Hyperbolic Sine Constitutive Equation Research Articles

Hot deformation behavior and process optimization of TC4-DT alloy fabricated by wire and arc additive manufacturing with in-situ forging

The near net shape forging of a preform fabricated using additive manufacturing (AM) technique has attracted significant attention due to its exceptional material utilization rate. However, the complexity of the parts hinders its further development. This study investigated the hot deformation behavior of TC4-DT titanium alloy fabricated by wire and arc additive manufacturing (WAAM) with in-situ forging. The isothermal compression samples underwent homogenizing treatment to eliminate layer bright lines before being subjected to deformation at temperatures ranging from 800 to 950 °C and strain rates ranging from 0.01 to 1 s−1 with the height reduction of 60%. Subsequently, the hot deformation constitutive equations and hot processing map were established to analyze the characteristics of hot deformation and microstructure evolution. The results demonstrate that the hyperbolic sine constitutive equation considering strain can accurately predict flow stress under arbitrary deformation conditions, with an average relative error of 7.23%. Furthermore, microstructure analysis under different deformation conditions validated the applicability of the hot processing map, which identified preferable and easily achievable in-situ hot forging regions at temperatures between 900 and 950 °C and strain rates between 0.05 and 1 s−1 with the strain exceeded 0.4. Finally, WAAM combined with optimized in-situ hot deformation processing enables the production of macrostructures consisting of fully equiaxed prior-β grains while maintaining isotropy in mechanical properties, thereby providing a solid foundation for direct additive manufactured complex forgings featuring uniformly fine equiaxed grains and highly comprehensive properties.

Study on hot processing map with ANN modification and DRX behaviors of a novel Mg-Ga-Sn anode for an air battery

The hot deformation behavior of Mg-Ga-Sn alloys at 360–450 °C and 0.001–1 s−1 was systematically studied by using a thermal simulator. The flow stress is affected by temperature and strain rate, which basically accords with hyperbolic sine constitutive equations. Based on the experimental data, the prediction accuracy of the stress correction model and the artificial neural network (ANN) model was comprehensively compared for the alloy system. The ANN model has good prediction accuracy and a certain degree of extrapolation and generalization ability. By observing the microstructures, the hot processing maps of the ANN modified model were ultimately determined to be closer to the real situation, and the hot processing maps were partially expanded (450–480 °C, 1-2 s−1). Based on the hot processing maps, the suitable processing range (360–450 °C, 0.001–0.01 s−1; 390–420 °C, 0.4–1 s−1) was determined, and a possible processing range (450–480 °C, 0.001–2 s−1; 390–450 °C, 1-2 s−1) was predicted. The EBSD results revealed two typical dynamic recrystallization mechanisms (CDRX and DDRX) in the alloy, corresponding to a strong <0001>//CD texture. In the region of higher temperature and lower strain rate, an obvious bimodal texture is found in the alloy, which is related to the promotion of nonbasal slip by Ga.

Hot Deformation Behavior and Mechanisms of SiC Particle Reinforced Al-Zn-Mg-Cu Alloy Matrix Composites

A systematic and comprehensive analysis of the hot deformation and mechanisms of SiC particle-reinforced aluminum matrix composites is significant for optimizing the processing of the composites and obtaining the desired components. Based on this, related research on 11 vol% SiCp particle-reinforced 7050Al matrix composites was carried out. Hot compression experiments were carried out on the Gleeble-3500 thermal simulator to study the hot deformation behavior of composites at the temperature of 370–520 °C and strain rate of 0.001–10 s−1. The hyperbolic sine constitutive equation of the material was established, and the processing map was calculated. Combining the typical metallograph and misorientation angle distribution, the microstructure evolution mechanism of composites was analyzed, and the effect of particles on recrystallization behavior was investigated. Under certain process conditions, the dominant deformation mechanism of composites changed from dynamic recovery (DRV) to dynamic recrystallization (DRX), and the grain boundary sliding mechanism began to play a role. In addition, high temperature tensile and elongation at break were tested, and it was found that the dominant form of fracture failure changed from brittle fracture of the particles to ductile fracture of the matrix as the temperature increased.

