Experimental Flow Curves Research Articles

Elevated Temperature Deformation Behavior of Novel NiTiAg Shape Memory Alloys: A Comparison Between Various Constitutive Models and Experimental Flow Curves

Elevated Temperature Deformation Behavior of Novel NiTiAg Shape Memory Alloys: A Comparison Between Various Constitutive Models and Experimental Flow Curves

Effect of dynamic strain ageing on flow stress and critical strain for jerky flow in Al-Mg alloys

A comprehensive approach addressing the flow behavior and the critical strain for the initiation of serrations in Al-Mg alloys is developed in the present work. The basic premise of the approach is that the solute atmosphere influences the friction as well as the strain hardening component of the flow stress. The friction effect of the solute cloud is modeled by considering the interplay between the characteristic solute migration time and the dislocation waiting time according to the cross-core diffusion mechanism. The impact on strain hardening is modeled by considering the apparent strengthening of the forest dislocations because of formation of solute aggregates near the vicinity of dislocation junctions. The apparent forest strengthening effect scales as the square root of the ratio of solute concentration in vicinity of the dislocation junctions and the bulk solute concentration. The modified constitutive model is validated against experimental flow curves obtained for strain rates varying over several orders of magnitude. It was observed that the modified constitutive model outperforms the standard constitutive model (considers only the friction effect of solute atmosphere) in predicting the flow curves in the dynamic strain aging domain. Furthermore, the modified constitutive model also accurately predicts the critical strain for the initiation of the jerky flow in both the normal and inverse regimes of the critical strain versus strain rate curve. Additional validation of the modified constitutive model is provided by dislocation character and density measurements via X-ray diffractograms, dislocation structure investigation via transmission electron microscopy along with fracture surface analysis.

Modeling the Evolution of the Dislocation Density and Yield Stress of Al over a Wide Range of Temperatures and Strain Rates

This paper introduces an extended model for the evolution of internal and wall dislocation densities in pure aluminum during plastic deformation. The approach takes the three internal state variables (3IVM) model as a starting point and advances it by taking into account the dynamic annihilation of immobile/locked dislocations as well as dislocations stored in the subgrain/cell walls. The strength of the material, as one of the properties affected by dislocation density, is used to validate the model. Experimental flow curves for pure Al are taken as the basis for calibration. Compression tests are performed at temperatures from − 196 °C to 500 °C with strain rates of 1, 0.1, and 0.01 s−1. The effect of temperature and strain rate on each state parameter is illustrated and discussed.

Integrated CFD-FEM approach for external gear pump vibroacoustic field prediction

In this work, a three-dimensional fluid-structural and vibro-acoustics coupled model of a gear pump is presented. Gear pumps represent the majority of the positive displacement machines used for flow generation in fluid power systems. Typically, the dynamics of gear pumps are dependent on the characteristics of the fluid dynamics inside the pump, which translates into vibrations to the housing. These vibrations then propagate to the surrounding medium and emit sound. The purpose of this study is to propose a three-dimensional fully integrated computational model to simulate the complete gear pump behaviour from the fluid dynamics to the structural vibrations, up to the vibroacoustic response. In this hybrid configuration, a transient CFD (Computational Fluid Dynamics) model is first developed to simulate the 3D flow field with a deforming and re-meshing approach to take into account the variation of the volume between the gears. Second, the internal pressure field calculated at each time step is then used as a loading into a structural FEM (Finite Element Method) model of the gear pump to compute the actual stresses and deformations of the housing. Third, the results of the structural response are used as excitation in a vibroacoustic sub-model to simulate the radiated noise using a high-order FEM technique. The comparison between the numerical and experimental flow curves validates the CFD model. The sound power calculations from the vibroacoustic model show good comparison with the sound intensity measurements around the pump casing, confirming the validity of the proposed coupled model. The described CFD-FEM approach proves to be a powerful gear pump design tool: it provides a reliable estimate of gear pump working parameters such as fluid power and vibroacoustic characteristics, starting from the CAD (Computer-Aided Design) geometry of the components. Furthermore, being one of the first multi-domain simulation models of a gear pump, this work can be useful to researchers as a starting point to correlate the noise emitted with the internal flow in full 3D conditions.

