Dynamic Material Model Research Articles

Hot deformation behavior and processing parameters optimization of SP700 titanium alloy

The Gleeble-3800 thermal simulator is used to perform isothermal and constant strain rate compression tests on SP700 titanium alloy under the conditions of deformation temperature of 700–950 °C and strain rate of 0.001–1 s−1. The processing map technology can be obtained based on dynamic material model, through this technology, its thermal deformation behavior can be studied and the appropriate processing parameter range can be optimized by combining the changes in the strain rate sensitivity exponent m, strain hardening exponent n and deformation activation energy Q. The results show that the flow stress of SP700 titanium alloy is sensitive to deformation temperature and strain rate. When the strain is 0.9, the strain rate sensitivity exponent m is greater than 0.5 when the deformation temperature is 800 °C and the strain rate is 0.001 s−1 and 1 s−1. Under this condition, the SP700 titanium alloy may have superplastic deformed. In addition, the analysis shows that when the deformation temperature is 775–825 °C, the strain rate is 0.3–1 s−1 and 0.001–0.002 s−1, this condition is the best processing parameter range of SP700 titanium alloy.

Hot deformation behavior and workfability of the homogenized Mg-5.8Zn-1.2Y–1Mn alloy containing I and W phases

In the present study, a thermo-mechanical simulator (Gleeble-1500D) is applied to conduct compression tests on homogenized Mg–6Zn-1.2Y–1Mn (wt.%) alloy and investigate features of this alloy in terms of flow behavior, dynamic recrystallization (DRX) evolution and hot workability. Different strain rates varying from 0.005 to 5 s−1 and different temperatures within the range of 200–400 °C are used in the experiments. An apparent mean deformation activation energy of 216.027 kJ/mol with a stress exponent of 10.88964 are achieved by regression analysis of Arrhenius type flow behavior equation. Using true stress-true strain data analysis, a kinetic model of dynamic recrystallization is presented as: XDRX=1−exp[−1.41((ε−εc)/ε∗)1.51]. Furthermore, the processing maps are developed and analyzed according to the dynamic material model (DMM). Based on the processing maps, the flow stability and instability domains are determined. It is found that the optimal hot working region of the alloy is temperature of 325–400 °C and strain rate of 0.005–0.05 s−1. Finally, a finite element analysis is carried out, and the reasonability of the optimal deformation parameters are verified.

Microstructure evolution and hot deformation behavior of 25Cr–6Mn–3Ni–1Mo–3W–0.1C–0.34N lean duplex stainless steel

Hot deformation characteristics of a 25Cr–6Mn–3Ni–1Mo–3W lean duplex stainless steel containing high C and N contents were elucidated. Hot compression tests were performed at temperatures of 600–1100 °C and strain rates of 0.01–10 s−1. Using the stress–strain curves from the hot compression tests, processing maps were established based on the dynamic material model. The hot working domains for the temperature range of 700–900 °C were found to be unstable, regardless of the strain rate. Transmission electron microscopy and electron backscatter diffraction analyses revealed that cracking occurred along the ferrite (α)/austenite (γ) phase boundaries during hot deformation in this unstable hot working regime, where coarse Cr23C6 carbide precipitated along the α/γ interphase. To further understand the hot deformation behavior, hot tension tests were carried out, which indicated that a ductility dip occurred at 700–900 °C due to the interphase precipitation of Cr23C6 carbide; this result was in accordance with the hot compression tests. Finally, the change in the precipitation behavior of Cr23C6 carbide upon deformation temperature and its effect on the hot workability were discussed through a time–temperature-precipitation diagram of Cr23C6 carbide.

An investigation of hot deformation behavior of Zn–22Al alloy and development of its processing maps during isothermal compression

In this paper, the hot deformation behavior of Zn–22Al alloy was investigated by performing hot compression tests under different deformation conditions. The Arrhenius-type constitutive model was developed and the constants were determined for this alloy. In addition, the processing map was constructed using the principle of the dynamic materials model (DMM). The results show that the Arrhenius-type model, with an activation energy of 63.722 kJ/mol, can provide an accurate prediction of the flow behavior of the alloy at various conditions. The higher energy dissipation efficiency was observed in the high-temperature ranges and low strain rates. The results showed that the unstable processing zone of Zn–22Al alloy has mainly occurred at high strain rates and low-temperature region. Besides, it is found that the strain has less significant effects on instability parameter and power dissipation efficiency.

