Zerilli-Armstrong Research Articles

Constitutive Modeling for Predicting High-Temperature Flow Behavior in Aluminum 5083+10 Wt Pct SiCp Composite

A constitutive model capable of predicting material flow behavior with high precision is essential for optimizing secondary processing parameters through simulation techniques. In this study, the hot deformation behavior of aluminum 5083+10 wt pct SiC particulate composite was predicted using constitutive equations based on the modified Johnson–Cook (JC), modified Zerilli–Armstrong (ZA), and strain-compensated Arrhenius models. The models were established on the basis of the true stress–strain values obtained from an isothermal hot compression test conducted on the INSTRON 8801 universal tensile testing machine under a temperature range of 473 K to 773 K and strain rate of 0.01 to 10 s−1. The prediction ability of the modified models was compared by calculating the correlation coefficient (R), average absolute relative error, and relative error. All the models could precisely predict the hot flow behavior of the composite. The modified ZA model had the highest accuracy. The JC model required the least number of material constants and had the lowest calculation time, followed by the modified ZA and strain-compensated Arrhenius models.

Constitutive Modeling for Hot Deformation Behavior of Al-5083 + SiC Composite

In the present research, isothermal hot deformation behavior of aluminum 5083 alloy + 15 (wt.%) SiC composite was obtained through compression test on INSTRON 8801 universal tensile testing machine (UTM) under a wide temperature range of 473-773 K and strain rate range of 0.01-10 s−1. The experimental true stress–strain data were employed to establish constitutive equations based on modified Johnson–Cook (JC) model and modified Zerilli–Armstrong (ZA) model to predict the hot flow behavior of the composite. The flow stress values obtained from these two models were plotted against the experimental flow curves to check the accuracy of these models. Suitability of the models was evaluated by comparing correlation coefficient (R), average absolute relative error and relative errors of prediction. The results show that the hot flow stresses of the present material depend on temperature and strain rate significantly. Both the models give good description of the hot deformation behavior of the composite. The prediction accuracy is found to be higher for modified ZA model compared to modified JC model, though the number of materials constants involved and time needed to evaluate them to establish the model are lower for modified JC model.

Crystal plasticity modeling of a near alpha titanium alloy under dynamic compression

The purpose of this study is to describe the dynamic behavior of near alpha titanium alloy at elevated temperatures using Crystal plasticity and other models. Three constitutive models: Johnson-Cook (J-C), Zerilli–Armstrong (Z-A), Cowper-Symonds (C–S) and J-C fracture models are established. Experimental results observed that material displayed strain rate sensitivity at various strain rates. The generated model constants have been incorporated into finite element code. Finite Element simulations of tensile tests under different strain rates have been performed using Autodyn software. A crystal plasticity model is established and shows that it can predict the stress strain response under dynamic loading conditions. The developed crystal plasticity model was implemented in the ABAQUS code to simulate high strain rate compression and showed good agreement. Subsequently, a Charpy impact test on specimen has also been simulated. The fracture surfaces of specimens tested under quasi static state at various temperatures were studied under scanning electron microscopy (SEM).

Physically-based constitutive model for flow behavior of a Ti-22Al-25Nb alloy at high strain rates

The objective of the study is to understand the dynamic flow behavior of Ti–22Al–25Nb alloy at high temperatures using a modified Zerilli–Armstrong (Z-A) model. To investigate the dynamic mechanical behavior of titanium alloy, the material was subjected to quasi static and dynamic compression testing. It is found out that the modified Z-A models possess better predictability in evaluating the flow behavior of the Ti–22Al–25Nb alloy at elevated strain rates and temperatures. The model well established the quasi-static and dynamic behavior of the titanium alloy, mainly the effects of strain hardening and thermal softening. The regimes of high strain rate deformation behavior represented by dynamic recrystallization (DRX), lamellar globularization and the instability flow have been discussed. Using transmission electron microscopy (TEM) studies, it is found that the dislocation density is directly associated with strain rate.

