Khan – Huang – Liang Research Articles

A comparative study of different constitutive models to predict the dynamic flow behaviour of a homogenised AT61 magnesium alloy

In the present work, phenomenological and physical models were established to predict the plastic flow behaviour of homogenised AT61 magnesium alloy. The models were developed using experimental data obtained from compression experiments under quasi-static and dynamic loading conditions over a wide range of strain rates (10−4–4000 s−1) and temperatures (25–250 °C). The quasi-static and high strain rate compression experiments were performed on a universal testing machine and a split Hopkinson pressure bar, respectively. Several types of basic and modified (m-) constitutive models, including Johnson-Cook (JC), Khan-Huang-Liang (KHL), and Zerrilli-Armstrong (ZA), were calibrated to predict the plastic flow behaviour of an AT61 alloy. The prediction capabilities of these constitutive models were compared statistically in terms of average relative error and correlation coefficient. It was noticed that the predictions of the models JC, m-JC, and m-KHL were quite similar to the experimental findings; however, ZA model deviates more from the experimental data.

Finite Element Modeling for Orthogonal Machining of AA2024-T351 Alloy With an Advanced Fracture Criterion

Abstract Numerical modeling of the plastic deformation and fracture during the high-speed machining is highly challengeable. Consequently, there is a need for an advanced constitutive model and fracture criterion to make the numerical models more reliable. The aim of the present study is to extend the recent advanced static Lou-Yoon-Huh (LYH) ductile fracture creation to high strain rate and temperature applications such as machining. In the present work, the LYH static fracture creation was extended to machining conditions by introducing strain rate and temperature dependency terms. This extended LYH fracture criterion was calibrated over the wide range of stress triaxialities and different temperatures. Modified Khan- Huang-Liang (KHL) constitutive model along with the variable friction model was employed to predict the flow behavior of work material during the machining simulation. Damage evolution method was coupled to identify the element deletion point during the machining simulation. Orthogonal machining experiments were carried out for an aerospace-grade AA2024-T351 at cutting speeds varying between 100 and 400 m/min with the feed rates varying between 0.1 and 0.3 mm/rev. To assess the prediction capabilities of extended LYH fracture criterion, numerical simulations were also carried out using Johnson-Cook (JC) fracture criterion under all experimental conditions. Specific cutting energy, chip morphology, and compression ratio predictions were compared with the experimental data. Numerical predictions with coupled extended LYH criterion showed good agreement with experimental results compared to coupled JC fracture criterion.

Understanding the deformation and fracture mechanisms in backward flow-forming process of Ti-6Al-4V alloy via a shear modified continuous damage model

A shear modified coupled damage criterion based on continuum damage mechanics has been proposed in this study. Khan-Huang-Liang (KHL) model is implemented to predict the constitutive behavior of Ti-6Al-4 V (Ti64) alloy. A VUMAT subroutine has been developed for the damage model using a stress integration algorithm. Multiple simulations with tensile, compression and shear geometries are carried out in Abaqus/Explicit and compared with the experimental results to benchmark the hardening and damage criteria. The flow forming process involves a complex triaxial state of stress. This study is focused on understanding the contribution of triaxiality and shear during deformation and fracture in the flow-forming process with different roller arrangements. For this purpose, the flow-forming processes with three different roller arrangements, single roller, three roller, and wedge roller, are modeled, and their formability is compared by implementing a shear modified continuous damage model. A single roller flow-forming (SRF) arrangement undergoes high triaxiality due to excessive material displacement by the roller and high strain gradient in the axial direction. The fracture occurs near the interface of the reducing and thinning zone. The three-rollers flow-forming (TRF) provided maximum reduction till fracture and material fails due to excessive strain in the thinning zone at a relatively large percentage reduction. The wedge roller flow-forming (WRF) suffers a lack of uniform material softening, and fracture occurs near the interface of the uplift and reducing zone under high triaxiality. 3-D process maps have been developed for predicting fracture strain as a function of stress triaxiality/Lode parameter and stress triaxiality/thermal softening factor (E/σ¯2). Finally, a summary chart correlating the parameters, and flow-formability has been developed.

