Modified Johnson Cook Research Articles

Application of Four Different Models for Predicting the High-Temperature Flow Behavior of 1420 Al–Li Alloy

In this paper, the high-temperature rheological behavior of 1420 aluminum–lithium alloy under experimental conditions (temperatures of 350–475 °C and strain rates of 0.01–10 s−1) was systematically investigated using a Gleeble-3500 thermal simulation tester (temperature 350~475 °C, strain rate of 0.01~10 s−1). Based on the flow stress curves of this alloy, four different types of high-temperature constitutive models of the alloy were constructed: the Arrhenius (AR) model, the Modified Johnson–Cook (MJC) model, the Modified Zerilli–Armstrong (MZA) model, and the VOCE model. The prediction accuracy of the four constitutive models was compared, and the response of the accuracy of the four constitutive models to the deformation parameters (temperature, deformation rate, and strain) was analyzed. The results showed that the VOCE, AR, and MZA models had high overall prediction accuracy with average absolute relative error (AARE) of 1.8933%, 3.9912%, and 7.8422%, respectively. The VOCE model could achieve the prediction of large strain deformation resistance under small strain with small batch experimental conditions for the corresponding conditions. The AR model had optimal prediction accuracy for the high-rate deformation process. The MJC model had the optimal prediction accuracy for the low-temperature low-rate deformation process. The MZA model had better prediction accuracy for the low-rate high-temperature deformation process. The 1420 aluminum–lithium alloy process parameters selection area constitutive model matching diagram was constructed.

Dynamic behavior and microstructural evolution of TiAl alloys tailored via phase and grain size

As a kind of promising aerospace material, TiAl alloys need to withstand extreme conditions such as high-rate impact loads and high temperatures. The mechanism on the failure and fracture of TiAl alloys under extreme conditions is related with the microstructure, including phase and grain size. In the present research, two kinds of TiAl alloys tailored with different microstructures, near lamellar (NL) and near gamma (NG), were fabricated by thermo-mechanical treatment. Microstructural characterization was analyzed by XRD and EBSD. The dynamic behavior of the TiAl alloys under different temperatures ranging from 293 K–873 K was investigated by a split Hopkinson pressure bar. The strain rate sensitivity and temperature sensitivity was analyzed. The microstructural evolution was concerned to understand the failure mechanism of the two kinds of the TiAl alloys. The NG-TiAl had the homogeneous deformation with synergy effect between homogeneous equiaxed grain and lamellar structure, and no failure occurred in NG-TiAl. However, the NL-TiAl showed heterogeneous deformation with both “orange peel effect” and cracks, which was attributed to large equiaxed grain and brittle γ-lamellae with similar orientation. Further, the cracks were easily nucleated and propagated from the interface between γ-lamellae structures, especially in the γ-lamellae structures parallel with the loading direction. Finally, the modified Johnson–Cook constitutive model was proposed to describe the deformation behavior, in which both strain rate hardening and temperature softening terms were expressed as a function of strain and strain rate.

Flow Stress Characteristics and Constitutive Modeling of Typical Ultrahigh‐Strength Steel under High Temperature and Large Strain

Hot compression experiments are conducted to explore the deformation behaviors of 300M steel under large strain, which can mimic the forging process of large components. It is found that the variations of flow stress are affected by the deformation parameters and the rivalry between work hardening and dynamic softening. A novel constitutive model is proposed to forecast the flow stress at different deformation parameters. The Pearson correlation coefficient between the experimental flow stress and the predicted flow stress by the newly proposed constitutive model is 3.489%, and the relative error is within the range of ±5%. It implies that the newly proposed constitutive model can describe the variations of flow stress appropriately. Furthermore, the prediction accuracy of the newly proposed constitutive model is compared with that of the strain‐compensated Arrhenius constitutive model, the modified Johnson–Cook constitutive model, and the Hensel–Spittel constitutive model. Results demonstrate that the novel constitutive model provides the highest accuracy, followed by the strain‐compensated Arrhenius constitutive model, then the Hensel–Spittel constitutive model, and the modified Johnson–Cook constitutive model has the weakest accuracy. The establishment of the novel constitutive model is helpful in accurately predicting the flow behavior of materials during the forging process.

