Constitutive modeling for the dynamic recrystallization evolution of AZ80 magnesium alloy based on stress-strain data

In order to improve the understanding of the dynamic recrystallization (DRX) behaviors of as-cast AZ80 magnesium alloy, a series of isothermal upsetting experiments with height reduction 60% were performed at the temperatures of 523 K, 573 K, 623 K and 673 K, and the strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1 s⁻¹ and 10 s⁻¹ on a Gleeble 1500 thermo-mechanical simulator. Dependence of the flow stress on temperature and strain rate is described by means of the conventional hyperbolic sine equation. By regression analysis, the activation energy of DRX in the whole range of deformation temperature was determined to be Q = 215.82 kJ mol⁻¹. Based on dσ/d? versus σ curves and their processing results, the ?ow stress curves for AZ80 magnesium alloy were evaluated that they have some characteristic points including the critical strain for DRX initiation (?_c), the strain for peak stress (?_p), and the strain for maximum softening rate (?*), which means that the evolution of DRX can be expressed by the process variables. In order to characterize the evolution of DRX volume fraction, the modified Avrami type equation including ?_c and ?* as a function of the dimensionless parameter controlling the stored energy, Z/A, was evaluated and the effect of deformation conditions was described in detail. Finally, the theoretical prediction on the relationships between the DRX volume fractions and the deformation conditions were validated by the microstructure graphs.     

Prediction of dynamic recrystallisation behaviour of AISI type 4140 medium carbon steel

Abstract

The aim of the present work was to establish quantitative relationships between the flow stress and the volume fraction of dynamic recrystallisation (DRX) as a function of processing variables such as strain rate, temperature, and strain for AISI type 4140 medium carbon steel, by means of torsion tests. Torsion tests were carried out in the temperature range 900-1100°C and the strain rate range 5·0 × 10­2 -5·0 × 10⁰ s^­1 to study the high temperature softening behaviour. For the exact prediction of flow stress, the effective stress—effective strain curves were divided into two regions, the work hardening and dynamic recovery region and the DRX region. The flow stress of the DRX region could be expressed in terms of the volume fraction of DRX. It was found that the calculated results were in agreement with the experimental flow stress and microstructure of the steel for any deformation condition.     

Study of the processing map and hot deformation behavior of a Cu-bearing 317LN austenitic stainless steel

The hot-working behavior of a Cu-bearing 317LN austenitic stainless steel (317LN–Cu) was investigated in the 950–1150 °C temperature and 0.01–10 s^− 1strain rate range, respectively. The effects of different deformation parameters and optimum hot-working window were respectively characterized through analyzing flow stress curves, constitutive equations, processing maps and microstructures. The critical strain for dynamic recrystallization (DRX) was determined by the inflection point on θ-σ and −∂θ/∂σ-σ curves. The peak stress was found to increase with decrease in temperature and increase in strain rate. Typical signs of DRX over a wide range of temperatures and strain rates were observed on the flow stress curves. The power dissipation maps in the strain range of 0.1–0.4 were basically similar, indicating the insignificant effect of strain on the power dissipation maps of 317LN–Cu. However, the instability maps showed strong strain sensitivity with increasing strain, which was attributed to the flow localization. The optimum hot-working window for 317LN–Cu was obtained in the temperature range 1100–1120 °C and strain rate range 0.01–0.018 s^− 1, with a peak efficiency of 38%. Microstructural analysis revealed fine and homogenized recrystallized grains in this domain.     

