Johnson-Cook Model Research Articles

Study on deformation behavior of Ti60 alloy based on multi-physics coupling

Titanium alloys are extensively employed in aerospace due to their superior performance, but their development is constrained by limited formability at room temperature, an electrically assisted forming (EAF) process emerges as a promising solution to reduce flow stress, improve formability, and accelerate material recrystallization. This study focuses on elucidating the interplay between pulse current, temperature, and flow stress in Ti60 alloy under combined electrical, thermal, and stress fields. To this end, electrically assisted tensile (EAT) tests were performed on Ti60 alloy using six different current densities. Currently, there is no unified theory for electro-plasticity in metal materials, and the absence of a suitable model hinders finite element simulation in EAF. The investigation encompasses four key areas: the impact of multi-physics coupling on temperature variations, the stress-strain curve characteristics, the microstructural analysis of tensile fractures, and the modification of the Johnson-Cook (MJC) model. Notably, temperature distribution proves more uniform across the width than the length. Tensile elongation initially rises and then falls with increasing current density, peaking at a critical current density (J=30 A/mm2). Higher current densities lead to a transition in fracture features, with deep, numerous dimples and tiny voids supplanting tearing ridges and facets. Despite this, brittle fracture remains the dominant mode, accompanied by granular oxide formation at J= 35, 40 A/mm2. The MJC model aligns closely with experimental outcomes, showing R and EAARE values of 92.7% and 7.15%, respectively. This model accurately predicts Ti60 alloy's deformation under multi-physics conditions, marking a significant advancement in integrating electro-plasticity into constitutive modeling.

Dynamic mechanical properties and constitutive model establishment of QSTE420 steel

The uniaxial tensile tests of QSTE420 steel under different strain rates were carried out using an electronic universal material testing machine, a high-speed tensile testing machine and a split Hopkinson tension bar (SHTB) device, the engineering stress-strain curves of steel within the range of 0.001– 1000 s−1 were obtained and the mechanical properties of steel at different strain rates were analyzed. The results show that in the static strain rate range of 10−3– 10−2 s−1, the yield strength and tensile strength of QSTE420 steel exhibit minimal variation, fluctuating between 430– 434 MPa and 507– 515 MPa, respectively; while the uniform elongation and elongation at break remain approximately at 12% and 35%, respectively. In the high strain rate range of 10−1– 103 s−1, both yield strength and tensile strength exhibit a consistent increase in direct correlation with the tensile rate. Specifically, the yield strength increases from 444 to 607 MPa and the tensile strength increases from 523 to 640 MPa as the strain rate escalates from 10−1 to 103 s−1. Moreover, the elongation at break demonstrates a general increasing trend and reaches its peak value of 45.65% at 100 s−1. The morphology of fracture surfaces under different strain rates are observed by Scanning Electron Microscopy (SEM). The fracture appearance analysis reveals numerous dimples in the fracture, indicating a ductile fracture. Furthermore, the comparison demonstrates that steel exhibits enhanced plasticity at a strain rate of 100 s−1. Based on the experimental results, the Johnson-Cook constitutive model was established and modified. The modified Johnson-Cook model exhibits a higher determination coefficient (R2) compared to the original version, signifying an improved fitting accuracy.

Failure analysis and design improvement of high-pressure seal cone head for vehicle hydrogen engine

