Experimental Flow Curves Research Articles

Thermo-mechanical Behaviour of 23/8 Austenitic Stainless Steel

The flow behaviour as well as initiation of dynamic recrystallization in Fe-23wt%Cr-8wt%Ni (23/8 steel) austenitic steel containing 0.28 wt% nitrogen was investigated using Gleeble 3800 thermomechanical simulator. Hot working was carried out in temperature range of 950–1100°C at strain rates ranging from 0.01 to 10 s–1. Based on experimental results a constitutive equation was predicted for peak flow stress embracing the Zener-Hollomon parameter. The deformation activation energy and stress exponent were calculated as 671.66 KJ/mole and 3.762 respectively. The critical stress for initiation of dynamic recrystallization was determined by the identification of an inflection point in the strain hardening rate versus stress plot. The average normalized critical stress for the metal was found as 0.806. The power dissipation efficiency and instability maps for the 23/8 austenitic stainless steel were developed adopting modified Dynamic material model (DMM). The power dissipation efficiency calculated using DMM was compared with that of modified DMM. The validity of power law during deformation process for the above material was analysed. The processing maps in connection with microstructures and experimental flow curves were used to interpret possible safe processing conditions of the above material during hot metal working. The peak efficiency of 35.91% at 0.6 strain was observed under 1100°C and 1 s–1 whereas the optimum processing condition was found under 1100°C and 0.1 s–1 having efficiency of 23.4%. Dominating damage mechanisms causing microstructure instability in this material are identified.

Thermodynamics of dynamic transformation of hot deformed austenite in four steels of increasing carbon contents

Recent observations regarding the dynamic transformation of deformed austenite at temperatures above the Ae3 are reviewed for four different steels of increasing carbon contents. The structures observed are Widmanstätten in nature and appear to have formed displacively. The effect of deformation on the Gibbs energy of austenite in these steels is estimated by assuming that the austenite continues to work harden after initiation of the transformation and that its flow stress and dislocation density can be derived from the experimental flow curve. By further taking into account the inhomogeneity of the dislocation density, Gibbs energy contributions are derived that are sufficient to promote transformation as much as 100°C above the Ae3. The present calculations indicate that the dislocation densities in the regions that experience transformation are 2–15 times higher than the average values. It is also suggested that, at the lower carbon levels, plate growth is followed by C diffusion, while it is accompanied by C diffusion at the higher carbon contents.

Simulation and experimental analyses of dynamic strain aging of a supersaturated age hardenable aluminum alloy

In this paper, dynamic strain aging (DSA) behavior in a temperature range of (25–235°C) and strain rate range of (10−4–5×10−2s−1) was investigated using a supersaturated age hardenable aluminum alloy. It was found that two mechanisms consisted of pinning of solute atoms to mobile dislocations and dynamic precipitation, were responsible for DSA in the testing conditions. The effects of both mechanisms on the macroscopic flow curve were studied using experimental and improved physically based material modeling approaches. It was shown that both phenomena lead to a negative strain rate hardening in the alloy. Dynamic precipitation acting at high temperature results in considerable work hardening and material strengthening. Taking into account these microstructural phenomena, the effects of deformation temperature and strain rate on the macroscopic flow behavior were discussed. The proposed modeling approach could successfully predict the experimental flow curve, possible jerky flow, and the corresponding serration types. Also, the spatial nucleation and propagation of the localized deformation bands along the specimen gauge length were recorded by a digital image correlation method and compared with the proposed model predictions.

Characterisation of microstructure and modelling of flow behaviour of bainite-aided dual-phase steel

This study aims to characterise the microstructure and model the flow curve behaviour of bainite-aided DP steel. First, combined electron backscatter diffraction (EBSD) and electron probe microanalysis (EPMA) measurements were applied to quantify the constituents (ferrite, martensite, and bainite) in the microstructure. Then, the flow behaviour of the material was modelled using the microscale finite element method by considering the effect of the microstructures using the representative volume element (RVE) approach based on real microstructure. The flow behaviour of single phases (ferrite, martensite, and bainite) was modelled using the dislocation-density-based work-hardening approach, whereas the model parameters were identified using microstructural features. The flow curves predicted from the 2D RVE calculations were correlated to 3D using a correlation factor. Good agreement between the 3D correlated and experimental flow curves was only achieved when bainite was considered in the RVE modelling. The presence of bainite reduces the internal stress gradients while increasing the overall strength of the material.

