A comparative study on modified Johnson Cook,modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict the hot deformation behavior in 28CrMnMoV steel

The true stress-strain data from isothermal hot compression tests on Gleeble-3500 thermo mechanical simulator, in a wide range of temperatures (1173–1473 K) and strain rates (0.01–10 s⁻¹), were employed to establish the constitutive equations based on modified Johnson Cook, modified Zerilli–Armstrong, and strain-compensated Arrhenius-type models respectively to predict the high-temperature flow stress of 28CrMnMoV steel. Furthermore, a comparative study has been made on the capability of the three models to represent the elevated temperature flow behavior of this steel. Suitability of the three models were evaluated by comparing the accuracy of prediction of deformation behavior, correlation coefficient, average absolute relative error (AARE) and relative errors of prediction, the number of material constants, and the time needed to evaluate these constants. The results showed that the predicted values by the modified Johnson Cook and Zerilli–Armstrong models could agree well with the experimental values except under the strain rate of 0.01 s⁻¹. However, the strain-compensated Arrhenius-type model could track the deformation behavior more accurately throughout the entire temperature and strain rate range.     

Artificial neural network and constitutive equations to predict the hot deformation behavior of modified 2.25Cr–1Mo steel

Hot compression tests of modified 2.25Cr–1Mo steel were conducted on a Gleeble-3500 thermo-mechanical simulator at the temperatures ranging from 1173 to 1473 K with the strain rate of 0.01–10 s⁻¹ and the height reduction of 60%. Based on the experimental results, an artificial neural network (ANN) model and constitutive equations were developed to predict the hot deformation behavior of modified 2.25Cr–1Mo steel. A comparative evaluation of the constitutive equations and the ANN model was carried out. It was found that the relative errors based on the ANN model varied from −4.63% to 2.23% and those were in the range from −20.48% to 12.11% by using the constitutive equations, and the average root mean square errors were 0.62 MPa and 7.66 MPa corresponding to the ANN model and constitutive equations, respectively. These results showed that the well-trained ANN model was more accurate and efficient in predicting the hot deformation behavior of modified 2.25Cr–1Mo steel than the constitutive equations.     

A modified Johnson–Cook constitutive model for Mg–Gd–Y alloy extended to 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 were lower than the reference temperature. Based on the impact compression data obtained by split Hopkins pressure bar technique, 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 stress–strain curves for a hot-extruded Mg–10Gd–2Y–0.5Zr alloy at both quasi-static and dynamic loadings under a wide range of temperatures ever though the current temperatures were lower than the reference temperature.     

Thermo-mechanical behavior of the Al–Si alloy coated hot stamping boron steel

Hot tensile tests of boron steels with and without an Al–Si coating were performed using a Gleeble 3500 test system, at temperatures of 700–850 °C and strain rates of 0.01–1/s. The phase and microstructure of the coating in as-coated and press-hardened conditions were observed under scanning electron microscopy (SEM) equipped with energy dispersive X-ray analysis and X-ray diffraction (XRD). Experimental results indicate that the Al–Si coating gave an unignorable influence on the thermo-mechanical properties of the boron steels. The ultimate tensile strength (UTS) of the Al–Si coated boron steel was almost equal to that of the uncoated under the lower strain rate at the same deformation temperature. At a higher strain rate, the UTS value appeared to be lower than that of the uncoated. Moreover, the UTS difference increased with the decreasing deformation temperature. The ductility of the Al–Si coated steel was lower than that of the uncoated under the described test conditions. Following the tensile tests, extensive cracks were visible in the Al–Si coating layer. SEM observation showed that microcracks and voids appeared after austenization, which may act as nucleation sites for the cracks. The cracks first propagated in the direction perpendicular to the coating/substrate interface and were identified as Type I cracks. The propagation was hindered by the substrate when these cracks reached the coating/substrate interface. This occurred because the interfacial bonding strength between the coating and the substrate was lower than the substrate strength. Following this initial failure, the cracks turned to propagate paralleled to the coating/substrate interface. In addition with the shear stress resulting from the substrate yielding, Type II cracks formed. Eventually, the cracked coatings were accompanied by interface decohesion from the substrate. The width and density of the cracks were found to increase with the decreasing deformation temperature and rising stain rate.     