Investigation of deformation behavior of Mg-2Ho alloy based on hyperbolic sine constitutive equation and PSO-BP neural network

In this study, uniaxial hot compression experiments were conducted on as-cast Mg-2Ho binary alloy that had undergone heat treatment. The hot deformation behavior of the alloy and the influence of strain rate (0.001–1 s−1) and deformation temperature (300–450 °C) on the mechanical properties were systematically studied. The microstructure and dynamic recrystallization (DRX) mechanisms of the alloy were analyzed in detail using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) techniques. A strain-compensated Arrhenius constitutive equation based on Zener-Hollomon parameter and a particle swarm optimization-backpropagation artificial neural network (PSO-BP ANN) based on machine learning (ML) were established to study the flow behavior of the alloy. The experimental results demonstrate that the flow stress decreases with increasing temperature and/or decreasing strain rate. The elevated temperature promotes the occurrence of DRX, resulting in a softening behavior observed in the stress-strain curve. The DRX mechanisms for alloys primarily involve continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). Further evaluation was conducted by using the correlation coefficient (R2) and mean squared error (MSE) to assess the constitutive equation and PSO-BP ANN. The prediction accuracy of the constitutive equation is poor (R2 =0.924), whereas the measured flow stress and predicted flow stress by PSO-BP ANN exhibit good consistency (R2 =0.99948), making it widely applicable for analyzing and predicting the hot deformation behavior of Mg-2Ho alloy under different experimental conditions.

Hot deformation behavior and microstructure evolution of flaky Ti3AlC2 particles reinforced pure Al composite

Optimizing the hot working parameters of metal matrix composites is beneficial for improving the microstructure of the matrix and the distribution of the reinforcements and eliminating materials defects. In this work, the hot deformation behaviors of the 20 vol% flaky Ti3AlC2 particles reinforced pure Al composite at strain rates of 10−3–1 s−1 and temperatures of 350–500 °C were investigated by hot compression tests. Friction correction equations were used to correct the flow stress data. The constitutive equations and processing maps were successfully established. The flow stresses of the Ti3AlC2/Al composite were precisely described through the hyperbolic sine constitutive equation. The true stress exponent was calculated to be 8, similar to the creep process with invariant microstructure. The particle rotation caused by the deformation of the Al matrix led to the alignment of the Ti3AlC2 flakes. The optimum hot working parameters of the composite are in the range of 410–500 °C, 0.18–1 s−1 based on the processing maps. Dynamic recrystallization (DRX) had a higher proportion in the optimum safe region. The high temperature-low strain rate unstable region was associated with superplastic. The instability in the low temperature-low strain rate region stemmed from the interface microcracks generated by the rotation of Ti3AlC2 flakes. The processing map theory can be well correlated with the microstructure evolution of the composite under different deformation parameters.

Dynamic recrystallisation and constitutive equation in hot deformed AISI H10 tool steel

ABSTRACT The compression deformation behavior of AISI H10 (DIN 32CrMoV12-28) hot work tool steel was investigated at temperatures ranging from 900°C to 1200°C and strain rates from 0.01 to 1 s−1. True stress-strain curves showed that a decrease in strain rate or increase in deformation temperature can promote the occurrence of DRX. It was found that the characteristic strains and stresses decrease with an increase in temperature or decrease in strain rate. The σc/σp ratio takes an average of 0.94; and the ϵc/ϵp ratio lies in range of 0.48-0.65 (average of 0.53). This suggests that DRV in H10 is not extensive and DRX starts at strains about half of the peak strain. However, the extensive softening by DRX keeps σp close to σc. Using the hyperbolic-sine constitutive equation, the deformation activation energy was calculated to be about 435.76 kJ mol−1.

Investigation of strain-rate sensitivity of T91 Steel Using Small Punch Testing

The Small Punch Test (SPT) is a useful technique for deriving location-dependent mechanical properties using small-sized specimens. In this work, we have investigated the tensile and fracture behavior of T91 steel, a candidate material for fusion and Gen IV fission nuclear reactors, by the SPT technique. Firstly, the hot shear flow behavior of T91 steel was investigated by SPT in the temperature range of 400 – 550 °C under quasi-static strain rates (0.003 mm/min and 0.3 mm/min). Further, the hot deformation material parameters in the exponential power-law and hyperbolic sine constitutive equations have been evaluated. The effect of temperature and strain rate variation on stress exponent in power-law and activation energy from hyperbolic sine equation have been correlated.

