Prediction Of Flow Stress Research Articles

Flow Behavior of AA5005 Alloy at High Temperature and Low Strain Rate Based on Arrhenius-Type Equation and Back Propagation Artificial Neural Network (BP-ANN) Model.

To realize the purpose of energy saving, materials with high weight are replaced by low-weight materials with eligible mechanical properties in all kinds of fields. Therefore, conducting research works on lightweight materials under specified work conditions is extremely important and profound. To understand the relationship of aluminum alloy AA5005 among flow stress, true strain, strain rate, and deformation temperature, hot isothermal tensile tests were conducted within the strain rate range 0.0003–0.03 s−1 and temperature range 633–773 K. Based on the true stress-true strain curves obtained from the experiment, a traditional constitutive regression Arrhenius-type equation was utilized to regress flow behaviors. Meanwhile, the Arrhenius-type equation was optimized by a sixth-order polynomial function for compensating strain. Thereafter, a back propagation artificial neural network (BP-ANN) model based on supervised machine learning was also employed to regress and predict flow stress in diverse deform conditions. Ultimately, by introducing statistical analyses correlation coefficient (R2), average absolute relative error (AARE), and relative error () to the comparative study, it was found that the Arrhenius-type equation will lose accuracy in cases of high stress. Additionally, owning higher R2, lower AARE, and more concentrative value distribution, the BP-ANN model is superior in regressing and predicting than the Arrhenius-type constitutive equation.

Hot deformation behavior of Sc/Nb modified AA2195 Al–Li–Cu alloys

The hot workability of third generation AA2195 (Al–Li–Cu–Ag–Mg–Zr) alloy with different Sc (0.15–0.25 wt%) and Nb (0.15–0.25 wt%) additions in the homogenized condition was investigated using processing maps approach. The additions of Sc and Nb were found to be beneficial in refining the as-cast grain size of AA2195 and changing the morphology from less dendritic grain structure to a globular or equiaxed form. Hot compression tests carried out in the temperature, T, range of 300–450 °C and strain rate, ε˙, of 10−3 – 10 s−1 were utilized to generate processing maps at a true strain, ε = 0.5. The flow curves of the alloys exhibit a typical dynamic recovery (DRV) characteristics and Arrhenius type constitutive equations successfully predicted flow stress of the alloys. The results obtained from the processing maps and complementary microstructural analysis of the deformed specimens revealed that 0.15 wt% additions of Sc and Nb (separately or in combination) are optimum to improve its workability. However, increasing Sc and Nb contents to 0.25 wt% relatively expanded flow instability regions. With the aid of the processing maps, deformed specimens microstructural analysis, activation energy and Zener-Hollomon parameter, Domain D-3 occurring at higher temperatures and strain rates were identified as the “safe” regimes for hot working of AA2195 with optimum Sc and Nb contents (0.15 wt% added separately or in combination). Limited pancake type grain morphology with higher fractions of dynamically recrystallized (DRX) grains was observed in Domain D-3. The microstructural manifestation in the flow instability regions was flow localization (at higher strain rates), cavities formation at the grain boundaries & precipitates, particles breakage and wedge cracking at the triple junctions at lower strain rates.

Establishing flow stress behaviour of Ti-6Al-4V alloy and development of constitutive models using Johnson-Cook method and Artificial Neural Network for quasi-static and dynamic loading

Ti-6Al-4V alloy is one of the most widely used material in both research as well as in commercial industries at present due to its high strength-to-weight ratio, low density and excellent high-temperature properties. Understanding the behaviour of this alloy at various deformation conditions (strain, strain rate and temperature) is crucial to fit the material in demanding applications. In our present work, the mechanical behaviour of α + β dual phase Ti-6Al-4V alloy is studied in the temperature ranging from 25 ℃ to 200 ℃ and rate of deformation ranging from 10-3 s−1 to 104 s−1. Tensile tests were done using uniaxial tensile tester for quasi-static range of deformation and Split-Hopkinson bar machine for dynamic range of deformation. Post deformation fracture surface analysis were carried out to understand the effects of strain rate and temperature variations on the deformation behaviour, and to establish a structure–property correlation. For the studied range of deformation parameters, constitutive models are developed. As Johnson-Cook model is one of the widely used model in various numerical analysis software, a modified Johnson-Cook model has been developed for the alloy. Moreover, artificial intelligence (AI) is found to be an efficient tool these days to solve complex problems in various fields of engineering. An attempt is also made in this study to develop an artificial neural network (ANN) framework for the prediction of flow stress at various deformation condition for Ti-6Al-4V alloy. Our study revealed that the AI based ANN technique is more efficient in calculating the flow stress as compared with the traditional Johnson-Cook model.

