Johnson-Cook Model Research Articles

Effects of mandrel velocity on residual stresses created in cold expansion process of adjacent holes for AA6016-T6 and AA1100 aluminum alloys

Cold expansion is a mechanical method for creating residual stresses. This method is a proven technique to increase the fatigue life, and checking the residual stress on it, is of particular importance. A cold expansion process is widely used to generate beneficial residual stresses into an annular region around the hole. In the present research work, AA 6016-T6 and AA 1100 aluminum alloys which are two strain rate sensitive materials, were subjected to cold expansion process with different mandrel velocities. In fact, the effect of mandrel velocity on the created residual stresses has been investigated. The constants of the Johnson-Cook material model have been determined for them and the process has been investigated, experimentally and numerically. The obtained results revealed that the values of the residual stresses created in the sheets depend on the velocity of the process especially at the edge of the sheets holes. By increasing the mandrel velocity from 5 to 500 mm/min, depending on the distance from the hole to the edge of the sheet, it is possible to enhance the hoop residual stress by 37.3–41.2% in AA 1100 aluminum alloy and by 37.6–38.1% in AA 6016-T6 aluminum alloy. This research showed that in all cases, the radial residual stresses created around the holes are negative. Also, it was cleared that due to the existence of material constraints and the movement of the sheet material, the amount of hoop residual stress created in the mid-thickness is more than the exit face and in the exit face is also more than the entrance face, exactly unlike the size of their zones.

Optimal prediction and validation of Johnson-Cook failure model for Al 6061 using genetic algorithm

Optimal prediction and validation of Johnson-Cook failure model for Al 6061 using genetic algorithm

Transient dynamics simulation of helicopter tail transmission shaft damage

Abstract Using the LS-DYNA explicit dynamic analysis software, a finite element model of projectile damage in helicopter tail transmission shaft was established with the Johnson-Cook intensity model. The dynamic response of the tail transmission shaft during bullet penetration was simulated dynamically, revealing that projectile damage is the primary mode of failure. Three typical angles were selected to simulate the penetration process, and results indicate that compared to vertical and 45°bullet penetrations, tail transmission shaft damage is more severe.

Low-Velocity Impact Behaviors of B4C/SiC Hybrid Ceramic Reinforced Al6061 Based Composites: An Experimental and Numerical Study

This study studied the low-velocity impact behavior of silicon carbide (SiC), boron carbide (B4C), and hybrid B4C/SiC reinforced aluminum 6061 alloy (Al 6061) matrix composites experimentally and numerically. The effect of hybridization, reinforcement volume fraction, and reinforcement type on low-velocity impact was investigated. 16 different metal-matrix composite materials were manufactured for the study, including 9 hybrid samples, 6 non-hybrid samples for each reinforcing ceramic particle, and 1 unreinforced sample. The powder metallurgy - hot press method was used in experimental production and then low-velocity impact tests were carried out. Numerical study was carried out using the non-linear finite element method (FEM). A Python algorithm running on ABAQUS/Explicit was utilized to determine ceramic particle distribution based on volume fraction, hybridization ratio, and random particle arrangement. The Johnson-Cook Plasticity Model was used for the non-linear relationship between stress and strain in the Al 6061 metal-matrix during impact. The results were interpreted with the contact force-time, contact force-displacement, and energy-time data obtained from low-velocity impact tests. In addition, the amount of collapse that occurred during the impact was measured and compared, and finally, SEM/EDX analysis was performed for the microstructure characterizations of the composite sample. Impact tests revealed that the collapse of composite samples ranged from 3.06mm to 3.58mm, with the unreinforced S6 sample collapsing 4.18mm, indicating that increased reinforcement elements reduce ductility, while a lower B4C ratio or higher SiC ratio in hybrid composites leads to greater collapse. Keeping the hybridization rate constant while increasing the reinforcement ratio leads to an increase in contact force and a decrease in contact time. Hybrid composites exhibited higher stiffness as SiC content increased, while B4C reinforced non-hybrid composites showed more significant stiffness. There is good agreement between the numerical and experimental results. Non-hybrid samples have a better match between numerical predictions and experimental results than hybrid samples.