3D processing map and high-temperature deformation behaviour of Fe–0.13P–0.05C–0.015N steel

Steels alloyed with high phosphorus should be developed for those applications where both strength and corrosion resistance are required. Structural steels such as rebars are manufactured using high-temperature deformation. Hence, thermo-mechanical behaviour of Fe-0.13P-0.05C -0.015N steel is considered using high temperature compression experiments after austenitization at 1050 °C for 10 s. The temperatures selected were between 750 and 1050 °C and at intervals of 50 °C. The rates of strain varied from 0.001 to 10 s−1. Microstructural evolution was studied with the help of optical and scanning electron microscopy. Modified dynamic materials model is used to draw a processing map. The processing map helps in determining the domains which are safe for hot working. This alloy steel can be safely processed in the area confined by the rates of strain between 1 and 10 s−1 as well as the temperature interval of 900 to 1000 °C.

Hot workability and microstructure control in Monel®400 (Ni–30Cu) alloy: An approach using processing map, constitutive equation and deformation modeling

Monel®400 alloy is widely used in marine and chemical industries due to its moderate strength and high resistance to corrosive environments. In the present work, hot workability of Monel®400 alloy in as-cast condition was studied using the processing maps approach. Hot-compression tests were performed in a Gleeble thermo-mechanical simulator in the temperature, T, range of 900–1200 °C and strain rate, ε˙, of 10−2 – 10+1 s−1. The data obtained from the tests was used to construct processing map at a true strain, ε, of 0.5 utilizing the modified dynamic material model (DMM) proposed by Murty and Rao. Processing map identified three stable domains for possible hot working occurring in the following T and ε˙ range - Domain-1: T = 900–1200 °C and ε˙ = 10−2-10−1.75 s−1; Domain-2: T = 1150–1200 °C and ε˙ = 10−1.75- 10−1 s−1; and Domain-3: T = 1100–1200 °C and ε˙ = 10+0 - 10+1 s−1. A broad flow instability regime in the form of flow localization was also identified at all temperatures and intermediate strain rates (ε˙ = 10−1.5 - 10+0 s−1). Complete recrystallized microstructure with discontinuous dynamic recrystallization (DDRX) as the dominating deformation mechanism was observed in Domain-3 (occurring at higher ε˙). In contrast, microstructural analysis of the deformed specimens in Domain-1 and Domain-2 occurring at lower ε˙ showed limited DRX at the serrated grain boundaries with dynamic recovery (DRV) and continuous DRX (CDRX) as the operating deformation mechanisms. With the aid of the processing map along with evolved microstructures of the deformed specimens, Domain-3 was identified as the optimum “safe” regime for thermo-mechanical processing. Results obtained from the processing map are then successfully validated through industrial trial forgings performed in the T range 950–1200 °C. The forging process was also simulated in identical process parameters using finite element method (FEM) software DEFORM®-3D to study the flow behavior and effective stress and strain distribution in the forged billets.

Hot working behaviour and processing maps of duplex cast steel

Abstract In this paper the hot working behaviour of medium carbon duplex cast steel is studied using uniaxial hot compression tests over a temperature range varying from 700 ˚C to 1 000 °C and at different strain rates ranging from 10–4 to 10–1 s–1. A model based on a variant of a dynamic materials model was employed to construct processing maps. These maps delineate the safe and unsafe domains. The safe domains, associated with dynamic recrystallization and dynamic recovery, can be chosen to optimize the hot workability of the studied material. Whereas, the unsafe domain is to be avoided because it is associated with plastic deformation instabilities. The domain associated with dynamic recrystallization is centred at 1000 °C and 10–4 s–1 with a peak energy dissipation efficiency of about 40%, while the domain associated with dynamic recovery is centred at 700 °C and 10–4 s–1 with a peak energy dissipation efficiency of about 27%. The unsafe hot working domain, spread over the entire temperature range and moderate to high strain rates, predicts the appearance of flow instabilities, in the form of shear bands and intergranular cracks. To validate the obtained results, microstructural observations corresponding to different processing conditions are presented.