Investigations on the Choice of Johnson–Cook Constitutive Model Parameters for the Orthogonal Cutting Simulation of Inconel 718

The Johnson–Cook model is the popular constitutive relation for the simulation of metal cutting process because of the availability of various sets of parameters for different materials. Different sets of Johnson–Cook parameters are observed to be available for a particular material due to dissimilarity in the initial condition of the material and experimental methods utilized for the calibration. Hence, it is difficult to choose an accurate parameter set for modeling the behavior of a material for the finite element simulation of its cutting process. In this regard, a strategy is proposed and validated in this study for choosing an accurate Johnson–Cook parameter set for Inconel 718. Twelve sets of Johnson–Cook parameters were collected from the literature for Inconel 718 and their flow stress predictions were investigated by comparing with experimental flow stress values for wide ranges of strain rates and temperatures as encountered during the cutting process. The Johnson–Cook parameter sets corresponding to the predicted flow stress curves that agree with the experimental values are chosen for modeling the behavior of Inconel 718. This comparison also helps in indexing the parameter sets according to the initial condition of the material since it is not reported mostly in the literature. The chosen material parameter sets are validated further for the orthogonal cutting simulation of Inconel 718 for a wide range of cutting conditions by comparing the cutting force and chip thickness predictions with the experimental values. Thus, the analysis of predicted flow stress values helps in choosing the accurate Johnson–Cook parameters for an Inconel 718 specimen which in turn helps in conducting accurate orthogonal cutting simulations. The finite element simulation of metal cutting helps in identifying the optimum cutting parameters which would help to reduce energy consumption and thus make the process more efficient and sustainable.

Application of unified constitutive model of 34CrNiMo6 alloy steel and microstructure simulation for flexible skew rolling hollow shafts

Flexible skew rolling (FSR) is a novel rolling process for shaft parts, which is capable of rolling the hollow shafts. The microstructure of shaft parts is very important to its service performance, and the application of finite element (FE) method has been widely used to simulate microstructure evolution. Firstly, hot compression tests were performed to obtain the flow curves and corresponding microstructure states of the steel under the conditions of 950–1100 °C and 0.1–10 s−1. Secondly, the average grain size (AGS) under different conditions was recorded. A unified viscoplastic constitutive model considering recrystallization is established to characterize the high-temperature deformation and microstructure evolution of 34CrNiMo6 alloy steel. A genetic algorithm (GA) is used to solve the material constants of the constitutive model. The error of the predicted flow stress is 3.632%, and the error of the predicted grain size is less than 10%, which indicates that the established constitutive model can precisely predict the flow stress and grain size variation of 34CrNiMo6 alloy steel. The constitutive model was coded and embedded into the FE software Simufact via a user-defined subroutine interface to simulate the grain evolution during a uniaxial hot compression test and microstructure evolution of alloy steel in the FSR process. The FSR trials of hollow shafts were conducted and the microstructure at different positions of rolled-part was observed to validate the correctness of the model. The FE simulation results of grain size are compared with the experimental results, and the results are in good agreement. The internal variable constitutive model established in this paper can predict and reveal the microstructure evolution of FSR hollow shafts very well, and the AGS of shaft parts rolled by FSR are distinctly refined.

