Johnson Cook Research Articles

An unresolved SPH-DEM model for simulation of ductile and brittle surface erosion by abrasive water-jet (AWJ) impact

The abrasive water-jet (AWJ) erosion process involves the complex interaction between fluid medium, abrasive particles and solid material, which brings great challenges to the establishment of numerical model. Because traditional grid-based methods are not suitable for the problems of local deformation and material removal, the meshfree method smoothed particle hydrodynamics (SPH), based on the unresolved coupling and the discrete element method (DEM), is adopted to establish the model for AWJ study. The fluid medium is treated as a weakly compressible viscous liquid, the solid material is treated as an elastic-plastic material, and the abrasives are treated as rigid bodies. The fluid and solid phases are discretized with SPH particles, and the abrasives are described with DEM particles. The Johnson-Cook (J-C) and Johnson-Holmquist-II (JH-2) constitutive models are used to describe the stress-strain behavior of ductile and brittle materials, respectively. The effectiveness of the numerical model is further verified by AWJ impact experiments. The plastic deformation and cumulative failure characteristics of ductile materials, and the crack formation and propagation characteristics of brittle materials are systematically analyzed. The results provide insight for the AWJ research and lay a foundation for investigation of other complex fluid-particle flow in a numerical way.

Numerical Study on the Development of Adiabatic Shear Bands During High Strain-Rate Compression of AISI 1045 Steel: A Comparative Analysis Between Plane-Strain and Axisymmetric Problems

This work studies numerically the development of adiabatic shear banding (ASB) during high strain-rate compression of AISI 1045 steel. Plane strain and cylindrical axisymmetric compressions are simulated in LS-DYNA, considering rectangular and cylindrical steel samples, respectively. Also, a parametric analysis in height-to-base ratio is conducted in order to evaluate the effect of geometry and dimensional ratio of the sample on ASB formation. Doubly structural-thermal-damage coupled finite element models are developed for the numerical simulations, implementing the thermo-viscoplastic Modified Johnson–Cook constitutive relation and damage criterion, while further damage-equivalent stress and strain fields are introduced for the damage coupling. The simulations revealed that plane strain compression promotes more ASB formation, providing lower critical strain for ASB initiation and wider and stronger ASBs compared with axisymmetric compression. Further, X-shaped ASBs initially form during plane strain compression, while as deformation increases, they transform into S-shaped ASBs in contrast to axisymmetric compression, where parabolic ASBs are developed. Also, a lower height-to-base ratio leads to greater ASB propensity, reducing critical strain in axisymmetric compression. Finally, thermal softening is found to precede damage softening and dominate the ASB genesis and its early evolution, while in contrast damage softening drives later ASB evolution and its transition to fracture.

Parametric Analysis and Improvement of the Johnson-Cook Model for a TC4 Titanium Alloy

Titanium alloys are widely used in the manufacture of gas turbines’ compressor blades. Elucidating their mechanical behavior and strength under damaged conditions is the key to evaluating the equipment’s reliability. However, the conventional Johnson-Cook (J-C) constitutive model has limitations in describing the dynamic response of titanium alloy materials under the impact of a high strain rate. In order to solve this problem, the mechanical behavior of a TC4 titanium alloy under high strain rate and different temperature conditions was analyzed by combining experiments and numerical simulations. In this study, the parameters of the J-C model were analyzed in detail, and an improved J-C constitutive model is proposed, based on the new mechanism of the strain rate strengthening effect and the temperature softening effect, which improves the accuracy of the description of strain sensitivity and temperature dependence. Finally, the VUMAT subroutine of ABAQUS software was used for numerical simulation, and the predictive ability of the improved model was verified. The simulation results showed that the maximum prediction error of the traditional J-C model was 23.6%, while the maximum error of the improved model was reduced to 5.6%. This indicates that the improved J-C constitutive model can more accurately predict the mechanical response of a titanium alloy under an impact load and provides a theoretical basis for the study of the mechanical properties of titanium alloy blades under subsequent conditions of foreign object damage.