Study of dynamic mechanical behavior of 1060-H112 aluminum alloy: Experimental and numerical simulation

1060-H112 aluminum alloy with high ductility is widely used in industrial engineering. The study of its dynamic mechanical behavior has theoretical and engineering application value. In this paper, quasi-static tensile tests from room temperature to 250°C and high strain rate compression tests were conducted using a universal material testing machine and a Hopkinson compression bar. By using a hybrid test-numerical simulation method, a modified Johnson-Cook (MJC) strength model and Cockcroft-Latham (C-L) fracture criterion parameters were calibrated. Subsequently, Taylor impact tests were performed on 1060-H112 aluminum alloy specimens with a diameter of 12.66 mm and a length of 50.64 mm in the range of 176.3–483.03 m/s. Upsetting and tensile tearing were observed in the tests. A 12.68 mm diameter blunt nosed projectile impact test on 2 mm 1060-H112 aluminum alloy plate was also conducted with a light gas gun system, and the speed related parameters and failure modes were obtained. Finally, a three-dimensional model corresponding to the test was established in ABAQUS/Explicit finite element simulation software, and the failure modes of the Taylor rod and the velocity parameters and failure modes of the target impact test were predicted. The results show that the MJC strength model and the C-L fracture criterion can predict the experimental results of the two tests accurately. It shows that the MJC strength model and C-L fracture criterion have high accuracy, and they will play an important role in the application of 1060-H112 aluminum alloy in industrial engineering.

A Modified Johnson–Cook Model and Microstructure Evolution of As-Extruded AA 2055 Alloy during Isothermal Compression

Isothermal compression behaviors of as-extruded AA 2055 alloy (T6 state) were studied at temperature of 320, 380, 440 and 500 °C with strain rate of 0.001, 0.01, 0.1 and 1 s−1 by a Gleeble-3800 testing machine. A modified Johnson–Cook model fitted by polynomial and power-exponential functions were established to describe the flow stress of the alloy. The constitutive models fitted by higher-order polynomials were more accurate than the ones fitted by second-order polynomial and power-exponential functions. The constitutive model fitted by a fourth-order polynomial was chosen for the optimal constitutive model in order to balance the prediction accuracy and model complexity. The modified Johnson–Cook constitutive model could predict the flow stress well, especially in high-temperature zone (around 500 °C) and low-temperature zone (around 320 °C). The dynamic precipitation and dissolution of the T1 phase during hot compression were discussed. The unusual dynamic precipitation of the T2 phase was investigated during hot compression by XRD and TEM. The massive dense fine precipitates effectively pinned dislocations or subgrain boundaries to accelerate DRV but suppressed DRX, leading to a low frequency of HAGBs in compressed samples.

Inverse Identification of a Constitutive Model for High-Speed Forming Simulation: An Application to Electromagnetic Metal Forming

Forming simulation requires a constitutive model whose parameters are typically determined with tensile tests assumed static. However, this conventional approach is impractical for high-speed forming simulation characterized by high strain rates inducing transient effects. To identify constitutive parameters in relation to high-speed forming simulation, we formulated the problem of constitutive modeling as inverse parameter estimation addressed by regularized nonlinear least squares. Regarding the proposed inverse constitutive modeling, we adopted the L-curve method for proper regularization and model order reduction for rapid simulation. For demonstration, we corroborated the proposed strategy by identifying the modified Johnson–Cook model in the context of a free bulge test with electromagnetic metal forming simulation. The L-curve method allowed us to systematically choose a regularization parameter, and model order reduction brought enormous computational savings. After identifying constitutive parameters, we successfully verified and validated the reduced and original simulation models, respectively, with a manufactured workpiece. In addition, we validated the numerically identified constitutive model with a dynamic material test using a split Hopkinson pressure bar. Overall, we showed that inverse constitutive modeling for high-speed forming simulation can be effectively tackled by regularized nonlinear least squares with the help of an L-curve and a reduced-order model.

