Johnson-Cook Constitutive Model Research Articles

Effect of the Layer Sequence on the Ballistic Performance and Failure Mechanism of Ti6Al4V/CP-Ti Laminated Composite Armor

The effect of the layer sequence on the ballistic performance of Ti6Al4V (35 mm)/CP-Ti (5 mm) laminated composite armor, against a 12.7 mm armor piercing projectile, was systematically investigated, both experimentally and computationally. By introducing the Johnson–Cook constitutive model and fracture criterion, the penetrating process of the composite plate was well-simulated. Furthermore, the influence of the layer sequence on the ballistic performance and failure mechanism of the composite plate was evaluated from the perspective of energy absorption and the stress distribution. Numerical simulation results of the macro morphology and penetration depth agreed well with the experimental results. The results showed that the energy absorption histories of each layer and stress distribution of the composite plate were found to be significantly affected by the arrangement sequence. The ballistic performance of Ti6Al4V/CP-Ti was far superior to that of CP-Ti/Ti6Al4V because more energy was absorbed in the early stage of the penetration process, thereby reducing the damage to the rear face. Further studies showed that the first principal stress in both structures was radially distributed in space, but was mainly concentrated at the rear face when the CP-Ti was placed at the front. Therefore, this stress induced cracking and failure in that region and, consequently, lowered the overall ballistic performance.

Effect of Microstructure on the Johnson-Cook Constitutive Model Parameters of Ti-6Al-4V Alloy

Constitutive models are widely used to predict the mechanical behavior of materials. In this research, the Johnson-Cook (J-C) constitutive model parameters of Ti-6Al-4V (Ti64) alloy with different microstructural details were fitted based on the mechanical properties over a broad range of strain rates and temperatures. The results indicate that the microstructural details have a significant effect on the mechanical properties and the J-C model parameters of Ti64. The five material parameters (A, B, n, C, m) in J-C model of Ti64 exhibit completely different varying trends as a function of the equiaxed primary α-phase volume fraction and α-platelet thickness. These changes in J-C model parameters of Ti64 can be attributed to the effect of microstructural details on the dislocation nucleation and motion under different deformation conditions.

Formability and deformation behavior of DP600 steel sheets during a hybrid quasi-static/dynamic forming process

The purpose of this work was to investigate the formability and deformation behavior of DP600 steel sheets during a hybrid forming process composed of quasi-static forming and dynamic high strain rate electrohydraulic forming (EHF) sequence. The results showed that the ultimate limit major strains under the uniaxial tensile strain path were 40–47%, and those under plane strain and biaxial tensile strain paths were 28–31% and 43–57%, respectively. Compared with quasi-static data, the hybrid data under these three strain paths were improved by 30%, 70%, and 36%, respectively, demonstrating a hyperplasticity characteristic. The quasi-static prestrain had little effect on the ultimate formability, and the hyperplasticity effect of the quasi-statically prestrained specimens mainly depended on the inertial effect and the change in constitutive behavior in the high strain rate EHF loading step. Furthermore, the optimized Johnson-Cook constitutive model of the quasi-statically prestrained sheet during high strain rate condition was obtained by means of dynamic Hopkinson tensile tests, and the numerical simulation results based on this material constitutive were in good agreement with that obtained by experiments, showing an error of less than 5%. Then, the numerical simulation reproduced the propagation and evolution process of the pressure wave from ellipsoid to sphere, and quantified the dynamic deformation behavior of the quasi-statically prestrained specimen during an EHF process. The maximum velocity and strain rate of the prestrained specimen during EHF step were 270 m/s and 3700/s, respectively, and the ultimate height of the deformed specimen was 43 mm.

Selective excitation of two-wave structure depending on crystal orientation under shock compression

Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations. However, little is known to date regarding how the shock response depends on crystal orientation, and especially why the two-wave structure depends on the crystal orientation. In this work, molecular dynamics simulations of shock compressions in copper single crystals are performed to investigate the orientation dependence of shock responses and the corresponding deformation mechanisms. Four copper single crystals with [001], [011], [012], and [123] crystal orientations along the depth direction are investigated. The [011], [012], and [123] crystal orientations of copper single crystals show distinct two-wave structures in their shock responses, while such a two-wave structure in the shock response is not seen for those orientations having a [001] crystal orientation. The potential causes are analyzed by considering the propagation velocities of both elastic and plastic waves. We develop a technique for identifying twin structures in face-centered cubic crystals and this technique can effectively identify the twin structure. The morphology of shock-induced defects (e.g., dislocations and twins) shows the significant dependence of crystal orientation and the mechanisms behind these are discussed in detail. Finally, the Johnson-Cook constitutive model describing dynamic deformations at high temperatures and high strain rates is used to analyze the relationships between the shock responses and microscopic defects. The predictions of the Johnson-Cook constitutive model are consistent with the results of the molecular dynamics simulations.