The dynamic transformation of deformed austenite at temperatures above the Ae3

Recent observations regarding the dynamic transformation of deformed austenite at temperatures above the Ae3 are reviewed. Experimental results obtained on four different steels over the temperature range from 743 to 917°C and at strains up to ε=5 are described. It is shown that there is a critical strain for the formation of superequilibrium ferrite and that the volume fraction of transformed ferrite increases with the strain. The structures observed are Widmanstätten in form and appear to have nucleated displacively. The effect of deformation on the Gibbs energy of austenite is estimated by assuming that the austenite continues to work-harden after initiation of the transformation and that its flow stress and dislocation density can be derived from the experimental flow curve by making suitable assumptions about two-phase flow. By further taking into account the inhomogeneity of the dislocation density, Gibbs energy contributions (driving forces) are derived that are sufficient to promote transformation as much as 100°C above the Ae3. The C diffusion times required for the dynamic formation of the cementite particles observed are estimated. These range from ∼25 to 100μs and are therefore consistent with the times available during rolling. The Gibbs energy calculations suggest that growth of the Widmanstätten ferrite is followed by C diffusion at the lower carbon contents, while it is accompanied by C diffusion at the higher carbon levels.

Disentangling glass and jamming physics in the rheology of soft materials

The shear rheology of soft particles systems becomes complex at large density because crowding effects may induce a glass transition for Brownian particles, or a jamming transition for non-Brownian systems. Here we successfully explore the hypothesis that the shear stress contributions from glass and jamming physics are `additive'. We show that the experimental flow curves measured in a large variety of soft materials (colloidal hard spheres, microgel suspensions, emulsions, aqueous foams) as well as numerical flow curves obtained for soft repulsive particles in both thermal and athermal limits are well described by a simple model assuming that glass and jamming rheologies contribute linearly to the shear stress, provided that the relevant scales for time and stress are correctly identified in both sectors. Our analysis confirms that the dynamics of colloidal hard spheres is uniquely controlled by glass physics while aqueous foams are only sensitive to jamming effects. We show that for micron-sized emulsions both contributions are needed to successfully account for the flow curves, which reveal distinct signatures of both phenomena. Finally, for two systems of soft microgel particles we show that the flow curves are representative of the glass transition of colloidal systems, and deduce that microgel particles are not well suited to studying the jamming transition experimentally.

Quantification of the effect of transformation-induced geometrically necessary dislocations on the flow-curve modelling of dual-phase steels

The current work aims to predict the work-hardening behaviour of dual-phase (DP) steel, focusing on the effect of transformation-induced geometrically necessary dislocations (GNDs). Equiaxed and banded microstructures were produced through suitable heat treatment cycles in a laboratory. Electron backscatter diffraction measurements were performed to characterise GNDs. The flow behaviour was modelled within the microscale finite element method, considering the effect of the microstructures using the representative volume element (RVE) approach. 2-D RVEs were created based on real microstructures. The flow behaviour of single phases was modelled using the dislocation-based work-hardening approach. The volume change during the austenite-to-martensite transformation was also modelled, and the resulting prestrained areas in ferrite were considered to be the storage place of GNDs. The thickness of the GND layer around martensite islands was quantified experimentally and numerically. Subsequently, three criteria were developed to describe the strength, thickness, and amount of prestrain in the GND zone as a function of microstructural features in DP steel. Then, numerical uniaxial loading in the rolling direction was applied on the RVEs to study the effect of GNDs on the stress and strain distribution in the microstructures, flow curve, and hardening behaviour of DP steel. A computational first-order homogenisation strategy was employed to obtain the true stress–true strain curves from the RVE calculations. The flow curves of simulations that took the GNDs into account were in better agreement with the experimental flow curves, compared with those of simulations that did not consider the GNDs.