Enhancing orthogonal finishing machining of Ti6Al4V with laser-ablated tool geometry modifications

Finishing machining of Ti6Al4V, known for its high strength and heat conduction resistance, demands optimisation to achieve high-quality end products. This study explores modifying the chip contact length on the rake face and altering the flank face with a cavity to minimise process forces and temperatures while maintaining cutting edge integrity. The research validates the manufacturability of ultra-short pulsed laser-ablated tool geometry modifications, indicating potential for industrial scale-up. Extensive experimental evaluations under dry conditions assess the impact of tool modifications at various feed rates for planing and turning. Significant reductions in process forces and temperatures were observed with rake face modifications, particularly at a cavity distance of approximately 34 µm. Ideal performance was noted for feed rates between 0.035 and 0.045 mm for planing and 0.040 to 0.045 mm/rev for turning. Smoothed Particle Hydrodynamics (SPH) simulations employing a Johnson-Cook material model were used to analyse chip formation and to predict the process forces. These simulations revealed a clear change in the chip formation and lower process forces and temperatures. The SPH results closely matched experimental outcomes, with a discrepancy of less than 7 % in cutting forces for both tool types, although feed forces were underestimated by about 50 %. The effect of the tool modification is reflected accurately at the respective feeds.

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.

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.

Dynamic Mechanical Behavior and Modified Johnson-Cook Model of Ti60 Alloy under High-temperature and High-strain-rate Conditions

Dynamic Mechanical Behavior and Modified Johnson-Cook Model of Ti60 Alloy under High-temperature and High-strain-rate Conditions

Grain disintegration and dynamic recrystallization during impact tests of additively manufactured nickel-based alloy 718

The high-temperature dynamic mechanical response of Alloy 718 produced via laser-powder bed fusion (LPBF) was investigated through compressive Split-Hopkinson Pressure Bar (SHPB) tests. Simulating the typical service conditions of Alloy 718, the tests were conducted at temperatures ranging from 298 K to 773 K and at strain rates of 1000 s−1 to 1500 s−1. Phenomenological material constitutive models, such as the modified versions of Johnson-Cook and Hensel-Spittel models, were developed based on the SHPB test results. Analysis of microstructural evolution under impact conditions highlighted that columnar grains with high Schmid factors tend to undergo preferential activation and dislocation pile-up. This process leads to the formation of adiabatic shear bands, grain disintegration, and intense lattice rotation, particularly at higher strain rates. Furthermore, increasing the dynamic deformation temperature facilitates the activation of discontinuous dynamic recrystallization (DRX), with strain accumulation promoting localized grain nucleation along heavily dislocated dendritic boundaries. Recognizing the limitations of phenomenological material constitutive models in accurately representing the underlying microstructural evolution, an artificial neural network (ANN)-based constitutive model employing a three-layer backpropagation learning algorithm was implemented, reducing the Average Absolute Relative Error (AARE) to 0.17%.

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.

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.

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.

Development of Johnson-Cook-Distinct Lattice Spring Model and its application in projectile penetration into metal targets

Projectile penetration into metal targets plays an important role in modern protective structure engineering, damage assessment in terrorist attacks, and car clash accident analysis, etc. The penetration process of metal target has been characterized by large deformation, high temperature, high pressure, and dynamic damage, which can be classified as a continuous-discontinuous dynamical process. To capture the dynamic responses of metal materials subjected to high-speed penetration, Johnson-Cook model has been implemented in a continuum-discrete model, namely, Distinct Lattice Spring Model (DLSM). This is achieved by redefining the constitutive model in DLSM, with plasticity hardening (plastic strain effects), strain rate, temperature, damage evolution, equation of state, etc., being taken into account, thus developing a new numerical model called JC-DLSM model. This model is validated through studying Taylor rod high-speed impact experiments, thin metal plate penetration experiments, and projectile impact experiments on titanium alloy targets. Good agreement between numerical modelling and experimental data has been achieved for all cases considered, thereby demonstrating the capability of JC-DLSM to reproduce the damage characteristics and ballistic limits of metals under high-speed impact/penetration. Then, the impacts of projectile shape, metal target surface configuration on the characteristics of penetration damage patterns have been investigated. This contributes to a better understanding of the damage mechanisms of metal targets upon penetration or impact, facilitating the computational means for analysing and optimizing the penetration resistance of protective engineering structures.

