Johnson-Cook Parameters Research Articles

Inverse material modeling and optimization of free-cutting steel with graphite inclusions

Graphite inclusions in steel are easing chip breakage and act as in situ lubricants. Therefore, graphitized steels are claimed to perform excellent in machining processes. They are considered as environmentally friendly alternatives to widely used Pb-alloyed steels. However, the effectiveness of graphite inclusions in different machining processes is not well understood. With the support of computer simulation techniques, a deeper understanding about chip formation and the role of internal friction (or lubrication) can be obtained. To enter into numerical analysis of material flow and chip formation, the quality of the applied constitutive law is crucial for close-to-reality simulation. In the present work, a most accurate determination of the Johnson-Cook constitutive law of partially graphitized steel 50SiB8 (hardness 214 HB) is aimed for. Johnson-Cook parameters are identified from dynamical compression tests, performed at strain rates up to 20s−1 and temperatures up to 800 °C. The material parameters are derived from two different numerical methods. The first standard method is based on minimizing the sum of squares of the differences between calculation and measurement. The parameters identified from this method are used as initial values for the second method, an inverse material modeling. The second method is based on a multi-case polynomial metamodel optimization in combination with finite element techniques. By applying inverse material modeling, the maximum discrepancy between measurement and calculation is reduced from 12% (regression with standard method) to 1%. A reliable parameter set for the Johnson-Cook model for graphitic steel 50SiB5 as input for future modeling of the chip formation is now available.

Bayesian calibration of strength parameters using hydrocode simulations of symmetric impact shock experiments of Al-5083

Predictive modeling of materials requires accurately parameterized constitutive models. Parameterizing models that describe dynamic strength and plasticity require experimentally probing materials in a variety of strain rate regimes. Some experimental protocols (e.g., plate impact) probe the constitutive response of a material using indirect measures such as free surface velocimetry. Manual efforts to parameterize constitutive models using indirect experimental measures often lead to non-unique optimizations without quantification of parameter uncertainty. This study uses a Bayesian statistical approach to find model parameters and to quantify the uncertainty of the resulting parameters. The technique is demonstrated by parameterizing the Johnson-Cook strength model for aluminum alloy 5083 by coupling hydrocode simulations and velocimetry measurements of a series of plate impact experiments. Simulation inputs and outputs are used to calibrate an emulator that mimics the outputs of the computationally intensive simulations. Varying the amount of experimental data available for emulator calibration showed clear differences in the degree of uncertainty and uniqueness of the resulting optimized Johnson-Cook parameters for Al-5083. The results of the optimization provided a numerical evaluation of the degree of confidence in model parameters and model performance. Given an understanding of the physical effects of certain model parameters, individual parameter uncertainty can be leveraged to quickly identify gaps in the physical domains covered by completed experiments.

Statistical calibration and uncertainty quantification of complex machining computer models

Abstract Finite element based machining process models are used in research and industry for process design and optimization. These models require a constitutive description of the material behavior to accurately model and predict process responses such as cutting forces, temperatures, and residual stress. Calibration of these models to low-strain uniaxial dynamic compression experiments can be troublesome since the machining process generally imposes much larger strains than uniaxial compression. Calibration of finite element models directly to machining data is generally difficult since the models are computationally expensive and nonlinear optimization methods for estimating the unknown calibration parameters yield non-unique solutions and require many iterations. In this work we utilize a nonstationary Gaussian Process surrogate model to emulate the finite element response and calibrate to experimental orthogonal cutting tests using a Bayesian inference framework. We assume that the material yield behavior can be described by the Johnson-Cook material flow model. We find that the nonstationary Gaussian Process model is an good surrogate for the complex finite element model. Cutting forces measured from orthogonal tube turning experiments were used for calibration. Validation is performed using a separate response variable - the cut chip thickness. Calibration results illustrate a preference for material models with low hardening rates, which alleviates issues such as over-prediction of strain hardening behavior when using the Johnson-Cook material flow model. The Bayesian formulation also captures the uncertainty in the Johnson-Cook parameters, which can be used to quantify the uncertainty in the machining process responses. The methods presented here are general and can be used for more complex constitutive and tribological models for machining and other complex manufacturing processes.