Hot deformation and constitutive model of as-cast Ni–Cr–Co nickel-base alloy

Abstract Nickel-based superalloys are widely used in thermal power, nuclear power, aerospace and other fields due to their excellent properties. Since the deformation resistance of Ni–Cr–Co superalloy is large and the forming range is narrow, the hot deformation behavior of Ni–Cr–Co superalloy was studied by hot compression experiments on a Gleeble-3800 under different deformation conditions (deformation temperature: 950–1200 °C, strain rate: 0.01–10 s−1, and deformation: 60 %). The modified Johnson–Cook, modified Zerilli–Armstrong and strain compensated Arrhenius models were constructed based on the stress–strain curves corrected for friction and temperature. The correlation coefficient (R) and average absolute relative error (AARE) were compared to verify the accuracy of the model. The results showed that the strain compensated Arrhenius model had high accuracy, the modified Zerilli–Armstrong had high accuracy in predicting the flow behavior above 1100 °C, while the modified Johnson cook had high accuracy only under the reference conditions. Electron back-scattered diffraction analysis showed that high-angle grain boundaries formed when the low-angle grain boundaries piled up to a certain extent, which is beneficial for refining the as-cast microstructure, and the increase in strain rate was beneficial for refining the microstructure and promoting the occurrence of recrystallization.

Modified Johnson–Cook Constitutive Model of 18CrNiMo7-6 Alloy Steel under Ultrasonic Surface Burnishing Process

Modified Johnson–Cook Constitutive Model of 18CrNiMo7-6 Alloy Steel under Ultrasonic Surface Burnishing Process

A Comparative Study of Three Constitutive Models concerning Thermo-Mechanical Behavior of Q345 Steel during Hot Deformation

The Gleeble-3800 thermal simulator was used to perform hot compression experiments on Q345 steel at a temperature of 1123~1373 K, a strain rate of 0.01~10 s−1, and 60% deformation. Analysis of the flow curves of Q345 steel revealed that flow stress decreases with the increase of deformation temperature and decrease of strain rate. According to the stress–strain curve of Q345 steel, three constitutive models of Johnson–Cook, Modified Johnson–Cook and strain-compensated Arrhenius were established. By comparison, it was found that the strain-compensated Arrhenius model has higher accuracy, and its correlation coefficient and average relative error are 0.995 and 4.93%, respectively. In addition, the thermal processing map of Q345 steel was established, and the optimal processing range was temperature 1253–1373 K, strain rate 0.5–10 s−1.

High strain rates deformation behavior of an as-extruded Mg–2.5Zn–4Y magnesium alloy containing LPSO phase at high temperatures

Mg–Zn–Y magnesium alloys comprising long-period stacking ordered (LPSO) phase have shown excellent strengthening effects, however, their deformation behavior and microstructure evolution under different strain rates and temperatures have not yet been thoroughly investigated. This work is based on the investigation of elevated temperature and high strain rate deformation behavior of an as-extruded Mg–2.5Zn–4Y magnesium alloy comprising LPSO phase, with the strain rates lying in the 700 s−1 to 2100 s−1 range, and temperature ranging from 293 K to 623 K. Electron backscattering diffraction (EBSD), scanning electron microscopy (SEM), and optical microscopy (OM) was employed for investigating the deformation microstructure. The results show that at early deformation the extension twinning coordinates the plastic deformation first, subsequently, pyramidal < c+a > slip and kinking of LPSO phase can also coordinate deformation for the experimental alloy at high strain rates at high temperatures. A peculiar phenomenon of misaligned LPSO phase structures (1600 s−1, 623 K) was also discovered. The fracture mode of the experimental alloy is mainly the cleavage fracture or the mixed ductile-brittle fracture during high-speed impact. A modified Johnson–Cook (J-C) constitutive model of the as-extruded Mg–2.5Zn–4Y was found to appropriately analyze the stress–strain values by comparing the computed results with the experimentally obtained data. It was, thus, demonstrated that the modified J-C model can make a reasonable prediction about the dynamic mechanical behavior of a Mg–2.5Zn–4Y magnesium alloy in its as-extruded condition throughout a range of high temperatures and strain rates with a high degree of accuracy.