An integrated Johnson–Cook and Zerilli–Armstrong model for material flow behavior of Ti–6Al–4V at high strain rate and elevated temperature

The Johnson–Cook (JC) model can give an accurate estimate of the flow stress at the low strain rate and temperature, but fails to predict the flow stress under high strain rate and elevated temperature due to the complex relationship among strain, strain rate and temperature. The Zerilli–Armstrong (ZA) model is capable to provide a higher prediction accuracy of material flow stress, but is unable to describe the material behavior above the limitation temperature (0.6Tm). In this research, an integrated JC–ZA model, which considers the grain size, strain hardening, strain rate hardening, thermal softening and the coupled effects of strain, strain rate and temperature, is proposed. The effects of strain rate and temperature on the flow stress of Ti–6Al–4V are investigated by quasi-static tensile test and dynamic split Hopkinson pressure bar test. It is proved that the integrated JC–ZA model has a similar accuracy with JC model at low strain rate and temperature with a prediction error of 2.180–2.358%, and a higher accuracy at high strain rate and elevated temperature with a prediction error in the range of 0.174–2.358%. Through this research, an accurate model by integrating JC model and ZA model for the flow stress of Ti–6Al–4V is given.

A modified Johnson-Cook model for FeCoNiCr high entropy alloy over a wide range of strain rates

The objective of the study is to perform experiments on FeCoNiCr high entropy alloy under different strain rates ranging from 0.01 to 3500/s and also at temperatures of 25, 200, 400 and 600 °C. Considering the effects of work hardening and thermal softening at high strain rates, the flow behavior is characterized by employing the modified Johnson-Cook (J-C) and Zerilli–Armstrong (Z-A) models. The triaxiality data showed the decrease in effective plastic strain at failure as triaxiality increases for all strain rates. Fracture constants have been evaluated.

Investigations on the effects of different constitutive models in finite element simulation of machining

Finite element (FE) modeling of a machining process in current industrial practice is highly essential to model and simulate the metal cutting process before resorting to costly and time consuming experimental trials. The current work describes a FE evaluation of machining process when simulating AA7075-T6 cutting process and comparison of predicted results with experimentally determined data like, cutting force, tool-chip contact temperature and chip thickness. Machining experiments and investigations into the effect of different constitutive models such as, Johnson-Cook (JC), Zerilli-Armstrong (ZA), Arrhenius (Arr) and Norton-Hoff (NH) models in turning of aluminum alloy AA7075-T6 were carried. The numerical simulation results indicate that the adeptness of FE model in forecasting machining performance is quite acceptable and predicted results are very close to experimental results.

Plastic flow behavior based on thermal activation and dynamic constitutive equation of 25CrMo4 steel during impact compression

To evaluate the dynamic mechanical properties of 25CrMo4 steel, the stress-strain curve of 25CrMo4 steel have been obtained by performing quasi-static and impact compression experiments at strain rates ranging from 0.001 s−1 to 4163 s−1. The 25CrMo4 steel displays an obvious strain rate effect and its hardening rate changes with the strain and strain rate. It even shows softening effect at high strain rates. Further, the grains of 25CrMo4 steel show features of both body-centered cubic (BCC) and face-centered cubic (FCC) structures and are severely stretched and fragmented during impact loading, as evidenced by microscopic observations. Based on these two points, the Zerilli-Armstrong (ZA) constitutive equations have been improved reasonably. These can provide the mechanical properties of 25CrMo4 steel during impact compression loading, which can in turn be used as reference values for practical engineering analysis.

Dynamic compressive behavior and fracture modeling of Titanium alloy IMI 834

A comprehensive study has been performed for understanding the constitutive behavior of titanium alloy IMI 834 under different strain rates, stress triaxialities and temperatures. Results confirmed an improvement in its strength with increase in strain rate and stress triaxiality. Experimental results obtained from the specimens of materials were employed to calibrate the material parameters of Johnson–Cook (J-C) strength and fracture model. The microstructure study has been undertaken to discuss the shear band and grain growth mechanisms. Three constitutive models: Johnson-Cook (J-C), Zerilli–Armstrong (Z-A) and Cowper-Symonds (C-S) models are established to determine the flow stress using dynamic compression data. The ballistic tests were performed in which 8 mm thick target plates were impacted by 7.62 AP projectiles with a velocity of 830 m/s. The ballistic test results were replicated through numerical simulations carried out using ABAQUS finite element code. It is observed that the residual velocities generated by simulations were in good agreement with the experimental results.