Superplastic behaviour of as received superplastic forming grade IN718 superalloy

Abstract

Tensile specimens of superplastic forming grade IN718 superalloy, containing banded microstructure in the as received state, were deformed at high temperatures T to investigate the stress σ versus strain rate ? · behaviour, the nature of the stress versus strain ? curves, ductility, and microstructure upon failure. The log σ–log ? · plot for the ? · range ～5 × 10^-6–3 × 10^-2 s^-1 at T = 1173–1248 K exhibited a strain rate sensitivity index m = 0·62 at low strain rates and m = 0·26 at high strain rates, representing region II and III behaviour, respectively. The activation energies were estimated to be 308 and 353 kJ mol^-1, respectively. All the σ–? curves, obtained at ? · = 1 × 10^-4 s^-1 for the temperature range 1173–1273 K, and at T = 1198 K for the strain rate range 1 × 10^-4–1 × 10^-2 s^-1, exhibited initial flow hardening, followed by flow softening. The microstructures revealed dynamic recrystallisation, grain growth, cavitation, and a variation in the amount of second phase particles. Grain growth and cavitation were found to increase with temperature in region II. Excessive grain growth at 1273 K led to the elimination of region II. Grain growth and cavitation were both found to be less pronounced as the strain rate increased in region III.     

Quantitative Analysis of Work Hardening and Dynamic Softening Behavior of low carbon alloy Steel Based on the Flow Stress

In this study, the constitutive equation and DRX(Dynamic recrystallization) model of Nuclear Pressure Vessel Material 20MnNiMo steel were established to study the work hardening and dynamic softening behavior based on the flow behavior, which was investigated by hot compression experiment at temperature of 950 °C, 1050 °C, 1150 °C and 1250 °C with strain rate of 0.01 s⁻¹, 0.1 s⁻¹ and 10 s⁻¹ on a thermo-mechanical simulator THE RMECMASTOR-Z. The critical conditions for the occurence of dynamic recrystallization were determined based on the strain hardening rate curves of 20MnNiMo steel. Then the model of volume fraction of DRX was established to analyze the DRX behavior based on flow curves. At last, the strain rate sensitivity and activation volume V^* of 20MnNiMo steel were calculated to discuss the mechanisms of work hardening and dynamic softening during the hot forming process. The results show that the volume fraction of DRX is lower with the higher value of Z (Zener–Hollomon parameter), which indicated that the DRX fraction curves can accurately predicte the DRX behavior of 20MnNiMo steel. The storage and annihilation of dislocation at off-equilibrium saturation situation is the main reason that the strain has significant effects on SRS(Strain rate sensitivity) at the low strain rate of 0.01 s⁻¹ and 0.1 s⁻¹. While, the effects of temperature on the SRS are caused by the uniformity of microstructure distribution. And the cross-slip caused by dislocation piled up which beyond the grain boundaries or obstacles is related to the low activation volume under the high Z deformation conditions. Otherwise, the coarsening of DRX grains is the main reason for the high activation volume at low Z under the same strain conditions.     

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.     

Hot deformation behaviour of precipitation hardening stainless steel

Abstract

The behaviour of 17-4 precipitation hardening (PH) stainless steel was studied using the hot compression test at temperatures of 950–1150°C with strain rates of 0·001–10 s^?1. The stress–strain curves were plotted by considering the effect of friction. The work hardening rate versus stress curves were used to reveal whether or not dynamic recrystallisation (DRX) occurred. Using the constitutive equations, the activation energy of hot working for 17-4 PH stainless steel was determined as 337 kJ mol^?1. The effect of Zener–Hollomon parameter Z on the peak stress and strain was studied using the power law relation. The normalised critical stress and strain for initiation of DRX were found to be 0·89 and 0·47 respectively. Moreover, these behaviours were compared to other steels.     

Dynamic and metadynamic recrystallization of Hastelloy X superalloy

Hot compression tests in the temperature range of 900–1150 °C and strain rates varying between 0.001 and 0.5 s⁻¹ were performed on Hastelloy X superalloy in order to investigate the kinetics of hot deformation. An Arrhenius-type equation was used to characterize the dependence of the flow stress on deformation temperature and strain rate. The results showed that dynamic recrystallization (DRX) as well as metadynamic recrystallization (MDRX) occurred during hot working. A novel technique has been developed for calculating the DRX kinetics parameters on the basis of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) and isothermal transformation rate equations. The variation of grain size in the DRX and MDRX regimes correlated with the standard Zener–Hollomon parameter.     