Numerical Studies on Low-Velocity Impact Failure Response of Al 1100 under Blunt and Hemispherical Impactors

Numerical simulation is performed to study the deformation and failure modes of Al 1100 plate of 2.4 mm thickness, subjected to low-velocity impact. Blunt and hemispherical nose shaped impactors are used in this study. The quasi-static tensile test is performed at a strain rate of 0.01/s to obtain the Johnson-Cook material parameters which are used in numerical simulation software, ABAQUS/CAE to perform impact analysis. Mesh convergence study is carried out to decide the appropriate number of elements for numerical analysis. The impact behavior of Al 1100 plate for each impactor shapes are studied at 22 J impact energy. Result indicate that increased in the nose radius of impactor will increase the amount of deformation energy for aluminium plate.

Anisotropic Visco-Elastoplastic Modeling of Quasi-Unidirectional Flax Fiber Reinforced Epoxy Behavior: An Investigation on Low-Velocity Impact Response

Based on experimental test results, flax fiber reinforced polymer composites are characterized by nonlinear visco-elastoplastic behavior. The aim of this work is to model the quasi-unidirectional flax fiber reinforced composite behavior through a three dimensional formulation with orthotropic elasticity and orthotropic plasticity using Hill criterion. The isotropic hardening and Johnson Cook parameters are identified from unidirectional tensile tests at different strain rates. The adjustment of Hill’s yield criterion is developed based on yield stresses obtained in tensile tests at different directions. The numerical integration of the constitutive equations is implemented in a user-defined material, UMAT subroutines for the commercial finite element code ABAQUS. Once model parameters are identified using tensile tests, the model needs to be validated by confronting it with other experimental results. That is why experimental and numerical three-point bending tests are carried out in order to validate the proposed model with tests that have not served for the identification. Finally, a numerical parametric study on low velocity impact of a flax/epoxy composite circular plate is investigated.

Mechanical properties and strain rate sensitivity of 3D laserdeposited Ti-6Al-4V alloy

Ti-6Al-4V has become the most common material in titanium alloy. Due to High specific strength, low density and excellent mechanical properties, it has been used in not only living, sports goods but also aerospace, defense industries. Usually these products have complex geometry, so there are a lot of limitations in general manufacturing process. Especially in weapon systems, applied loadings are severe therefore choice of materials is very important. 3D printing method is useful for manufacturing these complicated structure and suitable to discontinued, superannuated part of products. In this study, specimen for experiments is turned out by using 3d laser deposition technology which metal powder is injected into the focused beam of a high-powered laser. While lots of studies are mainly concerned with normal process, it is not commonly researched for metallic materials forming through 3D printing. In the 10-3~103/s strain rates range, two kinds of plate samples and LDAM Ti-6Al-4V were performed using universal testing machine and SHPB for dynamic material properties. Simplified Johnson-Cook constitutive equation parameters produced from these experiments.

Effect of Variation of Johnson-Cook Parameters on Kinetic Energy and Simulation of 4340 Steel Projectile

Computer simulations have been used for decades in the modelling of high velocity impact and general large deformation problems. Several computer codes have been developed to simulate these types of problems under a variety of geometric conditions and for any variety of materials. The Johnson-Cook material model is widely used in the simulation of high velocity impacts and even penetration of target structures. This research work represents the study of effects of variation of Johnson-Cook material constants on ballistic impact and its effect on residual kinetic energy of projectile. In the Johnson-Cook damage model, there are five material constants viz. D1, D2, D3, D4 and D5, and it is very difficult to find out all of these material constants by experiments. The main objective of the present research is to determine the most sensitive parameter out of these constants. To accomplish this target, experimental testing was done and additionally the impact physics was likewise recreated numerically utilizing ABAQUS. For the impact phenomenon 4340 steel, 10 mm diameter projectile and a 1006 steel target plate were chosen. From this study, it is concluded that the most sensitive Johnson-Cook damage model constant is ‘D3’

Influence of elevated strain rate on the mechanical properties of hollow structural sections

As protective design engineering becomes more prevalent, cold-formed steel hollow structural sections are often desired design components. As such, it is necessary to understand the behavior of hollow structural sections subject to air-blast loading, including the material response under elevated strain rates. Dynamic tensile tests have hence been performed on subsize tensile coupons taken from the flats and corners of cold-formed rectangular hollow section members. Dynamic yield stresses were obtained at strain rates from 0.1 to 18 s−1, which encompasses and exceeds the range recorded during far-field blast arena testing. The dynamic increase factor was calculated for each data point and synthesized with previous cold-formed rectangular hollow section tests at even higher strain rates (100–1000 s−1). The data set was used to determine Cowper–Symonds and Johnson–Cook parameters. The resulting material models can now be used to determine the strength increase of cold-formed rectangular hollow sections subject to a wide range of impulsive, elevated strain rate loads.

