared to homogenous pure structures while still preserving sufficient stiffness for diverse applications. Despite various research on drilling simulation concepts and ideas for these materials, there still needs to be an agreement on the process modeling. Researchers have looked into a lot of different numerical methods, including Lagrangian, Eulerian, arbitrary Lagrangian–Eulerian (ALE), and coupled Eulerian–Lagrangian (CEL), to find solutions to problems like divergence issues and too much mesh distribution, which become more of a problem at higher speeds. This research provides a global analysis of bottom-up meshing for eleven 1 mm layers using ABAQUS® software. It combines the internal surface contact approach with the Lagrangian domain’s kinematic framework. The model uses the Johnson–Cook constitutive equation to precisely predict cutting forces, stress, and strain distributions, optimizing cutting parameters to improve drilling performance. According to Taguchi analysis, the most favorable parameters for reducing cutting force and improving performance are a rotational speed of 700 rpm, a feed rate of 1 mm/s, and a depth of cut of 3 mm. The findings suggest that increasing the feed rate and depth of cut substantially affects the cutting force, while the rotational speed has a comparatively little effect. These ideal settings serve as a foundation for improving FGM drilling efficiency.

Investigation of oblique water entry of high-speed supercavitating projectiles using transient fluid-structure interaction simulation

This study employs a fluid-structure interaction simulation to examine the structural deformation of supercavitating projectiles during high-speed oblique water entry. A cavitation flow field simulation model is established using the VOF multiphase and cavitation models, while the structural dynamics model of the projectile is implemented using the Johnson-Cook constitutive equation. The transient fluid-structure interaction simulation is conducted through data transfer between the two models. Numerical simulations are then conducted with the assumptions of a rigid body, linear elasticity, and nonlinearity, respectively. The results indicate that the high-speed water entry induced substantial hydrodynamic force and plastic strain accumulation in the projectile, leading to considerable bending deformation. It was found that the deformation significantly influenced the hydrodynamic forces, highlighting the importance of fluid-structure interaction modeling. Moreover, the attack angle directly impacts the resulting deformation mode. Specifically, under high-speed conditions, three distinct deformation modes are observed at different attack angles: minimal deformation at low angles, an L-shaped bending at higher angles, and an S-shaped bending when the angle exceeds the threshold. This study highlights the importance of fluid-structure interaction methods in analyzing the deformation behavior of supercavitating projectiles during high-speed oblique water entry. The results show that the bidirectional dynamic interaction between fluid and structure significantly influences the structural stability of the supercavitating projectiles. The relevant conclusions can provide a reference for the optimal design of supercavitating projectiles to ensure the structural stability under high-speed conditions.

Improvement of Analytical Model for Oblique Cutting—Part I: Identification of Mechanical Characteristics of Machined Material

Analytical cutting models have recently become quite widespread due to the simplicity and rapidity of calculations as well as the stability of the solutions. This paper considers a procedure for determining the mechanical properties of machined material based on parameters for the analytical model of oblique cutting for a certain range of changes in cutting modes and inclination angles of the tool cutting edge. The model is based on the energy method of determining the main cutting process characteristics using the extreme assumptions of continuum mechanics. It is proposed to determine the parameters characterizing the mechanical properties of the processed material using the Johnson–Cook constitutive equation in two stages: preliminary determination of the constitutive equation parameters based on the results of mechanical compression specimen tests and experimental data of the oblique cutting process, and specifying the generalized values of the constitutive equation parameters using the inverse method through the finite element cutting model. The adequacy of the applied analytical cutting model is confirmed by comparing the kinetic characteristic values calculated using the analytical model of oblique cutting with the application of the specified parameters of the constitutive equation and the measured values of the kinetic characteristics. The deviation between the calculated and measured values of the cutting force components when changing the cutting depth (undeformed chip thickness) does not exceed 15%. The difference between the calculated and measured values of the cutting force components when the cutting speed is changed is about 20%.