Study of Khan-Huang-Liang (KHL) Anisotropic Deformation Model for Deep Drawing Behaviour of Inconel 718 Alloy

Study of anisotropic deformation behavior of a material plays a crucial role in optimizing hot working process parameters and trustworthy Finite Element (FE) analysis in sheet metal forming processes. In this work, Khan–Huang–Liang (KHL) phenomenological based constitutive model and anisotropic yield criteria has been formulated for Inconel 718 alloy. Firstly, uniaxial tensile tests have been conducted at different temperatures (room temperature -700°C) and slow strain rates (0.0001-0.1s-1) conditions. KHL constitutive model has been formulated and validated with experimental flow stress data. The prediction capability of the model is evaluated based on correlation coefficient (R), average absolute error, AAE (Δ) and its standard deviation (s). Subsequently, anisotropic yielding behavior of Inconel 718 alloy is predicted based on KHL yield criterion. Anisotropic coefficient (Lankford parameters) and tension compression asymmetry parameters have been calculated experimentally. The prediction capability of KHL yield criterion is analyzed based on yield locus, yield stress variation and anisotropic coefficient variation. The quality index of performance, namely global accuracy index (β) is evaluated. Further, Finite Element (FE) analysis has been carried out for deep drawing of Inconel 718 alloy using commercially available ABAQUS software. The developed KHL constitutive model and anisotropic yield criterion has been incorporated in FE simulation using UMAT/VUMAT code. The FE results are validated with experimental deep drawn cups at different process conditions.

Flow stress prediction of zircaloy-4 at elevated temperatures using KHL constitutive model

ABSTRACT Zircaloy-4 is widely used material for nuclear and high-temperature applications. This paper focuses on prediction of zircaloy-4 material flow stress at elevated temperatures using Khan-Huang-Liang (KHL) model. Three different routes of zircaloy-4 material namely low oxygen sheet, slab route sheet and tube route sheet are used for the experimental work. Uni-axial tensile tests are conducted at temperature range of 298–498K and at different strain rates of 0.001s−1, 0.005s−1 and 0.01s−1. The tensile test data has been used to predict the constants in KHL model for three different grades of zircaloy-4 material. The predicted flow stress with KHL model is compared with the experimental flow stress to check the accuracy of the model. The accuracy of model is also checked with statistical parameters such as correlation coefficient, average absolute error and root mean square standard deviation. This result reveal that the KHL model predicted flow stress is in good agreement with experimental flow stress data.

Influence of material modeling on warm forming behavior of nickel based super alloy

The present study helps in providing a systematic approach towards the investigation of deep drawing and stretch forming processes for Inconel 625 alloy. Firstly, the flow stress nature and material properties of Inconel 625 super-alloy have been investigated and it has been found that temperature and deformation rate significantly affects the flow stress behavior. By using experimental flow stress data, four different constitutive models namely; modified Jhonson-Cook (m-JC), modified Zerilli-Armstrong (m-ZA), modified Arrhenius (m-A), Khan–Huang–Liang (KHL) model have been formulated of which m-A has been found to have the best predictability for flow stress. Hill 1948 and Barlat 1989 anisotropic yield criterion have also been applied and it has been found that Barlat 1989 criteria more accurately capture the yielding behavior of Inconel 625 alloy. The deep drawing analysis has been carried out using target and noise performance measures for different process parameters viz., temperature, punch speed and blank holding pressure. Uniformity in thickness has been major cause of concern, hence experiment at 473 K, 5 mm/min speed and 20 Bar pressure was found to have least variation in thickness. Furthermore, the forming limit diagram (FLD) and fracture curve (FC) obtained from stretch forming analysis along five different strain paths was found to be significantly affected by temperature. Further, user defined material (UMAT) subroutine have been incorporated in ABAQUS 6.13 software to have effect of m-A model and Barlat 1989 yield criteria in finite element analysis (FEA) of deep drawing and stretch forming processes.