As hydrogen energy vehicle technology advances, the performance requirements of vehicle hydrogen engine components become increasingly stringent. The high-pressure sealing cone head is a vital connection of the vehicle's hydrogen engine, however, it is easily fractured during the loading test. To address this issue, this research combines finite element modeling and material characterization methodologies to perform failure analysis and re-optimization design of the sealing cone head. First, the parameters for the CL toughness fracture criteria and the Johnson-Cook constitutive model were obtained by the inversion technique and the tensile test, respectively. On the cold heading formation process of the cone head, finite element analysis and microstructure analysis were performed. The results show that machining defects on the outer surface are the root cause of failure. Fatigue cracking is the main failure mechanism, and the crack gradually expands under the effect of alternating loads, which eventually causes a fracture of the cone head. At the same time, there are bending-type folding defects caused by the instability of the cone head under pressure. Second, the critical structural and process factors that impact the mechanical behavior of the components are investigated, and the orthogonal experiment optimization method is utilized to find the optimal process parameters, using the damage value as the evaluation index. According to the findings, the die angle has a major impact on the damage value, but the eligible die angle that is too small would negatively affect the force of the cone head and nut. Finally, a multi-station cold heading procedure for the high-pressure seal cone head was innovatively presented, and its mechanism of action was unveiled. The aforementioned defects were effectively addressed by the optimized process, and as compared to the pre-optimization, the maximum principal stress of the optimized component in the C-region was reduced by 27%, which did not exceed the tensile strength. At the same time, the spindle load was decreased by 25% and the maximum damage value was decreased by 48%, reaching the safe range. The optimized process effectively improves the performance of the part and increases the quality stability.

Research on dynamic deformation behavior and constitutive relationship of hot forming high strength steel

To accurately characterize the dynamic deformation mechanical properties of hot forming steels 6Mn6 and 22MnB5 under collision conditions, quasi-static tensile tests (0.001s−1) and Hopkinson compression bar tests (∼2000s−1, ∼3000s−1, ∼4000s−1) were conducted to analyze the influence of strain rate on the material mechanical properties. Based on the experimental results, four constitutive models including Johnson-Cook (JC), modified JC (m-JC), Cowper-Symond (CS), and Khan-Huang (KH) models were established for both 6Mn6 and 22MnB5. Additionally, a modified model based on the Swift-Voce strain hardening model coupled with the Cowper-Symond model was proposed. A numerical simulation model for compression bar tests was developed using JC and m-JC models. The experimental results indicate that both hot forming steels exhibit strain rate sensitivity, with 6Mn6 performed a more pronounced effect than 22MnB5. The average absolute error (AARE) and correlation coefficient (R) of the m-JC and CS models were 0.99 and 0.29 %, 0.95 and 0.4 %, respectively. The dynamic deformation behavior of 6Mn6 and 22MnB5 at high strain rates was accurately predicted. Comparing with the JC model, the utilization of the m-JC user subroutine has resulted in a significant improvement in simulation accuracy by 58 % and 84 % for these two materials, which laying a solid foundation for high-precision vehicle collision simulation.

Surface crack analysis of 8Cr4Mo4V steel based on Crystal/Phase microstructure model by grinding

Metal polycrystalline materials tend to be homogeneous and isotropic at the macroscopic level, which leads it difficult to visually characterize the sprouting and expansion of cracks by traditional grinding simulation. In this study, the Johnson–Cook constitutive model was used for the finite element method (FEM) based on grinding characteristics with a high strain rate and large plastic deformation. The models are focused on the actual microstructure distribution, one of them contains grains and grain boundaries, and another contains phase organization (martensite and acicular martensite) and carbides. The study pinpoints the changes in microstructure under different grinding parameters during the grinding process and the influences on the formation of microscopic cracks. Ultimately, it was found that the shedding of large primary carbide is a critical factor for inducing surface cracks. The uncoordinated deformation between brittle carbides with the other phases is the main cause of carbide shedding. Therefore, this article visualized shows the influence of grinding parameters on surface cracks from the perspective of microstructure modeling, which is of great significance in guiding practical processing.

Modification of Johnson–Cook Constitutive Parameters in Ball Burnish Simulation of 7075-T651 Aluminum Alloy

The Johnson–Cook model is widely used because of its ability to meet the simulation material requirements in various situations. However, under different working conditions, the accuracy of the model may have errors. In this work, based on Abaqus (Abaqus R2022 Education Edition, Dassault Systèmes, Paris, France) simulation software, Johnson–Cook (JC) constitutive model parameters and compression parameters were selected to simulate the improvement of surface roughness during the ball milling of a 7075-T651 aluminum alloy. In the numerical simulation of ball polishing, the changes in the residual stress field when the Johnson–Cook parameters change are analyzed. By comparing the numerically simulated residual stress fields under the JC parameters calculated at different strain rates, a set of parameters that agrees with the experimental values is selected. The results show that the residual stresses are in line with the experimental values when the strain rate is 10−4s −1. The changes in roughness corresponding to the selected parameters are analyzed. The results indicate that the simulated trend of roughness variation is consistent with the experimental values, and the optimal surface roughness value under a static pressure of 300 N is obtained.

