Flow Stress Evolution Research Articles

Hot Workability of 300M Steel Investigated by In Situ and Ex Situ Compression Tests

In this work, hot compression experiments of 300M steel were performed at 900–1150 °C and 0.01–10 s−1. The relation of flow stress and microstructure evolution was analyzed. The intriguing finding was that at a lower strain rate (0.01 s−1), the flow stress curves were single-peaked, while at a higher strain rate (10 s−1), no peak occurred. Metallographic observation results revealed the phenomenon was because dynamic recrystallization was more complete at a lower strain rate. In situ compression tests were carried out to compare with the results by ex situ compression tests. Hot working maps representing the influences of strains, strain rates, and temperatures were established. It was found that the power dissipation coefficient was not only related to the recrystallized grain size but was also related to the volume fraction of recrystallized grains. The optimal hot working parameters were suggested. This work provides comprehensive understanding of the hot workability of 300M steel in thermal compression.

A continuous dynamic recrystallization model to describe the hot deformation behaviour of a Ti5553 alloy

A physical based model is developed to describe recrystallization phenomena of titanium alloys during hot working of the β phase. Continuous dynamic recrystallization is attributed as the restoration mechanism based on the progressive transformation of low angle boundaries (subgrains) into high angle boundaries (grains). The model describes both, the microstructure, and the flow stress evolutions during hot deformation with large strains. The microstructure is conceived as been formed by three different populations of dislocations, and high as well as low angle grain boundaries. Evolution rates of all microstructural features are determined based on the effects of generation, interaction and annihilation of dislocations during deformation due to dynamic recovery, continuous dynamic recrystallization and static recovery. Continuous dynamic recrystallization is modelled and is considered to occur homogeneously within the microstructure. The model is able to predict the formation of subgrains from a fully annealed microstructure and the progressive formation of high angle grain boundaries. The subgrain and grain sizes are also obtained as output of the model. The model was applied to describe the hot compression behaviour of a Ti5553 alloy deformed between 880°C to 920°C and strain rates from 0.001 s−1 up to 10 s−1. The model is validated with flow curves and microstructural characterisation of hot deformed, and with microstructural information of non-deformed samples. The critical strain rate increases with increasing strain rate and decreasing temperature, similar to the discontinuous dynamic recrystallization phenomenon. The model can be implemented to simulate the microstructure and predict flow stresses of titanium alloys in industrial processes.

Flow Behavior and Hot Processing Map of GH4698 for Isothermal Compression Process

An in-depth understanding of the flow behaviors of materials deformed at high temperatures is of paramount significance. However, insufficient research on the nickel-based GH4698 alloy has resulted in inaccurate material flow prediction or even cracking in the practical billet opening of GH4698 large forgings. In this study, hot compressions were performed at 950–1150 °C and 0.001–3 s−1. Single-peaked strain-stress curves were obtained under various conditions, owing to dislocation motions in dynamic recrystallizations. The Arrhenius model was formulated to accurately describe the flow stress evolutions and the mean prediction error of the flow stress was 5.90%. Processing maps were constructed at various hot working conditions. It was found that the hot working ability of GH4698 markedly decreased under lower temperatures (950–1080 °C) and higher strain rates (0.1–3 s−1). Optimal thermal processing parameters were suggested. In sum, this study systematically investigated the flow behaviors and hot working ability of GH4698 in isothermal compressions.

Effects of non-isothermal annealing on microstructure and mechanical properties of severely deformed aluminum samples: Modeling and experiment

Abstract In order to investigate the evolution of microstructure and flow stress during non-isothermal annealing, aluminum samples were subjected to strain magnitudes of 1, 2 and 3 by performing 2, 4 and 6 passes of multi-directional forging. Then, the samples were non-isothermally annealed up to 150, 200, 250, 300 and 350 °C. The evolution of dislocation density and flow stress was studied via modeling of deformation and annealing stages. It was found that 2, 4 and 6 passes multi-directionally forged samples show thermal stability up to temperatures of 250, 250 and 300 °C, respectively. Modeling results and experimental data were compared and a reasonable agreement was observed. It was noticed that 2 and 4 passes multi-directionally forged samples annealed non-isothermally up to 350 °C have a lower experimental flow stress in comparison with the flow stress achieved from the model. The underlying reason is that the proposed non-isothermal annealing model is based only on the intragranular dislocation density evolution, which only takes into account recovery and recrystallization phenomena. However, at 350 °C grain growth takes place in addition to recovery and recrystallization, which is the source of discrepancy between the modeling and experimental flow stress.