Milling Force Modeling Methods for Slot Milling Cutters

The slot milling cutter is primarily used for machining the tongue and groove of the steam turbine rotor, which is a critical operation in the manufacturing process of the steam turbine rotor. It is challenging to predict the milling force of a groove milling cutter due to variations in rake, rake angles and cutting speeds of the main cutting edge. Firstly, based on a limited amount of experimental data on turning, we have developed an equivalent turning force model that takes into account the impact of the rounded cutting edge radius, the tool’s tip radius and the feed rate on tool’s geometric angle. It provides a more accurate frontal angle for the identification method of the Johnson–Cook material constitutive equation. Secondly, the physical parameters, such as shear stress, shear strain and strain rate on the main shear plane, are calculated through the analysis of experimental data and application of the orthogonal cutting theory. Thirdly, the range of initial constitutive parameters of the material was determined through the split Hopkinson pressure bar (SHPB) test. The objective function was defined as the minimum error between the theoretical and experimental values. The optimal values of the Johnson–Cook constitutive equation parameters A, B, C, n and m are obtained through a global search using a genetic algorithm. Finally, the shear stress is determined by the governing equations of deformation, temperature and material. The axial force, torque and bending moment of each micro-segment are calculated and summed using the unit cutting force vector of each micro-segment. As a result, a milling force prediction model for slot milling cutters is established, and its validity is verified through experiments.

Study on dynamic mechanical properties of tungsten copper alloy and application of shaped charge

The tungsten-copper alloy liner has better performance than the copper liner. In order to better study the jet forming and penetration characteristics and dynamic mechanical properties of tungsten-copper alloy-shaped charge liner, this paper uses a multi-functional mechanical experimental machine and a Hopkinson bar device to carry out quasi-static tensile and dynamic impact tests, respectively, and fit the Johnson-Cook constitutive equation. The obtained parameters are used to carry out numerical simulations and compared with the experiment. The results show that the stress of the dynamic impact curve is higher than that of the quasi-static stress, and the strain rate strengthening effect is more obvious. There is an adiabatic temperature rise at the strain rate and an obvious thermal softening effect at different strain rates. At the highest strain rate, it shows an obvious strain rate strengthening effect and obvious plasticizing effect, and the tungsten-copper alloy has a certain sensitivity to strain rate. The precision of the Johnson-Cook constitutive model is higher, and it can better describe the plastic flow stress of tungsten-copper alloy at a high strain rate. When the parameters of the fitted Johnson-Cook model are used in the numerical simulation, the error between the numerical simulation and the actual is small. The obtained Johnson-Cook model and dynamic mechanical properties can help the follow-up study on the influencing factors of tungsten-copper jet forming and fracture, including the effect of material strength on injection instability, the integration of the shear band model with hydrodynamics, and the comparison of injection molding penetration with copper liners provide relevant data.

A response prediction method for clamped circular plates subjected to repeated blast loading

The aim of the present investigation is to study the behavior of metal circular plates that are clamped under the repeated blast loading at stand-off distances. In this paper, the Johnson-Cook constitutive equation involving the effects of material strain hardening and strain rate sensitivity is introduced into the empirical analysis equations used to predict the midpoint displacement of circular plates. Thus, a group of non-dimensional empirical equations are proposed for predicting the midpoint displacement of clamped metal circular plates subjected to both single and repeated blast loading. The proposed non-dimensional empirical analysis equations are verified with the simulation analysis and experimental results of previous papers. It indicates that the proposed non-dimensional midpoint displacement prediction equations demonstrate good consistency in predicting the deformation of clamped metal circular plates under both single and repeated blast loading conditions.

