Johnson-Cook Model Research Articles

Microstructural evolution and modified constitutive model of nanoscale Al2O3 dispersion-strengthened copper under high strain rate deformation

The dynamic mechanical properties and behaviors of an oxide dispersion strengthened copper alloy (ODS Cu) are investigated herein within a strain rate range of 1000–5000 s−1 using a split Hopkinson pressure bar to offer theoretical guidelines for potential applications. The mechanisms of plastic deformation and dynamic recrystallization of ODS Cu were studied by analyzing the microstructure evolution during dynamic compression. The results demonstrate that the strain rate sensitivity of ODS Cu exceeds that of pure Cu, which is beneficial for resisting dynamic high-speed impacts. The accumulation of dislocations and generation of an adiabatic temperature rise during high strain rate deformation promote the splitting of the original grains and the formation of dynamically recrystallized grains. The dominant Goss and cube textures transformed into R-cube textures with increasing strain due to the continuous rotation of subgrains and recrystallized grains. By considering the coupled effects of strain and strain rate, the Johnson-Cook model was modified according to the Voce hardening law. The modified Johnson-Cook model exhibits good agreement with the experimental data across a wide range of strain rates. This study provides insight into the dynamic mechanical behavior of ODS Cu.

Dynamic deformation and fracture surface investigation of rolled homogenous armor steel through Charpy impact testing

The amount of energy that can be absorbed by armor steel during dynamic loadings, such as a crash, impact, or blast, is crucial. To characterize the behaviour of material deformation under such loading, rigorous testing and a suitable material model are needed. Within the scope of this research, relevant tensile tests in the dynamic range are carried out to obtain the parameters necessary for three different material models, namely, the Johnson-Cook (J-C), Rusinek and Klepaczko (R-K), and a newly proposed modified Johnson-Cook (MJ-C) model. Tensile tests are simulated using these three material models, and the results are compared with the experimental results. The Charpy impact test at five different striking velocities, viz. 3, 4, 5, 6, and 8 ms−1 are numerically simulated using these material models. Upon comparing the obtained results with the experimental data, it becomes evident that the J-C model with modification (MJ-C) exhibits the best fit in prediction with regard to the specimen energy absorption and force versus displacement. A fractography investigation is also carried out to estimate the number of voids and void size with striking velocities. It shows that at higher strain rates, the number of voids increases. Additionally, the plastic deformation is restricted at high strain rates, leading to higher stress and reduced ductility.

Deformation and failure behavior of 2024-T42 sheet under impact loading

The deformation and failure behavior of 2024-T42 aluminum alloy sheet was investigated through a combined experimental-numerical method. Nine types of specimens were designed to cover a wide range of stress triaxialities and strain rates. Quasi-static and dynamic tests were carried out by electronic testing machine and split Hopkinson tensile bar respectively, and digital image correlation (DIC) method was introduced to measure the deformation. The phenomenological damage model GISSMO (generalized incremental stress state dependent damage model) and Johnson-Cook model were adopted to simulate all of the above tests and the load-displacement curves through numerical simulation were derived. An optimization method was developed to obtain all the model parameters by matching the load-displacement curves from simulation with those from tests by LS-OPT. Finally, drop weight tests and tensile tests of the central-hole plate were conducted. The applicability and accuracy of the damage models were verified by comparing the simulation results with the experiments, which indicates that GISSMO model predicts better the tests than the Johnson-Cook failure model.

Dynamic constitutive model of Fe–Cr–Ni stainless steel based on isothermal true stress-strain curves