Geometry and surface state effects on the mechanical response of Au nanostructures

Abstract A study of ultra-thin gold films and thin-walled nanoboxes has confirmed that length scales in terms of dislocation spacing can predict flow stress. Initial stages of deformation conform to linear hardening with average dislocation spacing controlled by the number of geometrically necessary dislocations in a pile-up. Later stages of deformation exhibit parabolic behavior with Taylor hardening interpreted in terms of a dislocation density described by the total line length of prismatic loops per unit volume. Comparisons of 20 and 40 nm thick planar films could be made to 205 nm high hollow gold nanoboxes with a wall thickness of 24 nm. These highly constrained, ultra-thin planar films demonstrated increased hardness from about 2 to 10 GPa with strains of 20 percent while less constrained nanoboxes increased from 0.8 to 4 GPa for the same strain magnitude.

A fully coupled crystal plasticity-cellular automata model for predicting thermomechanical response with dynamic recrystallization in AISI 304LN stainless steel

A microstructure-based multiscale framework was developed to physically correlate the microstructure evolution and mechanical behavior of AISI 304LN stainless steel during the thermomechanical process. The developed model couples a crystal plasticity finite element method (CPFEM) to simulate heterogeneous deformation and a probabilistic cellular automata (CA) approach with a dynamic recrystallization (DRX) model to simulate microstructure evolution. Specifically, the CA model was built with formulations with physical meaning and combined with CPFEM by updating algorithms with higher robustness. The developed model was validated by comparing it with the experimental results of AISI 304LN stainless steel under thermo-mechanical processing at various temperatures and strain rates. The predicted flow stresses, grain sizes, DRX volume fraction, and deformed texture match well with the experimental data. Additionally, the developed model can simulate microstructure evolution by the DRX process, whereby the evolutions of recrystallized grains and pole figures can be examined. Moreover, the mechanical responses during the nucleation and growth of recrystallized grains can be characterized by in-depth quantitative analysis considering grain-level deformation inhomogeneity.

Predicting High Temperature Flow Stress of Nickel Alloy A230 Based on an Artificial Neural Network

The high-temperature deformation behavior of metals and alloys undergoes complex mechanisms depending on the deformation conditions. The microstructure and mechanical properties after deformation are important factors that determine the strength and durability of the final product. Therefore, many studies to predict the microstructure and mechanical properties have been conducted. In this regard, numerous mathematical approaches for predicting microstructure and flow stress have been proposed over the past half century. Accordingly, many advances have been made in the field of material science. Nevertheless, there are limitations in the mathematical modeling method as there is a complex relationship between the deformation conditions and the mechanical properties. Therefore, in this study, flow stress prediction was performed by applying conventional constitutive equation and artificial intelligence technology, which is known to be effective in modeling complex relationships. As a result, it was confirmed that the flow stresses modeled by the artificial neural network showed a higher accuracy than the flow stresses modeled by the conventional Arrhenius hyperbolic sine equation.

Hot Deformation Behavior of Non-Alloyed Carbon Steels.

The hot deformation behavior of selected non-alloyed carbon steels was investigated by isothermal continuous uniaxial compression tests. Based on the analysis of experimentally determined flow stress curves, material constants suitable for predicting peak flow stress σp, peak strain εp and critical strain εcrDRX necessary to induce dynamic recrystallization and the corresponding critical flow stresses σcrDRX were determined. The validity of the predicted critical strains εcrDRX was then experimentally verified. Fine dynamically recrystallized grains, which formed at the boundaries of the original austenitic grains, were detected in the microstructure of additionally deformed specimens from low-carbon investigated steels. Furthermore, equations describing with perfect accuracy a simple linear dependence of the critical strain εcrDRX on peak strain εp were derived for all investigated steels. The determined hot deformation activation energy Q decreased with increasing carbon content (also with increasing carbon equivalent value) in all investigated steels. A logarithmic equation described this dependency with reasonable accuracy. Individual flow stress curves of the investigated steels were mathematically described using the Cingara and McQueen model, while the predicted flow stresses showed excellent accuracy, especially in the strains ranging from 0 to εp.