Scaling of bi-material sandwich panels subjected to impact loadings

Scaling is a widely used concept in impact and explosion engineering which is mainly utilized to predict the response behaviour of large-scale mechanical structures by conducting experiments on scaled trial models. However, the practical application of currently available conventional scaling methodologies for impact and explosive processes are significantly restricted by their inability to properly capture the scale effects of strain rate and strain hardening. Also, they are suffering from an insufficient number of independent degrees of freedom. Furthermore, the zeroth-order finite similitude theory, which can annihilate the non-scalability of rate and hardening effects, doesn’t provide us with efficient scaling methods when the investigated structure is made out of different materials. More precisely, the zeroth-order finite similitude theory and the classical dimensional analysis, which are suffering from a limited number of independent degrees of freedom, cannot scale the elastic-plastic behaviour represented by different parts of a structure made out of different materials. In other words, classical scaling methodologies including dimensional analysis and even the zeroth-order finite similitude theory cannot fix two different features having the same unit using different degrees of freedom, which make them useless for structures made of more than one material such as bi-material sandwich panels. In the presented paper, a new scaling methodology is developed based on the recently proposed first-order finite similitude theory which for the first time enables us to capture the rate dependent plastic behaviour of an impacted structure made out of two different materials. A sandwich panel made of two different materials which is subjected to an impact loading is considered as the case study in order to investigate the efficiency of the proposed first-order based scaling technique. The numerical results are determined using Abaqus finite element software in which the Johnson-Cook constitutive equation is utilized to take into account the rate and hardening effects on the initial yield stress. The results reveal that the behaviour of impacted full-scale bi-material sandwich panels can be predicted with a high accuracy when the extra degree of freedom provided us with the first-order finite similitude (i.e. R1) is set to vary between −1 and 1 (i.e. [Formula: see text]). Furthermore, it is found that the pure mechanical and thermo-mechanical behaviour of the impacted core honeycomb are highly accurately predicted using scaled-down trial models which are made from dissimilar materials and designed based on the zeroth-order finite similitude theory.

Estimation of temperature in the cutting area during orthogonal turning of grade 2 titanium

The authors introduce an experimental-analytical method for determining the average temperature values in the PSZ (primary shear zone) and the SSZ (secondary shear zone) during orthogonal turning of grade 2 titanium with a use of an uncoated carbide tool with a positive rake angle and a flat rake face. The presented method is based on an algorithm in which the values of shear stress in the PSZ and the SSZ are calculated by means of the Johnson–Cook constitutive equation and Oxley’s model of cutting mechanics. Average temperature values in the PSZ and the SSZ are determined by iteratively finding the minimum difference between the calculated stress values. As its inputs, the algorithm uses the values of the feed and the tangential cutting force components, the value of chip flow velocity on the rake face, and the constants of the Johnson–Cook constitutive equation. The model was validated with a use of empirical data collected during the experiments. The test rig consisted of a KNUTH Masterturn 400 precision lathe equipped with a dynamometer, a high-speed camera, and a thermal imaging camera.

Effect of Grain Size on Dynamic Compression Behavior and Deformation Mechanism of ZK60 Magnesium Alloy

The dynamic compression deformation of 3 µm, 15 µm and 25 µm grain size ZK60 alloys under high-strain-rate compression is systematically studied. Dynamic compression experiments at a strain rate of 1700 s−1 were conducted using a split Hopkinson pressure bar, and the microstructure of the specimen was characterized via electron backscatter diffraction and transmission electron microscopy, as well as via the calculation of Schmid factors. The results showed that the alloy exhibited the decrease in yield strength and peak stress as the grain size increased under dynamic compression. The grain refinement in the alloy was conducive to the activation of basic slip. In turn, an increase in the grain size caused the transition in the main deformation mechanism from pyramidal <a> slip to {10−12} tensile twinning and pyramidal <a> slip. Based on these deformation mechanisms, the Johnson-Cook constitutive equation with different grain sizes was modified, and the fitting results were in accordance with the experimental data.