Microstructure and flow behaviour of a quenching and partitioning steel at elevated temperatures

ABSTRACT Hot compression tests were carried out on a quench and partitioning steel in the temperature range of 850-1050 °C and strain rates of 10-3- 1 s-1. The single-peak flow curves were appeared at high strain rates and low temperatures and the multi-peaks at the opposite condition. It was found that the mechanism of dynamic recrystallization (DRX) changes by passing from 950 °C due to dynamic precipitation of carbide particles. The microstructural characterizations using optical microscopy and electron back scattered diffraction (EBSD) techniques revealed various mechanisms of DRX in different deformation conditions. EBSD results showed opposite variations of high and low angle grain boundaries with increasing deformation temperature and decreasing strain rate. By using the hyperbolic sine constitutive equation, the value of apparent activation energy at the typical strain of 0.5 was determined as 297.67 kJ/mol.

Hot Deformation Behavior and Development of Constitutive Equations on a Novel γ-γ/ Ni-base Superalloy: AD730

In this work, hot deformation behavior and microstructural evolution for a novel Ni-base superalloy, AD730, were analyzed using a hyperbolic sine constitutive equation. The hot compression tests were carried out at a wide range of temperatures (950oC-1200oC) and strain rates (0.001-1 s-1). The modeling was done at the overall deformation conditions, and then the obtained important constitutive parameters, i.e., n and Q, were calculated to be 5.44 and 820.26 kJ/mol, respectively. Microstructural evolution showed two distinct domains at higher temperatures (1100oC, 1150oC, and 1200oC) and lower ones (950oC, 1000oC, and 1050oC) accomplished by dynamic recrystallization (DRX) and non-DRX behavior due to absence and presence of γ/ particles, respectively. Furthermore, the constitutive equations were analyzed based on both separated temperature domains. The obtained parameters from this approach demonstrated better results as compared with the literature, i.e., the parameters of n and Q were calculated to be 8.60 and 1160.45 kJ/mol at the lower domain, in contrast with 3.69 and 468.32 kJ/mol which were at higher ones. Additionally, the stress prediction data based on correlation coefficient factor (R2) presented the best reliable prospective at two separated domains as 0.994, as compared with overall conditions prediction with 0.963. It was found that hot working of AD730 alloy as well as flow stress can be essentially affected by the γ/-phase. Therefore, the hot deformation behavior of AD730, as a γ/-containing superalloy, should be performed at identified domains considering the solution temperature of γ/-phase.

Hot Deformation Behavior and Constitutive Analysis of As-Extruded Mg–6Zn–5Ca–3Ce Alloy Fabricated by Rapid Solidification

The plasticity of Mg–6Zn–5Ca–3Ce alloy fabricated by rapid solidification (RS) at room temperature is poor due to its hexagonal-close-packed (HCP) structure. Therefore, hot deformation of RS Mg–6Zn–5Ca–3Ce alloy at elevated temperature would be a major benefit for manufacturing products with complex shapes. In the present study, hot deformation behavior of as-extruded Mg–6Zn–5Ca–3Ce alloy fabricated by RS was investigated by an isothermal compression test at a temperature (T) of 573–673 K and strain rate (ε˙) of 0.0001–0.01 s−1. Results indicated that the flow stress increases along with the declining temperature and the rising strain rate. The flow stress behavior was then depicted by the hyperbolic sine constitutive equation where the value of activation energy (Q) was calculated to be 186.3 kJ/mol. This issue is mainly attributed to the existence of fine grain and numerous second phases, such as Mg2Ca and Mg–Zn–Ce phase (T’ phase), acting as barriers to restrict dislocation motion effectively. Furthermore, strain compensation was introduced to incorporate the effect of plastic strain on material constants (α,Q,n,lnA) and the predicted flow stresses under various conditions were roughly consistent with the experimental results. Moreover, the processing maps based on the Murty criterion were constructed and visualized to find out the optimal deformation conditions during hot working. The preferential hot deformation windows were identified as follows: T = 590–640 K, ε˙ = 0.0001–0.0003 s−1 and T = 650–670 K, ε˙ = 0.0003–0.004 s−1 for the studied material.