Air‐Entraining Effect on Rheological Properties of Cement‐Based Mixtures

The rheological properties and stability of cement‐based materials determine the technological properties of concrete mixtures and significantly influence concrete properties. Polycarboxylate ether (PCE) and other plasticizing admixtures are widely used in construction practice to plasticize concrete mixtures. Experimental research on the rheological characteristics of cement mortar modified with PCE and air‐entraining admixtures (AIRs) was carried out with a rotation rheometer with coaxial cylinders and water bleeding tests. Herschel–Buckley or modified Bingham models were used to approximate experimental flow curves and assess rheological parameters such as yield stress, plastic viscosity, and shear thinning/thickening index. The rheological test was carried out at 5 and 90 min after mixing the cement mortar. The rheological test established that the modification of cement mortar by PCE in a dosage of 0.2% (in dry material) leads to a decrease in plastic viscosity of 25.0% with a reduction in water demand of 18% for the same workability. Modification of cement mortar by AIR in 0.3% dosage leads to a decrease in yield stress by 37.7% and a decrease in plastic viscosity by 35.4% compared to the control specimen without PCE. The combined modification by PCE and AIR admixtures shows a synergistic effect. It leads to a significant decrease in yield stress of cement mortar by 92.2% and a decrease in plastic viscosity to about 0 Pa·s. In addition, there is a significant coefficient of water bleeding reduction up to 0%, when additional water reduction was carried out in the mixture while maintaining the same workability. The cement mortar, with or without PCE and AIR, exhibited shear‐thinning characteristics for up to 90 min after mixing. The solid, liquid, and gas (air) phases’ influence yield stress and plastic viscosity in the analysis mixtures are presented in this paper. It has been established that a modified exponential Mooney dependency can be used to predict the yield stress and plastic viscosity of the modified cement mortar (both plasticized and air‐entrained).

Microstructure Based Flow Stress Modelling of Superalloy 718

In order to get the insights about microstructural changes that occurs under the thermo-mechanical processing conditions, the physics based modelling approach is very useful. Therefore, the flow curves of alloy 718 are theoretical simulated using a dislocation density dependent constitutive model for different conditions. Presented model considers the microstructural ingredients that are immobile dislocation density, effective grain size and dislocation cell size as the variables to address the creep. The simulated flow curves show a good agreement with the experimental flow curves. The magnitude of immobile dislocation density and dislocation cell size in between 3.87× 1014 - 3.87× 1014­ m-2 and 8.29-8.45 μm, respectively, at the completion of the simulation. Furthermore, this approach also provides the possibility to quantify and depict the variation in each strengthening contributions.

Data correction and verification of thermal simulation experiments under the influence of bulging belly

During the thermal simulation compression test, the formation of an obvious bulge in the specimen leads to a certain deviation between the calculated and actual values of the true stress. The finite element method was used to simulate the single-pass compression of specimens of 34CrNi3MoV steel and obtain the actual nonuniform deformation of the bulging belly during the compression process, and the results were applied to correct experimental flow curves. The results showed that the deformation conditions had a significant influence on the nonuniformity of the specimen deformation during the compression process, and all the modified flow curves were lower than the original ones. The size of the bulge and the metal flow line in the finite element simulation were consistent with the test results. The load value obtained by using the modified flow curve was similar to the load value measured in the test, which indicated that the modified flow curve was very close to the real flow force curve of the material. The method used to modify the flow force curve is simple and practical.

Characterization of Hot Deformation behavior for Ultra-High Strength (UHS) Steel containing Tungsten

The steel alloy of the current study contains 0.3% carbon with different amounts of Cr, and Mo, in addition to W. Single simulation hits were designed as isothermal passes for compressive hot deformation up to 0.5 true strain. Each simulation compressive pass was carried out at temperatures, 1050, 950, 850 and 750 oC, with strain rates 0.1 and 1.0 sec-1. A numerical computational model is used for formulation of the alloy hot flow behavior at the specified conditions. The model considers inseparable strain hardening mechanism and dynamic softening phenomenon. It is noticed that high deformation temperature lowers the flow stress value (σf), while the increase of the strain rate raises it. The flow curves reveal initial high strain hardening phenomena in combination with low dynamic softening features. With the increase of strain, the dynamic softening, becomes dominant, and the flow stress gradually drops until a relatively stable stress level. Predicted flow curves were then constructed and compared with their counterpart experimental flow curves. The predicted flow curves are typically matching the counterpart experimental ones.