Gleeble-based Johnson–Cook parametric identification of AISI 9310 steel empowered by computational intelligence

Gleeble-based Johnson–Cook parametric identification of AISI 9310 steel empowered by computational intelligence

Barrel rifling node offset detection and subsequent optimization based on thin film in-mold decoration characteristics of the Johnson–Cook model

In this paper, a nodal detection method for the detection and optimization of barrel helix offsets is proposed. The barrel used in this experiment is a 6-helix barrel. Moreover, the special properties of the film of Polyetheretherketone (PEEK) material are used to cover the surface of the barrel helix with a virtual in-mold decoration (IMD) film, and the unique nature of the film die offset in the IMD is utilized to detect the position of the barrel helix. The area with a large die index is the area with a large helix offset in the barrel, and the IMD die index is introduced to quantify the data. The IMD die index is used to determine the helix offset of the damaged barrel. The novelty of this work is that each node can use the die index to efficiently detect the position of the barrel helix deviation, carry out subsequent optimization and repair work through the optimization of the injection molding parameters and the design optimization of the barrel and verify the experiment by comparing the results. Through the steady-state simulation research mode, different permutations and combinations of the two process parameters are simulated to study their effects. Quantitative reference indicators include but are not limited to dependent variables such as the fluid flow velocity, shear rate, temperature distribution and phase transition, and the shear heating process of the injection screw is taken into account in the mold flow analysis to ensure that the die index value is more accurate. It can be seen from the analysis results that the temperature of the barrel changes after the groove depth and groove width are changed, and the effect ratio of the groove depth is lower than that of the groove width in the same degree of size change.

Investigations of three-dimensional fiber orientation on mechanical impact behavior of short glass-fiber-reinforced PEEK composites

This work presents experimental and numerical investigations of three-dimensional (3D) fiber orientation on mechanical impact behavior of short glass-fiber-reinforced polyether ether ketone (SGFR PEEK) composites. The incorporation of short fibers significantly enhances the stiffness and strength of the composites while reducing the ductility, thereby, making the study of their impact response essential. To this end, we firstly manufactured the composite components using injection molding, and used the micro-computed tomography (µCT) to measure the fiber orientation distribution in 3D space for mechanical behavior prediction. Then, by studying the molded components across the thickness based on the actual observation, a distinct laminate structure with seven layers was quantitatively evaluated. A representative volume element (RVE) micromechanical computational method was developed and compared with the experimental results. Furthermore, homogenization method with the periodic boundary condition was implemented to evaluate the effective mechanical properties of the molded components. Finally, the phenomenological Johnson Cook (JC) model with fracture behavior was conducted to analyze the impact response of the injected components with different fiber orientation distributions. The new framework is demonstrated by acceptable energy absorption capability prediction of the SGFR PEEK composites.

Prediction of flow stress of Ta–W alloys using machine learning

Abstract The primary aim of this article was to predict the flow stress of Ta–W alloys using the eXtreme Gradient Boosting (XGBoost) machine learning model and to explain the outcome using SHapley Additive exPlanations (SHAP). The article details the effect of temperature, strain rate, and alloying content on the deformation behavior. Though grain size, dislocation density, texture and impurities are also important factors affecting the deformation behavior, these have not been considered in this work. Data and constitutive models from the literature were used to find and compare the predictiveness of the flow stress in Ta–W alloys. XGBoost predicted flow stress with a root mean square error of 12 MPa during training and 40 MPa during testing, while constitutive models such as Johnson–Cook (JC), Zerilli–Armstrong (ZA) and mechanical threshold stress (MTS) models showed a root mean square error of 208, 131 and 149 MPa respectively. The linear correlation between the predicted and experimental flow stress at 10% strain was calculated using the Pearson correlation coefficient and found to be 0.64, 0.93, and 0.70 for JC, ZA and MTS models respectively, while XGBoost showed 0.99 during training and 0.98 during testing. The optimized XGBoost model was validated using five-fold and leave-one-group-out cross-validations. The flow stress at 10% strain was predicted using XGBoost at various temperatures, strain rates, and alloying content. The flow stress was low at temperatures above 1000 K and strain rates below 10−2 s−1. From SHAP analysis, it was found that the base flow stress value (at which the SHAP value is zero) was 477 MPa. For temperatures less than 275 K, strain rates greater than 1 s−1, and alloying content greater than 2.5 wt.% W, the flow stress showed an increase from its base value.