Hot deformation behavior and processing maps of hybrid SiC and CNTs reinforced AZ61 alloy composite

The hot deformation behavior of hybrid SiC and CNTs reinforced AZ61 alloy composite was investigated by hot compacting at the strain rate range of 10−4–0.1 s−1 and temperature range of 250–400 °C. The constitutive equation and processing maps were successfully established and checked. The results revealed that the composite exhibited typical flow behavior of metallic materials, and the flow stress increased as the temperature decreased and strain rate increased. The flow behavior was precisely described by using hyperbolic sine constitutive equation in this work. The average stress exponent and activation energy of the composite are 4.9 and 174 kJ/mol, respectively, indicating that the dominant deformation mechanism might be dislocation climb. The processing maps of the composite exhibited two instability zones and two safe zones (250–330 °C, 0.001–0.006 s−1 and 350–390 °C, 0.0001–0.0005 s−1) for selection of optimum processing parameters. Dynamic recrystallization (DRX) occurred in the safe zones, however, cracking and twinning were observed in the instability zones. In addition, the examination of microstructure evolution revealed that DRX gradually occurred more adequately as the temperature increased and strain rate decreased, and SiC particulates could promote the DRX of the composite due to the particle stimulating nucleation (PSN) effect.

Microstructural evolution, flow stress and constitutive modeling of Al−1.88Mg−0.18Sc−0.084Er alloy during hot compression

To explore the hot compression behavior and microstructural evolution, fine-grained Al−1.88Mg−0.18Sc− 0.084Er (wt.%) aluminum alloy wires were fabricated with Castex (continuous casting−extrusion) and ECAP-Conform, and their hot compression behavior was investigated at temperatures of 673−793 K and strain rates of 0.001−10 s−1; the microstructures were characterized by optical microscope, X-ray diffractometer, transmission electron microscope, and electron backscattered diffractometer, and the flow stresses were obtained by thermal compression simulator. Microstructural evolution and flow curves reveal that dynamic recovery is the dominant softening mechanism. Continuous dynamic recrystallization followed by dynamic grain growth takes place at a temperature of 773 K and a strain rate of 0.001 s−1; the yielding drop phenomenon was discovered. Hyperbolic sine constitutive equation incorporating dislocation variables was presented, and a power law constitutive equation was established. The stress exponent is 3.262, and the activation energy for deformation is 154.465 kJ/mol, indicating that dislocation viscous glide is the dominant deformation mechanism.

Research on dynamic recrystallization behavior of Ni[sbnd]Fe[sbnd]Cr based alloy

The dynamic recrystallization (DRX) behavior of Ni-Fe-Cr based alloy was studied in temperature range of 980–1130 °C and strain rate range of 0.01–10s−1. By systematically analyzing the stress-strain data and microstructure evolution of NiFeCr based alloy, the influences of strain rate, temperature and strain on the critical conditions for DRX behavior were investigated. Meanwhile, the constitutive equation of the correlation between peak stress and Z parameters was established by using hyperbolic sine constitutive equation. The DRX critical strain model, kinetics model and grain size model of the studied alloy were also established. The deformation activation energy is 496.92 kJ/mol. The DRX behavior of the studied alloy is sensitive to deformation temperature and strain rate. With the decrease of strain rates or the increase of deformation temperatures, the critical strain of DRX softening decreases, and the volume fraction of DRX increases. In addition, the three models can accurately predict and characterize DRX behavior of the studied alloy.

Determination of Constitutive Equation and Thermo–Mechanical Processing Map for Pure Iridium

Deformation behavior of pure iridium has been studied during thermal compression testing with the help of Gleeble-1500D in the temperature range of 1200 °C~1500 °C and strain rate range of 10−1 s−1~10−2 s−1. Resistance to deformation, microstructural evolution and hot workability of pure iridium have been used to analyze in detail. Frictional coefficient has been used to modify the experimental stress–strain curve of thermal compression test, and it has been found effective in reducing the influence of friction during thermo–mechanical testing. The hyperbolic sine constitutive equation of pure iridium has been established to give a material processing model for numerical simulation. A very high value of activation energy for iridium, 573 KJ/mol, clearly indicates that it is very hard to deform this material. The deformation mechanism of pure iridium is dependent upon temperature as well as strain rate. At low temperature and strain rate (temperature range of 1200 °C~1300 °C and strain rate range of 10−1 s−1~10−2 s−1), dynamic recovery is active while dynamic recrystallization becomes operative as temperature and stain rate are increased. On further increase in temperature and decrease in strain rate (temperature range of 1400 °C~1500 °C and strain rates of 10−2 s−1~10−3 s−1), abnormal grain growth takes place. On the basis of a constitutive model and processing map, suitable forming process parameters (temperature range of 1400 °C~1500 °C and strain rate range of 0.1 s−1~0.05 s−1) for pure iridium have been worked out.