EFFECT OF SHORTENINGS ON THE RHEOLOGY OF GLUTEN‐FREE DOUGHS: STUDY OF CHESTNUT FLOUR WITH CHIA FLOUR, OLIVE AND SUNFLOWER OILS

ABSTRACTEffects of chia flour (CHF, up to 7.5%), olive oil (up to 10.0%) and sunflower oil (up to 10.0%) on mixing and rheological behavior for chestnut flour (CF) doughs were studied using Mixolab device and a controlled‐stress rheometer. Steady‐shear (0.01 to 10/s) and oscillatory (1 to 70 rad/s at 0.1% strain) tests were carried out at 30C. Apparent viscosity of doughs at each shear rate and storage modulus at each angular frequency decreased with increasing additives content. Elastic properties at CHF content higher than 4.0% remained constant with increasing additive. Experimental flow curves and mechanical spectra were successfully fitted using Williamson and power models, respectively. Gelatinization temperatures increased with CHF and remained constant with oils addition.PRACTICAL APPLICATIONSAs celiac disease is becoming more common nowadays the consumers' demand for gluten‐free products with high nutritional and taste quality is increasing. This work deals with the study of the impact of shortenings (chia flour, olive and sunflower oils) on the rheological performance of gluten‐free doughs based on chestnut flour (CF) using different experimental techniques. Tested additives are studied over a content range of industrial interest. The effect of these additives on the CF doughs is essential in order to get formulations with a suitable technological aptitude. Finally, this study tries to provide additional economic value to seasonal products as chestnut fruit by means of the industrial manufacture of new flour products.

Transformation-Induced, Geometrically Necessary, Dislocation-Based Flow Curve Modeling of Dual-Phase Steels: Effect of Grain Size

The flow behavior of dual-phase (DP) steels is modeled on the finite-element method (FEM) framework on the microscale, considering the effect of the microstructure through the representative volume element (RVE) approach. Two-dimensional RVEs were created from microstructures of experimentally obtained DP steels with various ferrite grain sizes. The flow behavior of single phases was modeled through the dislocation-based work-hardening approach. The volume change during austenite-to-martensite transformation was modeled, and the resultant prestrained areas in the ferrite were considered to be the storage place of transformation-induced, geometrically necessary dislocations (GNDs). The flow curves of DP steels with varying ferrite grain sizes, but constant martensite fractions, were obtained from the literature. The flow curves of simulations that take into account the GND are in better agreement with those of experimental flow curves compared with those of predictions without consideration of the GND. The experimental results obeyed the Hall-Petch relationship between yield stress and flow stress and the simulations predicted this as well.

Modeling the Flow Curve of Hot Deformed Austenite

A 0.02%C plain carbon and a 0.22%C TRIP steel were tested in compression in the temperature range 900°C to 1150°C and strain rate range 0.05s-1 to 1s-1. Thirty-two experimental flow curves were obtained in this way. The critical conditions for the initiation of dynamic recrystallization were determined by the double differentiation method. Using a dislocation density model to describe the austenite flow stress, the work hardening parameters r and h were derived and are used to model the flow curve in the absence of dynamic recrystallization. The latter was employed to calculate the fractional softening attributable to dynamic recrystallization. The kinetics of dynamic recrystallization are then described using Avrami kinetics. Finally, the dependences of the Avrami and work hardening parameters on Z, the Zener-Hollomon parameter, are used to model compression flow curves at strain rates an order of magnitude greater than the ones employed in the tests.