Austenitic Fe–Cr–Ni stainless steel is widely used in aviation, chemistry, energy, due to its excellent properties of high-temperature performance. In this study, the splitting Hopkinson pressure bar with high-temperature system was employed to evaluate the dynamic mechanical properties of Fe–Cr–Ni stainless steel. The true stress-strain curves were obtained under varying conditions, including variable strains, strain rates and temperatures. The true stress increases and levels off as the true strain increases, while increases as the strain rate increases, but decreases sharply as the deformation temperature rises. The deformation temperature is consist of healing temperature and adiabatic temperature. The adiabatic temperature rise related to the specific heat capacity was calculated. The actual deformation temperatures were calculated under different strains by combining the true stress-strain curves. The true stress-strain curve under variable temperature was corrected to the stress-strain curve under isothermal state by using the thermal softening rate, which decoupled the strain and temperature. The Power-Law and Johnson-Cook constitutive models were fitted based on the real stress-strain isothermal curve. The fitting accuracy of Power-Law model was 1.61% for different strain rates at room temperature in average, 3.51% for fixed strain rate at different temperatures. While the fitting accuracy of Johnson-Cook model was 2.94% for different strain rates at room temperature in average, 6.18% for fixed strain rate at different temperatures.

Optimization of flow behavior models by genetic algorithm: A case study of aluminum alloy

Prediction of the flow stress of materials using a flow constitutive model provides strong support for engineering practice and promotes the continuous development of aluminum alloys and relevant application fields. Optimizing the parameters of flow constitutive models is a key concern to explain and predict the flow behavior. In this study, a genetic algorithm (GA) is used to optimize the parameters of flow constitutive models widely used for the flow behavior of Al alloy including modified Johnson-Cook model, hyperbolic sinusoidal Arrhenius-type model, SK-Paul model, modified Zerilli-Armstrong model, Kobayashi-Dodd model, and modified Fields-Backofen model. AA6061−T6 alloy is used in this study since it has been used as a representative Al alloy. The performance of the models optimized by GA was evaluated through comparative analysis with mechanical test. The Gleeble-3800 thermal simulation testing apparatus was employed to conduct unidirectional thermal compression tests under multi conditions, including different temperatures (573 ∼ 783 K), diverse strain rates vary from 0.001 to 1 s−1, and a range of strains (0 ∼ 0.8). The performance of all the models optimized by GA is enhanced, and the optimization effect of GA on SK-Paul model is most pronounced, which exhibits a maximum correlation coefficient (R) of 0.99731 and a minimum average absolute relative error (AARE) of 6.53%. The findings highlight the validity of GA optimization in flow constitutive models in the prediction of the flow behavior of Al alloy.

Multi-stage Johnson–Cook Model for Collision Analysis: Impact Experiments and Simulations

Multi-stage Johnson–Cook Model for Collision Analysis: Impact Experiments and Simulations

Deformation behavior, constitutive modeling and microstructure evolution of 2195 Al-Li alloy deformed at high strain rates and cryogenic temperatures

High-speed and cryogenic-temperature forming technologies have exhibited great potential for fabricating advanced Al-Li alloy components for aircraft due to their ability to enhance materials’ formability. However, there remains an urgent need to study the high-accuracy constitutive model and complex deformation mechanism of Al-Li alloys deformed at high strain rates and cryogenic temperatures. In this study, the flow stress behavior and microstructure evolution of 2195 Al-Li alloy were investigated over a wide stain rate range (from 2000 s−1 to 5000 s−1) and temperature range (from 298 K to 123 K). The flow stress increases by ∼ 32% at 2000 s−1 and ∼ 37% at 5000 s−1 as the deformation temperature drops from 298 K to 123 K, but only increases by ∼ 4% at 298 K and ∼ 8% at 123 K as the strain rate increases from 2000 s−1 to 5000 s−1. At the high strain rate of 5000 s−1, the T1 phases exhibit bending (at 298 K) and fracturing (at 123 K), with increased lattice distortion and substructure generation around the intersections of T1 phases. A new constitutive model (g-Johnson-Cook model) is developed, which shows a higher accuracy than both the Arrhenius model and Johnson-Cook model in describing the deformation behavior.

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.