An Improved Johnson–Cook Constitutive Model and Its Experiment Validation on Cutting Force of ADC12 Aluminum Alloy During High-Speed Milling

Because of the massive work and high cost of milling experiments, finite element analysis technology (FEA) was used to analyze the milling process of ADC12 aluminum alloy. An improved Johnson–Cook (J–C) constitutive equation was fitted by a series of dynamic impact tests in different strain rates and temperatures. It found that the flow stress gradually increases as the strain rate rises, but it decreases as the test temperature rises. Compared with the J–C constitutive model, the predicted flow stress by the improved J–C constitutive model was closer to the experimental results when the strain rate was larger than 8000 s−1 and the temperature was higher than 300 °C. A two-dimensional cycloidal cutting simulation model was constructed based on the two J–C constitutive equations which was validated by milling experiments at different cutting speeds. The simulation results based on the improved J–C constitutive equation were closer to the experimental results and showed the cutting force first increased and then decreased, with cutting speed increasing, reaching a maximum at 600 m/min.

Multiscale simulation of grain refinement induced by dynamic recrystallization of Ti6Al4V alloy during high speed machining

During high speed machining (HSM), the strong thermal-mechanical coupling can lead to the microstructure evolution in the deformation zone of workpiece. Grain refinement may occur, which has great effects on the mechanical behavior, and even on the fatigue strength and corrosion resistance of the machined surface. The development of multiscale models to predict the microstructure evolution is gaining rising interest. This study aims to investigate the grain refinement induced by dynamic recrystallization (DRX) occurring in HSM of Ti6Al4V, through finite element (FE) and cellular automata (CA) methods. An orthogonal cutting model for HSM of Ti6Al4V is developed combining a modified Johnson-Cook constitutive model (TANH) and Johnson-Mehl-Avrami-Kolmogorov (JMAK) DRX model. The CA model is proposed considering dislocation density evolution, grain nucleation and growth. The 2D mesoscopic microstructure evolution is simulated successfully by the CA model in which the input deformation parameters come from the FE simulations of the orthogonal cutting process. Finally, the grain size and microstructure morphology calculated by both FE and CA methods are compared with those characteristics obtained experimentally by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Identical microstructure predictions from both CA and FE methods show a reasonable agreement with the TEM results, on the condition that twinning and phase transformation are not considered in the simulations. This work proves that the combination of FE and CA methods is an effective approach to achieve a more comprehensive understanding of the microstructure evolution and its effect on mechanical behavior during HSM. It shows that the rise of both DRX volume fraction and DRX grain size finally results in the slightly decreasing of average grain size of serrated chips with the increase of cutting speed, which leads to the strain softening phenomenon of flow stress.

A novel finite element investigation of cutting force in orthogonal cutting considering plough mechanism with rounded edge tool

The plough phenomenon generated by the micro-scale cutting edge plays an important role in tool wear, chip formation and surface integrity. In this study, the plough mechanism in orthogonal cutting with rounded edge tool is investigated by finite element method (FEM). The separation line is developed to determine the contact behavior between rounded edge tool and workpiece. Especially, the workpiece material flow is explored in detail with the definition of separation line. Three contact regions are identified and three frictional force components along the cutting edge are proposed. Then, the Johnson-Cook constitutive model and Johnson-Cook ductile damage criteria are used to describe the plastic deformation and damage mechanics in the cutting simulation with ABAQUS. A developed method based on finite element analysis is proposed to identify three force components individually, including separation line determination based on nodal displacement and three contact region determination with partition function. The accuracy and correctness of the novel FEM model are validated by a series of orthogonal cutting processes. Moreover, the nonlinearly increase relationship between specific cutting energy and edge radius is discussed considering size effect.