On the Study of Cyclic Crystal Plasticity Ratchetting Constitutive Model for Polycrystalline Pure Copper

With the hypothesis of a small deformation, the novel cyclic visco-plasticity constitutive model (CV-CM) is constructed to study the cyclic deformation responses of polycrystalline metals. In this model, a modified Armstrong–Frederick nonlinear kinematic hardening (NKH) law is adopted to simulate the ratchetting deformation more precisely. The cyclic hardening characteristic of FCC polycrystalline copper is investigated with the use of flow stress evolution of slip system. For the issue of the transition from single crystal to polycrystalline crystals, the explicit [Formula: see text] rule is introduced to compute the polycrystalline response. Finally, through comparison with the experimental data, the proposed model is verified. It is demonstrated that the uniaxial ratchetting response of FCC metal can be precisely captured. The ratchetting response of copper single crystal and its relation with the crystallographic directions can be exactly traced by the present model as well.

Flow Stress Evolution in Further Straining of Severely Deformed Al

To investigate the flow stress evolution in further straining of severely deformed Al sheets, a comprehensive model which considers both mechanical and metallurgical alterations is needed. In this study, constrained groove pressing (CGP) as a severe plastic deformation method, and a flat rolling process for further straining are utilized. Using basic mechanical models, strain and strain rate were calculated for this process. Dislocation density and flow stress evolutions were predicted by utilizing initial mechanical data, considering the ETMB (Y. Estrin, L. S. Toth, A. Molinari, and Y. Brechet) dislocation density model. Based on these model predictions, the combination of the CGP process with a further rolling process results in higher flow stresses than repeating the specific process discretely. This phenomenon can be attributed to the ability of the rolling process to produce a greater strain rate, which, in turn, leads to the higher flow stresses. Thorough data from the mechanical tests as well as X-ray diffraction profiles strongly support the validity of the model in the prediction of flow stress and dislocation density, respectively.

A phenomenological hardening model for an aluminium-lithium alloy

A phenomenological hardening model based on the extended Voce law is proposed to capture the plastic flow of a third generation aluminium-lithium alloy. The model includes a simple precipitation law, which accounts for pre-ageing plastic deformation, and a hardening law that accounts for hardening of the matrix, and for the interaction of matrix glide dislocations with anisotropic and isotropic precipitates. Flow stress evolution in solution treated, underaged, and peak-aged samples is measured through uniaxial tensile tests on specimens cut at 0∘, 45∘, and 90∘ to the rolling direction. The measured flow stress evolution in all the tempers is captured well by the model. Model parameters offer insights into the sub-structural evolution that accompanies plastic deformation.

Crystal Plasticity modeling of dynamic recrystallization in CP Ti

The present work is an attempt at modeling the phenomenon of dynamic recrystallization (DRX) in commercial purity α-titanium. DRX is associated with increase in number of grains along with loss of strength. Thus it is critical to understand its occurrence while structural metal components and parts are processed. A dislocation density hardening based approach accounts for the occurrence of DRX subject to achieving a critical value of dislocation density for each grain. A model describing nucleation and probability of DRX is integrated into a polycrystal plasticity framework. Only slip deformation modes are considered. In the present work, multiple parametric studies have been carried out. The formation of new DRX grains with deformation has been highlighted. Due to applying a probabilistic criterion for addition of new DRX grains, this number is less than the number of grains having dislocation density more than critical value that is required for occurrence of DRX. The average dislocation density over all grains has been shown to decrease with deformation due to nucleation of new grains. A modified algorithm for modeling dynamic recrystallization has henceforth been demonstrated for CP Ti via evolution of flow stress, dislocation density and grain weights of ‘old’ and ‘new’ grains with deformation.