A Simple Procedure for the Post-Necking Stress-Strain Curves of Anisotropic Sheet Metals

Modelling the anisotropic plasticity of a metal requires the derivation of various experimental flow curves from specimens machined along different orientations and, depending on the anisotropy model, tested under different loading modes (tension, compression, torsion). The derivation of stress–strain curves from tensile experiments is a common practice within the uniform straining range but still presents some uncertainties after necking onset. Modern sheet metals, for structural applications where significant energy absorption is required, may exhibit early necking and prolonged post-necking ductility; when such alloys also exhibit pronounced anisotropy, the derivation of their flow curves may be challenging, whatever the loading mode or the specimen direction. This work examines the experimental procedures for determining the true-stress–true-strain curve and the anisotropic strain ratio, extended over the post-necking range and up to failure, from representative tensile tests along the rolling direction of PHS-1800 steel and aluminum 6181 alloy. The validity ranges of different standard procedures for stress–strain derivation are investigated to understand when and how fast the typical true-stress–true-strain data start to depart from the effective material response. Other considerations, based on simple experimental and post-processing procedures, aim at a procedure delivering useful information about the material response over the post-necking range and up to failure. The procedure to retrieve post-necking true curves and anisotropy ratios is then applied to tensile tests at static, intermediate, and high strain rates on the two sheet metals of interest.

Interpolation and Extrapolation Performance Measurement of Analytical and ANN-Based Flow Laws for Hot Deformation Behavior of Medium Carbon Steel

In the present work, a critical analysis of the most-commonly used analytical models and recently introduced ANN-based models was performed to evaluate their predictive accuracy within and outside the experimental interval used to generate them. The high-temperature deformation behavior of a medium carbon steel was studied over a wide range of strains, strain rates, and temperatures using hot compression tests on a Gleeble-3800. The experimental flow curves were modeled using the Johnson–Cook, Modified-Zerilli–Armstrong, Hansel–Spittel, Arrhenius, and PTM models, as well as an ANN model. The mean absolute relative error and root-mean-squared error values were used to quantify the predictive accuracy of the models analyzed. The results indicated that the Johnson–Cook and Modified-Zerilli–Armstrong models had a significant error, while the Hansel–Spittel, PTM, and Arrhenius models were able to predict the behavior of this alloy. The ANN model showed excellent agreement between the predicted and experimental flow curves, with an error of less than 0.62%. To validate the performance, the ability to interpolate and extrapolate the experimental data was also tested. The Hansel–Spittel, PTM, and Arrhenius models showed good interpolation and extrapolation capabilities. However, the ANN model was the most-powerful of all the models.

Effect of varying shear rates at different resting times on the rheology of 3D printable concrete

3D printing offers a paradigm shift in the construction industry. The material undergoes different stages like mixing, pumping, extruding, and printing with disparate shearing patterns and the effect of shear rates must be brought into consideration. The rheological properties of 3D printable concrete with varying shear rates at different resting times were studied. The designed mix has an ultra-high compressive strength of 110 MPa. Different hystresis curves with shear rates of 0–25 s−1 (P1) and 0–50 s−1 (P2) are studied. The tests were conducted at 10 min intervals up to 30 min resting time. The experimental down flow curves are further analyzed using the Bingham model, the modified Bingham model, and the Herschel-Bulkley model. It is observed that the rheological properties of 3D printable concrete are highly dependent on the resting time, and the applied shear rates and demand judicious selection of rheological models to predict yield stress and plastic viscosity. The comparison between experimental and analytical models indicates better predictability with the modified Bingham and Herschel- Bulkley model. The yield stress values for the modified Bingham model were found to be varying from 95 Pa to 178 Pa and Herschel-Bulkley model from 130 Pa to 177 Pa for P1 and P2, respectively.