Transient growth of a micro-void in an infinite medium under thermal load with modified Zerilli–Armstrong model

In this paper, the transient growth of a spherical micro-void under remote thermal load in an infinite medium is investigated. After developing the governing equations in the problem domain, the coupled nonlinear set of equations is solved through a numerical scheme. It is shown that a small cavity can grow rapidly as the temperature increases in a remote distance and may damage the material containing preexisting micro-voids. Conducting a transient thermal analysis simultaneously with a structural one reveals that the material may experience a peak in the radial stress distribution, which is five times larger compared to the steady-state one, and shows the importance of employing a time-dependent approach in this problem. Furthermore, utilizing a sensible yield criterion, i.e., the modified Zerilli–Armstrong model, discloses that there is a large discrepancy in the results assuming perfectly plastic constitutive model. It is verified that the obtained results do not violate the proportional loading conditions that is the basis for development of the governing formulation in this work. The monotonic alteration of the plastic strain components versus time proves that we do not encounter any elastic unloading during the void growth, which is a basic assumption in the present work. Some numerical examples are also presented to investigate the features of the presented model.     

Hot tensile deformation behaviors and constitutive model of an Al–Zn–Mg–Cu alloy

The hot tensile deformation behaviors of an Al–Zn–Mg–Cu alloy are studied by uniaxial tensile tests under the deformation temperature of 340–460 °C and strain rate of 0.01–0.001 s⁻¹. The effects of deformation temperature and strain rate on the hot tensile deformation behaviors and fracture characteristics are discussed in detail. The Arrhenius-type constitutive model is developed to predict the peak stress under the tested deformation condition. The results show that: (1) The true stress–true strain curves under all the tested deformation conditions are composed of four distinct stages, i.e., elastic stage, uniform deformation stage, diffusion necking stage and localized necking stage. The flow stress decreases with the increase of deformation temperature or the decrease of strain rate. (2) The elongation to fracture increases with the increase of deformation temperature. Under the tested conditions, the strain rate sensitivity coefficient varies between 0.1248 and 0.2059, which indicates that the main deformation mechanism is the lattice diffusion-controlled dislocation climb. (3) The localized necking causes the final fracture of specimens under all the deformation conditions. Microvoids coalescence is the main fracture mechanism under relatively low deformation temperatures. With the increase of deformation temperature, the intergranular fracture occurs. (4) The peak stresses predicted by the developed model well agree with the experimental results, which indicate the validity of the developed model.     

The hot deformation behavior and processing map of Ti–47.5Al–Cr–V alloy

The high temperature flow behavior of as-extruded Ti–47.5Al–Cr–V alloy has been investigated at the temperature between 1100 °C and 1250 °C and the strain rate range from 0.001 s^− 1 to 1 s^− 1 by hot compression tests. The results showed that the flow stress of this alloy had a positive dependence on strain rate and a negative dependence on deformation temperature. The activation energy Q was calculated to be 409 kJ/mol and the constitutive model of this material was established. By combining the power dissipation map with instability map, the processing map was established to optimize the deformation parameters. The optimum deformation parameter was at 1150 °C–1200 °C and 0.001 s^− 1–0.03 s^− 1 for this alloy. The microstructure of specimens deformed at different conditions was analyzed and connected with the processing map. The material underwent instability deformation at the strain rate of 1 s^− 1, which was predicted by the instability map. The surface fracture was observed to be the identification of the instability.     

Plastic deformation behavior of ultrafine-grained Al–Mg–Sc alloy

Ultrafine-grained (UFG) Al–Mg–Sc alloy was obtained by friction stir processing. The UFG alloy was subjected to uniaxial tensile testing to study the tensile deformation behavior of the alloy. An inhomogeneous yielding (Lüdering phenomenon) was observed in the stress–strain curves of UFG alloy. This deformation behavior was absent in the coarse-grained alloy. The Lüdering phenomenon in UFG alloy was attributed to the lack of dislocations in UFG microstructure. A strong dependence of uniform ductility on the average grain size was exhibited by the UFG alloy. Below a critical grain size (0.5 μm), ductility was very limited. Also, with the decrease in grain size, most of the plastic deformation was observed to be localized in necked region of the tensile samples. The negative strain rate sensitivity (SRS) observed for the UFG alloy was opposite of the SRS values reported for UFG alloys in the literature. Based on activation volume measurement, grain boundary mediated dislocation-based plasticity was concluded to be the micro-mechanism operative during plastic deformation of UFG Al–Mg–Sc alloy.     