Simulation of micro-milling Inconel 718 considering scale effect

To study the scale effect during micro-milling process, we establish a modified Johnson-Cook (JC) constitutive model to describe the strengthening behavior of materials on microscale based on the theory of strain gradient plasticity. The VUMAT constitutive subroutine of Inconel 718 is programmed. The radius of the tool edge and its influence on the rake angle are considered. Based on the modified JC constitutive equation, the simulation of micro-milling Inconel 718 process is achieved. The micro-milling Inconel 718 experiments are conducted. The accuracy of the simulation of micro-milling Inconel 718 process considering scale effect is verified by comparing cutting force from experiments with simulation outputs based on the traditional as well as modified JC constitutive equation. It is proved that the simulation outputs of the micro-milling process based on the modified JC constitutive equation are more consistent with the experimental results.

A modified Johnson-Cook model for dynamic behavior of spray-deposition 17 vol.% SiCp/7055Al composites at high strain rates

In this study, the dynamic impact tests of spray-deposited 17 vol% SiCp/7055Al composites at various strain rates were performed with a Split Hopkinson Pressure Bar (SHPB). In these tests, the strain rate was 392 s−1–2002 s−1, and the temperature was 293 K–623 K. Subsequently, the Johnson-Cook (JC) was used to describe the flow behaviors under high speed impact deformation, and its effectiveness was assessed. Results show that the stress values predicted by the JC model could be inconsistent with the experimental ones. A modified JC constitutive model of 17 vol% SiCp/7055Al composites was developed by modifying the strain rate hardening term and considering coupling effects of strain, temperature and strain rate. According to the comparison between the experimental data and the results assessed with the modified JC model, the proposed model could assess the stress-strain values more accurately, especially in the beginning of plastic deformation. This indicates that the composites exert the joint effects of strain rate hardening and temperature softening during high-speed impact deformation.

Energy absorption and impact resistance of sandwich composite alloy structures under dynamic impact

Abstract A new sandwich composite structure is prepared based on warm rolling process. The dynamic mechanical property of the sandwich composite structure is investigated through split Hopkinson pressure bar (SHPB) experiment. The Johnson–Cook constitutive model is modified based on the SHPB experiment result, taking into account the synergy between strain softening and strain rate softening. Projectile penetration simulation is performed on the sandwich composite structure using projectile penetration schemes for different angles and different structural dimensions to examine how penetration angle and structural dimensions affect the dynamic energy absorption property of sandwich composite structures. Vibration equations of sandwich structures are inferred based on Hamilton’s theory to reveal the dynamic energy absorption mechanisms of these structures. The results show that symmetric structures have better damping performance than asymmetric structures; maximum stress will display a rise-fall-rise profile with increasing penetration angle; for symmetric structures with damping layer thickness of 4 mm, the projectile deflection angle will first increase and then reduce with increasing penetration angle and the projectile deflection angle will approximate 40°at penetration angle 10°.

Prediction of machining-induced residual stress in orthogonal cutting of Ti6Al4V

In addition to having significant effects on the service life of machined parts, residual stress can cause large deformations during machining of thin-walled parts in aerospace field. The residual stress in machined part surface layer is induced by mechanical and thermal stress in the machining process of parts. Therefore, it is essential to accurately predict the generated residual stress due to the machining process. To address this issue, an improved prediction model of the residual stress for orthogonal cutting process based on analytical method is presented by taking the mechanical and thermal stress into consideration. Oxley’s cutting force model and Waldorf’s plowing force model are used to calculate the chip formation force and plowing force based on the contact mechanics, Johnson-Cook constitutive model, and slip line theory. The cutting temperature is predicted according to our previous work based on the Huang-Liang model and the Komanduri-Hou model. The final residual stress is predicted by calculating the loading and relaxation of mechanical and thermal stress. The presented prediction method of residual stress is validated by orthogonal cutting of a Ti6Al4V pipe. It is found that the prediction values of the presented model show a good agreement with the experimental results, which indicates that the presented model can be adopted to predict the residual stress of Ti6Al4V during orthogonal cutting.

Sensitivity analysis of Johnson-Cook material parameters on adiabatic shear in different directions

ABSTRACT This study investigates the effects of strain, strain rates, and forming directions (RD-rolling direction, TD-transverse direction, and ND-normal direction) on adiabatic shear, via dynamic impact compression tests using the Split Hopkinson Pressure Bar (SHPB) apparatus. A modified Johnson-Cook (J-C) constitutive model is proposed, which used to analyse the influence of the constitutive parameters on the sensitivity of adiabatic shear, employing a finite element software. The different sensitivities of adiabatic shear under different directions are explained by combining microscopic analysis and results from mechanical responses. The results show that the sensitivity of adiabatic shear can be related to the time of stress collapse in the following trend: ND > TD > RD; the sensitivities of these constitutive parameters on adiabatic shear are calculated and compared.