Dynamic tensile characteristics of elliptically shaped Ni8Ti9Cr1 rings

Thin-walled tubes with elliptically shaped annular sections are widely applied in fuel ducts and exhaust pipes. However, the tensile mechanical properties of these structures have remained elusive due to the lack of accurate testing methods. This study aims to fill this gap by establishing circumferential tensile testing methods for static and dynamic conditions by employing a split Hopkinson tensile bar and an electronic universal tensile machine. The quasistatic and dynamic tensile characteristics of two distinct elliptically shaped Ni8Ti9Cr1 rings with different aspect ratios were investigated at room temperature, revealing a significant loading rate effect. The tensile curves exhibited considerable fluctuations, which diminshed as aspect ratios decreased. These fluctuations were attributed to stress waves propagating back and forth between the specimen, the clamp, and the bars, causing superimposition. The Johnson‒Cook (JC) model was established based on the experimental results and then incorporated into the finite element model to gain deep insights into the mechanical responses of the Ni8Ti9Cr1 rings under tension. Our findings reveal that dynamic tensile testing of elliptically shaped Ni8Ti9Cr1 rings induces a complex stress state, which leads to nonuniform necking effects and structural vibrations, revealing complex behaviors previously unexplored. This investigation significantly advances the understanding of quasistatic and dynamic tensile responses in elliptically shaped ring structures, shedding light on their mechanical intricacies across varying conditions.

Nanomechanical inhomogeneities in CVA-deposited titanium nitride thin films: Nanoindentation and finite element method investigations

Refractory metals that can withstand at high temperatures and harsh conditions are of utmost importance for solar-thermal and energy storage applications. Thin films of TiN have been deposited using cathodic vacuum arc deposition at relatively low temperatures ∼300 °C using the substrate bias ∼ −60 V. The nanomechanical properties of these films were investigated using nanoindentation and the spatial fluctuations were observed. The nanoindentation results were simulated using finite element method through Johnson-Cook model. A parametric study was conducted, and 16 different models were simulated to predict the hardening modulus, hardening exponent, and yield stress of the deposited film. The predicted values of elastic modulus, yield stress, hardening modulus and hardening exponent as 246 GPa, 2500 MPa, 25000 MPa and 0.1 respectively are found to satisfactorily explain the experimental load-indentation curves. We have found the local nitridation plays an important role on nanomechanical properties of TiN thin films and confirms that the nitrogen deficient regions are ductile with low yield stress and hardening modulus. This study further opens the opportunities of modelling the nanoscale system using FEM analysis.

Minimization of residual stress, surface roughness and tool wear in Electro Discharge Machining of inconel 625

Electro Discharge Machining (EDM) is a well-known non-traditional machining technique which is widely used to make die castings and turbine blades out of difficult-to-cut materials like Inconel 625. The machined part's surface quality and dimensional accuracy are affected by the EDM electrode's wear. Moreover, surface roughness and residual stress augmentation of EDM-machined components can reduce the workpiece's lifespan by decreasing the fatigue life of machined parts. To enhance the precision and durability of EDM machined components, residual stress, tool wear, and surface roughness should be evaluated and minimized. The majority of published research works for the assessment and optimization of EDM machining parameters are based on experimental works which are limited to testing, workpiece materials, and machining conditions. In order to improve the quality of machined surfaces and reduce tool wear and residual stress during Inconel 625 EDM processes, a virtual machining approach has been developed in the research work. To predict the cutting temperature during EDM operations, the modified Johnson Cook model of Inconel alloys is used. The finite element approach is then used to calculate the generated residual stress during the EDM process. The proposed virtual machining approach is also applied in order to predict the surface roughness of EDM machined parts. To minimize the residual stress, tool wear, and surface roughness during EDM operations of Inconel 625, the machining parameters of gap voltage, peak current, pulse-off time, and pulse-on time are optimized using the Taguchi optimization approach. Experiments and simulations are then conducted to verify the developed virtual machining system in the study. So, using the optimal machining parameters, the residual stress, surface roughness of machined items and wear of EDM electrode are minimized by 24.5 %, 25.4 %, and 25.4 % respectively. Thus, the quality and reliability of components made using EDM processes may be enhanced by the suggested virtual machining system.