Research on Thermal Deformation Behavior of Marine Crankshaft S34MnV Steel

Hot deformation behavior of S34MnV steel was studied by isothermal compression tests. According to the experimental results, the influence of strain rate and deformation temperature on flow stress is analyzed. The results indicate that for S34MnV steel with same deformation, the flow stress decreases with the increase in deformation temperature when the strain rate is constant, and increases with the increase in strain rate when the temperature is fixed. It established that a five‐order polynomial Arrhenius‐type constitutive equation which based on strain compensation. The correlation coefficient R between the predicted value and the experimental value is 0.9943, and the average absolute relative error (AARE) (%) value is calculated to be 3.9749%. The dynamic material model (DMM) diagram of thermal processing map is also drawn to investigate the workability of S34MnV steel, and it suggests that the best thermal processing conditions for S34MnV steel are predicated to be within the strain rate range of 0.03–0.6 s−1 and deformation temperature range of 1030–1150 °C. In the suggested domains, the peak value of the power dissipation efficiency is between 34% and 39%.

Identification of plastic constitutive Johnson–Cook model parameters by optimization-based inverse method

Abstract Because the design of most products incorporates numerical analysis such as the finite element method, these days, accurate determination of dynamic material model parameters is significant. Usually, the dynamic constitutive model parameters such as those in the Johnson–Cook (JC) model are determined by fitting stress–strain curves obtained by split Hopkins pressure bar (SHPB) tests at various strain rates and temperatures. However, the determination of model parameters by fitting cannot consider potential three-dimensional heterogeneities of stress propagation because the stress and strain are calculated with the assumption of one-dimensional wave propagation. In this study, to accurately determine plastic constitutive model parameters considering all of the potential heterogeneities of stress propagation, an optimization-based inverse method was proposed. Multiple objectives were defined with multiple experimental data that were obtained by SHPB tests at different conditions. The error was defined using transmitted and reflected bar signals obtained in experiments and finite element analysis with candidate model parameters. JC model parameters were set as design variables and determined to minimize the error. To show the reliability of the proposed method, experimental data were generated numerically by FE analysis with known model parameters. The parameters determined by the proposed method were compared with the known exact values. Model coefficients were also determined by fitting the stress–strain relations to show the superiority of the proposed method. Though the fitting of stress–strain curves can also reasonably determine the model coefficients, it was shown that the model parameters could be determined accurately by the proposed optimization-based inverse method.

Characterization of Hot Deformation Behavior of Ti-Al-Nb-Zr-Mo-Cr Alloy

The hot deformation behavior of Ti-Al-Nb-Zr-Mo-Cr titanium alloy has been investigated using a Gleeble-1500D thermal simulation test machine in the temperature range of 855°C~1015°C,at constant strain rate from 0.01 s-1 to 10s-1 and with height reduction of 45%. The flow curves characteristic under different deformation parameters show significant difference. According to the stress-strain curves of the alloy and its stress characteristics, the Arrhenius constitutive equation was obtained. The average activation energy is about 541 kJ/mol in the α+β field, and about 243 kJ/mol in the β field, respectively. Based on the dynamic materials model, the processing map is generated, which shows that the peak efficiency domain appears at the temperature of 874°C~900°C and the strain rate of 0.001 s-1~0.06s-1 with a peak efficiency of 0.58 at about 887°C/0.001s-1.

Hot deformation characterization of Ti–Nb alloy based on GA-LSSVM and 3D processing map

Abstract The thermal compression tests of Ti–Nb alloy under T = 790–940 °C and e ˙ = 0.001–10s−1 were carried out on the thermal simulation testing machine of Gleeble-3500. The flow stress curves were obtained, and the high-temperature rheological properties of the alloy were analyzed. The 3D activation energy maps were calculated and constructed. The LSSVM model of constitutive relation was established, and the penalty coefficient γ and kernel parameter δ of the LSSVM model were optimized by the genetic algorithm (GA). The constitutive model of the alloy based on the GA-LSSVM algorithm was constructed. The predicted value of the model was also compared with the experimental data. The polar reciprocity model (PRM) and dynamic material model (DMM) were used to establish the 3D processing map of the alloy and appropriate thermal processing parameters. The results indicated that T and e ˙ have a great influence on the flow stress of Ti–Nb alloy. Ti–Nb alloy is a negative temperature-sensitive and a positive strain rate-sensitive material. The correlation coefficient (R) of the GA-LSSVM algorithm constitutive model is 0.9958. The model has high prediction accuracy and strong generalization ability, which provide a new method for establishing a high-temperature constitutive model of materials. The PRM processing map is more accurate in optimizing the processing parameters of Ti–Nb alloy than that of the DMM processing map through analyzing the 3D processing map and observing the microstructure. The instability modes in the instability region of the alloy mainly include local flow. The stability region's predominant deformation mechanism is DRX. The 870–940 °C and 0.001–0.01s−1 are the best parameters during the processing of Ti–Nb alloy.