Flow curves up to peak strength of hot deformed D2 and W1 tool steels

Abstract

A high carbon, high chromium cold work die steel (D2) and a water hardenable carbon tool steel (W1) were hot deformed in torsion between 900 and 1150°C for the alloy steel and 900 and 1200°C for the carbon steel, at strain rates from 0·1 to 4 s^-1. The slope of the stress–strain curves, which represents strain hardening, decreased linearly then changed gradually to a slower linear decline before decreasing quickly to zero at the peak stress. On further strain, stress decreased to a steady state regime, indicative of dynamic recrystallisation. Kocks–Mecking analysis provided an activation enthalpy with an average comparable to the activation energy derived from a sinh modified Arrhenius analysis of peak stress. The alloy carbides of the D2 steel have the effect of raising its strength to over twice that of the carbon steel, accelerating the onset of dynamic recrystallisation but drastically lowering its ductility.     

Hot Deformation Behavior,Dynamic Recrystallization,and Texture Evolution of Ti–22Al–25Nb Alloy

The hot deformation behavior, dynamic recrystallization, and texture evolution of Ti–22Al–25Nb alloy in the temperature range of 950–1050 °C and strain rate range of 0.001–1 s^?1 is investigated by plane‐strain compression testing on the Gleeble‐3500 thermo‐mechanical simulator. The results show that the flow stress decreases with the increase of temperature and decrease of strain rate. Besides, the flow curves appear a serrate oscillation at a strain rate of 0.1 s^?1 for all the temperature ranges, which may result from instability such as flow localization or micro‐cracking. The flow behavior can be expressed by the conventional hyperbolic sine constitutive equation and the calculated deformation activation energy Q in the (α₂ + B2) and B2 regions are 631.367 and 304.812 kJ mol^?1, respectively. The microstructure evolution is strongly dependent on the deformation parameters, and dynamic recrystallization (DRX) is the dominant softening mechanism in the (α₂ + B2) region, including discontinuous dynamic recrystallization (DDRX), and continuous dynamic recrystallization (CDRX). In addition, the η_bcc‐fiber of {110} <001> is the dominant texture component in deformed Ti–22Al–25Nb alloy. It is observed that the weakening of the deformation texture is accompanied by the occurrence of DRX, which can be attributed to the large misorientation between DRX grains and neighboring B2 matrix induced by the rotation of DRX grains toward the preferred slip systems.

     

The rate of dynamic recrystallization in 17-4 PH stainless steel

The hot working behavior of 17-4 PH stainless steel (AISI 630) was studied by hot compression test at temperatures of 950–1150 °C with strain rates of 0.001–10 s⁻¹. The progress of dynamic recrystallization (DRX) was modeled by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) kinetics equation. The flow softening was directly related to the DRX volume fraction and the DRX time was determined by strain rate. For quantification of recrystallization rate, the reciprocal of the time corresponding to the DRX fraction of 0.5% or 50% was used. Analysis of the sigmoid-shaped recrystallization curves revealed that the rate of DRX increases with increasing deformation temperature and strain rate. The Zener-Hollomon parameter (Z) was found to be inappropriate for analysis of DRX kinetics. Therefore, the dynamic recrystallization rate parameter (DRXRP) was introduced for this purpose. The DRXRP may be determined readily from the Avrami analysis and can precisely predict the rate of DRX at hot working conditions.     

新型奥氏体耐热钢CHDG-A的动态再结晶行为及其动力学模型

进行新型奥氏体耐热钢(CHDG-A)的热压缩实验,研究了在900~1100℃、应变速率为0.01-10 s^-1条件下这种钢的热变形特征。结果表明:随着变形温度的提高或应变速率的降低这种钢的流变应力显著降低。基于Arrhenius模型构建了这种材料的本构方程,得到CHDG-A热变形激活能Q为515.618 kJ/mol。微观组织分析结果表明,动态再结晶(DRX)是该材料在实验热变形条件下最主要的软化方式,DRX形核主要通过晶界弓出,变形温度的升高和应变速率降低均有利于再结晶形核。基于真应力-应变曲线求得动态再结晶用Z参数表示的峰值和临界值(σ_p、ε_p、σ_c和ε_c),并确定了ε_c/ε_p,σ_c/σ_p的比值分别为0.52和0.98。同时,还基于Avrami方程建立了CHDG-A的DRX动力学模型。     