Comparison of Modified Johnson–Cook Model and Strain–Compensated Arrhenius Constitutive Model for 5CrNiMoV Steel during Compression around Austenitic Temperature

Isothermal compression behaviors of 5CrNiMoV steel were studied at temperatures of 870, 800, 750, and 700 °C, with strain rates of 0.001, 0.005, 0.01, 0.05, and 0.1 s−1, the compression temperatures 870 and 800 °C are above Ac3, as well as 750 and 700 °C below Ac3 temperature. The Modified Johnson–Cook (MJC) model and the Strain–Compensated Arrhenius (SCA) model were employed to demonstrate the relationship between the flow stress and the compression parameters. The correlation coefficient (R) and average absolute relative error (AARE) between the calculational and experimental flow stress were used to evaluate the accuracy of the two models. The results show that the effect of dynamic softening on flow stress is much more significant at higher temperatures and lower strain rates, while this effect is not obvious when the strain rate exceeds 0.005 s−1 with the temperature below Ac3. The MJC model has a good accuracy close to the reference conditions (0.001 s−1 and 700 °C), and it is suitable to predict the plastic behavior when the flow stress is lower than 200 Mpa. The unbiased AARE values were 6.82 and 5.71 for MJC model and SCA model, respectively, which implied the SCA model has a higher accuracy than the MJC model. The SCA model was believed to be capable of being used to illustrate the thermomechanical behavior of 5CrNiMoV tool steel in a wide range of plastic deformation conditions.

On Dynamic Mechanical Properties of 3003 Aluminum Alloy Based on Generalized Incremental Stress-State-Dependent Damage Model with Modified Johnson–Cook Equation

On Dynamic Mechanical Properties of 3003 Aluminum Alloy Based on Generalized Incremental Stress-State-Dependent Damage Model with Modified Johnson–Cook Equation

Dynamic Mechanical Properties of TC11 Titanium Alloys Fabricated by Wire Arc Additive Manufacturing.

To study the compressive mechanical properties and failure modes of TC11 titanium alloy fabricated by wire arc additive manufacturing (WAAM) technology in a large strain rate range at room temperature, the quasi-static and dynamic compression tests were carried out. In addition, optical microscopy (OM) and scanning electron microscopy (SEM) were employed to observe the metallographic structure and fracture morphology, respectively. The stress–strain curves in the range of 0.001 s−1–4000 s−1, original and post-deformation microstructures, macroscopic damage patterns, and microscopic fracture morphology were obtained at two different loading directions, including the scanning and deposition directions, respectively. In uniaxial compression experiments, the material showed little difference in mechanical properties between the scanning and deposition directions, exhibiting a strain rate strengthening effect. However, the strain rate sensitivity of the material under quasi-static loading conditions is much less than that under dynamic loading conditions. In addition, combining the stress–strain curve with the fracture morphology analysis, the plasticity in the scanning direction is better than in the deposition direction. Based on the experimental results, a modified Johnson–Cook (JC) constitutive model considering strain rate sensitivity and the effect of strain rate on strain hardening was proposed, and the parameters were determined using a Multiple Population Genetic Algorithm (MPGA). The obtained constitutive model is in good agreement with the experimental data, which can provide a reference for the engineering numerical calculation of TC11 titanium alloy for WAAM. This study also provides a fundamental databank for the application and design of WAAM TC11 alloy in the manufacturing of large and complex structural parts.