Dynamic deformation behavior of single phase VNbTa medium-entropy alloys

In this study, the deformation behavior of body-centered-cubic (BCC) VNbTa medium-entropy alloy (MEA) was studied under different strain rates ranging from 10−3 s−1 to 5000 s−1 using screw-driven testing machine and split Hopkinson pressure bar (SHPB), respectively. The alloy presents an outstanding synergy of strength and plasticity without any adiabatic shear bands even at a strain rate of 5000 s−1. Moreover, the yield strength of the alloy displays an obvious strain rate dependence, increasing by ∼94.4% from 842 MPa at 10−3 s−1 to 1637 MPa at 5000 s−1. The strain rate sensitivity (SRS) factor m and highest temperature rise under dynamic loading is calculated to be 0.2991 and 182 K, respectively, which means a strong strain rate hardening and thermal softening resistance. Microstructure evolution analyses demonstrate a transition of deformation mechanism from single dislocation slip controlling in low strain rate to a synergy of mechanical twinning and dislocation slip in high strain rate. Therefore, the excellent dynamic mechanical properties could be attributed to the synergistic effects of the strong strain rate hardening and thermal softening resistance, the mechanical twins, and the cell structures and microbands derived from dislocation slip controlling. In addition, the dynamic deformation behavior of VNbTa could also be described by a classical Johnson-Cook model. Combining the excellent cryogenic temperature mechanical properties (tensile strength of ∼1930 MPa and fracture elongation ∼27%), the present work further indicates that the VNbTa MEA has great potential for engineering applications under some extreme circumstances.

A modified Johnson–Cook model for the plastic behavior of metals in ultrasonic vibration-assisted upsetting processes

In this work, we present a constitutive description of the plastic behavior of the metals and alloys under Ultrasonic Vibration (UV). When UV is imposed, it induces a softening effect on the plastic deformation of metals and alloys, referred to as the acoustoplastic phenomenon. The volumetric softening mechanism of the acoustoplasticity must consider stress superposition and acoustic softening. Taking the Johnson–Cook (JC) constitutive model as the reference for metal thermo-plasticity, the flow stress reduction due to UV is introduced by three types of softening terms: subtractive, multiplicative, and coupled. Those different configurations will be quantified via physical and phenomenological assumptions. For the study and validation of the proposed constitutive models, we focus on a well-known material, 6063 aluminum alloy. The ultrasonic vibration is modeled by an assisted upsetting process of an aluminum billet and compared with experiments. The impact of variations of the strain rate, ultrasonic amplitude, and frequency on the softening behavior of the models are analyzed and compared with available experimental results. We find out that the subtractive and coupled models agreed well with the experimental results showing the errors ranging from 2.4–4.8% and 4.4%–8%, respectively. However, the predictive ability of the multiplicative model exhibits large discrepancies at the low stage of strains following the acceptable predictions at high stains. By understanding the impact of the UV on the acoustoplastic deformation of the metals and alloys we can establish a reliable theoretical framework for prospective numerical studies of the UV-assisted manufacturing processes which is the goal of the current research presented here.

Effects of strain rate on dynamic deformation behavior and microstructure evolution of Fe-Mn-Cr-N austenitic stainless steel

In this work, the effects of strain rate on dynamic hot deformation behavior and microstructure evolution of Fe-Mn-Cr-N steel were studied under quasi-static and dynamic loading conditions using a Gleeble-3800 thermal-mechanical simulator and Split-Hopkinson pressure bar (SHPB) system. The stress-strain curves show that the yield and flow stresses are both significantly dependent on strain rate, also the strain rate sensitivity increases from 0.050 at a low strain rate (0.001–0.1 s−1) to 1.507 at a high strain rate (4500–5500 s−1). At a low strain rate (0.001–0.1 s−1), the microstructure evolution is dominated by dislocation slip and dynamic recovery (DRV). When strain rates are increased to 2500–3500 s−1, dislocation slip and mechanical twining together coordinate plastic deformation. When the strain rate was 4500–5500 s−1, the dynamic recrystallization (DRX) based on twinning formed in the deformation bands, and its fraction increased with the increasing strain rate due to adiabatic temperature rise (ΔT). The high micro-hardness value was obtained mainly because of the strain rate hardening (2500–3500 s−1), but the decrease at the strain rate of 4500–5500 s−1 is primarily attributed to recrystallization softening after deformation. The modified Johnson-Cook (J-C) model considering adiabatic temperature rise agrees with experimental results. It can be used to predict the plastic deformation behavior of Fe-Mn-Cr-N steel under high strain rate loading.