Modeling of constitutive relationship of Ti–25V–15Cr–0.2Si alloy during hot deformation process by fuzzy-neural network

In this paper, an adaptive fuzzy-neural network model has been established to model the constitutive relationship of Ti–25V–15Cr–0.2Si alloy during high temperature deformation. The network integrates the fuzzy inference system with a back-propagation learning algorithm of neural network. The experimental results were obtained at deformation temperatures of 900–1100 °C, strain rates of 0.01–10 s⁻¹, and height reduction of 50%. After the training process, the fuzzy membership functions and the weight coefficient of the network can be optimized. It has shown that the predicted values are in satisfactory agreement with the experimental results and the maximum relative error is less than 10%. It proved that the fuzzy-neural network was an easy and practical method to optimize deformation process parameters.     

Hot deformation behavior of spray-deposited Al–Zn–Mg–Cu alloy

The flow behavior of spray-deposited Al–10.21Zn–2.76Mg–1.45Cu–0.16Zr (wt.%) alloy has been systematically investigated by thermal compression tests with temperature and strain rate ranging from 613 K to 733 K and 0.001–1 s⁻¹, respectively. Microstructural observations revealed that the average grain size of spray-deposited alloy was below 25 μm due to the high cooling rate. Both relatively high temperature and low strain rate could promote the formation of dynamic recrystallization (DRX). The stress level of the alloy decreased with increasing deformation temperature and decreasing strain rate, which could be characterized by a Zener–Hollomon parameter in the hyperbolic-sine equation. Furthermore, the strain-dependent constitutive equation could lead to a good agreement between the calculated and measured flow stresses in the elevated temperature range for spray-deposited alloy. The deformation activation energy for spray-deposited alloy was relatively lower than that of the as-cast alloy owing to ultrafine grains and high supersaturated solid solubility.     

Constitutive analysis of the hot deformation behavior of Fe–23Mn–2Al–0.2C twinning induced plasticity steel in consideration of strain

In this study, constitutive analysis has been carried out on Fe–23Mn–2Al–0.2C twinning induced plasticity (TWIP) steel. For this purpose, hot compression tests were conducted on a Gleeble-3500 thermo-mechanical simulator in the temperature range of 900–1150 °C and the strain rate range of 0.001–20 s⁻¹. The effects of deformation heating and friction on flow stress were analyzed and corrected. On the basis of Sellars–Tegart–Garofalo equation, the strain-dependent constitutive equations of the steel were derived. The results show that deformation heating has a significant influence on the flow stress at lower temperatures and higher strain rates, while the frictional effect is slight even at the highest strain level investigated. Comparison of the calculated flow stress with the experimental data suggests that the developed constitutive equations can adequately describe the relationships between the flow stress, strain rate, temperature and strain of the steel during hot deformation. This is supported by a high correlation coefficient (R = 0.996) and a low average absolute relative error (AARE = 3.31%) for the entire deformation condition range investigated.     

Hot deformation behavior of an austenitic Fe–20Mn–3Si–3Al transformation induced plasticity steel

Hot deformation behavior of an austenitic Fe–20Mn–3Si–3Al transformation induced plasticity (TRIP) steel was investigated by hot compression tests on Gleeble 3500D thermo-mechanical simulator in the temperature ranges of 900–1100 °C and the strain rate ranges of 0.01–10 s⁻¹. The results show that the flow stress is sensitively dependent on deformation temperature and strain rate, and the flow stress increases with strain rate and decreases with deformation temperature. The peak stress during hot deformation can be predicted by the Zener–Hollomon (Z) parameter in the hyperbolic sine equation with the hot deformation activation energy Q of 387.84 kJ/mol. The dynamic recrystallization (DRX) is the most important softening mechanism for the experimental steel during hot compression. Furthermore, DRX procedure is strongly affected by Z parameter, and decreasing of Z value lead to more adequate proceeding of DRX.     

An analysis of hot deformation of an Al–Cu–Mg alloy produced by powder metallurgy

The high-temperature plasticity of a 2014 aluminium alloy produced by powder metallurgy was investigated in a wide range of temperatures and strain rates. When the strain rate was plotted as a function of stress (either peak flow stress in torsion, or applied stress in tensile creep), the alloy exhibited the same threshold-like behaviour observed in similar materials. The microstructure of representative torsioned samples was analysed in a transmission electron microscope (TEM) and the characteristics of particles and precipitate distribution were estimated. The dependence on stress and temperature was analysed by means of the conventional constitutive equations used for describing the hot-working behaviour and by means of a modified form of the sinh-equation, where the stress was substituted by an effective stress i.e. by the difference between the actual stress and a threshold stress. This temperature-dependent threshold stress was found to be a constant fraction (15%) of the Orowan stress generated by the dispersion of alumina particles and of precipitated intermetallic phases.     