Numerical Modeling of Titanium Alloy Ti10V2Fe3Al Milling Process

The simulation of material machining using finite element models is a powerful tool for the optimization of simulated processes and tools, as well as for the determination of cutting process characteristics that are difficult or practically impossible to determine by experiment. The paper presents results of the numerical simulation of the titanium alloy Ti10V2Fe3Al (Ti-1023). The behavior of the machined material was modeled with the Johnson–Cook constitutive equation, and its damage mechanism was modeled using the Cockcroft and Latham model. The parameters of the constitutive equation for machined material behavior and damage were determined using a DOE sensitivity analysis during orthogonal cutting. The values of the cutting force components, as well as the minimum and maximum chip thicknesses, were used as target functions for the DOE analysis. The generalized values of the constitutive equation parameters and the fracture stress values determined by the DOE analysis were calculated as the set intersection of individual multitude values of these parameters. The simulation results of the studied cutting processes showed an acceptable agreement with the experimental data when the cutting speed and tool feed changed significantly. The deviation in the simulated values of the cutting forces from their measured values ranged from about 10% to about 20%.

절삭 시뮬레이션에 사용되는 구성방정식 종류별 절삭력 예측

The constitutive equation shows the difference in the predicted result value related to cutting according to the coefficient value and type. Therefore, in this study, the cutting force and chip shape obtained from the cutting test for each cutting condition were applied as standards. And the simulation results applying the constitutive equation were compared. The constitutive equations used in this study are the Power-Law, Johnson-Cook, and S-K constitutive equations. Since the Power-Law constitutive equation is basically applied to the cutting simulation, it was used as the internal material property, and the Johnson-Cook constitutive equation and the S-K constitutive equation determined the coefficient value and performed simulation as a user property. As a result, it was confirmed that the tangential force and chip shape prediction in the cutting force and chip shape prediction of AAl7075 material were valid through simulation using the S-K constitutive equation.

Dynamic Behavior of a Novel High-Strength and Ductile Near-α Titanium Ti-Al-Mo-Zr-Fe-B Alloy

In this study, the dynamic compression properties of a new high-strength (>1000 MPa) and ductile (>15%) near-α titanium Ti-6Al-1Mo-2Zr-0.55Fe-0.1B alloy were investigated at high strain rates of 1620 s−1~2820 s−1 by a split Hopkinson pressure bar (SHPB). The microstructural evolution of the samples before and after the dynamic deformation was analyzed by electron backscatter diffraction (EBSD). The results indicated that the strength of the alloy enhanced significantly under the dynamic loading compared with the quasi-static compression and increased with the increase in the strain rate. An abundance of deformation twins released the dislocation pile-up and coordinated the plastic deformation of alloy during the dynamic loading. The dynamic plasticity constitutive equation of the alloy was obtained by fitting high strain rate experimental data at room temperature by the Johnson–Cook constitutive equation with the modified temperature term.

Determination of the Shear Angle in the Orthogonal Cutting Process

Determination of the shear angle by experimental and analytical methods, as well as by numerical simulation, is presented. Experimental determination of the shear angle was performed by analyzing the chip roots obtained by the method of cutting process quick stop through purposeful fracture of the workpiece in the area surrounding the primary cutting zone. The analytical determination of the shear angle was carried out using the chip compression ratio and was based on the principle of a potential energy minimum. Measurement of the shear angle in the numerical simulation of orthogonal cutting was performed using the strain rate pattern of the machined material at the selected simulation moment. It was analyzed how the parameters of the Johnson–Cook constitutive equation and the friction model affect the shear angle value. The parameters with a predominant effect on the shear angle were determined. Then the generalized values of these parameters were established with a software algorithm based on identifying the intersection of the constitutive equation parameter sets. The use of generalized parameters provided the largest deviation between experimental and simulated shear angle values from 9% to 18% and between simulated and analytically calculated shear angle values from 7% to 12%.