Performance study of explosively formed projectile using CoCrFeNi high-entropy alloy as a liner

Based on mechanical tensile experiments on the CoCrFeNi high-entropy alloy (HEA), this study explores the forming patterns of the eccentrically shaped sub-hemispherical lined explosively formed projectile (EFP) made of the HEA material. The CoCrFeNi HEA material is initially prepared, and mechanical tensile tests are conducted at various temperatures and strain rates. The Johnson–Cook (J–C) constitutive equation for this material is derived by fitting the experimental data. Scanning electron microscopy and the energy dispersive spectrometer characterize the fracture surface of the tensile specimens, providing insights into the mechanical ductility and fracture mechanism of CoCrFeNi HEA. The EFP forming process under various charge configurations is simulated using AUTODYN software, leading to the identification of the optimal charge configuration. In addition, the damage performance is evaluated. This study provides a theoretical basis for applying HEA materials in the field of shaped charges and offers new ideas and methods for designing more efficient shaped charge warheads.

An Interactive Fluid–Solid Approach for Numerical Modeling of Composite Metal Foam Behavior under Compression

Composite metal foams (CMF) are renowned for their high strength‐to‐density ratio, high stiffness, and energy absorption capabilities. Homogenized finite element models of CMF have been numerically solved to understand the mechanical behavior of the material under a variety of external loading conditions. This work aims to pioneer a comprehensive finite element model for steel–steel composite metal foam by incorporating the interactions between embedded stainless‐steel hollow spheres with entrapped air inside stainless‐steel matrix. The material behavior of hollow spheres, surrounding matrix, and air are modeled using Johnson–Cook (JC) plasticity, Deshpande–Fleck (D–F) foam, and linear polynomial equation of state in LS DYNA. Further, the finite element model utilizes a combination of Lagrangian solid elements and meshfree smooth particles hydrodynamics with appropriate contacts to effectively model the interaction of entrapped air within stainless‐steel hollow spheres with surrounding metallic spheres and matrix. The strain rate and the crosshead velocity of 65 s−1 and 2.4765 m s−1 are used for quasistatic compression analysis. Finally, the results obtained from the computational model are compared and validated using previously reported experimental quasistatic compression data. The numerical model corroborates stress–strain response of CMF with 5.6% error for plateau stresses average within 25% and 30% strain.

Research on Dynamic Mechanical Behavior of Reinforcing Steel Under Ultrahigh Strain Rate

The strain rate effect significantly influences the dynamic mechanical behavior of reinforcing steel under impact loads. To investigate the effect of strain rate on the dynamic mechanical behavior of reinforcing steel, this study conducts dynamic compression tests on four types of reinforcing steel using a Split Hopkinson pressure bar. The results show that there is a significant strain rate effect on the reinforcing steel when the strain rate reaches 103–104 s−1. The experimental results are analyzed using the Johnson–Cook model (J–C model), and the original model is modified based on the error between the model predictions and the experimental results. The results indicate that the modified J–C model, which includes an enhanced strain rate effect term, better predicts the dynamic mechanical behavior of reinforcing steel at ultrahigh strain rates.

Determination and Verification of the Johnson–Cook Constitutive Model Parameters in the Precision Machining of Ti6Al4V Alloy

Numerical simulations of the cutting process play a key role in manufacturing and cost optimization. Inherent in finite element analysis (FEA) simulations is the correct description of material behavior during machining. For this purpose, various material models are used to describe the behavior of the material in the range of high deformation, high temperature values, and high strain rates. Very often the Johnson–Cook (JC) material model is used for this purpose; however, the correct determination of the material constants of this model is a key aspect. Therefore, this paper presents a procedure for determining the material constants of the JC model using an analytical method based on normalized tensile and compression testing of the material for different strain rates over a wide temperature range. After determining the material constants, the authors conducted numerical simulations of the orthogonal turning of Ti6Al4V titanium alloy using the obtained constants. Validation of the obtained results with those obtained in experimental studies was also carried out. The outcomes demonstrated that the difference between FEM simulation and experimental tests did not exceed 0.02 mm (14%) in the case of chip thickness,. Much smaller differences were obtained for the temperature in the cutting zone, where the maximum difference was about 45 °C (4%). Comparing the components of the cutting force, we found that, in the case of the main cutting force, in most cases, the differences did not exceed 70 N (8%). After the verification of the obtained results, it was also found that the determined material constants of the Johnson–Cook model can be successfully used in FEM modeling of the cutting process of Ti6Al4V titanium alloy for the adopted range of values of technological parameters.