Application of advanced analytical techniques to study structure–property relationship of hot rolled high strength low alloy steel

Abstract

The microstructure–property relationship in conventional high strength low alloy (HSLA) steel was evaluated using data obtained from transmission electron microscopy (TEM) and atom probe tomography (APT). Atom probe tomography allowed the characterisation of fine TiC particles with average radius of 3±1·2 nm that were not observed by TEM. The increase in the yield strength of steel due to the presence of fine precipitates was calculated to be 128 MPa.     

Deformation behavior of an Al–Cu–Mg–Mn–Zr alloy during hot compression

Deformation behavior of an Al–Cu–Mg–Mn–Zr alloy during hot compression was characterized in present work by high-temperature testing and transmission electron microscope (TEM) studies. The true stress–true strain curves exhibited a peak stress at a critical stain. The peak stress decreased with increasing deformation temperature and decreasing strain rate, which can be described by Zener–Hollomon (Z) parameter in hyperbolic sine function with the deformation activation energy 277.8 kJ/mol. The processing map revealed the existence of an optimum hot-working regime between 390 and 420 °C, under strain rates ranging from 0.1 to 1 s⁻¹. The main softening mechanism of the alloy was dynamic recovery at high lnZ value; continuous dynamic recrystallization (DRX) occurred as deformed at low lnZ value. The dynamic precipitation of Al₃Zr and Al₂₀Cu₂Mn₃ dispersoids during hot deformation restrained DRX and increased the hot deformation activation energy of the alloy.     

Static recrystallisation and recrystallisation during hot deformation of Al–1Mg–1Mn alloy

Abstract

Plane strain compression tests at 5 s^?1 and at temperatures of 270–480°C have been carried out on an Al–1Mg–1Mn alloy containing a bimodal distribution of intermetallic particles and after a prior heat treatment to coarsen all particles to greater than 1 μm in size. During the heat treatment, recrystallisation of the initially hot worked material only proceeded with coarsening of the fine particles. During subsequent hot deformation, thin foil electron microscopy revealed that identical subgrain structures were developed in the two materials by dynamic recovery at temperatures below 450°C. At higher temperatures, the initially recrystallised material showed localised particle stimulated dynamic recrystallisation. The subsequent static recrystallisation rate was more than 10³ times faster in the material free from small particles.

MST/751     

Comparison of torsion and compression constitutive analyses for elevated temperature deformation of Al–Li–Cu–Mn alloy

Abstract

Experimental alloy 2090 (Al – 2.1Li – 2.6Cu – 0.4Mn) was deformed in torsion and compression at temperatures T=300, 400, and 500°C and strain rates ε?=10^–2 to 10 s^–1. The torsion and compression results were analysed using equation A(sinh ασ)ⁿ=Z=ε? exp(Q_HW/RT), where Z is the Zener – Hollomon parameter. The variation of stress exponent n, Arrhenius slope s, and activation energy Q_HW were calculated with variation of the stress multiplier a from 0.01 to 0.08 MPa^–1. The change of α caused the stress exponent to decrease at a declining rate and Arrhenius slope s to increase linearly, thus causing the activation energy Q_HW to become stable above α=0.04 MPa^–1. The two experimental test techniques gave very similar flow stresses and constitutive constants. At α=0.052 MPa^–1 activation energy values showed reasonable consistency with other age hardenable aluminum alloys. The compression tests were also analysed using the power law expression ε? exp(Q′_HW/RT)=Z=A″σ^n′.     

Study of hot forging behavior of as-cast Mg–3Al–1Zn–2Ca alloy towards optimization of its hot workability

Mg–3Al–1Zn–2Ca (AZX312) alloy has been forged in the temperature range of 350–500 °C and at speeds in the range of 0.01–10 mm s⁻¹ to produce a rib-web shape with a view to validate the processing map and study the microstructural development. The process was simulated through finite-element method to estimate the local and average strain rate ranges in the forging envelope. The processing map exhibited two domains in the following ranges: (1) 350–450 °C/0.0003–0.05 s⁻¹ and (2) 450–500 °C/0.03–0.7 s⁻¹ and these represent dynamic recrystallization (DRX) and intercrystalline cracking, respectively. The optimal workability condition according to the processing map is 425–450 °C/0.001–0.01 s⁻¹. A wide flow instability regime occurred at higher strain rates diagonally across the map, which caused flow localization that should be avoided in forming this alloy. The experimental load–stroke curves correlated well with the simulated ones and the observed microstructural features in the forged components matched with the ones predicted by the processing map.