Research on Conventional and High-Speed Machining Cutting Force of 7075-T6 Aluminum Alloy Based on Finite Element Modeling and Simulation

In current industrial practice, the finite element modeling of the metal cutting process is essential. In this paper, finite element analysis of conventional and high-speed cutting of 7075-T6 aluminum alloy is carried out. A finite element model of the 7075-T6 aluminum alloy was developed using the Johnson Cook instant on equation to investigate the milling behavior of the alloy under conventional and high-speed conditions. The cutting forces in the X-direction, Y-direction, and Z-direction were predicted analytically for five groups of different Johnson Cook models with different material constants, and the predicted results were compared with the experimentally determined cutting forces to investigate the influence of the Johnson Cook constitutive model parameters on the simulation of the cutting forces of the 7075-T6 aluminum alloy. The results showed that the constitutive model parameters are inconsistent for conventional and higher speed cutting conditions. Under conventional cutting conditions, the JC4 model predicts the material factor cutting forces in good agreement with the experimental results, while under high-speed cutting conditions, the JC5 model predicts the material factor cutting forces in good agreement with the experimental results, but that the finite element model has good applicability in predicting machining performance. Only the experimental data obtained by covering the real strain, strain rate and temperature range to determine the material constant of the Johnson Cook constitutive equation can accurately predict the cutting force in all directions.

Experimental and numerical study on micro-blasting process of 3A dental implant titanium alloy: A comparison between finite element method and smoothed particle hydrodynamics

In the present study, solid particle erosion due to micro-blasting of dental implants (3A) made of titanium alloy under the impact of multiple alumina particles with an average diameter of 85 μm was analyzed, experimentally and numerically. The numerical investigation was conducted using finite element (FE) and smoothed particle hydrodynamics (SPH) methods. The erosive behavior of this alloy was simulated as impacts in micro-scale based on Johnson-Cook constitutive equations. By focusing on the particles impacts, a representative volume element (RVE) technique was proposed to simulate the arbitrary multiple particle impacts. The results of FE and SPH models are validated and compared with the experimental results. The effects of particle velocity and impact angle on the erosion rate of the alloy are then investigated. Finally, an equation is presented for prediction of the erosion rate versus velocity and angle of impact. The results indicate that for all impact velocities, the combination of penetration and cutting can create a critical condition of erosion damage for the titanium alloy.

A modified Johnson-Cook constitutive model for structural steel after cooling from high temperature

High temperature has a significant impact on the mechanical properties of steel structural members, which can develop a potential collapse. Currently, various studies have been concentrating on the post-fire mechanical properties of different steels, while few of them considered the corresponding constitutive model. Therefore, in this paper, the classical Johnson-Cook constitutive equation is selected as a benchmark and is modified to fit the conditions in which the effects of heating and cooling on the mechanical properties of fire-affected steel are considered. To this end, three commonly used structural steels, namely Q345B, Q460 and Q690D, are selected in this paper. First, the specimens were heated to different target temperatures, and then naturally cooled down to the ambient temperature in the air. After cooling from the exposure temperatures, the subsequent tensile tests were performed on the fire-affected specimens to capture the failure modes and study the residual mechanical properties. To verify the proposed constitutive model, an Abaqus subroutine (UMAT) program was developed in this study. The experimental data of water-cooled specimens obtained in our previous studies were also selected to further test the feasibility of this new model. The results show that the exposure temperature and steel grade have significant effects on the residual mechanical properties of the structural steel specimens when the target temperature exceeds 700 °C. Meanwhile, the modified Johnson-Cook constitutive is able to predict the stress –strain behavior precisely, regardless of the cooling method. The results obtained in this study are helpful for both further research and engineering application when doing a numerical study of the fire-affected steel structures.