Hot Ductility Analysis and Flow Stress Prediction of (C-Mn-S-Al-Nb-V-Ti) Micro-alloyed Steel

The objective of this work is to study the hot ductility of (C-Mn-S-Al-Nb-V-Ti) micro-alloy steel of industrial production whose initial structural state is rolling stock. To simulate the thermomechanical treatments imposed we have deformed by pulling our samples after subjecting them to a solution treatment at 1200 °C and a precipitation treatment cycle before deformation. Hot deformations were carried out at temperatures from 700 °C and 1150 °C and deformation rates ranging between 10-2 s-1 and 5.10-4 s-1. The results show a decrease in hot ductility. Minimum values of hot ductility are determined at 800°C, and another decrease in hot ductility was observed at 900°C. Ferrite precipitation is observed at austenitic grain boundaries in the intercritical temperature range, causing intergranular embrittlement. Precipitation makes the hot ductility curve wider and deeper around 900°C. Hot ductility losses can explain by the presence of precipitates in the austenitic region and the presence of the two-phase structure in the intercritical region. Finally, based on experimental stress-deformation data, artificial neuron network (ANN) methods were used to predict flow stress of (C-Mn-S-Al-Nb-V-Ti) micro-alloy steel. This model is more effective in predicting flow stress and results can also be used in the mathematical simulation of hot metal formation processes.

Prediction of flow stress characteristics of P92 steel using a simple physically-based constitutive modelling

This study reports the flow stress behavior of three P92 steels with different compositions. Uniaxial compression tests were conducted in the deformation temperature range of 575 °C to 650 °C and strain rate range of 0.001-0.5 s-1 using a Gleeble® 3500 thermo-mechanical simulator. A simple physically-based constitutive model was used to analyse the effects of deformation conditions (temperature and strain rate) on the metal flow stress behavior during the deformation process. The method accounts for the temperature dependence of Young’s modulus and the lattice self-diffusion coefficient of Fe in the ferrite. Constitutive equations describing the flow stress behavior of the three P92 steels were developed. From the results, the stress exponent n of 26.13(steel A), 21.61(steel B) and 27.55 (steel C) were obtained using the self-diffusion activation energy in the physically-based constitutive equation. From the results, the three steels had variation in the stress exponent values, which was attributed to differences in elemental content, such as chromium and tungsten. The developed constitutive equations were verified using statistical parameters: Pearson’s correlation coefficient (R) and average absolute relative errors (AARE). Statistical analysis showed that the three steels had the same R of 0.98, while AARE was: 1.68 (steel A), 1.72 (steel B), and 1.82 (steel C). The constitutive equations developed showed a good correlation between the experimental and predicted flow stress data. Hence, the method is applicable in describing flow stress behavior in the metalworking process in the industry.

Predicting flow stress of Ni steel based on machine learning algorithm

This article builds a stress–strain prediction model based on production data from the steel industry by using machine learning algorithms. Based on the stress–strain data of 9Ni steel hot deformation behavior, the prediction model of flow stress constitutive equation of 9Ni steel is established. Four models, including Arrhenius-type model considering strain compensation, Arrhenius-type model of Stochastic Configuration Networks (SCNs) neural network, Arrhenius-type model of Multi-objective Particle Swarm Optimization (AMPSO) and Support Vector Machine (SVM) model, are adopted in this research. The results show that the Arrhenius-type model considering strain compensation can predict the stress trend under different deformation conditions, but its prediction accuracy has some deviation. The prediction model based on SVM algorithm has the best prediction accuracy. The square of Correlation Coefficient (R2), the Average Absolute Relative Error (AARE), and Mean Square Error (MSE) are 0.99996, 0.002455, and 0.1998, respectively. Based on the data of 9Ni steel hot deformation behavior, the prediction models of machine learning algorithm have good application prospects in steel industry.