Numerical simulation method and structural optimization for shearing capacity of ram blowout preventers

With the increasing demand for energy in the country, there has been a notable rise in the deployment of deep and ultra-deep wells. Consequently, drilling operations have become more complex, with greater intricacies in drilling techniques, challenging operating conditions, and varying geological factors. The size of the drill pipes has grown larger, and higher steel grades are being used, surpassing the design requirements of conventional ram blowout preventers. As a result, issues have arisen, including inadequate shear force of the ram blowout preventer to cut through the drill pipes and the potential for cut debris from the drill pipes to fall and damage the sealing elements, compromising the sealing integrity and posing a risk of blowouts.To address these issues encountered in the field, a shear analysis model for the ram blowout preventer was established based on the Johnson-Cook constitutive model and the Shear Damage fracture criterion. The reliability and accuracy of the simulation were validated through comparative experiments between simulation and laboratory trials. Furthermore, the structure of the ram blowout preventer was optimized to mitigate these challenges. Additionally, the response surface method was employed to optimize the parameters of the novel ram structure for the ram blowout preventer, followed by indoor experiments using the selected parameters. The experimental results demonstrated a significant improvement in both the shear performance and sealing capability of the novel ram blowout preventer compared to the conventional ram blowout preventer design. This advancement provides valuable insights and practical reference for on-site operations.

Modified constitutive models for Inconel 718 considering current density and temperature in electrically assisted forming process

Electrically Assisted Forming (EAF) technology has obvious advantages in material forming. To develop an effective constitutive model considering electrical effects, room temperature and electrically assisted quasi-static uniaxial tensile tests were conducted using ultrathin nickel-based superalloy plates with a thickness of 0.25 mm. The research focused on the two most widely recognized effects: the Joule thermal and the electric athermal effects. The mechanism of current action can be divided into two scenarios: one considering the Joule thermal effect only, and the other considering both effects simultaneously. Two basic constitutive models, namely the Modified-Hollomon model and the Johnson-Cook (J-C) model, were selected to be optimized through the classification of two different situations, and four optimized constitutive models were proposed. It was found that the J-C model with simultaneous consideration of the Joule thermal effect and electric athermal effect had the best prediction effect by comparing the results of these four models. Finally, the accuracy of the optimization model was verified by finite element simulation of the electrically assisted stretching optimization model. The results show that the constitutive model can effectively predict the temperature effect caused by the Joule heat effect and the athermal effect of current on the material.

Identification of Johnson-Cook material model parameters for laser shock peening process simulation for AA2024, Ti–6Al–4V and Inconel 718

This paper addresses the identification of Johnson-Cook material model parameters for the simulation of high strain rate processes such as laser shock peening. A combined numerical and experimental approach is described for the identification of the material parameters for AA2024-T3, Ti–6Al–4V, and Inconel 718 alloys. Validation of the parameters was performed based on depth-resolved residual stress profile evaluation after both experimental and numerical laser shock peening application. However, it has been observed that the strain rate-dependent coefficient identified at low strain rates is insufficient for accurately representing the behavior of the Ti–6Al–4V alloy. Consequently, there is a need to identify and determine the appropriate parameter specifically tailored to the strain rates that are relevant to the intended application of the material. The outcomes of this study provide significant insights into the accurate identification of Johnson-Cook material model parameters for laser shock peening simulations. The findings emphasize the critical importance of considering the strain rate-dependent coefficient C in the Johnson-Cook material model to enhance the accuracy and precision of representing material behavior in simulation efforts.