Ballistic resistance of 2024 aluminium plates against hemispherical, sphere and blunt nose projectiles

Numerical investigation has been carried out on 2024 aluminium plate targets against 12.7mm diameter hardened steel projectiles. The ballistic resistance of 1.27mm thick target was studied against a spherical ball as well as the hemispherical and blunt nosed cylindrical projectiles. The simulations were performed on ABAQUS/Explicit finite element code by modelling the target as deformable and the projectiles as rigid three dimensional surface. The Johnson-Cook (JC) elasto-viscoplastic material model was employed to predict the flow and fracture behaviour of the target. The objective of the study was to investigate the efficiency of the JC model to numerically reproduce the maximum target deflection and peak impact force caused by three distinct shaped projectiles during target perforation. Three different sets of JC parameters calibrated by different authors [20,21] for 2024 aluminium alloy were considered to simulate the performance of the target against each projectile and the results thus obtained were compared and validated through available experiments [24]. The failure mode, deflection and impact force obtained have been noticed to have significant influence of the material models. The ballistic limit of 1.27mm thick target was numerically computed against each of the three projectiles and validated through the Recht-Ipson model. The effective span and target thickness were also varied to investigate the influence on the maximum deflection and peak impact force.

Computational and Split-Hopkinson Pressure-Bar studies on the effect of the jacket during penetration of an AK47 bullet into ceramic armour

In this paper we probe the effect of a bullet's jacket on its ability to enhance penetration of a bullet core into a ceramic-faced target. This is achieved through computational modelling using ANSYS AUTODYN® and by Split-Hopkinson Pressure-Bar compression testing of a core, with and without a jacket. The focus of this work was on an AK47 mild-steel-cored (MSC) bullet. The objective of this work was to investigate the role of the jacket in the penetration process and to better understand if there is any protective benefit of stripping a bullet's jacket prior to making contact with ceramic armour. Further, new Johnson-Cook parameters for the AK47 steel core are presented.

On the importance of the choice of the parameters of the Johnson-Cook constitutive model and their influence on the results of a Ti6Al4V orthogonal cutting model

A wide range of parameters is available in the literature for the Johnson-Cook constitutive model, the most used flow stress in metal cutting modelling. This strength of the Johnson-Cook model is also a weakness as it is therefore difficult to choose the set that will provide the most accurate results. Indeed, for a given material, several parameters are available due to different identification conditions (strain, strain rates and temperature range). This paper gathers the sets of Johnson-Cook parameters from the literature for Ti6Al4V before comparing them based on their stress-strain curves. The twenty identified sets are then introduced in a Coupled Eulerian-Lagrangian (CEL) finite element orthogonal cutting model and their results are compared at fixed cutting conditions. This comparison is then extended for the three most characteristic sets to two other uncut chip thicknesses. All the numerical results are compared to an experimental reference in the same cutting conditions. Links between the parameters of the Johnson-Cook flow stress and outputs of the model are then highlighted; they are still valid when the uncut chip value is modified. A set is finally recommended to obtain an accurate estimation of the cutting force and average feed force and chip thickness values.

Using FEM simulations of cutting for evaluating the performance of different johnson cook parameter sets acquired with inverse methods

Material model parameters are the primary source of error in the finite element analysis (FEM) of cutting processes. Expensive and time consuming material testing is required in order to describe the material's behavior in high temperature and high strain rate conditions during cutting. An alternative approach has been suggested in research papers; inverse analysis using cutting experiments together with FE analysis or analytical models. The latest approach is to combine an analytical model together with a material model capable of describing flow stress in terms of strain, strain rate and temperature, and using cutting experiments to acquire input parameters for inverse analysis, from which the material model parameters can be solved. In this paper, performance evaluation is done for five different sets of Johnson Cook parameters for AISI 1045, acquired with materials testing, inverse analysis with FEM, and the proposed combined inverse analysis with an analytical model and cutting experiments. The performance is evaluated by running simulations with a wide range of cutting parameters and comparing the simulated results of cutting forces and temperature to known experimental results found in literature. It was found that the proposed inverse method produces better performing model parameters than those found in literature.