ANALYSIS OF THE PROPERTIES OF A NONLINEAR SHEAR FLOW MODEL OF THIXOTROPIC MEDIA TAKING INTO ACCOUNT THE MUTUAL INFLUENCE OF STRUCTURAL EVOLUTION AND DEFORMATION PROCESS

A systematic analytical study was conducted on the mathematical properties of the previously proposed prototype of a nonlinear Maxwell-type constitutive equation for describing the shear flow of thixotropic media (viscous liquid polymers, viscoelastic melts, concentrated solutions, pastes, emulsions), which takes into account the mutual influence of the deformation process and structural evolution (the kinetics of formation and breaking of intermolecular bonds) on viscosity and shear modulus and the effect of the deformation process on this kinetics. In the uniaxial case, the constitutive equation is governed by a nondecreasing material function and six positive parameters. The equation is reduced to a system of two nonlinear autonomous differential equations for the stress and the structuredness parameter. It is proved that the equilibrium position of this system is unique. The dependences of the position coordinates on all material parameters and on the shear rate for an arbitrary nondecreasing material function are investigated in general form, and all the dependences are proved to be monotonic. Equations for the flow and viscosity curves are derived and investigated. It is proved that the model leads to an increasing dependence of the equilibrium stress on the shear rate and to a decreasing apparent viscosity curve, which reflect the typical properties of the experimental flow curves of pseudoplastic media. Using six arbitrary material parameters and a material function that control the model, we analytically study the phase portrait of the nonlinear system of two differential equations, to which the model is reduced, for dimensionless stress and the degree of structuredness in the vicinity of its only equilibrium position. It is proved that the equilibrium position is always stable and can be of three kinds only: a stable node, a degenerate node, or a stable focus. Criteria for each kind are found in the form of explicit constraints on the material function, model parameters, and shear rate. The existence of a stable focus indicates the nonmonotonicity of the system solutions and the existence of deformation modes with (damped) fluctuations of stress and structuredness when stationary values are reached. The influence of the material parameters and material function on the type of equilibrium point and on the behavior of the model integral curves is analyzed.

Understanding the rheology of kaolinite clay suspensions using Bayesian inference

Mud is a suspension of fine-grained particles (sand, silt, and clay) in water. The interaction of clay minerals in mud gives rise to complex rheological behaviors, such as yield stress, thixotropy, and viscoelasticity. Here, we experimentally examine the flow behaviors of kaolinite clay suspensions, a model mud, using steady shear rheometry. The flow curves exhibit both yield stress and rheological hysteresis behaviors for various kaolinite volume fractions (ϕk). Further understanding of these behaviors requires fitting to existing constitutive models, which is challenging due to numerous fitting parameters. To this end, we employ a Bayesian inference method, Markov chain Monte Carlo, to fit the experimental flow curves to a microstructural viscoelastic model. The method allows us to estimate the rheological properties of the clay suspensions, such as viscosity, yield stress, and relaxation time scales. The comparison of the inherent relaxation time scales suggests that kaolinite clay suspensions are strongly viscoelastic and weakly thixotropic at relatively low ϕk, while being almost inelastic and purely thixotropic at high ϕk. Overall, our results provide a framework for predictive model fitting to elucidate the rheological behaviors of natural materials and other structured fluids.

Analysis and Modeling of Stress-Strain Curves in Microalloyed Steels Based on a Dislocation Density Evolution Model.

Microalloyed steels offer a good combination of desirable mechanical properties by fine-tuning grain growth and recrystallization dynamics while keeping the carbon content low for good weldability. In this work, the dislocation density evolution during hot rolling was correlated by materials modeling with flow curves. Single-hit compression tests at different temperatures and strain rates were performed with varying isothermal holding times prior to deformation to achieve different precipitation stages. On the basis of these experimental results, the dislocation density evolution was evaluated using a recently developed semi-empirical state-parameter model implemented in the software MatCalc. The yield stress at the beginning of the deformation σ0, the initial strain hardening rate θ0, and the saturation stress σ∞—as derived from the experimental flow curves and corresponding Kocks plots—were used for the calibration of the model. The applicability for industrial processing of many microalloyed steels was assured by calibration of the model parameters as a function of temperature and strain rate. As a result, it turned out that a single set of empirical equations was sufficient to model all investigated microalloyed steels since the plastic stresses at high temperatures did not depend on the precipitation state.