Ultrasonic welding of Cu cables bonding: Tensile, porosity and evolution of microstructure

Tensile strength, porosity and microstructure evolution of ultrasonic bonding for BVR2.5 Cu cables at different welding energies were investigated. By X-ray computed tomography and modification of the Johnson-Cook model, the predictive model of porosity was developed for the first time to assess joint strength. When the porosity was lower than 19%, the joint formed a good bond and reached the tensile strength of 585.7 ± 17.9 N. The maximum joint tensile strength was achieved at about 10% porosity. The Cu grains at the interface underwent plastic deformation, discontinuous dynamic recrystallisation and dynamic recovery to form a good bond. Interfacial grains are refined by ultrasonic vibrations, but the reduction of the porosity is the critical factor in improving joint strength.

Numerical-experimental analysis of laser-welded small energy absorbers with direct impact Hopkinson method

This research paper presents a comprehensive numerical-experimental analysis of the phenomena observed during the compression of small energy absorbers (EAs) with dimensions 23 × 23 mm and a thickness of 0.6 mm. This study uses the direct impact Hopkinson (DIH) method. The locus is the detailed prediction of the strength of laser-welded joints in terms of energy absorption under both quasi-static and dynamic loading conditions. Furthermore, the paper explores the potential utility of the described methodology for modeling and predicting the failure mechanisms of small energy absorbers. This investigation delves into key factors that affect the distribution of cracks in deformed energy absorbers. These include: the detail of the reproduction of the absorber geometry, the impact of finite element formulations and modeling method (2D/3D elements) and the complexity of the material model for propagated cracks. Two material models are considered, the simplified Johnson–Cook model and the tabulated Johnson-Cook with Hockett–Shelby extrapolation model, which incorporate linear damage dependent on the stress triaxiality and Lode angle. The study also highlights the advantages and disadvantages of the DIH test method. Some features cannot be effectively observed through experimental testing alone. The experimental procedure involved initial testing and calibration of the material models for both the parent material and the welded joints at three different strain rates. Subsequently, the validated energy absorber models are subjected to static and dynamic crushing. The results are subsequently compared with the virtual results obtained using the gravity hammer method, which is a more readily accessible testing approach. Remarkably, a very high correlation between the numerical simulation and experimental data is observed, providing a comprehensive understanding of the research problem related to laser-welded absorbers.

Strain rate-temperature effects and constitutive models for Q690D QT steel

This paper investigates the mechanical properties of the high-strength structural steel Q690D QT (Quenched and Tempered) over a wide temperature range and a wide strain rate range. Firstly, a series of quasi-static and dynamic tests adopting the universal testing machine and Split Hopkinson Pressure Bar were carried out to investigate the mechanical properties at strain rates from 0.00025 s−1 to 5000 s−1 and temperatures from room temperature (20 °C) to 700 °C. Stress-strain curves and dynamic yield strength increase factors were extracted and investigated. Test results show that Q690D QT exhibits different strain rate effects at different temperatures, more significant at the temperatures of 600 and 700 °C, as well as the high-temperature softening effect. Dynamic strain aging effect is identified at temperatures between 300 − 600 °C for plastic strain rates of 800 s−1 and 2300 s−1, nevertheless, this effect is observed at a higher temperature range of 500–700 °C for higher plastic strain rates of 4000 s−1 and 6400 s−1. From the analysis, the adiabatic thermosoftening effect cannot be ignored when the plastic strain rates reach 4000 s−1. Finally, an improved form of the Johnson-Cook model is proposed for capturing the adiabatic temperature effects at different temperatures and validated by the test data. A parameter dynamic temperature factor is proposed to describe the comprehensive effect of strain rate, test temperature, and adiabatic thermosoftening.