Applying extended Oxley’s machining theory and particle swarm optimization to model machining forces

Oxley’s parallel-sided thick zone model is the mostly used analytical approach to simulate the cutting process. In order to apply this approach, the flow stress needs to be calculated as a function of the strain, the strain rate, and the temperature. Among the various models that describe the materials’ plastic behavior, the Johnson-Cook (JC) equation has been extensively used. Therefore, the prediction of the JC parameters for a given material is a laborious and costly task. Using the extended Oxley’s theory and experimental results, the coefficients can be found in an inverse procedure. This optimization process can be solved using particle swarm optimization (PSO). Hence, this work deals with the prediction and analysis of the JC equation parameters obtained by an inverse procedure applying PSO. The simulated parameters are used to calculate the machining forces. The results show that the presented approach can predict the cutting and thrust forces very well.

Consistent constitutive modeling of metallic target penetration using empirical, analytical, and numerical penetration models

Abstract Historically, there has been little correlation between the material properties used in (1) empirical formulae, (2) analytical formulations, and (3) numerical models. The various regressions and models may each provide excellent agreement for the depth of penetration into semi-infinite targets. But the input parameters for the empirically based procedures may have little in common with either the analytical model or the numerical model. This paper builds on previous work by Riegel and Anderson (2014) to show how the Effective Flow Stress (EFS) strength model, based on empirical data, can be used as the average flow stress in the analytical Walker–Anderson Penetration model (WAPEN) (Anderson and Walker, 1991) and how the same value may be utilized as an effective von Mises yield strength in numerical hydrocode simulations to predict the depth of penetration for eroding projectiles at impact velocities in the mechanical response regime of the materials. The method has the benefit of allowing the three techniques (empirical, analytical, and numerical) to work in tandem. The empirical method can be used for many shot line calculations, but more advanced analytical or numerical models can be employed when necessary to address specific geometries such as edge effects or layering that are not treated by the simpler methods. Developing complete constitutive relationships for a material can be costly. If the only concern is depth of penetration, such a level of detail may not be required. The effective flow stress can be determined from a small set of depth of penetration experiments in many cases, especially for long penetrators such as the L/D = 10 ones considered here, making it a very practical approach. In the process of performing this effort, the authors considered numerical simulations by other researchers based on the same set of experimental data that the authors used for their empirical and analytical assessment. The goals were to establish a baseline with a full constitutive model and to determine if the EFS could be estimated from a standardized constitutive model. We were unable to accomplish this. Several papers detailing simulations using the Johnson–Cook (JC) constitutive model were located and used as a basis for comparison. The authors were somewhat surprised to find that the JC parameters employed in those studies were not actually developed for the target materials that were evaluated experimentally. More disconcerting was the fact that a number of different sets of JC parameters were published for presumably the same material. Although not intended to be a critique of the JC model, this research raises a serious concern regarding the manner in which the model has been applied to terminal ballistics problems. The details of the study are included in this paper because the authors believe it helps put the discussion of EFS into proper context.

Inverse Analysis Procedure to Determine Flow Stress and Friction Data for Metal Cutting Finite Element Modeling

This paper describes an automated procedure developed for the identification of Johnson-Cook (JC) law material parameters and Coulomb friction coefficient at the tool-chip interface, in the specific case of metal cutting FE analysis. The procedure has been developed in iSight environment, through the integration between AdvantEdge metal cutting FE code and an appropriately selected optimization algorithm. The identification of JC and friction parameters, in fact, has been performed considering it as an optimization problem, in which the objective function is the numerical/experimental error function minimization (in the specific case, it is related to the forces and temperatures responses). The calibration and validation phases have been performed using forces and temperatures experimental data, collected in orthogonal cutting test on SAF2507 superduplex steel.