INVESTIGATING CUTTING FORCE AND CUTTING POWER WHEN TURNING AA6082-T4 ALLOY AT CUTTING DEPTHS SMALLER THAN TOOL NOSE RADIUS

Aluminum alloys are widely preferred engineering materials in the manufacturing industry due to their high formability, good mechanical strength, and low density. Machining problems in aluminum alloys include built-up-edge formation, chip rupturing, and low surface quality, particularly in the 6xxx series due to the high Si content in the machining area. The aim of this study was to investigate the influence of cutting depth smaller than the tool corner radius, and various cutting parameters on cutting force and cutting power in machining AA6082-T4 alloy. In this context, the Johnson-Cook material model was established for AA6082-T4 alloy, and machining behaviors in terms of cutting force, and cutting power were investigated by performing finite element method (FEM) analyses using a full factorial design and variance analyses with different machining parameters. In conclusion, the lowest cutting forces were achieved with a cutting depth of 0.3 mm and a feed of 0.1 mm/rev, and the lowest cutting power was obtained with a cutting speed of 300 m/min, a cutting depth of 0.3 mm, and a feed of 0.1 mm/rev. In addition, the most effective machining parameters have been determined as cutting depth with a ratio of 91.74% for cutting force and cutting speed with a ratio of 33.13% for cutting power based on the results of variance and regression analysis.

Study on thermal deformation constitutive model of NiCoFeAlCrMo high-entropy alloy with FCC / L12 coherent structure

Due to its multi-principal component characteristics, high-entropy alloys exhibit excellent comprehensive mechanical properties and become a new generation of engineering structure alternative materials. At present, a single constitutive model is used to describe the change of flow stress in the study of hot deformation behavior of high-entropy alloys, and there are some problems such as inaccurate prediction accuracy or inapplicability of the model in some hot processing intervals. In this paper, three different constitutive models are combined to fully consider the applicability of the model in different temperature ranges, and the change of flow stress behavior is accurately described, which is of great significance for subsequent deformation mechanism research, hot processing process optimization, numerical simulation and so on. Thermal compression experiments on cast Ni28.5Co18.6Fe18.2Al16.3Cr10.5Mo4 Ti2.3Nb0.6W0.9C0.2 high-entropy alloy were carried out using a Gleeble-3800 thermal simulation tester with deformation temperatures in the range from 900 ℃ to 1150 ℃ and strain rates from 0.001 s−1 to 1 s−1. The constitutive relationships between true stress and strain, temperature and strain rate were established, while the heat deformation process of this alloy under different deformation conditions by Arrhennius, Modified Johnson-Cook and Modified Fields-Backofen models were characterized. The results indicate that Arrenius model describe the rheological behavior of the alloy better in a wider temperature range and at a wider strain rate range. Comparatively, the model shows the highest prediction accuracy in the high-temperature region and slightly lower accuracy in the mesothermal and low-temperature regions. The modified J-C and F-B models have better prediction accuracy in the low-temperature and medium-temperature regions, respectively. Due to the different deformation conditions, dislocation configurations such as dislocation tangles, dislocation networks, and subcrystalline junctions can be observed in the plastic deformation region. The dislocation density of this alloy increases with increasing strain rate and decreasing deformation temperature after deformation.

NUMERICAL ANALYSIS OF V-SHAPED PROTECTIVE PLATES AT VARIOUS ANGLES SUBJECTED TO BLAST LOADING – A COMPARATIVE ANALYSIS

The mechanical response of blast-resistant vehicles, such as Infantry Fighting Vehicles (IFVs), Mechanized Infantry Combat Vehicles (MICVs), Armored Personal Vehicles (APVs), and Mine-Resistant Ambush-Protected (MRAP) vehicles, is crucial for their effective design. When designing armored vehicles, it is important to achieve a balance between rigid designs that transmit blast forces to the troop's cabins and softer designs that prevent excessive structure deformation hazardous to the troops. This study investigates the performance of V-shaped plates at different angles under blast loading. The focus is on modeling blast effects using the Conventional Weapon (ConWep) method and the Johnson-Cook material model. The material used for V-shaped protective plates STRENX700 (S690QL) armor steel is commonly used for blast protection in Anti-Landmine (ALM) Vehicles. The blast-wave induces large deformation, erosion, high strain rates, non-linear material behavior and fragmentation. The numerical simulation results are presented in the form of vertical displacement of the central node on the protective plate, von Mises equivalent stress, and equivalent plastic strain.