Hot Deformation Behavior and Processing Maps of a New Ti-6Al-2Nb-2Zr-0.4B Titanium Alloy.

The hot deformation behaviors of a new Ti-6Al-2Nb-2Zr-0.4B titanium alloy in the strain rate range 0.01–10.0 s−1 and temperature range 850–1060 °C were evaluated using hot compressing testing on a Gleeble-3800 simulator at 60% of deformation degree. The flow stress characteristics of the alloy were analyzed according to the true stress–strain curve. The constitutive equation was established to describe the change of deformation temperature and flow stress with strain rate. The thermal deformation activation energy Q was equal to 551.7 kJ/mol. The constitutive equation was On the basis of the dynamic material model and the instability criterion, the processing maps were established at the strain of 0.5. The experimental results revealed that in the (α + β) region deformation, the power dissipation rate reached 53% in the range of 0.01–0.05 s−1 and temperature range of 920–980 °C, and the deformation mechanism was dynamic recovery. In the β region deformation, the power dissipation rate reached 48% in the range of 0.01–0.1 s−1 and temperature range of 1010–1040 °C, and the deformation mechanism involved dynamic recovery and dynamic recrystallization.

Compressive response and microstructural evolution of in-situ TiB2 particle-reinforced 7075 aluminum matrix composite

The hot forming behavior, failure mechanism, and microstructure evolution of in-situ TiB2 particle-reinforced 7075 aluminum matrix composite were investigated by isothermal compression test under different deformation conditions of deformation temperatures of 300–450 °C and strain rates of 0.001-1 s−1. The results demonstrate that the failure behavior of the composite exhibits both particle fracture and interface debonding at low temperature and high strain rate, and dimple rupture of the matrix at high temperature and low strain rate. Full dynamic recrystallization, which improves the composite formability, occurs under conditions of high temperature (450 °C) and low strain rate (0.001 s−1); the grain size of the matrix after hot compression was significantly smaller than that of traditional 7075Al and ex-situ particle reinforced 7075Al matrix composite. Based on the flow stress curves, a constitutive model describing the relationship of the flow stress, true strain, strain rate and temperature was proposed. Furthermore, the processing maps based on both the dynamic material modeling (DMM) and modified DMM (MDMM) were established to analyze flow instability domain of the composite and optimize hot forming processing parameters. The optimum processing domain was determined at temperatures of 425-450 °C and strain rates of 0.001-0.01 s−1, in which the fine grain microstructure can be gained and particle crack and interface debonding can be avoided.

Constitutive model and microstructural evolution of hot deformation of investment-cast Ti-4Al-0.005B alloy

Hot compression tests of investment-cast Ti-4Al-0.005B (TA5) alloy were conducted over a wide temperature range of 750 °C–850 °C at strain rates of 0.01–1 s−1. Based on the flow stress curve and dynamic material model, a constitutive equation is established. The thermal deformation behavior and microstructural evolution of investment-cast TA5 alloy at high temperatures is systematically analyzed. The results show that the Zener-Hollomon parameter′s formula calculates the apparent activation energy of TA5 as 469893 J · mol−1, α is 0.0032, and the apparent value of n is 12.34. The peak flow stress decreases with increasing deformation temperature and decreasing strain rate. At high strain rates, the grains appear nonuniform and exhibit microcracks. Thus, high temperature and low-strain rate are beneficial to the occurrence of slip. Under these conditions, grain boundaries can sufficiently migrate, the microstructure remains compact and stable, and dynamic recrystallization grains distribution is more uniform. Therefore, the high-temperature and low-strain zone is most suitable for processing TA5 alloy.