Dynamic tensile behaviour of 7A04-T6 aluminium alloy at elevated temperatures

As typical light engineering metals, aluminium alloys are widely employed in modern manufacturing and construction sectors. Among them, 7A04-T6 high-strength aluminium alloy (AA7A04-T6), alloying with Zn, Mg and Cu and manufactured via the T6 temper process, is a good alternative to steel in construction and is now attractive to engineers and researchers. The structural members made from 7A04-T6 High-strength aluminium alloy are also vulnerable to a variety of accidental actions, such as impact and blast which expose the AA7A04-T6 material to both high strain rates and elevated temperature. To date, investigations into the mechanical properties of AA7A04-T6 material under the loading conditions with strain rates and temperatures coupled are still limited. Dynamic tensile tests were conducted under the rate-temperature coupling test conditions in this work, to study the influence of strain rate and temperature on the stress-strain response of AA7A04-T6 material. The ranges of the test strain rate and temperature were from 0.001 s−1 to 102 s−1 and from 20 ℃ to 200 ℃, respectively. Based on the classical Johnson-Cook model and Cowper-Symonds model, a modified model was proposed for AA7A04-T6 material and good agreement is achieved in the comparison between the predictions and the measured stress-strain curves, which could facilitate the relevant fine analysis and resilient design in the future.

Simulating equal channel angular pressing of commercially pure aluminium using Johnson–Cook model

Optimizing the Equal Channel Angular Pressing (ECAP) process for a new material can be a complex endeavour, given the multiple variables such as Coefficient of Friction (COF), channel angle, temperature, etc. To address the need for a material model that can account for temperature-dependent plastic flow, the present study applies the Johnson-Cook plasticity model for simulating ECAP. The present study reports the effects of varying the channel angle (90°, 120°, 150°) and COF (ranging from 0 to 0.15) at room temperature. The results show that the channel angle plays a significant role in influencing the behaviour of the aluminium, with stress and strain exhibiting an inverse relationship with the channel angle. Additionally, the aluminium material experiences a maximum stress distribution and higher flow stress within the COF range of 0 to 0.15 for a channel angle of 90°, as compared to 120° and 150°. This behaviour can be attributed to the restriction of movement at higher COF values. Notably, a maximum shear stress of 56 MPa was observed when the channel angle was set to 90° with a COF of 0.15. Furthermore, across all simulations involving channel angles of 90°, 120°, and 150°, an increase in COF lead to a decrease in curvature. These simulated results are consistent with existing literature. Thus, the Johnson-Cook plasticity model, with appropriate modifications, serves as a viable approach for studying the ECAP process.

Strain rate and temperature rate behavior of ultra-high-strength 1770 steel: Base for transverse impact analysis

The investigation was motivated by the widespread use of ultra-high-strength steels in cable-stayed bridges and armor steel plates. These structures are exposed to elevated risks from extreme loads, including vehicle impacts and blast loadings. The study aimed to investigate the mechanical properties of 1770 steel for applications in extreme conditions. The strain rates and temperatures ranged from 0.00095 s−1 to 1303 s−1 and 20 °C–900 °C, respectively. Tensile tests were conducted at various strain rates using a Split Hopkinson Tension Bar for dynamic testing and a universal testing machine for quasi-static testing at room temperature (20 °C). Quasi-static tension at elevated temperatures was carried out using an electromechanical testing machine coupled with a heating device. A uniform temperature distribution inside the specimens was ensured by a 30-min holding time. The results of the tensile test indicate that the 1770 steel displays notable thermal softening effects and strain rate hardening that differ from mild steel. The standard Johnson-Cook (J-C) model was found to be inadequate in accurately predicting the strain rate effects of this specimen. To address this issue, the strain rate parameter C in the standard model was adjusted to create the modified J-C model, which demonstrated good agreement with the experimental results. To further demonstrate the modified model and the identified parameters, drop hammer impact tests and corresponding numerical simulations were conducted. The impact test and numerical simulation results showed good agreement in terms of deformation and contact force. The mechanical properties and the constitutive models can serve as a design reference for the ultra-high-strength 1770 steel in extreme envirnments, as well as a theoretical basis for fitting material models of similar ultra-high-strength steels.