Modeling of mass flow behavior of hot rolled low alloy steel based on combined Johnson-Cook and Zerilli-Armstrong model

Accuracy and reliability of numerical simulation of hot rolling processes are dependent on a suitable material model, which describes metal flow behavior. In the present study, Gleeble hot compression tests were carried out at high temperatures up to 1300 °C and varying strain rates for a medium carbon micro-alloyed steel. Based on experimental results, a Johnson-Cook model (JC) and a Zerilli-Armstrong (ZA) model were developed and exhibited limitation in characterizing complex viscoplastic behavior. A combined JC and ZA model was introduced and calibrated through investigation of strain hardening, and the coupled effect of temperature and strain rate. Results showed that the combined JC and ZA model demonstrated better agreement with experimental data. An explicit subroutine of the proposed material model was coded and implemented into a finite element model simulating the industrial hot rolling. The simulated rolling torque was in good agreement with experimental data. Plastic strain and stress distributions were recorded to investigate nonlinear mass flow behavior of the steel bar. Results showed that the maximum equivalent plastic strain occurred at 45° and 135° areas of the cross section. Stress increased with decreasing temperature, and the corresponding rolling torque was also increased. Due to the extent of plastic deformation, rolling speed had limited influence on the internal stress of the bar, but the relative rolling torque was increased due to strain rate hardening.

Constitutive Equations and ANN Approach to Predict the Flow Stress of Ti-6Al-4V Alloy Based on ABI Tests

The flow behavior of Ti-6Al-4V alloy was studied by automated ball indentation (ABI) tests in a wide range of temperatures (293, 493, 693, and 873 K) and strain rates (10−6, 10−5, and 10−4 s−1). Based on the experimental true stress-plastic strain data derived from the ABI tests, the Johnson-Cook (JC), Khan-Huang-Liang (KHL) and modified Zerilli-Armstrong (ZA) constitutive models, as well as artificial neural network (ANN) methods, were employed to predict the flow behavior of Ti-6Al-4V. A comparative study was made on the reliability of the four models, and their predictability was evaluated in terms of correlation coefficient (R) and mean absolute percentage error. It is found that the flow stresses of Ti-6Al-4V alloy are more sensitive to temperature than strain rate under current experimental conditions. The predicted flow stresses obtained from JC model and KHL model show much better agreement with the experimental results than modified ZA model. Moreover, the ANN model is much more efficient and shows a higher accuracy in predicting the flow behavior of Ti-6Al-4V alloy than the constitutive equations.

Dynamic Deformation Behaviors of an In Situ Ti-Based Metallic Glass Matrix Composite

Quasi-static and dynamic deformation behaviors, fracture characteristics, and microstructural evolution of an in situ dendrite-reinforced metallic glass matrix composite: Ti50Zr20V10Cu5Be15 within a wide range of strain rates are investigated. Compared with the quasi-static compression, the yielding stress increases, but the macroscopic plasticity significantly decreases upon dynamic compression. The effects of the strain rate on strain hardening upon quasi-static loading and flow stress upon dynamic loading are evaluated, respectively. The Zerilli-Armstrong (Z-A) model based on dendrite-dominated mechanism is employed to further uncover the dependence of the yielding stress on the strain rate.

Mechanical Properties and Microstructure of the CoCrFeMnNi High Entropy Alloy Under High Strain Rate Compression

The equiatomic CoCrFeMnNi high entropy alloy, which crystallizes in the face-centered cubic (FCC) crystal structure, was prepared by the spark plasma sintering technique. Dynamic compressive tests of the CoCrFeMnNi high entropy alloy were deformed at varying strain rates ranging from 1 × 103 to 3 × 103 s−1 using a split-Hopkinson pressure bar (SHPB) system. The dynamic yield strength of the CoCrFeMnNi high entropy alloy increases with increasing strain rate. The Zerilli-Armstrong (Z-A) plastic model was applied to model the dynamic flow behavior of the CoCrFeMnNi high entropy alloy, and the constitutive relationship was obtained. Serration behavior during plastic deformation was observed in the stress-strain curves. The mechanism for serration behavior of the alloy deformed at high strain rate is proposed.

A Comparative Study on Johnson Cook, Modified Zerilli–Armstrong and Arrhenius-Type Constitutive Models to Predict High-Temperature Flow Behavior of Ti–6Al–4V Alloy in α + β Phase

AbstractTrue stress and true strain values obtained from isothermal compression tests over a wide temperature range from 1,073 to 1,323 K and a strain rate range from 0.001 to 1 s–1 were employed to establish the constitutive equations based on Johnson Cook, modified Zerilli–Armstrong (ZA) and strain-compensated Arrhenius-type models, respectively, to predict the high-temperature flow behavior of Ti–6Al–4V alloy in α + β phase. Furthermore, a comparative study has been made on the capability of the three models to represent the elevated temperature flow behavior of Ti–6Al–4V alloy. Suitability of the three models was evaluated by comparing both the correlation coefficient R and the average absolute relative error (AARE). The results showed that the Johnson Cook model is inadequate to provide good description of flow behavior of Ti–6Al–4V alloy in α + β phase domain, while the predicted values of modified ZA model and the strain-compensated Arrhenius-type model could agree well with the experimental values except under some deformation conditions. Meanwhile, the modified ZA model could track the deformation behavior more accurately than other model throughout the entire temperature and strain rate range.