On the prediction of hot deformation mechanisms and workability in Al6063/Nip and Al6063/steelp composites using hyperbolic-sine constitutive equation

The present study investigates the hot deformation mechanisms and workability in novel AA6063-Nip and AA6063-Steelp composites using hyperbolic-sine constitutive equation. The AA6063-Nip and AA6063-Steelp composites were produced with AA 6063 as matrix, and 6 wt% Ni or 6 wt% steel particles as reinforcement for each of the composite, with the adoption of double stir casting method for the composite production. Axisymmetric compression testing was performed using Gleeble 3500 thermomechanical simulator at temperature and strain rate of 200–400 °C and 0.01–10 s−1 respectively to a global strain of 0.5, while constitutive model was used to study the hot working characteristics of AA6063-Nip and AA6063-Steelp composites. The results showed that anomalous flow stress oscillations and partial insensitivity to strain rate, characterised the flow stress patterns displayed by both composites. The activation energies (QHW) values derived at incremental strain, were within the range of 83.8 to 218.4 kJ/mol for AA 6063/Nip and 14.2 to 271.9 kJ/mol for AA 6063/Steelp composites. The highest values of the QHW, for AA 6063/Nip was 53% and for AA 6063/Steelp was 91% higher than that for self-diffusion of Aluminium (QSD ∼142 kJ/mol), which suggest that the deformation controlling mechanism was work hardening facilitated by dispersion strengthening. This was supported by the stress exponent values which exceeded 5 for both composites – affirming dispersion strengthening to dominate the deformation process. Also, the QHW of the composites was intermediate in comparison with the range of 111 – 509 kJ/mol reported for AMCs of similar reinforcement composition in literature, indicating that both composites have intermediate workability.

Study on hot deformation behavior of AISI 414 martensitic stainless steel using 3D processing map

Hot deformation of AISI 414 martensitic stainless steel was studied over the temperature and strain rate intervals of 950−1150 °C and 0.001 to 1 s−1, respectively. Based on the extracted data from hot compression tests a hyperbolic sine constitutive equation with correlation coefficient (R) of 0.99 was developed to model the flow behavior. The dynamic materials model (DMM) was used to establish the three-dimensional (3D) processing maps as a function of deformation temperature, strain rate, and strain. The analysis of the maps revealed that applied strain had a significant effect on power dissipation efficiency (η) and flow instability (ξ). Based on the generated processing maps four domains with the highest value of η were identified which represent the safe regions for hot working. Microstructural observation showed the significant effects of the temperature and strain rate on grain size evolution during hot deformation. From the microstructure analysis, the optimum hot working conditions were determined to be in the 1000−1130 °C temperature and 0.1–1 s−1 strain rate ranges. Dynamic recrystallization was identified as the dominant restoration mechanism under these conditions. The influence of carbides on size of the dynamic recrystallized grain was also studied and correlated with grain size evolution. On the basis of the obtained results, a correlation between the dynamically recrystallized grain size and Zener–Hollomon parameter is proposed.

Hot deformation behaviour of 40CrNi steel and evaluation of different processing map construction methods

40CrNi steel is a low alloy steel with medium hardenability and has been widely used in the manufacturing of crankshafts, wind turbine forgings, etc. As forging is usually involved in the manufacturing of these components, optimization of the hot deformation process of 40CrNi steel is quite critical. Towards this, the prediction of flow stress and the determination of optimal processing parameter windows are of great importance. In this research, isothermal uniaxial hot compression tests were carried out for 40CrNi steel with true strain rates of 0.01, 0.1, 1, 10 and 30 s−1 and temperatures of 850–1200 °C. Both the strain compensated hyperbolic sine constitutive equation and the modified Johnson-Cook model were adopted to predict the flow stress curves, with average absolute relative errors of 0.034 and 0.061, respectively. Processing maps of the tested steel were constructed to determine the optimal deformation parameter windows, and the characteristics of the prior austenite microstructure generally correspond very well to the processing map established. Furthermore, different processing map construction methods were compared and it was found that power-dissipation efficiency maps strongly rely on the σ- ε˙ relationship. Assuming a certain type of constitutive equations leads to monotonic efficiency value patterns. Calculation methods based on experimental results are helpful to reflect the meaningful information carried by the experimental σ- ε˙ relationships.