Room temperature strengthening mechanisms, high temperature deformation behavior and constitutive modeling in an Al-3.25Mg-0.37Zr-0.28Mn-0.19Y alloy

To improve the ambient strength and high temperature ductility, a novel Al-3.25Mg-0.37Zr-0.28Mn-0.19Y (wt.%) alloy has been fabricated by multidirectional forging and warm rolling. Microstructures and mechanical properties were investigated by light microscope, X-ray diffraction apparatus, transmission electron microscope, and tensile tester. The ultimate tensile strength, yield strength, and elongation of 354.67 ± 0.04, 254 ± 3 MPa, and 18.47% were achieved in the processed alloy, respectively, at room temperature. The maximum superplasticity of 412.5% was demonstrated in this fine-grained (grain size of 8.80 ± 1.06 μm) alloy at 793 K and 8.33 × 10−4 s−1. An ambient strengthening sequence was obtained: grain boundary strengthening > dislocation strengthening > Orowan strengthening > solid solution strengthening. The occurrence of Portevin–Le Chatelier effect or serrated flow in as-annealed alloy was confirmed by theoretical model estimation and experimental evidence. Microstructural evolution and flow stress curves confirmed that dynamic recovery and dynamic grain growth occurred at elevated temperatures; Sotoudeh-Bate curves were discovered at higher temperatures and lower strain rates. Solute Mg, dynamic grain growth, and flow localization were responsible for the formation of Sotoudeh-Bate curves. Modified Johnson–Cook constitutive equation considering dislocation variables and power-law constitutive equation were established. In this fine-grained alloy at 793 K and 8.33 × 10−4 s−1, the number of dislocations inside a grain was 6, the stress exponent was 2, the grain size exponent was 2, and the average activation energy for deformation was 140.10 kJ/mol. These pieces of evidence demonstrated that grain boundary sliding accommodated by intragranular dislocation controlled by lattice diffusion governs the rate-controlling process.

Numerical and experimental investigation of the ballistic performance of the armor structure with in-layer deflector against bullets

This is a study to investigate ballistics performance of armor structures with in-layer deflector against projectiles. For this purpose, the armor structure, which consists of a v-cross section sheet metal array covered with aluminum and steel plates, has been designed and optimized. Firstly, numerical simulations were studied using the finite-element method (FEM). The ANSYS LS-DYNA FE software is used for the ballistic analysis. The Johnson-Cook constitutive equation and damage model were used to model the behavior of metal armors under impact in the ballistic simulations. In the next step, experimental studies were carried out. Penetration depths were measured; including the magnitude of plate bending in front of the target plate and bulging behind it. Comparisons between the results of the finite element analysis (FEA) and the tests reveal that a bullet with a velocity of 868 m/s penetrated the target, but the target could not be penetrated at a firing speed of 631 m/s Furthermore the experimental and numerical results were in good agreement.

Investigation of cold drawing process of thin-walled ribbed steel tube

Cladding tube is an important part of nuclear power components. This paper presents a simulation and experimental study on the cold drawing process of one kind of cladding tubes, namely thin-walled ribbed steel tube. Three kinds of drawing processes are studied: single pass drawing, tube sinking and fixed-plug combined drawing process, and two pass fixed-plug drawing process. The finite element (FE) simulation model considering Johnson-Cook constitutive equation is established to analyze the effective stress, effective plastic strain, and contact force in different drawing processes. Different out diameter (OD) and wall thickness (WT) 316L stainless steel (SS) tubes are used to investigate the forming process of the ribbed tube. Furthermore, experiments with the same parameter settings are compared with the simulations. It is found that the simulation and experimental results are in good agreement, the ribs height highly depends on the tube OD and WT. The results show that the formation of tube ribs is caused by the extrusion of the drawing die. In addition, during the forming of the tube ribs, inner grooves will be formed on the inner wall of tube, and the fixed-plug drawing process can effectively reduce the depth of the inner groove. Finally, the microstructure and hardness of the ribbed tube at different position are investigated. This work provides a reference for the integrated forming process of the ribbed tube.