An exponential strain dependent Rusinek–Klepaczko model for flow stress prediction in austenitic stainless steel 304 at elevated temperatures

In this paper, to predict flow stress of Austenitic Stainless Steel (ASS) 304 at elevated temperatures the extended Rusinek–Klepaczko (RK) model has been modified using an exponential strain dependent term for dynamic strain aging (DSA) region. Isothermal tensile tests are conducted on ASS 304 for a temperature range of 323–923K with an interval of 50K and at strain rates of 0.0001s−1, 0.001s−1, 0.01s−1 and 0.1s−1. DSA phenomenon is observed from 623 to 923K at 0.0001s−1, 0.001s−1 and 0.01s−1. Material constants are calculated using data obtained from these tensile tests for non-DSA and DSA region separately. The predicted results from the RK model are compared with the experimental data to check the accuracy of the constitutive relation. It is observed that to find out the constants of this model, some initial assumptions are required, and these initial values affect the predicted values. Hence, Genetic Algorithm (GA) is used to optimize the constants for RK model. Statistical measures such as the correlation coefficient, the average absolute error and standard deviation are used to measure the accuracy of the model. The resulting values of the correlation coefficient for ASS 304 for non-DSA and DSA region using modified extended RK model are 0.9828 and 0.9701. This modified, extended RK model is compared with Johnson–Cook (JC), Zerilli–Armstrong (ZA) and Arrhenius models and it is observed that specifically in DSA region, the modified extended RK model gives highly accurate predictions.

Constitutive modelling of the flow behaviour of a β titanium alloy at high strain rates and elevated temperatures using the Johnson–Cook and modified Zerilli–Armstrong models

The objectives of this work are to characterize the flow behaviour of the Ti–6Cr–5Mo–5V–4Al (Ti6554) alloy at high strain rates and elevated temperatures using the Johnson–Cook (JC) model and a modified Zerilli–Armstrong (ZA) model, and to make a comparative study on the predictability of these two models. The stress–strain data from Split Hopkinson Pressure Bar (SHPB) tests over a wide range of temperatures (293–1173K) and strain rates (103–104s−1) were employed to fit parameters for the JC and the modified ZA models. It is observed that both the JC and the modified ZA models have good capacities of describing the flow behaviour of the Ti6554 alloy at high strain rates and elevated temperatures in terms of the average absolute error. The modified ZA model is able to capture the strain-hardening behaviour of the Ti6554 alloy better as it incorporates the coupling effects of strain and temperature. However, dynamic recovery or dynamic recrystallization that may happen at elevated temperatures should be taken into consideration when selecting data set for parameters fitting for the modified ZA model. Also the modified ZA model requires more stress–strain data for the parameters fitting than the JC model.

Comparison of Material Flow Stress Models toward More Realistic Simulations of Friction Stir Processes of Mg AZ31B

Utilizing a proper material model for describing the mechanical behavior of any material is key for a successful simulation of friction stir processing (FSP) where temperature, strain, and strain rate gradients vary abruptly within, and when moving away, from the stirring zone. This work presents a comparison of how faithfully do three different constitutive equations reproduce the state variables of strain, strain rate, and temperature in an FEM simulation of a test-case FSP (1000 rpm spindle speed, and 90 mm/min feed). The three material models considered in this comparison are namely: Johnson-Cook (JC), Sellars-Tegart (ST), and Zerilli-Armstrong (ZA). Constants for these constitutive equations are obtained by fitting these equations to experimental mechanical behavior data collected under a range of strain rates and temperatures of twin-rolled cast wrought AZ31B sheets.It is widely recognized that JC-based models over predicts stress values in the stir zone whereas ST-based models are incapable of capturing work hardening outside of the stir zone. Therefore, a ZA model, being a physical based-HCP specific model, is hereby investigated for its suitability as a material model that would overcome such drawbacks of JC-and ST-based models. The equations from the constitutive models under consideration are fed into an FEM model built using DEFORM 3D to simulate the traverse phases of a friction stir process. Amongst these three material models, comparison results suggest that the HCP-specific ZA model yield better predictions of the state variables: strain, strain rate, and temperature, and, consequently, the estimated values for flow stresses.