Assessment of predicting temperature distribution of friction stir welded AA6061 induced by pin profiles for developing sustainable industry

Nowadays, the aspects of energy and environmental pollution have been becoming a big challenge in developing sustainable industries. Using green technology is considered as priority solution for any manufacturing process. Friction stir welding (FSW) is invented as green technology applied widely in many field industries. To evaluate its applicability, this study focused on the prediction of temperature distribution of FSWed AA6061 induced by various pin profiles. Research efforts are being made to gain a better understanding of FSW process, to explore different tool configurations, and their influence on the heat generation. The numerical model was developed in Abaqus software, utilizing the coupled Eulerian Lagrangian method, the Johnson-Cook material model, and the mass scaling technique. The model’s accuracy is verified by comparing its simulated temperature values with experimental data in Stir zone (SZ) and Heat-affected zone (HAZ). The numerical results show the high correlation with the experimental study, with the deviation around 10%. It is shown that tool pin profiles with the combination of thread and flat features generated the highest temperature.

Towards a Simulation-Assisted Prediction of Residual Stress-Induced Failure during Powder Bed Fusion of Metals Using a Laser Beam: Suitable Fracture Mechanics Models and Calibration Methods

In recent years, Additive Manufacturing (AM) has emerged as a transformative technology, with the process of Powder Bed Fusion of Metals using a Laser Beam (PBF-LB/M) gaining substantial attention for its precision and versatility in fabricating metal components. A major challenge in PBF-LB/M is the failure of the component or the support structure during the production process. In order to locate a possible residual stress-induced failure prior to the fabrication of the component, a suitable failure criterion has to be identified and implemented in process simulation software. In the work leading to this paper, failure criteria based on the Rice-Tracey (RT) and Johnson-Cook (JC) fracture models were identified as potential models to reach this goal. The models were calibrated for the nickel-based superalloy Inconel 718. For the calibration process, a conventional experimental, a combined experimental and simulative, and an AM-adapted approach were applied and compared. The latter was devised to account for the particular phenomena that occur during PBF-LB/M. It was found that the JC model was able to capture the calibration data points more precisely than the RT model due to its higher number of calibration parameters. Only the JC model calibrated by the experimental and AM-adapted approach showed an increased equivalent plastic failure strain at high triaxialities, predicting a higher cracking resistance. The presented results can be integrated into a simulation tool with which the potential fracture location as well as the cracking susceptibility during the manufacturing process of PBF-LB/M parts can be predicted.

Improved Analytical Model for Thermal Softening in Aluminum Alloys Form Room Temperature to Solidus

In advanced solid-state manufacturing processes such as friction stir welding, the metal’s temperature ranges from room temperature to the solidus temperature. The material strength in the temperature range is generally required for investigating the mechanical behaviors. In this communication paper, an analytical model is proposed for describing the thermal softening of aluminum alloys for room temperature to solidus temperature, in which the concept of temperature-dependent transition between two thermal softening regimes is implemented. It is demonstrated that the proposed model compares favorably to the well-known Sellars–Tegart model and Johnson–Cook model. The constants of the proposed model for nine typical engineering commercial aluminum alloys are documented.