The modified temperature term on Johnson-Cook constitutive model of AZ31 magnesium alloy with {0002} texture

Abstract The dynamic compression experiments with Split-Hopkinson Pressure Bar(SHPB) were performed on AZ31 magnesium alloy rolled sheet specimens in the normal direction (AZ31-ND) with {0002} texture at the temperature of 293–523 K and the strain rate of 0.001–2200 s−1. The temperature term in Johnson-Cook(JC) constitutive model had been reasonably modified. This advantage made constitutive model promising for decribing the dynamic deformation behavior of AZ31-ND with {0002} texture more accurately. The obtained true stress-true plastic strain curves agreed well with the measured results in a wide range of strain rates and temperatures. The thermal softeninging, strain and strain rate hardening effect on the AZ31-ND with {0002} texture were discussed. The adiabatic shear band (ASB) of AZ31-ND with {0002} texture hat shaped specimen was successfully predicted by combining modified JC constitutive model and numerical simulation, which was also validated by Electron Back-Scattered Diffraction (EBSD) map under the same boundary condition.

The identification of improved Johnson-Cook constitutive model in a wide range of temperature and its application in predicting FLCs of Al–Mg–Li sheet

For the Al–Mg–Li alloy sheet, a series of uniaxial tensile tests are firstly carried out under different temperatures (25–450°C) and strain rates (0.00025–0.01s−1). Then, to describe the flow behavior of the sheet, the improved Johnson-Cook constitutive model (hereinafter abbreviated as ‘improved J-C model’) is employed, in which the coefficients are respectively determined in different temperature ranges of 25–150°C, 200–300°C and 350–450°C. Afterwards, the improved J-C model is introduced into the modified M-K model to predict the FLCs of the sheet, which are finally compared with the experimental FLCs obtained by Nakazima tests. It is found that the improved J-C model can accurately describe the stress-strain relationship for the Al–Mg–Li alloy sheet in a wide temperature range within 25–450°C and give an accurate prediction of FLCs under 25°C and 150°C. However, the predicted FLCs are much lower than the experimental ones when the forming temperature is equal or greater than 250°C and the reasons that may cause this great difference are analyzed in detail.

Investigation on experiment and simulation of the grinding process of cast iron

Grinding is used to reduce form error and improve the surface quality of workpiece in metal cutting. To investigate the grinding process of cast iron, a series of grinding tests and simulation of cast iron were carried out. At the same time, the finite element method was used to establish a finite element model to simulate the grinding process of cast iron. In the model, the dynamic effects, thermo-mechanical coupling, Johnson–Cook constitutive model, material damage model, and contact model were taken into account. Then, the grinding process of cast iron was simulated using the established finite element model in the ABAQUS software. Material remove, residual stress, grinding force, and cutting temperature were achieved through the simulation. In addition, the effect of the main grinding parameters (depth of grinding and spindle speed) on residual stress, grinding force, and surface quality in the grinding of cast iron was investigated.

Study on modified Johnson-Cook constitutive material model to predict the dynamic behavior Mg-1Al-4Y alloy

An accurate prediction of high speed impact behavior of metals by considering the combined effects of strain, strain rate and temperature is essential for understanding dynamic impact deformation of metals. To understand the effect of strain, strain rate and temperature on the high-speed impact behavior of Mg-1Al-4Y alloy, the dynamic impact compression experiments for Mg-1Al-4Y alloy were carried out by split Hopkinson pressure bar (SHPB). The mechanical properties of Mg-1Al-4Y alloy specimens were studied at different strain rate and temperature. The number of {10–12} extension twins decreases with the strain rate increasing from the electron backscatter diffraction (EBSD) technology, because of the formation of extension twins is suppressed with the strain rate increases, and dislocations become the main mode of dominant deformation. It is also found that the increase of strain rate has a positive effect on the strength of the material. But, the temperatures have a negative impact on the strength of the material. A modified Johnson-cook model has been presented, which shows good predictions with experimental results at different strain rates and temperatures. Especially, the predictions of the Johnson-cook equation are completely consistent with experimental results in small deformation stage.