Corrected Method for Scaling the Structural Response Subjected to Blast Load

In scale-down tests of ship structures subjected to a blast load, the accuracy of the predicted response of a prototype is affected by the material substitution and geometric distortion between a scaled model and a full-size structure; this is known as incomplete similarity. To obtain a more accurate response from a prototype during small-size tests, a corrected method for scaling the response of thin plates and stiffened plates under a blast load was derived. In addition, based on numerical simulations of explosion responses by employing the elastic–plastic model and the Johnson–Cook constitutive model, it was found that using the average yield stress derived from the equivalent plastic strain energy in the ideal elastic–plastic model can obtain consistent structural responses. Moreover, a method for calculating the distortion factor caused by the yield stress of different materials was proposed. Furthermore, it was demonstrated that the average effective plastic strain between the prototype and the corrected model is equal, and based on this, a similarity prediction method was established to correct the distortions caused by yield stress and the thickness of blast loaded plates. The results indicate that the proposed correction method can compensate for the differences caused by distorted factors of yield stress and thickness, with the maximum error in the structure’s peak displacement being less than 3%.

Shear Band Formation with Split Hopkinson Bar Experiments

The essence of dynamic failure is closely linked to dramatic shear deformations which often lead to the formation of adiabatic shear bands (ASB). Under high loading velocities and the subsequent rapid temperature increase, the localization of shear strain is crucial in view of safety issues of systems in mechanical and aircraft engineering, especially with respect to fast rotating components and diverse crash scenarios. In this research, we perform high speed impact tests at the split Hopkinson pressure bar (SHPB) setup and use particular hat-shaped specimen geometries that resemble the stresses and failure conditions at the component level.In the first step, we specify a notched specimen geometry using finite element (FE) simulations to ensure pure shear. Further, quasi-static compressive tests and a series of impact tests at high strain rates of 103−104s−1 are conducted on specimens manufactured from a fine-grain structural steel with the properties of S355. Optical microscopy and electron backscatter diffraction (EBSD) of the sheared zones unveil significant localization to maximal shear strains of about 0.9 accompanied by grain refinement by factors 5 to 14. The displacements across the surface of the specimens are captured with subset-based local digital image correlation (DIC) during the impact time, and serve as an objective to validate a viscoplastic constitutive relationship. More precisely, the deformation distribution is accurately reproduced by the widely recognized Johnson-Cook (JC) model, which features an enhanced description of damage evolution. Thus, combining experimental and characterization techniques, continuum mechanics and reasonable optimization strategies for the identification of model parameters provides an efficient approach for comprehensive insights into the strain localization behaviour and its impact on the mechanical performance of S355 under extreme strain rates and deformations.

Pore collapse, shear bands, and hotspots using atomistics-consistent continuum models for RDX (1,3,5-trinitro-1,3,5-triazinane): Comparison with molecular dynamics calculations