Research on the dynamic recrystallization behavior of GCr15 steel

The dynamical recrystallization (DRX) of GCr15 steel was investigated at deformation temperatures of 950–1150 °C and strain rates of 0.1–10 s^?1 on a Gleeble-3800 thermo-mechanical simulator. The stress–strain curves at lower strain rates are typical of the occurrence of DRX and exhibit a peak in the flow stress before reaching steady state. The flow stress at higher strain rates increases rapidly to the maximum too, but followed by a steady region. The microstructures after deformation certify that DRX takes place in all specimens. And the results show that DRX occurs more easily with the decrease of strain rate and the increase of deformation temperature. Using regression analysis, the DRX activation energy of the steel, the relationship of critical strain and deformation conditions were determined. In order to determine the recrystallized fraction under different conditions, an approximate model based on the stress–strain curves was investigated, and the kinetic model for DRX was established.     

Serrated yielding in Nb–V dual phase steel

Abstract

The characteristics of serrated yielding (the Portevin–Le Chatelier effect) in a Nb–V dual phase steel have been studied in the temperature range 85–210°C at strain rates between 1·2 × 10^?5 and 1·2 × 10^?2 s^?1. Serrated yielding was found to initiate only after a critical strain ?_c was reached. The strain between two successive serrations ??_s increases almost linearly with strain, while the stress drop ?σ_c increases with strain up to ?σ_max, then decreases. The exponent β in the mobile dislocation density–plastic strain relationship (ρ_m= ?^β) is 1·09 in the temperature range 85–140°C and 1·34 in the temperature range 140–210°C. The results also indicate that in the same temperature ranges there are two values of activation energy for type A serrations, i.e. 79 and 119 kJ mol^?1 respectively. The results are discussed in terms of substitutional–interstitial solute atom interaction and changes of concentration of interstitial atoms.

MST/934     

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.     

Influence of oxygen on the processing maps for hot working of electrolytic tough pitch copper

Processing maps for the hot deformation of electrolytic tough pitch (ETP) copper (100 ppm oxygen) have been developed in the temperature range 600–950 °C and strain rate range 0.001–100 s^− 1, and compared with those published earlier on ETP copper with higher oxygen contents (180, 220 and 260 ppm). These reveal that dynamic recrystallization (DRX) occurs over a wide temperature and strain rate range and is controlled by different diffusion mechanisms. In ETP copper with 100 and 180 ppm oxygen, the apparent activation energy in the DRX domain occurring in the strain rate range 0.001–10 s^− 1 and temperature range 600–900 °C is about 198 kJ/mol which suggests lattice self-diffusion to be the rate-controlling mechanism. This DRX domain has moved to higher temperatures and lower strain rates in ETP copper with higher oxygen content. In the second domain occurring at strain rates in the range 10–100 s^− 1 and temperatures > 700 °C, the apparent activation energy is 91 kJ/mol and DRX is controlled by grain boundary self-diffusion. This domain is absent in the maps of ETP copper with oxygen content higher than 180 ppm and this is attributed to the pinning of the grain boundaries by the oxide particles preventing their migration.     