Comparison of Material Flow Stress Models toward More Realistic Simulations of Friction Stir Processes of Mg AZ31B

Utilizing a proper material model for describing the mechanical behavior of any material is key for a successful simulation of friction stir processing (FSP) where temperature, strain, and strain rate gradients vary abruptly within, and when moving away, from the stirring zone. This work presents a comparison of how faithfully do three different constitutive equations reproduce the state variables of strain, strain rate, and temperature in an FEM simulation of a test-case FSP (1000 rpm spindle speed, and 90 mm/min feed). The three material models considered in this comparison are namely: Johnson-Cook (JC), Sellars-Tegart (ST), and Zerilli-Armstrong (ZA). Constants for these constitutive equations are obtained by fitting these equations to experimental mechanical behavior data collected under a range of strain rates and temperatures of twin-rolled cast wrought AZ31B sheets.It is widely recognized that JC-based models over predicts stress values in the stir zone whereas ST-based models are incapable of capturing work hardening outside of the stir zone. Therefore, a ZA model, being a physical based-HCP specific model, is hereby investigated for its suitability as a material model that would overcome such drawbacks of JC-and ST-based models. The equations from the constitutive models under consideration are fed into an FEM model built using DEFORM 3D to simulate the traverse phases of a friction stir process. Amongst these three material models, comparison results suggest that the HCP-specific ZA model yield better predictions of the state variables: strain, strain rate, and temperature, and, consequently, the estimated values for flow stresses.

Constitutive modeling of two-phase metallic composites with application to tungsten-based composite 93W–4.9Ni–2.1Fe

The two-phase metallic composites, composed by the metallic particulate reinforcing phase and the metallic matrix phase, have attracted a lot of attention in recent years for their excellent material properties. However, the constitutive modeling of two-phase metallic composites is still lacking currently. Most used models for them are basically oriented for single-phase homogeneous metallic materials, and have not considered the microstructural evolution of the components in the composite. This paper develops a new constitutive model for two-phase metallic composites based on the thermally activated dislocation motion mechanism and the volume fraction evolution. By establishing the relation between microscopic volume fraction and macroscopic state variables (strain, strain rate and temperature), the evolution law of volume fraction during the plastic deformation in two-phase composites is proposed for the first time and introduced into the new model. Then the new model is applied to a typical two-phase tungsten-based composite – 93W–4.9Ni–2.1Fe tungsten heavy alloy. It has been found that our model can effectively describe the plastic deformation behaviors of the tungsten-based composite, because of the introduction of volume fraction evolution and the connecting of macroscopic state variables and micromechanical characteristics in the constitutive model. The model's validation by experimental data indicates that our new model can provide a satisfactory prediction of flow stress for two-phase metallic composites, which is better than conventional single-phase homogeneous constitutive models including the Johnson–Cook (JC), Khan–Huang–Liang (KHL), Nemat-Nasser–Li (NNL), Zerilli–Armstrong (ZA) and Voyiadjis–Abed (VA) models.

Dynamic Deformation Behavior of Dual Phase Ferritic-Martensitic Steel at Strain Rates From 10−4 to 2000 s−1

The deformation behavior of the dual phase steel (DP 1000 steel) was studied by the quasi-static tensile experiment and the dynamic tensile experiment. The experiments were carried out at strain rates ranging from 10−4 to 2000 s−1 at room temperature. Then the stress-strain curves of DP1000 steel in the strain rate range of 10−4–2000 s−1 were measured. By introducing the strain rate sensitivity factor m, Zerilli-Armstrong model was optimized. The constitutive equation parameters which formulate the mechanical behavior of DP1000 steel were fitted based on the Johnson-Cook (JC) constitutive model and the optimized Zerilli-Armstrong (ZA) constitutive model, respectively. By comparing indicators of “accuracy-of-fit”, R2 terms, for the two models, the optimized Zerilli-Armstrong constitutive model can reflect plastic deformation behavior both at the low and high strain rates more accurately. The reasons why the optimized Zerilli-Armstrong constitutive model is more advantageous than the Johnson-Cook model were discussed by using the yield strength and ultimate tensile strength (UTS) versus strain rates, and strain hardening rate versus effective plastic strain analytical methods.