A discontinuous dynamic recrystallization model incorporating characteristics of initial microstructure

Abstract In order to describe and predict the kinetic process of discontinuous dynamic recrystallization (DDRX) during hot working for metals with low to medium stacking fault energies quantitatively, a new physically-based model was proposed by considering the characteristics of grain size distribution, capillary effect of initial grain boundaries (GBs) and continuous consumption of GBs. Using Incoloy 028 alloy as a model system, experiments aiming to provide kinetic data (e.g., the size and volume fraction of recrystallized grain) and the associated microstructure were performed. Good agreement is obtained between model predictions and experimental results, regarding flow stress, recrystallized fraction and grain size evolution. On this basis, a thermo-kinetic relationship upon the growth of recrystallized grain was elucidated, i.e., with increasing thermodynamic driving force, the activation energy barrier decreases.

Constitutive modeling and inverse analysis of the flow stress evolution during high temperature compression of a new ZE20 magnesium alloy for extrusion applications

The high temperature deformation behavior of a new magnesium alloy, ZE20 (Mg-2.4%Zn-0.2%Ce), using uniaxial isothermal compression testing, is investigated within the paper. A set of experiments was conducted at temperatures of 350–425 °C, and strain rates in the range of 0.01 s−1 to 10 s−1, and samples were compressed by 70% of their original length. An inverse analysis approach was used to evaluate flow stress curves based on load displacement measurements for each deformation condition. Flow stress evolution for the new alloy under these test conditions showed higher flow stress and lower work softening than commercially available magnesium casting alloys. Finally, constitutive equations predicting flow stress as a function of strain, strain rate, and temperature were applied to modeling mechanical response of the new alloy. Predictions from three constitutive models of steady state stress were validated against uniaxial compression data. It was found that all three models evaluated reliably predict the high strain stress values to within 15% of measured values.

Cellular Automaton Modeling of Dynamic Recrystallization of Nimonic 80A Superalloy Based on Inhomogeneous Distribution of Dislocations Inside Grains

A modified cellular automaton (CA) model in the time and space scale is developed to simulate the dynamic recrystallization (DRX) mechanism of Nimonic 80A nickel-base superalloy during hot deformation. Some necessary thermo-mechanical parameters used as input data in CA approach such as work hardening and softening coefficient are fitted according to the previous hot compression experiments. Based on the experimental results, nucleation kinetics is modified as a function of Zener-Holloman parameter. A dislocation density model at transient recrystallization boundary is proposed, in which the dislocation density is a function of temperature, strain rate and annealed dislocation density. The simulated results are in good agreement with experimental results, proving that the modified CA model is capable of predicting both flow behavior and microstructural evolution of Nimonic 80A during hot deformation. According to the experimental and simulated results, the DRX behavior is discussed in detail. It demonstrates that the flow stress and microstructural evolution of DRX have a relationship with the deformation temperature and strain rate.

Uniaxial compression behaviour of porous copper: Experiments and modelling

Uniaxial compression behavior of porous copper samples having a wide range of initial porosity prepared by Spark Plasma Sintering (SPS) process is presented. Simple analytical model is developed for evolution of porosity and flow stress during uniaxial compression based on the Gurson model which was initially developed for low porosity solids (<10%) having simple pore geometry. A unique linear relationship was observed for normalized porosity (porosity/initial porosity) with strain and normalized flow stress (flow stress/flow stress of matrix). The model predictions are in good agreement with the experimental results over a wide range of porosity (2–25%) and strain (0–0.26). Furthermore, a new model for strain hardening rate is developed which explains the significant strain hardening observed in the uniaxial compression tests. The observed strain hardening rate of the porous samples depends not only on the strain hardening rate of the matrix material but also on the extent of pore closure during compression. While the relative contribution of the strain hardening rate of the matrix largely dominates the observed response, the contribution due to pore closure is significant for samples with high initial porosity, especially at higher values of strain.