Hot deformation behavior of an extruded Mg-Li-Zn-RE alloy

A new Mg-7.8%Li-4.6%Zn-0.96%Ce-0.85%Y-0.30%Zr alloy has been developed. α phase, β phase and RE-containing intermetallics formed in the alloy. It is found that the alloy can easily be extruded at 260 °C with σ_0.2 = 256 MPa, σ_b = 260 MPa and δ = 14%. Hot deformation behavior of the extruded alloy was studied using the processing map technique. Compression tests were conducted in the temperature range of 250-450 °C and strain rate range of 0.001-10 s⁻¹ and the flow stress data obtained from the tests were used to develop the processing map. The different efficiency domains and flow instability region corresponding to various microstructural characteristics have been identified as follows: (1) Domain I occurs in the temperature range of 250-275 °C and strain rate range of 1-10 s⁻¹, with a peak efficiency of about 50% at 250 °C/10 s⁻¹. Incomplete DRX process has occurred in β phase and DRX process hardly occurs in α phase; (2) Domain II occurs in the temperature range of 250-275 ?C and strain rate range of 0.001-0.003 s⁻¹, with a peak efficiency of about 42% at 250 °C/0.001 s ⁻¹. Incomplete DRX process has occurred in β phase and α phase; (3) Domain III occurs in the temperature range of 400-450 °C and strain rate range of 1-10 s⁻¹, with a peak efficiency of about 42% at 450 °C/10 s⁻¹. Complete DRX process has occurred in β phase and α phase. No cracking, cavity and band of flow localization are observed in flow instability region. The optimum parameters for hot working of the alloy are 250 °C/10 s⁻¹ and 250 °C/0.001 s⁻¹, at which fine dynamic recrystallization microstructure will be achieved. RE-containing intermetallics and α phase accelerate the DRX process in β phase. The softer β phase reduces the driving force for DRX process in α phase, so DRX process in α phase is retarded.     

Comparison of dynamic softening in 301, 304, 316 and 317 stainless steels

The mechanical torsion data in the form of flow curves and strain hardening rates from both as-cast and worked 300 series austenitic stainless steels, tested in the range 1200-900°C and 0.1 to 5.0 s-1, have been analysed to deepen understanding of dynamic softening mechanisms. The critical strain for dynamic recrystallization (DRX) is determined from the downward inflection of the strain hardening rate-stress curves, and completion of DRX is taken from the start of the steady-state regime. The rate of softening can be described by means of the Avrami equation with a mean k value of 1.27. These conclusions, based upon mechanical data, have been confirmed by optical metallographic methods. The peak strain (e _p) at which there is about 30% DRX is shown to be a function of the Zener-Hollomon parameter (Z) and the original grain size (D₀). The transition from multiple-peak grain coarsening to single-peak grain refinement behaviour has been determined. While the DRX grain size is a linear function of the steady-state flow stress with a power of -1.23, the subgrain diameter function has a power of -1. The stress and strain for subgrain formation were determined from changes in slope of the strain hardening-stress curves.     

Evolution of dynamic recrystallisation in AISI 304 stainless steel

Abstract

The nucleation and development of dynamic recrystallisation (DRX) has been studied via hot torsion testing of AISI 304 stainless steel. The DRX behaviour was investigated with microstructural analysis and slope changes of flow stress curves. The characteristics of serrated grain boundaries observed by SEM, electron backscattered diffraction and TEM indicated that the nucleated DRX grain size was similar to that of the bulged part of the original grain boundary. The DRX of the alloy was nucleated and developed by strain induced grain boundary migration and by the necklace mechanism. Before the steady state in the flow curve at 1000 ° C and 0.5 s^-1, the dynamically recrystallised grains did not remain a constant size and gradually grew to the size of fully DRX grains at steady state (30 μm). The calculation of the grain size was based on X _DRX (volume fraction of dynamically recrystallisation) under the assumption that the nucleated DRX grains grow to the steady state continuously. It was found that the calculated grain size of the alloy was good agreement with that of the observed grain size. It is expected that a fine grained steel can be obtained by controlling hot deformation conditions on the basis of newly developed equations for predicting DRX behaviour.     

Effect of nitrogen on tensile flow behaviour of type 316 LN austenitic stainless steel

Abstract

The influence of nitrogen content on the tensile flow behaviour of type 316 LN austenitic stainless steel has been studied. Nitrogen content in the steel has been varied in the range 0·07 to 0·22 wt-%. Tensile tests were carried out over the temperature range of 300–1123 K at a nominal strain rate of 3×10^?3 s^?1. The tensile flow behaviour of the steels has been analysed based on the constitutive equation proposed by Voce. The Voce’s parameters of initial stress (σ_i) and saturation stress (σ_s) were found to increase linearly with increase in nitrogen content at all the test temperatures. Tensile properties of the steels were predicted from Voce constitutive equation parameters.