An insight into the mechanical behavior and failure mechanism of CFRP/Al adhesively bonded structures subjected to low-velocity impact

Experimental and numerical methods are used to investigate the effects of different impact surfaces and energies on the mechanical properties and failure behavior of CFRP/Al adhesively bonded structures. To predict the damage initiation and propagation of CFRP laminates, interlaminar and adhesive layer, and aluminum alloy plates, the integrated finite element model containing both low-velocity impact (LVI) and axial tensile after impact (TAI) processes is developed by combining continuum damage mechanics model, cohesive zone model, and Johnson-Cook model. Additionally, LVI and TAI tests have been performed on the corresponding adhesively bonded structures with aluminum alloy 5182 (AA5182) and CFRP laminate as impact surfaces, which verify the effectiveness of the proposed integrated FEM. The results indicate that AA5182, as the impact surface, produces greater impact damage (maximum crater depth and opening width) in the center of the overlap region in comparison with the CFRP. The residual bearing capacity of the joints is the result of the competition between impact behavior and mechanical interlocking. The tensile strength, stiffness, and failure displacement of the joints decrease with the increase of impact energy. The failure modes of the joints include annular and circular cohesive failure of the adhesive layer in the impact region, interface failure, cohesive failure and peeling failure in the non-impact region, delamination damage, and fiber pullout and matrix cracking of the CFRP laminate. This investigation can provide good technical support for the structural design of heterogeneous material connections.

Simulation analysis of the circular sawing process of medium density fiberboard (MDF) based on the Johnson–Cook model

Simulation analysis of the circular sawing process of medium density fiberboard (MDF) based on the Johnson–Cook model

Effect of different friction coefficient models on numerical simulation of inertia friction welding of 2219 Al alloy to 304 stainless steel

In inertia friction welding (IFW) of Al alloy to steel, the friction coefficient of interface influences the friction heat production and determines the accuracy of the numerical simulation of welding process. A fully coupled three-dimensional model was established to simulate the IFW process of 2219 Al alloy to 304 stainless steel. By taking different simplifications in the influencing factors (i.e., temperature, sliding velocity, and pressure) of friction coefficient, three types of friction coefficient models were established and utilized in the simulation of IFW process. The strain compensated Arrhenius and Johnson-Cook models were employed to describe the deformation behavior of Al alloy and steel, respectively. Both Al alloy and steel were assumed to be the elastic-plastic body, and the friction stress was calculated by the Coulomb friction model. The friction interface temperature, angular velocity attenuation, axial shortening distance, and joint appearance were measured to verify and compare the accuracy of the established models. The temperature and stress evolutions during the IFW process were also analyzed. With the smallest error in validation, the friction coefficient model, which was a function of temperature, sliding rate, and pressure, showed the best accuracy in describing the friction behavior. By considering the effect of pressure, a more accurate shear stress at the center region of the interface was calculated with a lower value. It means that the friction resistance at the region was lower, promoting the flow of internal Al alloy and the formation of curly-shape flash.

Comparison of Measurement of Aluminium Alloy in High Strain Rate

Abstract This article describes the Split Hopkinson Pressure Bar test of aluminium alloy EN AW 7075-T6. This test is used for material testing at a high strain rate. Two approaches in measurement. In the first case was used one size of specimen and different initial pressure. In the second case was set one initial pressure and three different lengths of specimen. Based on measured data, constants of Johnson-Cook material model for FEM analysis were found.

Hot compressive deformation behavior and microstructural evolution of the spray-formed 1420 Al–Li alloy

The 1420 Al–Li alloy has been widely used in the aerospace field. To investigate the hot workability of the alloy, a series of hot compression tests were carried out on the spray-formed alloy in the temperature range of 300°C–450 °C with strain rates of 0.0001s−1-10s−1. First, an improved Johnson-Cook model was developed by considering the coupling effect of strain, strain rate, and temperature, and the prediction error of the model was reduced to 5.3 %. Subsequently, processing maps with various strains were established. In addition, the microstructural evolution under various deformation conditions was systematically studied using the electron backscatter diffraction (EBSD) technique. The alloy exhibited uniform deformation under the synergistic effect of the continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX) mechanisms. Finally, the feasible hot working windows were identified as 425°C–450°C and 0.01s−1-0.1s−1 based on processing maps and microstructural evolution results. This work could offer comprehensive guidance for the hot working process of 1420 Al–Li alloy from both the macro and the micro aspects.