The Parameters Identification of High-Temperature Constitutive Model Based on Inverse Optimization Method and 3D Processing Map of Cr8 Alloy Steel.

As a novel kind of cold roller steel, Cr8 alloy steel has the characteristics of high hardness, high wear resistance and good toughness, which can effectively prolong the service life of the roller that is an important part of the steel rolling mill. How to accurately define the constitutive model parameters of metal materials is the major problem, because it seriously affects the accuracy of numerical simulation results of the roller hot forming process. In the study of Cr8 alloy steel’s thermal deformation behavior of the present paper, the high temperature compression test was done on a Gleebel-1500D thermal/force simulation testing machine. A novel method of parameter identification was proposed based on inverse optimization. The Hansel–Spittel constitutive model was established by using the inverse optimization method. To carry out the verification on the accuracy of the established constitutive model, the predicted flow-stress of constitutive model was made a contrast to the experimental flow-stress, and the standard statistical parameters were also applied to further evaluation. The results showed a relatively high prediction accuracy of the Hansel–Spittel constitutive model based on the inverse optimization algorithm. Meanwhile, to obtain optimal parameters of Cr8 alloy steel in the thermal processing, 3D thermal processing maps concerning strain-rate, strain and temperature were built based on the dynamic material model. According to the 3D processing map, the most adequate thermal processing parameters of Cr8 alloy steel were obtianed as follows: strain 0.2–0.4, strain-rate 0.05–0.005 s−1, temperature 1100–1150 °C.

Hot deformation behavior and microstructure evolution of an Fe–30Cr–2Mo ultra-pure super ferritic stainless steel

The hot deformation behavior and microstructure evolution of an Fe–30Cr–2Mo ultra-pure super ferritic stainless steel were investigated at the temperature range of 950–1150 °C and strain rate varying from 0.01 to 10 s−1. A strain compensated constitutive equation based on the Arrhenius-type model was established to predict the flow stress. The hot processing map based on the dynamic materials model was achieved to identify the optimum processing parameters. In addition, the features of microstructure evolution combined with the processing map were systematically investigated. The experimental results revealed that the flow stress increased with decreasing deformation temperature or increasing strain rate. Dynamic recovery was confirmed to be the predominant softening mechanism. The values of flow stress predicted by the strain compensated constitutive equation agreed well with the experimental values. The extent of dynamic recrystallization and recrystallized grain size increased with increasing deformation temperature or decreasing strain rate, and the continuous dynamic recrystallization was attributed to be the predominant mechanism of recrystallization during hot deformation. The optimum hot working parameters were determined to be the deformation temperature of 1070–1150 °C and strain rate of 0.1–1 s−1 with a peak power dissipation efficiency of 42%.

Application of the Strain Compensation Model and Processing Maps for Description of Hot Deformation Behavior of Metastable β Titanium Alloy.

The flow behavior of metastable β titanium alloy was investigated basing on isothermal hot compression tests performed on Gleeble 3800 thermomechanical simulator at near and above β transus temperatures. The flow stress curves were obtained for deformation temperature range of 800–1100 °C and strain rate range of 0.01–100 s−1. The strain compensated constitutive model was developed using the Arrhenius-type equation. The high correlation coefficient (R) as well as low average absolute relative error (AARE) between the experimental and the calculated data confirmed a high accuracy of the developed model. The dynamic material modeling in combination with the Prasad stability criterion made it possible to generate processing maps for the investigated processing temperature, strain and strain rate ranges. The high material flow stability under investigated deformation conditions was revealed. The microstructural analysis provided additional information regarding the flow behavior and predominant deformation mechanism. It was found that dynamic recovery (DRV) was the main mechanism operating during the deformation of the investigated β titanium alloy.