Identification of constitutive laws’ parameters by means of experimental tests on AlSi-PE abradable coating

Abradable coatings are a part of dynamic seals used in aircraft engines to diminish inter-stage leakages by reducing rotor/stator clearances of the low and high-pressure compressors. However, interactions may occur during running between the rotating blades and the coating sprayed onto the casing. Due to the complexity of reproducing experimentally rotor/stator interactions, modeling approaches are used to optimize the choice of abradable coating, making constitutive laws necessary input data for rotor/stator interaction studies. Previous experimental researches were done to explore the dynamic and quasi-static compressive thermomechanical behavior of AlSi-PE abradable coating [1,2]. Using results from these investigations and from a complementary experimental characterization coupled with a high speed camera, parameters of a standard Johnson–Cook constitutive law have been identified for the wide ranges of strain-rate and temperature explored. Although modeling data were in satisfactory agreement with the experimental results, an original constitutive law formulation has been proposed to better predict the thermomechanical behavior of AlSi-PE abradable material at high temperatures. As an introduction of damage into the modeling, a standard and modified Johnson–Cook damage law, describing a strain criterion from which failure theoretically begins, has been included and analyzed when modeling the coating’s behavior by considering only quasi-static conditions.

Impact Forming of AA5052-H32 Sheets With Friction Stir Spot Welds Using a Shock Tube and Failure Assessment

Abstract In this present study, both the experimental and numerical investigations are carried out to understand the formability of AA 5052-H32 sheets of 1.5 mm thickness with friction stir spot weld (FSSW). A shock tube experimental facility is utilized in which a rigid hemispherical striker is propelled at a high velocity and deforms the FSSW sheets at high strain rates. In this analysis, the effect of different tool rotational speed and plunge depth on the FS spot welding outputs and forming outputs are understood. Furthermore, DEFORM-3D finite element (FE) code is used to perform FE simulation of both the FS spot welding and forming of the welded sheets interactively. During the forming analysis, a new strategy is followed to identify the rate-dependent mechanical properties that are incorporated during FE simulation. The tensile data obtained from the unwelded section of the sheet deformed using the shock tube is fit to the modified Johnson–Cook (MJC) model. In the case of the FS spot-welded region, a hardness-based multiplying factor is identified and used to obtain stress–strain data by fitting it to MJC model. The predicted temperature evolution during the FSSW is validated with the experimental data and a good correlation has been observed. The predicted material flow phenomenon gives an insight into the joint formation during FSSW. Various forming outputs such as deformation profile, crack pattern, and effective strain distribution predicted by MJC model in combination with Freudenthal damage model are compared with the experimental data, and the results have a fair agreement.

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.

RETRACTED: Dynamic mechanical properties and modification of fracture criteria of 6061-T651 aluminum alloy

In order to investigate the effects of stress triaxiality, Lode angle, temperature and strain rate on the fracture characteristics of 6061-T651 aluminum alloy materials, the mechanical property tests of materials are carried under different stress states, temperature and strain rate using universal material testing machine. Firstly, the mechanical property test results show that the fracture strain of 6061-T651 aluminum alloy material decreases with the increase of stress triaxiality. And also, the fracture strain of material related to the Lode angle parameter, especially the effect of the Lode angle more significantly at the range of lower stress triaxiality. When the temperature less than 250 ℃, the temperature of material has significant influence on its flow stress, while the influence of temperature on its fracture strain can be ignored. While the temperature more than 250℃, the temperature of material has greatly influence on its flow stress and fracture strain. Moreover, the strain rate has no significant effect on the fracture strain of 6061-T651 aluminum alloy. Subsequently, basing on the test results of mechanical properties, the Modified Johnson-Cook(MJC) criterion is obtained by modifying Johnson-Cook(J-C) fracture criterion, and the parameters of MJC and Modified Mohr-Coulomb(MMC) fracture criterion are calibrated. Finally, the impact test of sphere projectile penetrating the 6061-T651 aluminum alloy target plate is conducted on a one-stage gas gun, and also the ballistic limit velocity and failure mode of target are obtained. In order to verify the validity of the model and parameters, and the corresponding 3D model of projectile impact target is established by using ABAQUS/Explicit finite element software. The results showed that the prediction results of Lode angle dependent MMC fracture criterion is closer to the test compared with the Lode angle independent MJC fracture criterion.