Effect of Deformation Temperature, Strain Rate and Strain on the Strain Hardening Exponent of Copper/Aluminum Laminated Composites

In order to investigate the strain hardening behaviour of Cu/Al laminated composites, isothermal compression tests were conducted in the temperature range of 300–450 °C and stain rate range of 0.01–1 s−1. Based on the experimental data, stain hardening exponent n was calculated to evaluate the strain hardening ability of Cu/Al laminated composites during the deformation process. The results show that deformation temperature, strain rate, strain and laminated structure are all responsible for the evolution of flow stress during the isothermal compression. The highly non-linear character of Ln σ - Ln ε curves shows the dynamic competition between work hardening and dynamic softening, and dynamic softening gradually plays a dominant role with the increase of strain. Furthermore, strain hardening exponent n is more sensitive to deformation temperature than strain rate. Lower deformation temperature and higher strain rate contribute to the enhancement of strain hardening exponent n.

Effect of multipass deformation at elevated temperatures on the flow behavior and microstructural evolution in Ti-6Al-4V

Simulated multipass deformation experiments were carried out via torsion testing on a Ti-6Al-4V alloy in the two-phase region under both isothermal and continuous cooling conditions. Flow softening was observed during the isothermal multipass deformation tests as indicated by the evolution of the mean flow stress (MFS). The MFS values increased with interpass time from 2 s to 32 s. Using BSE-SEM characterization techniques, dynamic phase transformation (alpha to beta) and coarsening of the alpha phase took place. The quantitative results indicate that the alpha phase transforms into beta during straining, but it retransforms statically into alpha by amounts that increase with interpass time. The flow softening observed is the net result of softening by dynamic transformation and hardening by reverse transformation.

A novel unified model predicting flow stress and grain size evolutions during hot working of non-uniform as-cast 42CrMo billets

The cast preformed forming process (CPFP) is increasingly considered and applied in the metal forming industries due to its short process, low cost, and environmental friendliness, especially in the aerospace field. However, how to establish a unified model of a non-uniform as-cast billet depicting the flow stress and microstructure evolution behaviors during hot working is the key to microstructure prediction and parameter optimization of the CPFP. In this work, hot compression tests are performed using a non-uniform as-cast 42CrMo billet at 1123–1423 K and 0.01–1 s−1. The effect laws of the non-uniform state of the as-cast billet with different initial grain sizes on the flow stress and microstructure are revealed deeply. Based on experimental results, a unified model of flow stress and grain size evolutions is developed by the internal variable modeling method. Verified results show that the model can well describe the responses of the flow stress and microstructure to deformation conditions and initial grain sizes. To further evaluate its reliability, the unified model is applied to FE simulation of the cast preformed ring rolling process. The predictions of the rolling force and grain size indicate that it could well describe the flow stress and microstructure evolutions during the process.

Hot deformation behavior and constitutive model of GH4169 superalloy for linear friction welding process

In order to realize a better description about the plastic flow behavior in linear friction welding process of GH4169 superalloy, especially at the friction interface where rather elevated temperature and severe deformation happened, it is necessary to adopt an accurate constitutive model of GH4169 superalloy suitable for the high temperature range. The isothermal hot compression tests of GH4169 superalloy at different deformation temperatures and strain rates were designed and conducted using Gleeble-3500 thermo-simulation machine. Based on the measured flow stress-strain data, three constitutive equations were derived on the basis of the modified Field-Backofen (F-B) model, Johnson-Cook (J-C) model and strain compensated Arrhenius model, respectively. The experimental results show that the plastic flow stresses of GH4169 superalloy are significantly affected by the strain rate and temperature. The comparisons of plastic flow stress between the experimental and the calculated results based on three constitutive models show that there are great errors in the calculation on the plastic flow stress at high strain rates by using the modified F-B model and the J-C model, while the strain compensated Arrhenius model can describe exactly the plastic flow stress evolution because the coupled influences of temperature, strain and strain rate are considered. Furthermore, linear friction welding (LFW) experiment and corresponding finite element simulation based on the established constitutive equations were carried out. The comparisons of flash shape and its dimension between the simulated and experimental results indicate that the strain compensated Arrhenius model is more suitable for the LFW numerical simulation of GH4169 superalloy.