Shock-induced energy localization is a crucial mechanism for determining shock sensitivity of energetic materials (EMs). Hotspots, i.e., localized areas of elevated temperature, arise when shocks interact with defects (cracks, pores, and interfaces) in the EM microstructure. The ignition and growth of hotspots in a shocked energetic material contribute to rapid chemical reactions that can couple with the passing shock wave, potentially leading to a self-sustained detonation wave. Predictive models for shock-to-detonation transition must correctly capture hotspot dynamics, which demands high-fidelity material models for meso-scale calculations. In this work, we deploy atomistics-guided material models for the energetic crystal RDX (1,3,5-trinitro-1,3,5-triazinane) and perform tandem continuum and all-atom molecular dynamics (MD) simulations. The computational setup for the continuum and MD simulations are nearly identical. The material models used for the calculations are derived from MD data, particularly the equations of state, rate-dependent Johnson–Cook strength model, and pressure-dependent shear modulus and melting temperature. We show that a modified Johnson–Cook model that accounts for shear-induced localization at the pore surface is necessary to represent well—relative to MD as the ground truth—the inelastic response of the crystal under a range of shock conditions. A head-to-head comparison of continuum and atomistic calculations across several metrics of pore collapse and energy deposition demonstrates that the continuum calculations are in good overall agreement with MD. Therefore, this work provides improved RDX material models to perform physically accurate meso-scale simulations, to enhance understanding of hot spot formation, and to use meso-scale hot spot data to inform macro-scale shock simulations.

Hydrogen susceptibility of Al 5083 under ultra-high strain rate ballistic loading

Abstract The effect of hydrogen on the ballistic performance of aluminum (Al) 5083H131 was examined both experimentally and numerically in this study. Ballistics tests were conducted at a 30° obliquity in accordance with the ballistic test standard MIL-DTL-46027 K. The strike velocities of projectiles were ranged from 240 m s−1 to 500 m s−1 level in the room temperature. Electrochemical hydrogen charging method was utilized to introduce hydrogen into material. Chemical composition of material was analyzed using energy dispersive X-ray (EDX) analysis. Instant camera pictures were captured using high-speed camera to compare H-uncharged and H-charged specimen ballistics tests. The volume loss in partially penetrated specimens were assessed using the 3D laser scanning method. Microstructural examinations were conducted utilizing scanning electron microscopy (SEM). It was observed that with the increased deformation rate, the dominance of the HEDE mechanism over HELP became evident. Furthermore, the experimental findings were corroborated through numerical methods employing finite element analysis (FEM) along with the Johnson–Cook plasticity model and failure criteria. Inverse optimization technique was employed to implement and fine-tune the Johnson–Cook parameters for H-charged conditions. Upon comparing the experimental and numerical outcomes, a high degree of consistency was observed, indicating the effective performance of the model.

Experimental Determination and Simulation Validation: Johnson–Cook Model Parameters and Grinding Simulation of 06Cr18Ni11Ti Stainless Steel Welds

Hydrogen permeation resistance in the welded region of 06Cr18Ni11Ti steel is relatively weak due to surface defects, which need high integrity surface machining. The parameters of the welding material for 06Cr18Ni11Ti steel are currently unavailable, which causes some inconvenience for simulation studies. To fill the lack of 06Cr18Ni11Ti steel weld material parameters in the relevant literature at the present stage, the quasi-static tensile test at different strain rates and notch specimen tensile tests were conducted in this paper and determined the Johnson–Cook (J-C) constitutive model parameters and Johnson–Cook failure model parameters. Subsequently, a multi-grain grinding simulation model was built based on W-M fractal dimension theory by using the determined material parameters. The influence of processing parameters on grinding heat was analyzed. Grinding experiments were conducted to analyze the influence of processing parameters on grinding heat and grinding force. By comparing the simulation and experimental results, it is revealed that the average error is 9.37%, indicating relatively small discrepancy. It is demonstrated that the grinding simulation model built in this paper could efficiently simulate the grinding process, and the determined weld material parameters of 06Cr18Ni11Ti steel have been verified to possess high accuracy and reliability.

Continuum models for meso-scale simulations of HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) guided by molecular dynamics: Pore collapse, shear bands, and hotspot temperature