Experimental and numerical investigation on the ballistic resistance of 2024-T351 aluminum alloy plates with various thicknesses struck by blunt projectiles

As one of the most commonly used aerospace aluminum alloys, 2024-T351 aluminum alloy plates are frequently exposed to impact loadings. In this study, the ballistic resistance of 2, 4, 4.82 and 8 mm thick 2024-T351 aluminum alloy plates struck by blunt projectiles was investigated both experimentally and numerically. Ballistic impact tests of 2024-T351 aluminum alloy plates of different thicknesses were carried out using a one-stage gas gun, and the initial-residual velocities and the ballistic curves were determined experimentally. It was found that the plates failed by shear plugging regardless of target thickness and the enhancement of ballistic limit velocity decreased with an increase in the target thickness. In parallel with experiments, numerical simulations were carried out by ABAQUS/Explicit. Deformation behavior of the plates was described by a modified Johnson-Cook (MJC) plasticity model accompanied with either the Lode-dependent modified Mohr-Coulomb (MMC) fracture criterion or the Lode-independent modified Johnson-Cook (MJC) fracture criterion (MJC). Numerical simulations showed that the ballistic limit velocities and the fracture path predicted by the Lode-dependent MMC fracture criterion were in better agreement with the experimental ones. Detailed analysis on the fracture path was performed and it was found that the normalized Lode angle was close to zero while the stress triaxiality was negative except for the 2 mm thick targets. Within such a stress state region, the Lode independent MJC fracture criterion obviously overpredicted ductility of the material and thus predicted much higher ballistic limit velocities. The main objective of the study is to reveal the necessity of incorporating Lode angle into a fracture criterion in predicting ballistic resistance of 2024-T351 aluminum alloy plates with various thicknesses struck by blunt projectiles through finite element (FE) simulations.

Effect of grain refiner, modifier and graphene on the mechanical properties of hyper eutectic Al-Si alloys by experimental and numerical investigation

The present work focuses on the study of mechanical properties of die cast hypereutectic Al-16Si alloys that are subjected to grain refinement and modification. It further deals with the study of the influence of the reinforcement of graphene to the sample that is simultaneously grain refined and modified. Hyper eutectic Al-16Si alloys are die casted with five different compositions. The Vickers hardness test and tensile strength test are performed on the all the casted samples. The Optical microstructure examination of the specimens is performed. The numerical simulation data derived from finite element analysis of the tensile test is validated against experimental tensile test results and both were found to coincide. Using experimental data, two alternative constitutive models, namely the modified Johnson Cook (m-JC) model and the integrated JC-ZA model, were formulated on the investigated materials for precise flow stress behaviour prediction. The JC-ZA model's integration is expected to improve prediction power in relevant consideration conditions.

Inverse Determination of Johnson-Cook Parameters of Additively Produced Anisotropic Maraging Steel.

In powder bed-based additive manufacturing (AM), complex geometries can be produced in a layer-wise approach. Results of material science experiments regarding material property identification, e.g., tensile strength, show interdependencies between the test load direction and the layer orientation. This goes hand-in-hand with the measured cutting force, changing with the relative angle between cutting direction and layer orientation in orthogonal cutting tests. However, due to the specific process characteristics, the layer orientation results in anisotropic material properties. Therefore, during machining, the material behaves depending on the buildup direction, which influences the cutting process. To predict this behavior, a simplified inverse approach is developed to determine the buildup direction-dependent parameters of a modified Johnson–Cook model for cutting simulation. To qualify these cutting models, mainly the cutting force and additionally the chip formation examined during orthogonal cuts are used. In the present paper, the influence of the laser-powder-bed-fusion (LPBF) process parameters on subtractive post-processing are shown. A good agreement between verification experiments and simulations is achieved.