Flow Curve Modelling of an Austenitic Stainless Steel at High Temperatures Starting from the One-Parameter Model of Strain Hardening

The flow curves of an austenitic stainless steel deformed at temperatures 700-1000°C with strain rates 10-5-10-2 s-1 were modelled with the Voce equation. The parameters needed to draw the Voce equation, are the saturation stress σV that defines the height of the flow curve, the critical strain εC that defines the velocity to achieve σV, and the stress σo, namely the back-extrapolated flow stress to zero strain. A modified strain hardening analysis based on the one-parameter model was used to analyze the strain hardening rate dσ/dε vs. the flow stress σ in order to obtain σV and εC. The modified approach was based on the assumption that the dislocation multiplication component of strain hardening was temperature and strain rate dependent through the thermal activation term s of flow stress. A parameter s’ proportional to s was obtained from the strain hardening analysis and a relationship between s’ and temperature and strain rate was found. Relationships between σV, σo, εC and s’ were finally established and at this stage the Voce equation could reproduce the experimental flow curves at any imposed deformation conditions of temperature and strain rate.

Modeling the viscosity and aggregation of suspensions of highly anisotropic nanoparticles

The rheology of nanofiber suspensions is studied solving numerically the Population Balance Equations (PBE). To account for the anisotropic nature of nanofibers, a relation is proposed for their hydrodynamic volume. The suspension viscosity is calculated using the computed aggregate size distributions together with the Krieger-Dougherty constitutive equation. The model is fitted to experimental flow curves for Carbon NanoFibers (CNF) and for NanoFibrillated Cellulose (NFC), giving a first estimation of the microscopic anisotropy parameter, and yielding information on the structural properties and rheology of each system.

Flow stress behavior of commercial pure titanium sheet during warm tensile deformation

The flow stress behavior of commercial pure titanium (CP-Ti) sheet was studied by uniaxial warn tension tests at temperatures ranging from 623 K to 773 K and strain rates from 5.0 × 10 −2 to 8.3 × 10 −4 s −1. A mathematical model using an updated Fields–Backofen (FB) equation was established to describe the flow stress behavior of CP-Ti during warm tensile testing. The results show that the flow stress of CP-Ti is evidently affected by both deformation temperature and strain rate, i.e., the flow stress decreases with the decrease of strain rate and the increase of deformation temperature, and a typical characteristic of dynamic recrystallization softening. The flow stress curves analyzed by FB equation shows good agreement with experimental flow curves for different temperatures and strain rates for CP-Ti sheet.

Prediction of hot compression flow curves of Ti–6Al–4V alloy in α + β phase region

Prediction of material flow behavior is essential for designing the forming process of any material. In this research, experimental flow curves of Ti–6Al–4 V alloy were obtained using the isothermal hot compression test done at 750–950 °C with 50 °C intervals and constant strain rates of 0.001, 0.005 and 0.01 s −1. For prediction of hot deformation flow curves two methods of modeling were applied. In the first method, an entire flow curve was modeled using Sellars equation. In the second one, modeling of a flow curve up to the peak point was carried out with Cingara model, and modeling beyond that was performed with a model developed based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory. The accuracy of each model was examined through a statistical method. Results showed that flow curve modeling using Cingara model and JMAK theory leads to results that are more consistent with the experimental data.

Modeling Rheological Properties of Oil Well Cement Slurries Using Artificial Neural Networks

An artificial neural network (ANN) model was developed to predict the rheological properties of oil well cement slurries. The slurries were prepared by using Class G oil well cement with a water-cement ratio (w/c) of 0.44 and incorporating three different chemical admixtures, including a new-generation polycarboxylate-based high-range water-reducing admixture (PCH), polycarboxylate-based midrange water-reducing admixture (PCM), and lingosulphonate-based midrange water-reducing admixture (LSM). The rheological properties were investigated at different temperatures in the range of 23 to 60°C by using an advanced shear-stress/shear-strain controlled rheometer. A back-propagation neural network was designed and trained by using the experimental flow curves. The shear rate, dosage of admixture, and test temperature were considered as input parameters, and the measured shear stress was the output parameter. The trained ANN was not only capable of accurately predicting the shear flow used for its training, but c...

Modeling Uniaxial, Temperature, and Strain Rate Dependent Behavior of AZ31 Alloy by Softening Model

In the present study, a softening model proposed for warm forming behavior of Al-Mg alloys is applied to AZ31 alloy in order to determine the applicability of the model to magnesium alloys AZ31 alloy is tested at several temperatures (room temperature to 300 oC) and strain rates (0.0083-0.17 s-1). The results indicate that the model shows good agreement with experimental flow curves for different temperatures and strain rates for AZ31 alloy.