Constitutive modeling of multiscale polycrystals considering grain structures and orientations

Traditional macro-scaled plasticity theories may not be fully valid and accurate in study of meso-/micro-scaled deformation due to the existence of size effects (SEs). In meso/microforming, there are only several to ten grains in the deformation zone. The anisotropy of individual grains significantly affects the mechanical responses and deformation behaviors of polycrystalline metallic materials. Meanwhile, grain boundaries are isotropic and generally considered as barriers to plastic deformation. In this research, the constitutive modeling considering the orientation and boundary-interior difference of grains was developed and validated by the SE-based experiments and simulations with different specimens and grain sizes. In compression tests, discontinuous shear bands are found to be generated with a zig-zag distribution in the coarse-grained specimen, but long and continuous shear bands appear in the fine-grained specimen. In tensile and meso-heading tests, microcracks initiate at grain boundary regions and grow along grain boundaries. More and smaller microcracks exist in the fine-grained material, while coarse grains facilitate the formation of larger cracks. Furthermore, compared with the crystal plasticity simulation, the simulation using the proposed modeling loses a little accuracy in prediction of freeform geometry in compression but has the advantages of high simulation efficiency and accurate prediction of flow stress. This modeling is thus suitable for addressing the meso-/micro-scaled engineering deformation problems of polycrystalline materials.

Constitutive modelling of hot deformation behaviour of metallic materials

The complexity of hot deformation behaviours of metallic materials is acknowledged in decades of study. The present work uses a new constitutive model by Zhu-Ou-Popov (ZOP model) and its modifications to predict the hot deformation behaviours of metals. The ZOP model and its modifications are introduced firstly. The basic idea of these models is centred on a set of piecewise and transition functions: the piecewise functions are used to predict flow stress at different strain ranges, whilst the transition functions enable a smooth shifting from small strain to large strain ranges. The methods for identification of four variant models are developed and given in detail. Hot compressive flow stress curves of 42CrMo at different strain rates and temperatures are used to show the validity of these models. Results show that, all of the developed models are able to predict the hot compressive behaviour of 42CrMo. Using the Arrhenius type equation and modified Zener-Holloman parameter to predict the flow stress from the yield point, the Modified model Ⅲ gives the most favourable prediction accuracy with R2 of 0.9569, whilst other models are also effective with R2 higher than 0.91. The modifications of the ZOP model can be used to predict the yield stress and to reflect the peak stress. In addition, the applicability and advancement of the presented constitutive models are discussed. The models are considered to be effective in reflecting the occurrence and completion of dynamic recrystallization (DRX) in hot deformation of metallic materials. It is shown that the studied models are capable of predicting the peak strain and completion strain of DRX, with comparable results obtained to experimental data.

Processing Workability and Artificial Neural Network of AA1070 to the Prediction of Hot Flow Stress

Processing Workability and Artificial Neural Network of AA1070 to the Prediction of Hot Flow Stress

A modified Zerilli–Armstrong constitutive model for simulating severe plastic deformation of a steel alloy

A modified Zerilli–Armstrong model has been proposed and validated in previous works for simulating distinct deformation mechanisms of continuous-shear and shear-localization during severe plastic deformation of a face centered cubic alloy. In this paper, the validity of the modified Zerilli–Armstrong model has been further tested by using it for modeling the severe plastic deformation of another face centered cubic material, a steel alloy. In particular, the modified Zerilli–Armstrong model is used as a constitutive relation for simulating behavior of AISI 1045 steel alloy while undergoing severe plastic deformation through orthogonal and plane-strain machining. Accordingly, the performance of the constitutive relation in predicting flow stress distribution along the primary shear zone is validated by comparing with forecasts made using the distributed primary zone deformation, the original Zerilli-Armstrong and Johnson-Cook models. Furthermore, finite element simulations of orthogonal cutting of this steel alloy were carried out, and good agreement was observed between the predicted chip morphology and attendant cutting forces with experimental values reported in literature for a range of cutting conditions. The force predictions also fared better compared to those predicted by using the Zerilli-Armstrong and Johnson-Cook models. These validations provide further corroboration of using the modified Zerilli–Armstrong model as a constitutive relation for simulating the behavior of face-centered cubic materials under conditions of high plastic strains and also high strain-rates.