Constitutive-damage modeling and computational implementation for simulation of elasto-viscoplastic-damage behavior of polymeric foams over a wide range of strain rates and temperatures

The material behavior and damage of polymeric foams (e.g., polyurethane foam and polystyrene foam) are extremely complex under compression, depending on strain rates and temperatures. In the present study, the elasto-viscoplastic-damage behavior of polymeric foams over a wide range of strain rates and temperature is evaluated and predicted using the modified Gurson-Tvergaard-Needleman-Lemaitre (GTNL) model and the modified Khan-Huang-Liang (KHL) model. A modified GTNL model is introduced to describe phenomena of decreasing void volume fraction and elastic modulus for polymeric foams under uniaxial compression. The modified KHL model is proposed to evaluate the nonlinear strain rate- and temperature-dependent material behavior of polymeric foams. The full derivation of the implicit integration algorithm of the proposed modified GTNL-KHL model is introduced, and a user-defined material (UMAT) subroutine for commercial finite element analysis code (i.e., ABAQUS) is established. Using the UMAT, the damage characteristics (e.g., void volume fraction and elastic modulus changes) and the nonlinear material behavior (e.g., linear elastic, softening/plateau and densification) of polymeric foams under uniaxial compression with various strain rates and temperatures are successfully simulated.

Prediction of flow stress behaviour by materials modelling technique for Inconel 718 alloy at elevated temperature

ABSTRACT Tensile flow behaviour attracts a continue attention in enhancing material processing and ensuring secure performance during metal forming processes. In present study, tensile deformation behaviour of Inconel 718 alloy have been investigated from room temperature (RT) to 700°C, strains (from 0.01 to 0.3 with interval of 0.01) at strain rates of 0.0001-0.01 s−1. From experimental observation, it is observed that flow stress behaviour was considerably influences by temperature and strain rate variation. Additionally, constitutive models, mainly Khan–Huang–Liang (KHL) and modified Fields–Backofen (mFB) models have developed to predict flow stress behaviour. Statistical parameters, mainly average absolute error (Δ), correlation coefficient (R) and root mean square error (s), have been evaluated the prediction capability of models. KHL model has given highest coefficient of correlation (R = 0.9182); this signifies suitability of KHL model for flow prediction of Inconel 718 alloy.

On the Constitutive Models for Ultra-High Strain Rate Deformation of Metals

Ultra-high strain rate deformation (> 104 s−1) is common in high speed manufacturing and impact engineering. However, a general constitutive model suitable for describing the material deformation at ultra-high strain rates is still unavailable. The purpose of this study is of two-folds. The first is to systematically evaluate the performances of four typical constitutive models, Johnson-Cook (J-C), Khan-Huang-Liang (KHL), Zerilli-Armstrong (Z-A), and Gao-Zhang (G-Z), in predicting the dynamic behaviors of materials. The second is to obtain an improved constitutive model to better describe the deformation of materials under ultra-high strain rates. To this end, high strain rate tests were carried out on different crystalline structures, i.e., BCC, FCC, and HCP over a wide range of strain rate from 102 s−1 to 1.5 × 104 s−1. It was found that before the critical strain rate, around 104 s−1, all of the previous models can predict the flow stresses. When the strain rate passes a critical point, however, these models fail to predict the sudden upsurge of the flow stresses. The improved model developed in this paper, by considering the dislocation drag mechanism, can successfully characterize the dynamic behaviours of materials over the whole range of strain rates.

Enhanced Constitutive Model for Aeronautic Aluminium Alloy (AA2024-T351) under High Strain Rates and Elevated Temperatures

Success of the numerical simulations depends on the accuracy of the material constitutive relations. Most of the ductile materials exhibit increased strain rate sensitivity at higher strain rates (> 103 s−1) compared to low and medium strain rates. Meanwhile, plastic deformation of any ductile material under high strain rate conditions results in heat generation due to plastic work. Hence, a reliable constitutive model should be able to predict the accurate thermo-mechanical response of the material over a wide range of strain rate loading conditions. In the present work, an enhanced constitutive model for high strain rate and elevated temperature is proposed. For calibration purpose, the stress-strain response of AA2024-T351 is studied under quasi-static and dynamic loading conditions using uniaxial compression and split Hopkinson compressive pressure bar (SHPB) respectively at various temperatures. A threshold strain rate value is identified and used to improve the prediction capabilities of the present model. Later, the proposed model is compared with Johnson-Cook (JC) and Khan-Huang-Liang (KHL) models using the different statistical parameters. This analysis revealed the improved stress-strain prediction capability of the proposed model compared to the others.