Meso-scale calculations of energy localization and initiation in energetic material microstructures must capture the deformation and collapse of pores and high-temperature shear bands, which lead to hotspots. Because chemical reaction rates depend sensitively on temperature, predictive continuum models need to get the pore-collapse dynamics and resulting hotspot temperatures right; this imposes stringent demands on the fidelity of thermophysical model forms and parameters and on the numerical methods employed to perform high-resolution meso-scale calculations. Here, continuum material models for β-HMX are examined in the context of shock-induced pore collapse, treating predictions from all-atom molecular dynamics (MD) simulations as ground truth. Using atomistics-consistent material properties, we show that the currently available strength models for HMX fail to correctly capture pore collapse and hotspot temperatures. Insights from MD are then employed to advance a Modified Johnson–Cook (M-JC) strength model, which is shown to capture key aspects of the physics of shock-induced localization in HMX. The study culminates in a MD-guided strength model for β-HMX that produces continuum pore-collapse results in better alignment on several aspects with those predicted by MD, including pore-collapse mechanism and rate, shear-band formation in the collapse zone, and temperature, strain, and stress fields in the hotspot zone and the surrounding material. The resulting MD-informed/MD-determined M-JC model should improve the fidelity of meso-scale simulations to predict the detonation initiation of HMX-based energetic materials in microstructure-aware multi-scale frameworks.

Parameter identification of Johnson–Cook constitutive model based on genetic algorithm and simulation analysis for 304 stainless steel

Addressing the significant discrepancy between actual experimental cutting force and its predicted values derived from traditional constitutive model parameter identification methods, a reverse identification research of the Johnson–Cook (J-C) constitutive model for 304 stainless steel was conducted via genetic algorithm. Considering actual cutting zone and the influence of feed motion on the rake (flank) angle, an unequal division shear zone model was established to implement the theoretical calculation for shear zone stress. Through cutting experiments, the spindle speed was negatively correlated with the cutting force at first, and then became positively correlated; The empirical formula (EXP model) for turning force was corrected, revealing that the EXP model was unable to provide optimal predicted values for cutting force. The influence of the J-C constitutive parameter C on the cutting morphology was firstly investigated through simulation analysis, and determined an appropriate value for C, then obtained the precise values for the other four constitutive parameters by genetic algorithm. Moreover, the simulated values of cutting force in JC1 model (obtained from the Split Hopkinson Pressure Bar test) and JCM model (the improved model using genetic algorithm) were obtained by three-dimensional (3-D) simulation via FEM software. The results indicated that, the maximum error between actual experimental cutting force and its simulated values (by JCM model) was 14.8%, with an average error of 6.38%. These results outperformed the JC1 and EXP models, suggesting that the JCM model identified via genetic algorithm was more reliable.

Constitutive model and microstructure evolution of thermal deformation behavior of in situ TiB2p/Al-Zn-Mg-Cu composites with high Zn content

The deformation behavior of in situ TiB2 particle reinforced Al-Zn-Mg-Cu matrix composites with high Zn content was investigated through thermal compression tests. A comparative analysis of several constitutive models was performed, including the phenomenological modified Johnson-Cook (JC) and strain-compensated Arrhenius-type models, as well as the physically based modified and optimized Zerilli-Armstrong (ZA) models. In contrast to other materials, it is found that the accuracy of the modified JC and ZA models is significantly affected by the reference strain rate. When this was factored in, the optimized ZA model demonstrated superior accuracy, with a correlation coefficient (R) of 0.9986 and an average absolute relative error (AARE) of 2.15 %, while requiring the fewest calculation efforts amongst all of the models attempted. The mechanisms of the microstructural evolution in the composites after thermal deformation were also investigated. This work advances the understanding of TiB2p/Al-Zn-Mg-Cu composites and introduces an improved modeling framework, which is expected to benefit future material design and performance.

Determination of stress triaxiality by experiment-simulation and obtaining of johnson-cook damage criterion for Al-Mn alloy

Abstract Al-Mn alloy is extensively implemented in new energy vehicles. Damage prediction is the key to its safety application. The Johnson-Cook (JC) constitutive relationship parameters of Al-Mn alloy were first determined by standard tensile tests to predict the damage behavior of Al-Mn alloy. Subsequently, different notch specimens were designed to study the influence of stress state on damage behavior. By combining tensile tests and simulations, the stress triaxiality of Al-Mn alloy under different stress states was accurately obtained. On this basis, the JC damage criterion parameters were obtained. Finally, the obtained JC constitutive relationship and damage criterion parameters were imported into the tensile simulation models. The results showed that the force-displacement curves of the tensile experiments and simulations matched well, which can effectively simulate the deformation and fracture behavior of the Al-Mn alloy.