Hot Deformation Behavior of a Beta Metastable TMZF Alloy: Microstructural and Constitutive Phenomenological Analysis

A metastable beta TMZF alloy was tested by isothermal compression under different conditions of deformation temperature (923 to 1173 K), strain rate (0.172, 1.72, and 17.2 s−1), and a constant strain of 0.8. Stress–strain curves, constitutive constants calculations, and microstructural analysis were performed to understand the alloy’s hot working behavior in regards to the softening and hardening mechanisms operating during deformation. The primary softening mechanism was dynamic recovery, promoting dynamic recrystallization delay during deformation at higher temperatures and low strain rates. Mechanical twinning was an essential deformation mechanism of this alloy, being observed on a nanometric scale. Spinodal decomposition evidence was found to occur during hot deformation. Different models of phenomenological constitutive equations were tested to verify the effectiveness of flow stress prediction. The stress exponent n, derived from the strain-compensated Arrhenius-type constitutive model, presented values that point to the occurrence of internal stress at the beginning of the deformation, related to complex interactions of dislocations and dispersed phases.

Prediction of Flow Stress of Annealed 7075 Al Alloy in Hot Deformation Using Strain-Compensated Arrhenius and Neural Network Models.

Hot compression experiments of annealed 7075 Al alloy were performed on TA DIL805D at different temperatures (733, 693, 653, 613 and 573 K) with different strain rates (1.0, 0.1, 0.01 and 0.001 s−1.) Based on experimental data, the strain-compensated Arrhenius model (SCAM) and the back-propagation artificial neural network model (BP-ANN) were constructed for the prediction of the flow stress. The predictive power of the two models was estimated by residual analysis, correlation coefficient (R) and average absolute relative error (AARE). The results reveal that the deformation parameters including strain, strain rate, and temperature have a significant effect on the flow stress of the alloy. Compared with the SCAM model, the flow stress predicted by the BP-ANN model is in better agreement with experimental values. For the BP-ANN model, the maximum residual is only 1 MPa, while it is as high as 8 MPa for the SCAM model. The R and AARE for the SCAM model are 0.9967 and 3.26%, while their values for the BP-ANN model are 0.99998 and 0.18%, respectively. All these reflect that the BP-ANN model has more accurate prediction ability than the SCAM model, which can be applied to predict the flow stress of the alloy under high temperature deformation.

Development of an Integrated Flow Stress and Roll Force Models for Plate Rolling of Microalloyed Steel

The hot deformation behavior of Nb–V–Ti containing high‐strength steel is studied using compression test. Based on the data generated during hot compression tests, a deep neural network (DNN) flow stress model is developed for the experimental microalloyed steel. The predicted flow stress by the DNN model is compared with flow stress predicted by conventional strain‐compensated Arrhenius constitutive equation. Results using the DNN model are found to be superior to the constitutive equation with overall correlation coefficient (R) greater than 99.8%. The accuracy of the developed DNN flow stress model finds to be significantly higher even at higher strain rates. A DNN roll force model is also developed for the plate rolling of the experimental steel. The predicted flow stress from the DNN flow stress model for the given rolling condition is also used as an input to the roll force model. It is found that DNN model is able to predict the roll force accurately by >98.4% as it takes care of various nonlinear process variable which cannot be accounted mathematically. It also validates the accuracy of DNN flow stress model.

Novel flow stress prediction and work hardening behavior of aluminium alloy AA7075 at room and elevated temperatures

The strength and deformation behavior of the aluminium alloy AA7075 was crucial information for engineering and manufacturing design. Tensile tests were performed in a temperature range of 25–300 °C on the aluminium alloy AA7075-T651. Flow curves at different temperatures were shown. The work hardening behavior was analyzed using the Kocks-Mecking and Crussard-Jaoul models. Flow curves in hardening regimes were predicted using constitutive models, i.e., Hollomon, Ludwigson, Ludwik, Swift, and Voce. At high temperatures involved with softening phenomenon, Voce model combined with linear softening or Voce softening were used to predict flow stresses. A novel approach, Voce hardening and softening models combined with the piecewise nonlinear regression technique, was introduced. It was found that the plastic deformation of aluminium alloy AA7075 was dominated by only one mechanism indicated by one slope of stage III in the K-M plot. The hardening regime was found at room and elevated temperatures and could be predicted reasonably using all constitutive equations. At elevated temperatures, the novel approach predicted flow stresses with great accuracy.