Rate dependent behaviour and dynamic strain localisation of three novel impact resilient titanium alloys: Experiments and modelling

The tensile behaviour of three ductile titanium alloys, Ti0.7Al4V, Ti1Al4V and Ti3Al2.5V, conceived for impact containment applications, is characterised at quasi-static, intermediate and high strain rates. Tests have been performed using a screw driven mechanical system and a bespoke in-house developed split Hopkinson tension bar equipped with ultra-high speed photographic equipment. The three alloys present noticeable strain rate sensitivity. Ti1Al4V is characterised by the lowest flow stress and highest ductility of the three alloys. Ti3Al2.5V higher flow stress but lowest strain to failure while Ti0.7Al4V has similar flow stress but larger engineering failure strain compared to Ti3Al2.5V. The dynamic true strain rate, determined by measuring the time history of the minimum cross-section diameter during necking, reaches values up to one order of magnitude higher than the nominal strain rate. This phenomenon, occurring during dynamic strain localisation, is of fundamental importance for understanding and modelling the dynamic behaviour of ductile alloys designed to withstand impact loading. The experimental results are used to determine the material parameters of the Johnson-Cook (JC) and Khan–Huang–Liang (KHL) models, which are incorporated in the ABAQUS/explicit code for finite element simulations of the dynamic tensile tests. It is found that the KHL model predicts the experimentally measured strain field, deformed geometry, effective strain rate and macroscopic force-displacement response during the high strain rate experiments with significantly better agreement than the JC model.

Constitutive Modeling of High-Temperature Flow Stress of Armor Steel in Ballistic Applications: A Comparative Study

Armox 500T is one of the armor grade steels extensively used as armor against bullet penetration in ballistic applications. In such applications, the material undergoes plastic deformation at large strain rates (103 s−1) at temperatures of the order of 673-1373 K. In the present work, an attempt has been made to predict strain rate and temperature-dependent flow behavior of Armox 500T steel through physical-based model like modified Zerilli–Armstrong (M-ZA) and phenomenological-based models like Cowper Symonds (CS), modified Johnson–Cook (M-JC), Arrhenius (Arr.) and Khan–Huang–Liang (KHL) constitutive material model. Isothermal uniaxial compression tests at low strain rates (10−3-10−1 s−1) and dynamic compression tests at high strain rates (600-3000 s−1) in the temperatures range of 673-1373 K have been carried out to determine constitutive material model parameters. In addition, an artificial neural network (ANN) model that works on multilayer perceptron (MLP) based back propagation neural network (BPNN) has also been developed. The results from all these models have been compared in terms of three statistical parameters namely correlation coefficient (R), mean absolute percent error (MAPE) and its standard deviation (Δ). The results revealed that M-JC model shows highest correlation coefficient and lowest average absolute error. Further, ANN model prediction has the highest accuracy with R = 0.999 and MAPE = 1.052.

Experimental and Numerical Investigations on Hot Deformation Behavior and Processing Maps for ASS 304 and ASS 316

AbstractA thorough understanding of hot deformation behavior plays a vital role in determining process parameters of hot working processes. Firstly, uniaxial tensile tests have been performed in the temperature ranges of 150 °C–600 °C and strain rate ranges of 0.0001–0.01s−1 for analyzing the deformation behavior of ASS 304 and ASS 316. The phenomenological-based constitutive models namely modified Fields–Backofen (m-FB) and Khan–Huang–Liang (KHL) have been developed. The prediction capability of these models has been verified with experimental data using various statistical measures. Analysis of statistical measures revealed KHL model has good agreement with experimental flow stress data. Through the flow stresses behavior, the processing maps are established and analyzed according to the dynamic materials model (DMM). In the processing map, the variation of the efficiency of the power dissipation is plotted as a function of temperature and strain rate. The processing maps results have been validated with experimental data.

Analysis of Flow Stress Behaviour of Inconel Alloys at Elevated Temperatures Using Constitutive Model

A reliable and accurate prediction of flow behaviour of metals considering the coupled effects of strain, strain rate and temperature is vital in analyzing the workability of the metal. In this study, Khan-Huang-Liang (KHL) phenomenological based constitutive models has been developed for flow stress prediction of Inconel 625 and 718 alloys. Firstly, uniaxial tensile tests have been performed from room temperature to 400°C at an interval of 100°C and slow strain rate ranges of 0.0001–0.01s−1. KHL constitutive model has been developed using uniaxial tensile test data. The predicted flow behaviour has been compared with experimental stress-strain data. The prediction capability of these models has been verified using various statistical measures such as correlation coefficient (R), average absolute error (Δ) and its standard deviation (S). Based on the analysis of statistical measures revealed that KHL model has good in agreement with experimental flow stress behaviour.