High Strain‐Rate Material Model Validation for Laser Peening Simulation

Finite element modeling can be a powerful tool for predicting residual stresses induced by laser peening; however the sign and magnitude of the stress predictions depend strongly on how the material model captures the high strain rate response. Although a Johnson-Cook formulation is often employed, its suitability for modeling phenomena at very high strain rates has not been rigorously evaluated. In this paper, we address the effectiveness of the Johnson-Cook model, with parameters developed from lower strain rate material data (∼103 s–1), to capture the higher strain rate response (∼105–106 s–1) encountered during the laser peening process. Published Johnson-Cook parameters extracted from split Hopkinson bar testing were used to predict the shock response of aluminum samples during high-impact flyer plate tests. Additional quasi-static and split Hopkinson bar tests were also conducted to study the model response in the lower strain rate regime. The overall objective of the research was to ascertain whether a material model based on conventional test data (quasi-static compression testing and split Hopkinson bar measurements) can credibly be used in FE simulations to predict laser peen-induced stresses.

Determination of material model parameters from orthogonal cutting experiments

Flow stress models in finite element analysis of metal cutting require material parameters that are essential considering the accuracy of the simulations. This article presents a method to acquire material parameters from cutting experiments using the extended Oxley’s shear zone theory. The novelty in this approach is to use measured chip geometry and temperature instead of determining them analytically to calculate strain and strain rate. These values are used to calculate the resultant cutting forces with the extended Oxley’s model and Johnson–Cook flow stress model. Flow stress model parameters are optimized to fit the calculated forces to those measured from cutting experiments. The Johnson–Cook parameters acquired with this method perform better than those found in the literature.

Inverse Identification at Very High Strain Rate of the Johnson–Cook Constitutive Model on the Ti‐6Al‐4 V Alloy With a Specially Designed Direct‐impact Kolsky Bar Device

ABSTRACTIn the present work, an inverse identification of the Johnson–Cook constitutive model is performed on the titanium alloy Ti‐6Al‐4 V at three strain rates until about 2·104 s−1 (till about 1.1·104 s−1 of plastic strain rate) on a specially designed direct impact Kolsky bar device. First, the design of such a device must meet several criteria, and is shown to be the solution of an optimization problem. A systematic design procedure for such a device is then introduced. Second, an inverse analysis using the finite element code ABAQUS is carried out to identify the Johnson–Cook parameters on experimental data obtained with the designed system.

Numerical modeling of laser assisted machining of a beta titanium alloy

Laser assisted machining is a promising new machining technology that can be used to assist with the fabrication of components from difficult to machine materials such as beta titanium alloys. To understand the mechanism behind this process, a reliable numerical machining model is needed. This study employed an SPH method to the problem of laser assisted machining of Ti–6Cr–5Mo–5V–4Al alloy. The SPH method has several advantages when dealing with large-deformation problems compared with traditional finite element methods. A laser scanning model was developed beforehand to predict the temperature elevation due to laser heating and the temperature results were used as initial conditions for the SPH/FE machining models. Johnson–Cook parameters and Zerilli–Armstrong parameters of Ti–6Cr–5Mo–5V–4Al alloy were acquired based on experimental data from the Split Hopkinson Pressure Bar (SHPB) test and were implemented in the machining models. The cutting force predictions of machining models using these two material models were discussed in this study. Both conventional machining (CM) and laser assisted machining (LAM) were simulated. The main cutting force predictions and the temperature predictions were compared with experimental results to validate the models.

Determination of Johnson–Cook Parameters for Cast Aluminum Alloys

A series of experiments were conducted to determine the Johnson–Cook parameters for three different cast aluminum alloys, namely, A356, A357, and F357. Room temperature compression experiments were performed under varying rates of loading ranging from 10−3 s−1 to 5000 s−1. High temperature compression (235 °C and 435 °C) experiments were performed at an average strain rate of 5000 s−1. A split Hopkinson pressure bar (SHPB) apparatus was utilized in conjunction with an induction coil heating system for applying dynamic loading at elevated temperatures. In addition, experiments were performed under high strain rate tensile loading using tensile SHPB apparatus, and the fractured specimens were examined under scanning electron microscope (SEM) to understand the failure modes in these alloys. High-speed photography was used to capture the chronological progression of the deformation under dynamic tensile loading. The results indicated that all the three cast aluminum alloys were sensitive to strain rate and temperature. A356 exhibited the least value of flow stress under both static and dynamic loading conditions, and the highest elongation before break under dynamic tensile loading. The SEM images of the fractured specimens under dynamic tensile loading showed characteristics of transcrystalline ductile fracture in these cast aluminum alloys.