Steady shear flow of magnetic fiber suspensions: Theory and comparison with experiments

This paper is focused on the rheology of magnetic fiber suspensions in the presence of a magnetic field applied perpendicular to the flow. At low Mason numbers, Mn<0.1, the experimental flow curves show a steep initial section corresponding to the inclination and stretching of the gap-spanning aggregates formed upon magnetic field application. At higher Mason numbers, aggregates no longer stick to the walls and the flow curves reach a Bingham regime, with the dynamic yield stress growing with the magnetic field intensity. This yield stress appears to be about three times higher for the fiber suspensions than for the suspensions of spherical particles. Such difference, measured at relatively low magnetic field intensities, H0<30 kA/m, is explained in terms of the enhanced magnetic susceptibility of the aggregates composed of fibers compared to the aggregates composed of spherical particles. For weak magnetic fields, the forces of solid friction between fibers are expected to play a minor role on the stress...

Deformation induced FCC to HCP transformation in a Co–27Cr–5Mo–0.05C alloy

In this work, the role played by plastic straining on the FCC(γ) → HCP(ɛ) strain induced transformation (SIT) ɛ-martensite in a Co–Cr–Mo–0.05C alloy was investigated. It was found that alloy plastic deformation at room temperature promotes the development of ɛ-martensite giving rise to the formation of intragranular striations. Moreover, aging at 800 °C of pre-strained specimens initially promotes SIT ɛ-martensite. This is followed by a time plateau (1 h) delay after which isothermal ɛ-martensite develops. Apparently, prior plastic straining leads to increasing incubation times for the onset of the isothermal ɛ-martensite transformation. In addition, tensile specimens containing various amounts of isothermal ɛ-martensite were tested all the way to fracture and their respective stress–strain properties were experimentally determined. Comparisons between experimental and simulated flow curves using the rule of mixtures indicated some deviations in the simulations at volume fractions above 0.25 ɛ-martensite. In contrast, predictions of yield and tensile strength were in good agreement with the experimental outcome. In particular, linear trends were exhibited by both, the yield and tensile strength as a function of the volume fraction of ɛ-martensite. Finally, the alloy elongation remained nearly constant with the volume fraction of ɛ-martensite in the range of the 0.15 < HCP < 0.55. Higher or lower values lead to a rapid decrease in the exhibited elongation.

Modelling of Microstructure and Flow Stress Evolution during Hot Forging

AbstractA phenomena based description of the microstructure and flow stress evolution of metals subjected to hot working is presented. The change in dislocation density with time was determined from the dislocation generation and recovery rates. Dynamic recrystallization was assumed to initiate when the dislocation density became greater than a critical value. The flow stress was calculated as a function of the overall dislocation density of the deformed and the recrystallized grains. To validate the model a set of single hit hot compression tests were carried out on two different AFP (Ausscheidungshärtende Ferritisch‐Perlitische or precipitation hardened ferritic‐pearlitic) steels at different strain rate and temperature combinations. The agreement between the calculated and experimental flow curves is quite encouraging.

Dynamic Plastic Response of the Mg-Gd-Y Alloy over a Wide Range of Temperatures

In this paper, a new phenomenological and empirically based constitutive model was proposed to change the temperature term in the original Johnson-Cook constitutive model. The new model can be used to describe or predict the stress-strain relation of the metals deformed over a wide range of temperatures even though the current temperatures are lower than the reference temperature. Based on the impact compression data obtained by split Hopkins pressure bar (SHPB) apparatus about one hot-extrudedMg-10Gd-2Y-0.5Zr alloy, the material constants in the new model can be experimentally determined using isothermal and adiabatic stress-strain curves at different strain rates and temperatures. Good agreement is obtained between the predicted and the experimental flowcurves for the hot-extrudedMg-10Gd-2Y-0.5Zr alloy at both quasi-static and dynamic loadings under a wide range of temperatures ever though the current temperatures are lower than the reference temperature.