Study of Hot Deformation Behavior Using Phenomenological Based Constitutive Model for Austenitic Stainless Steel 316

A reliable and accurate prediction of flow behavior of metals considering the coupled effects of strain, strain rate and temperature is crucial in understanding the workability of the metal and optimizing process parameters for hot forming process.In this study, two phenomenological based constitutive models namely; modified Fields-Backofen (m-FB) and Khan-Huang-Liang (KHL) have been developed for flow stress prediction of Austenitic Stainless Steel (ASS) 316. Uniaxial tensile tests have been performed in the temperature ranges of 150°C– 600°C and strain rate ranges of 0.0001– 0.01s-1 for analyzing the deformation behavior. The prediction capability of these models have been verified with experimental data using various statistical measures such as correlation coefficient (R), average absolute error (Δ) and its standard deviation (S). Based on the analysis of statistical measures revealed Khan-Huang-Liang (KHL) model has good agreement with experimental flow stress data.

Constitutive modeling and fracture behavior of a biomedical Ti–13Nb-13Zr alloy

The dynamic compression tests were performed at various strain rates (0.01, 1700, 2700 and 3500/s) and temperatures (25, 200, 400 and 600°C) for a biomedical Ti–13Nb-13Zr alloy. Based on experimental data, constitutive models were established using the Modified Johnson-Cook (J-C) model, Modified Khan–Huang–Liang (KHL) model and Artificial neural network (ANN) model, respectively. The new modified J-C model considers the coupled effects of strain hardening, strain rate hardening and thermal softening. In this work, a radial basis function artificial neural network (RBF-ANN) model was also developed to predict the high strain rate flow curves of Ti–13Nb-13Zr alloy. The results demonstrate that the flow behavior of Ti–13Nb-13Zr alloy is considerably influenced by the strain rate and temperature. The modified KHL model and ANN significantly enhance the predictability. The deformation behavior represented by dynamic recrystalization (DRX) and the instability flow has been discussed with reference to microstructural evolution during high strain rate compression. The validation of the developed constitutive model is embedded in the finite element analysis (FEA) to perform numerical simulations with ABAQUS/Standard to obtain the charpy impact energy.

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.

The Use of genetic algorithm and neural network to predict rate-dependent tensile flow behaviour of AA5182-O sheets

In this study, the tensile flow behaviour of AA5182-O sheet was experimentally obtained in different material directions (RD, DD, and TD) at strain rates ranging from 0.001 to 1000s−1 and predicted by means of both phenomenological models and neural networks (NNs). Constants in Johnson–Cook (JC), Khan–Huang–Liang (KHL), and modified Voce were calculated using genetic algorithm (GA) and linear regression analysis and used to simulate the uniaxial tension tests. Two types of feed-forward back-propagation neural networks were also trained and validated to predict the rheological behaviour of the alloy without the limitations of a mathematical function. The weights and bias values of each network were then used to simulate uniaxial tensile deformation. Subsequently, the results were compared with experimental flow curves and accuracy parameters were calculated. It was found that the modified Voce constitutive equation was able to predict the flow behaviour of AA5182-O with better accuracy than JC and KHL models. Also, the NN was found to be the most accurate method of predicting the anisotropic rate-dependant behaviour of AA5182-O.

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.

Comparative study of constitutive modeling for Ti–6Al–4V alloy at low strain rates and elevated temperatures

An accurate prediction of flow behavior of metals considering the combined effects of strain, strain rate and temperature is essential for understanding flow response of metals. Isothermal uniaxial tensile tests have been performed from 323K to 673K at an interval of 50K and strain rates 10−5, 10−4, 10−3 and 10−2s−1. In this study prediction of flow behavior of Ti–6Al–4V alloy sheet is done using four constitutive models namely; Johnson–Cook (JC), Fields–Backofen (FB), Khan–Huang–Liang (KHL) and Mechanical Threshold Stress (MTS). The predictions of these constitutive models are compared using statistical measures like correlation coefficient (R), average absolute error (Δ) and its standard deviation (δ). Analysis of statistical measures revealed that FB model has more deviation from the experimental values. Whereas, the predictions of all other models (JC, KHL, and MTS) are very close to the experimental results. JC and KHL are better models for predicting the flow stress. However, considering the fact that MTS model is a physical based model, MTS model is preferred over other models.