A study on magnetorheological and sedimentation properties of soft magnetic Fe58Ni42 particles

In this study, the samples with two volume fractions (ϕ) of Fe58Ni42 (permalloy) i.e. (ϕ1 = 25 and ϕ2 = 30 %) were used as magnetic particles, silicone oil as a carrier fluid, and aluminium disterate as an additive. As received Fe58Ni42 particles surface morphology and composition of the Fe58Ni42 were investigated using field emission scanning electron microscopy (FESEM) coupled with energy dispersive spectroscopy (EDS), respectively. The X-ray Diffraction (XRD) structural information analysis confirmed Fe58Ni42 particles have a face-centered cubic phase, corresponding with the result of the high resolution transmission electron microscopy (HRTEM) characterization technique. The magnetorheological properties were tested via rotational rheometer at four different magnetic field strengths. The results show that sample PMRF-30 has a maximum shear stress, shear viscosity, and dynamic modulus greater than the PMRF-25 sample. In addition, experimental shear stress flow curves are well fitted with Herschel-Bulkley rather than Bingham and Casson rheological models. The permalloy based magnetorheological fluid (PMRF) samples were prepared with a 25 % volume fraction and a 30 % volume fraction of permalloy particles with a sample abbreviation of PMRF-25 and PMRF-30, respectively. Furthermore, the sedimentation stability of suspensions of both the samples was observed using visual inspection. This method result shows the sedimentation ratio with respect to time of 72 h was 31 % and 29 %, respectively.

Thermo-mechanical approach to study the residual stress evolution in part-scale component during laser additive manufacturing of alloy 718

Laser Additive Manufacturing (LAM) is a promising technology for manufacturing gas turbine components with enhanced design capability and a significant reduction in part weight. Additive manufacturing of alloy 718 using Laser Powder Bed fusion (L-PBF) process poses certain challenges pertaining to complex residual stress, micro-segregation of Nb, and undesired Laves phase formation in the as-printed state. The built-up residual stress and undesired brittle phase may lead to cracks and build failures. This article studied residual stress evolution during L-PBF of alloy 718 using Finite Element (FE) thermo-mechanical simulation implemented in Simufact Additive® software. The model adopted the bundling of physical powder in voxel mesh to minimize the computational time and mimic the actual process scenario during part-scale simulation. Experimental flow curves generated from Gleeble 3800® tests at elevated temperatures were utilized to calibrate material property for better accuracy in the FE simulation. The calibrated model was used to study the residual stress evolution during support structure removal. Verification and validation of simulated results were performed using X-ray diffraction (XRD) measurements. The simulated value agrees well with the experimental value with a maximum deviation of 7%. Finally, the experimentally validated model was used to correlate the effect of layer thickness variation on residual stress evolution.

Shallow and deep learning of an artificial neural network model describing a hot flow stress Evolution: A comparative study

In recent years, the utilization of artificial neural networks (ANNs) as regression models to solve the issue of hot flow stress forecasting has become a standard approach. In a connection with this kind of regression issue, employed ANNs are usually learned via a shallow learning technique while only limited attention has been paid to a deep learning method. In the frame of the submitted research, the shallow learning approach is thoroughly compared to the deep learning techniques which are based on the use of a Restricted Boltzmann Machine (RBM) and an Auto-Encoder (AE). To do so, these learning techniques are applied on a feed-forward multi-layer ANN describing the experimental hot flow curve dataset of micro-alloyed medium carbon steel. In comparison with the shallow learning method, both deep learning approaches provided higher accuracy in the network response – especially in the case of a higher number of hidden layers. The results have also shown that neither the RBM-based deep learning method nor the AE-based method had a significant effect on the duration of the necessary calculations. However, it turned out that the RBM-based method can, under certain conditions, lead to a more reliable network performance.