Simulation and experimental study of 7A09 aluminum alloy milling under double liquid quenching

To explore the influence of double liquid quenching on the cutting performance of the 7A09 aluminum alloy, quasi-static compression and dynamic impact tests were carried out on the 7A09 aluminum alloy after double liquid quenching using an MTS810.23 universal testing machine and split-Hopkinson pressure bar (SHPB). The experimental data were fitted to obtain the Johnson–Cook constitutive model parameters of the alloy. Simulations of the machining process were carried out using the Deform-3D finite element software. The results showed that the rheological stress increased with the increase in strain rate and the decrease in temperature. The increase in the cutting speed and feed caused the cutting temperature to rise sharply, whereas the influence of the cutting amount on the cutting temperature was weak. Because of the presence of chip nodules, there was extremum in the cutting force vs cutting speed curves. The increase in the feed and cutting depth increased the cutting area Ac, so the cutting force also increased. The simulation results were verified by experiments. The simulation predictions were in good agreement with the test values, and the cutting force and temperature variations with the cutting parameters were the same. Thus, the correctness of the 7A09 aluminum alloy finite element model was verified.

High strain rate behaviour of stainless-clad bimetallic steel

To study the dynamic mechanical properties and to develop constitutive models of stainless-clad (SC) bimetallic steel at high strain rates, 11 groups of standard specimens (i.e. cylinders of 6 mm in diameter and 6 mm in height) are designed. Four different loading directions and clad ratios varying from 0.2 to 0.5 are considered. 123 compression tests are carried out at six strain rate levels (0.0005 s−1, 1000 s−1, 1500 s−1, 2000 s−1, 3000 s−1 and 4000 s−1). Johnson-Cook (J-C) constitutive model is used to fit the test data, and the fitting results are in good agreement with the experimental results. It can be found that the strain rate hardening has a prominent effect on stress development of the SC bimetallic steel at high strain rate compared with that in the quasi-static condition. With an increase of the clad ratio, the stress of the SC bimetallic steel grows slightly as the strain hardenability and sensitivity of the strain rate decrease. The SC bimetallic steel can be considered as an isotropic material in terms of high strain rate behaviour because different loading directions result in no obvious distinction. In addition, a formula for dynamic increase factor (DIF) for strengths as well as a general constitutive equation of J-C model for the SC bimetallic steel are developed and validated, which can be adopted in structural design under impact loading and promote engineering application of the SC bimetallic steel.

Effect of cutting edge microgeometry on surface roughness and white layer in turning AISI 52100 steel

Abstract In high precision cutting, cutting edge microgeometry largely influences the machining performance and wear behavior of cutting tool. This study systematically analyses the effect of cutting edge microgeometry on surface roughness and white layer formation. A series of orthogonal cutting experiments of AISI 52100 steel is established with various edge preparations. Meanwhile, 2D finite element cutting model based on ABAQUS/EXPLICIT general software is developed to investigate the formation of white layer. In the proposed numerical model, the Johnson-Cook constitutive model is used to describe the elastic and plastic deformation of machined surface layer. Then, surface topography of machined workpiece is achieved to get 2D surface roughness. Besides, the phase transition mechanism with the consideration of the combination of stress and strain is used to predict the white layer. The investigation results show that enlarging chamfer width can improve surface roughness, while increasing chamfer angle has less effect on surface roughness. Moreover, both large rounded edge and large chamfered edge can contribute to white layer formation.

Depth of cut prediction in abrasive waterjet turning using a new finite element model

Abrasive waterjet turning (AWJT) is an advanced machining process that could be used for turning cylindrical workpieces with the advantages of low vertical forces and negligible thermal distortion. Radial-mode AWJT is characterised by better utilisation of jet energy and high material removal rate. However, the prediction of depth of cut (DOC) is difficult due to the interaction of several process parameters. In this paper, a new finite element (FE) model was developed to predict the DOC in radial-mode AWJT. The workpiece material is AISI 4340 alloy steel and it is modelled with Johnson-Cook (JC) constitutive model. Two AWJT parameters: waterjet pressure and abrasive flow rate, were considered in the FE model with three levels for each parameter. A full factorial design was selected to evaluate the combined effect of these independent parameters. The resulting crater profile was utilised to estimate the DOC at each parameter combination. In order to evaluate the model accuracy, the DOC results were compared with published experimental data from the literature at the same AWJT conditions. The comparison showed a good agreement between the FE results and the published experimental results.