Dislocation density based model for Al-Cu-Mg alloy during quenching with considering the quench-induced precipitates

The accurate prediction of residual stress for as-quenched Al-Cu-Mg alloy requires profound knowledge on the materials' constitutive behavior. In present work, the flow stress of as-quenched Al-Cu-Mg alloy is modelled using a dislocation density based model which considers the influences of precipitation, solid solution and forest dislocation. The radii and volume fractions of precipitates at different cooling rates and temperatures are predicted by a multi-class precipitation kinetics model. Parameters of the constitutive model are obtained by calibration using isothermal tensile tests. The model predictions are in good agreement with experimental data in terms of the flow stress and volume fraction evolution. The results show that volume fraction of precipitates decreases with the increasing temperature and cooling rate, in contrast to the increasing trend for radius of precipitates. The quench-induced precipitates have an influence only on the magnitudes of flow stress at low temperatures. However, for the large precipitates, the dislocation loops, i.e. geometrically necessary dislocations (GND's), can influence both the strain hardening rates and magnitudes of flow stress.

Consistency of dynamic recrystallization models from the perspective of physical metallurgy and continuum mechanics

AbstractDynamic recrystallization (DRX) is characterized by the nucleation and growth of new grains, which takes place concurrently to plastic deformation. DRX processes are used in industrial hot forming operations to control the microstructure and properties of the workpiece. Various models have been developed that consider the coupled evolution of microstructure and flow stress during hot deformation processes, some from a perspective of physical metallurgy, some from continuum mechanics. It is widely accepted that the onset of DRX is characterized by an inflection point of the strain hardening rate as a function of stress. This criterion was derived by Poliak and Jonas using results from the thermodynamics of irreversible processes. The present paper analyses the conditions that need to be met by DRX models to be consistent with the criterion by Poliak and Jonas. It is shown that for models which use classical Avrami kinetics to describe the evolution of the recrystallized volume fraction, the Avrami exponent should exceed a value of 3 to ensure that the Poliak‐Jonas criterion is not violated. Based on this observation, a framework for consistent DRX kinetics is presented and discussed. (© 2017 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Microstructure and flow stress evolution during hot deformation of 304L austenitic stainless steel in variable thermomechanical conditions

Most of industrial hot deformation processes are performed in variable conditions where the strain rate and/or deformation temperature are not constant. In this work, hot compression tests in both constant and varying strain rate conditions were performed on 304L austenitic stainless steel using a Gleeble 3800 machine. The variations in microstructure and flow stress during and after the transient deformation stage are carefully analysed. It is clearly shown that, following the abrupt increase of strain rate, both the flow stress and substructural changes are subjected to a transient period over strains of ~0.2, before reaching states similar to those developed through constant strain rate conditions at the new strain rate. When the strain rate was rapidly decreased, the flow stress transient stage extended over a lower strain interval than the substructure transient period. It is shown that local misorientation distributions are good indicators of the deformation microstructure of low SFE materials as they capture small variations in deformation structures which cannot be analysed from stress-strain curves alone.

Development of a Model for Dynamic Recrystallization Consistent with the Second Derivative Criterion.

Dynamic recrystallization (DRX) processes are widely used in industrial hot working operations, not only to keep the forming forces low but also to control the microstructure and final properties of the workpiece. According to the second derivative criterion (SDC) by Poliak and Jonas, the onset of DRX can be detected from an inflection point in the strain-hardening rate as a function of flow stress. Various models are available that can predict the evolution of flow stress from incipient plastic flow up to steady-state deformation in the presence of DRX. Some of these models have been implemented into finite element codes and are widely used for the design of metal forming processes, but their consistency with the SDC has not been investigated. This work identifies three sources of inconsistencies that models for DRX may exhibit. For a consistent modeling of the DRX kinetics, a new strain-hardening model for the hardening stages III to IV is proposed and combined with consistent recrystallization kinetics. The model is devised in the Kocks-Mecking space based on characteristic transition in the strain-hardening rate. A linear variation of the transition and inflection points is observed for alloy 800H at all tested temperatures and strain rates. The comparison of experimental and model results shows that the model is able to follow the course of the strain-hardening rate very precisely, such that highly accurate flow stress predictions are obtained.