Characterization of Ti-6Al-4V alloy in the temperature range of warm metal forming and fracture analysis of the warm capping process

The flow behavior of a Ti–6Al–4V alloy during warm forming was characterized, and the results were analyzed to reveal the causes of fracture during warm forging of a small Ti–6Al–4V alloy bolt. The experimental flow curves obtained by compression test of cylindrical specimens at the warm forming conditions were fitted by a general extended C–m model after post-processed by a high-accuracy temperature correction scheme. Finite element analyses of the compression tests were conducted at various sample temperatures and strain rates using the flow model, revealing that the predicted compression loads were consistent with the experimental results. Flow behavior was also analyzed to reveal the metallurgical and macroscopic instabilities of the Ti–6Al–4V alloy. The flow behavior, macroscopic instability indices, and predicted forming load-stroke curves of Ti–6Al–4V alloy and SCr420H alloy steel were compared. The results study revealed that fracturing of the material in the capping stage during the automatic multi-stage warm forging of the small Ti–6Al–4V alloy bolt was caused by the sharp decrease in the forming load in an unpredictably early stroke from macroscopic instability, as indicated quantitatively by its macroscopic instability index.

Analytical model of the in-plane torsion test

In research and industry, the in-plane torsion test is applied to investigate the material behaviour at large plastic strains: a sheet is clamped in two concentric circles, the boundaries are twisted against each other applying a torque, and simple shear of the material arises. This deformation is analysed within the scope of finite elasto-plasticity. An additive decomposition of the Almansi strain tensor is derived, valid as an approximation for arbitrary large plastic strains and sufficiently small elastic strains and rotations. Constitutive assumptions are the von Mises yield criterion, an associative flow rule, isotropic hardening, and a physically linear elasticity relation. The incremental formulation of the elasticity relation applies covariant Oldroyd derivatives of the stress and the strain tensors. The assumptions combined with equilibrium conditions lead to evolution equations for the distribution of stresses and accumulated plastic strain. The nonzero circumferential stress must be determined from the equilibrium condition because no deformation is present in tangential direction. As a result, a differential-algebraic-equation (DAE) system is derived, consisting of three ordinary differential equations combined with one algebraic side condition. As an example material, properties of a dual phase steel DP600 are analysed numerically at an accumulated plastic strain of 3.0. Radial normal stresses of 3.1% and tangential normal stresses of 1.0% of the shear stresses are determined. The influence of the additional normal stresses on the determination of the flow curve is 0.024%, which is negligibly small in comparison with other experimental influences and measurement accuracies affecting the experimental flow curve determination.

The Correlation between Solidification Rates, Microstructure Integrity and Tensile Plastic Behaviour in 4.2 wt.% Silicon Strengthened Ductile Iron

High Silicon Strengthened Ductile Iron (HSiSDI) with 4.2 wt.% of silicon was produced in Y-blocks with different thicknesses to investigate the effects of the solidification rate on microstructure integrity and tensile mechanical properties. With decreasing solidification rates, the graphite degeneracy with the appearance of chunky graphite became more significant at the highest silicon contents, so chemical ordering and graphite degeneracy seemed to be qualitative explanations of tensile property degradation. However, a deeper analysis of the relationship between solidification rate, microstructure and tensile properties was realized through an innovative approach based on the Matrix Assessment Diagram (MAD), where the parameters of Voce equation resulting from best-fitting the experimental tensile flow curves of a significant number of HSiSDI samples, were plotted. For 3.5 wt.% silicon content, the MAD analysis indicated that the microstructure was sound for any solidification rate, while for 4.5 wt.% the microstructure was sound only for the fastest solidification rates. For 4.2 wt.% silicon content the MAD analysis pointed out that the tensile plastic behaviour and the microstructure integrity was in between the 3.5 and 4.5 wt.% silicon contents, representing a composition threshold where the reliable microstructures were only found with the fastest solidification rates, while considerable variability was found for the slowest ones. Support to the MAD analysis results was given from microstructure observations.