Microstructure Evolution during High-Temperature Deformation of Ti-5Al-5V-2Mo-1Cr-1Fe Alloy under Compression

Hot isothermal compression testing of Ti-5Al-5V-2Mo-1Cr-1Fe alloy exhibiting lamellar (α/β) microstructure was performed using a deformation simulator. The flow curves of the alloy were obtained as a function of temperature around its beta transus (‘Tβ’, the allotropic transformation temperature from HCP to BCC phase) at different strain rates in the range of 10−2-10 s−1. The apparent activation energy ‘Q’ for the alloy under these hot working conditions was found to be ~ 644 and ~ 317 kJ mol−1 in two-phase (α + β) and single-phase β regimes, respectively. Distinct constitutive relationships for the alloy have been established at various temperature regimes. Dynamic material model was employed to generate the processing maps and thereby evaluate the stable domains for hot working of this alloy. Deformation below the ‘Tβ’ led to α lamellae kinking followed by fragmentation and dynamic recrystallization of α phase. While deformation above ‘Tβ’ resulted in serrated β boundary, an indicative of dynamic recovery (DRV) of β phase. The processing maps along with the detailed post-deformed microstructural examination showed that the optimum/safe working domains for processing of the alloy are ‘T’ = 1123-1163 K and ‘ $$\dot{\varepsilon }$$ ’ = 10−2-10 s−1.

Identification of the Constitutive Model Parameters by Inverse Optimization Method and Characterization of Hot Deformation Behavior for Ultra-Supercritical Rotor Steel.

X12 (X12CrMoWVNbN10-1-1) ferritic heat resistant steel is an important material for the production of new-generation ultra-supercritical generator rotors. Hot compression tests of X12 ferritic heat-resistant steel were performed via a Gleeble-1500D testing machine under temperatures of 1050–1250 °C and strain rates of 0.05–5 s−1. In order to provide material model data for finite element simulations and accurately predict the hot deformation behavior, a reverse optimization method was proposed to construct elevated temperature constitutive models of X12 ferritic heat-resistant steel in this paper, according to the Hansel–Spittel constitutive model. To verify the accuracy of the model, the predicted and experimental values of the constitutive model were compared. The results indicated that the model had a high prediction accuracy. Meanwhile, the correlation coefficient between the experimental value and the predicted value of constitutive model was 0.97833. For further verification of the accuracy of the model, it was implemented in finite element FORGE@ software to simulate the compression tests of different samples under different conditions. Comparing actual displacement–load curves with displacement–load curves acquired through finite element simulations, the results indicated that displacement–load curves predicted by the model were very consistent with actual displacement–load curves, which verified the accuracy of the model. Moreover, to research the optimal processing parameters of the material, hot processing maps were drawn according to the dynamic material model. In terms of microstructure evolution, a characteristic area distribution map of the hot processing map was established. Therefore, the optimal hot forming parameters regions were in the range of 1150–1200 °C/0.05–0.62 s−1 for X12 ferritic heat-resistant steel.

Hot Deformation Behaviors in Ti-6Al-4V/(TiB + TiC) Composites

Thermal compression testing was investigated using the Gleeble 3800 thermal simulator, and thermal deformation behavior of particle-reinforced titanium matrix composites (TMCs) was studied under deformation temperatures of 750–900 °C, strain rates of 0.001–1 s−1, and experimental deformation of 60%. According to obtained flow stress curves, the hot deformation characteristics were analyzed. Based on the Arrhenius hyperbolic sinusoidal model, the constitutive equation at high temperature was established. Based on the theory of dynamic material models, a hot processing map of TMCs at high temperature was established, and the peak region of power dissipation rate and the instability region in the hot processing map were both determined. At the same time, the corresponding microstructures in the peak power dissipation rate and rheological instability regions were observed. The results showed that flow stress decreased with increasing deformation temperature and increased with increasing strain rate. The thermal deformation activation energy of titanium matrix composites was 301.8 kJ/mol. The Ti-6Al-4V/(TiB + TiC) composites possessed only one instability zone under high-temperature compression at a strain of 0.5, with corresponding temperatures at 750–840 °C and strain rates at 0.1–1 s−1. The optimal thermal deformation parameters included corresponding temperatures of 830–880 °C and strain rates of 0.001–0.05 s−1. The microstructures corresponding to optimal hot working parameters in processing maps were more homogeneous than the microstructures in the instability zone, including the distribution uniformity of reinforcement and the degree of dynamic recrystallization, and no instability phenomena including abnormal grain growth, microcracks or intensive fracture of reinforcements were found, indicating that the hot processing map had a positive guiding effect on the option of desirable material thermal-working parameters.