High temperature behavior of severely deformed AA 5083 through equal channel lateral extrusion

Describing the high temperature behavior of a fine-grained AA 5083 aluminum alloy using an improved constitutive model is the focus of this paper. Dual Equal Channel Lateral Extrusion (DECLE) was utilized to create fine-grain microstructure in AA 5083 aluminum alloy. EBSD confirmed the formation of fine-grain microstructure after 5 passes of DECLE. The hot deformation behavior of the DECLEd alloy was assessed by hot compression tests at temperatures of 200–275 °C and strain rates of 10−4-10−1 s−1. The material constants, A, n and Q, in the hyperbolic-sine constitutive equation were calculated at peak stresses. The results suggested that the grain size affects the values of α and n, while the activation energy (Q) is more or less independent of the grain size. The values of α and n for the fine-grain material were obtained as 0.004357 (MPa−1) and 9.97, respectively. These calculated values (α and n) are respectively lower and higher than those reported for a coarse-grain one in the literature. This result was related to the high flow stress of the refined microstructure. The value of Q showed that the dislocation-dispersoid interactions are the rate-controlling mechanism during hot deformation. By iterating the calculation of constants at various strains, a strain-compensated constitutive equation was proposed for the prediction of flow stress over a wide range of strain. Finally, the processing maps were developed for the AA 5083 alloy at various strains.

Effects of Mn addition and related Mn-containing dispersoids on the hot deformation behavior of 6082 aluminum alloys

The hot deformation behaviors of 6082 aluminum alloys containing different Mn contents (0.05–1.0 wt%) were systematically investigated by uniaxial compression tests in a temperature range of 400–550 °C and strain rate range of 0.001–1 s-1. Prior to the hot deformation, a low-temperature homogenization (450 °C for 6 h) was carried out on direct-chill cast billets to promote the precipitation of Mn-containing dispersoids. The large numbers of dispersoids in the Mn-containing alloys yielded significantly increased high-temperature flow stresses, compared to that of the base alloy without dispersoids. The material constants and activation energies for hot deformation were determined using the hyperbolic-sine constitutive equation and experimental peak flow stress data. The activation energy increased from 191 kJ/mol for the base alloy to 286 kJ/mol for the alloy with 0.5% of Mn. With further increase in Mn content, the activation energy increased only moderately to 315 kJ/mol for the alloy with 1.0% of Mn. The influences of the Mn content and deformation conditions on the dynamic recovery and recrystallization were quantitatively analyzed. The precipitation of dispersoids in the Mn-containing alloys promoted the retardation of the dynamic recovery and inhibition of the recrystallization owing to their strong pinning effect on the dislocation movement and subgrain migration.

A comparative study on the hot deformation behavior of Ti[sbnd]5Al[sbnd]5Mo[sbnd]5V[sbnd]3Cr and newly developed Ti[sbnd]4Al[sbnd]7Mo[sbnd]3V[sbnd]3Cr alloys

Hot deformation behavior of Ti-5553 and newly-developed Ti-4733 β-Ti alloys were compared by hot compression tests at 930–1080 °C and strain rates of 0.001–1 s−1. The flow curves and microstructures showed that dynamic recovery and partial continuous dynamic recrystallization are the dominant microstructural mechanisms at hot working condition. It was observed that the flow stress of Ti-4733 lies over that of Ti-5553. Using the M¯d¯-B¯O¯diagram, Mo equivalent number and the valence electron count, it was shown that β-phase in Ti-4733 is more stable than that in Ti-5553. The higher strength of Ti-4733 was attributed to the more stability of β and its higher Mo equivalent number. While the β quenched microstructure in Ti-5553 contained parallel layers of α′ martensite, it was absence in Ti-4733 due to the more stability of β. Using the hyperbolic-sine constitutive equation the values of apparent activation energy for Ti-5553 and Ti-4733 were determined as 380 and 315 kJ/mol, respectively. The Kocks-Mecking dislocation evolution model was used to model the flow curves. The recovery and hardening parameters for Ti-4733 in the developed model were found lower than those for Ti-5553. The model could satisfactorily predict the experimental flow curves at various conditions.