Analytical temperature model for spindle speed selection in additive friction stir deposition

This paper describes a physics-based, analytical model for additive friction stir deposition (AFSD) spindle speed selection to achieve a desired deposition temperature. In the model, power input to the feedstock, which enables plastic flow and deposition, is related to the material temperature rise and subsequent flow stress reduction using Fourier’s conduction rate equation. Power input is modeled as frictional heating at the deposit-surface interface and adiabatic heating due to plastic deformation. The flow stress is predicted using the strain, strain rate, and temperature-dependent Johnson-Cook constitutive model for the selected feedstock alloy. Model predictions are compared to AFSD numerical simulation results available in the literature and experiments for aluminum alloys.

Mechanical properties and JC constitutive modification of tungsten alloys under high strain rates and high/low temperatures

The original Johnson-Cook model's poor prediction of W90 alloy stress at high strain rate and high and low temperatures restricts research and utilization of this alloy. This study used a Split Hopkinson Pressure Bar (SHPB) device to conduct dynamic compression tests on W90 alloy over a temperature range of [-90℃,700℃] and analyze its mechanical behavior. We examined the material's different plastic phase characteristics at high and low temperatures and conducted microstructure research on impact test specimens. Then, we analyzed the stress-strain data from SHPB experiments and quasi-static compression tests on the classical Johnson-Cook model. The original Johnson-Cook model was calibrated using the stress-strain data from SHPB and quasi-static compression tests, and the modified Johnson-Cook model was established and verified. The results show that: low temperature significantly strengthens the material's stress, while increasing temperature thermal softening reduces stress; increasing strain rate increases the strain generated by the workpiece, causing faster strain hardening and thermal softening effects, resulting in higher and more stable stress; low temperature makes thicker grain boundaries, increasing plastic stress, and increasing strain rate also increases plastic stress, as well as making the material's grain boundaries thicker. The increase of strain rate makes the grain more dense, which will also show up in the increase of stress on the macroscopic level; the modified Johnson-Cook model in this paper has high agreement with experimental data, with a mean value of MAPE of only 1.85 %,which is 90.20 % lower than the traditional model, and the average value of the RMSE is 85.56 % lower than the traditional model. The modified model significantly outperforms the traditional model in predicting stress and better describes stress changes in W90 at different temperatures.

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.

Crashworthiness and optimization design of additive manufacturing double gradient lattice enhanced thin-walled tubes under dynamic impact loading

It is of paramount importance to ensure the protection of both infrastructure and personnel in scenarios characterized by a high strain rate dynamic impact. In order to develop lighter weight and higher crashworthiness energy-absorbing structures, this paper incorporates the bionic design of lattice reinforced thin-walled tube structures in the form of double gradient, as a means of achieving the aforementioned objectives. Material mechanical properties and the designed structures at high strain rate were researched using Split Hopkinson Pressure Bar (SHPB) experiment. The effects of gradient form and gradient parameters on the deformation pattern and crashworthiness of lattice enhanced thin-walled tubes are researched by means of the validated finite element model and the experimentally fitted Johnson-Cook material model. The results indicate that the specific energy absorption of the double gradient lattice enhanced thin-walled tube (T3L3) is increased by 36.19 % and the peak crush force is reduced by 21.19 % compared to the lattice enhanced thin-walled tube without gradient. Finally, the multi-objective optimization analysis of the T3L3 with the objective of achieving the maximum SEA and minimum PCF is carried out by Response Surface Methodology (RSM) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to find the Pareto optimal solution set. Double-gradient bionic structure offers a new idea for designing energy-absorbing structures under high-speed impact conditions.