Flow Stress Strain Curves Research Articles

Effects of Trace Ce Addition on Hot Deformation Behavior of Cu-0.8 Mg Alloy

Hot deformation tests of Cu-0.8 Mg and Cu-0.8 Mg-0.15 Ce alloys were carried out with a Gleeble-1500D thermal simulator in the temperature range of 500-850°C and the strain rate range of 0.001-10 s−1. Based on compression tests, flow stress–strain curves and processing maps of Cu-0.8 Mg and Cu-0.8 Mg-0.15 Ce alloys were plotted, and constitutive equations of the two alloys were constructed. The microstructure of the two alloys under different hot deformation conditions was observed and analyzed by optical microscopy. The trace addition of Ce restricted the movement of dislocations, promoted dynamic recrystallization, increased the flow stress and activation energy for hot deformation and enlarged the hot working region compared to the alloy without trace Ce addition.

Investigation on superplastic deformation behavior and microstructure evolution of TNW700 titanium alloy

TNW700 titanium is a near-α high temperature titanium alloy, which can be used at 700°C for a short time. The superplasticity behavior and microstructure evolution of TNW700 alloy were investigated by means of isothermal tensile test within the temperature and strain rate ranges from 900° to 975°C and 0.01s-1 to 0.0005s-1, respectively. The flow stress-strain curves show that deformation temperature, strain rate and strain all play an important role in the superplasticity test of the TNW700 alloy. Flow stress decreases with increasing temperature and decreasing strain rate, and increases with increasing strain. Meanwhile, the TNW700 alloy exhibits a longer hardening stage, especially at the lower strain rates, which may be related to the presence of (ZrSi) precipitated phases. The microstructure evolution observed by scanning electron microscope (SEM) indicate that (ZrSi) precipitated phases are mainly distributed at α and β phase boundaries. The volume fraction and the grain size of β phase gradually increase with increasing temperature and decreasing strain rate, and the influence of temperature on it is greater than that of the strain rate, especially at high temperatures. Grain coarseness caused by dynamic and static growth is the main cause of stress hardening. The strain rate sensitivity exponent (m) was calculated to identify the dominant deformation mechanisms under various deformation parameters.

Constitutive Model and Flow Behavior of B1500HS High-Strength Steel During the Hot Deformation Process

Hot compression tests were carried out on a Gleeble-3800 thermal mechanical simulator in the temperature range from 700 to 900 °C and strain rate range from 0.005 to 10 s−1 to investigate the hot deformation behavior of B1500HS high-strength steel. Softening mechanisms of B1500HS high-strength steel under different deformation conditions were analyzed according to the characteristics of flow stress–strain curves. By analyzing and processing the experimental data, the values of steady flow stress, saturated stress, dynamic recovery (DRV) softening coefficient, and other factors were solved and these parameters were expressed as functions of Zener–Hollomon factors. Based on the dislocation density theory and the kinetic model of dynamic recrystallization (DRX), constitutive models corresponding to different softening mechanisms were established. The flow stress–strain curves of B1500HS predicted by a constitutive model are in good agreement with the experimental results and the correlation coefficient is . The comparison results indicate that the constitutive models can accurately reflect the deformation behavior of B1500HS high-strength steel under different conditions.

Study on Dynamic Mechanical Properties and Constitutive Model Construction of TC18 Titanium Alloy

In order to investigate the static and dynamic mechanical properties of TC18 titanium alloy, the quasi-static stress–strain curve of TC18 titanium alloy under room temperature was obtained by DNS 100 electronic universal testing machine (Changchun Institute of Mechanical Science Co., Ltd., Changchun, China). Meanwhile, the flow stress–strain curves under different temperatures and strain rates are analyzed by split Hopkinson pressure bar (SHPB) device with synchronous assembly system. On the basis of the two experimental data, the JC constitutive model under the combined action of high temperature and impact load is established using the linear least squares method. The results show the following: the yield strength and flow stress of TC18 titanium alloy increase slowly with the increase of the strain rate, and the strain value corresponding to the yield strength is reduced. With the increase of strain, the flow stress increases at first and then decreases at different temperatures. The strain value corresponding to the transition point rises with the temperature increase, and the corresponding stress value remains basically unchanged. With the increase of experimental temperature, the flow stress shows a downward trend, and the JC constitutive model can predict the plastic flow stress well.

Plastic flow behavior of twinning induced plasticity steel from low to warm temperatures

This work investigates the tensile behavior of twinning induced plasticity (TWIP) steel under room to warm temperatures. Stress-strain flow curves have been obtained from steady-state uniaxial tensile tests performed at different temperatures, that is, from 20 to 800°C, and different engineering strain rates, 0.003 and 0.5s−1. The yield and ultimate tensile strength, elongation at fracture, reduction of area, strain hardening exponent and strain hardening rate have been defined to describe the plastic behavior of TWIP steel. It has been found that the plastic flow behavior of TWIP steel is characterized by negative strain rate sensitivity and strain hardening, at temperatures from 20 to 300°C, until the twinning mechanism occurs. At these temperatures, dynamic strain aging starts at the beginning of plastic deformation, with the appearance of fluctuations in the work hardening rate and local strain rate. Pronounced local serrations also appear at 300°C and 0.003s−1. Plastic deformation is mainly driven by dislocation gliding at 550 and 800°C, and mechanical twins are absent. As a result, negative strain rate sensitivity and local serrations disappear in the stress-strain curves. Creep also contributes notably to plastic deformation at 800°C, as was also observed on the fracture surfaces of tensile samples. Mechanical twins were only visible for the lower temperatures. The grains in the sample tested at 800°C and 0.003s-1 were fully recrystallized.

Study on constitutive model and dynamic recrystallization softening behavior of AZ80A magnesium alloy

The microstructures of as-cast AZ80A magnesium alloy before and after homogenization treatment were studied. The flow behaviors of the homogenized alloy under different deformation conditions were studied by isothermal compression tests. Based on the flow stress-strain curves of the homogenized alloy, the constitutive model was established by the strain compensation method. The strain rate sensitivity index maps with different strains were constructed to quantify the dynamic recrystallization softening behavior of the homogenized alloy. Based on this, the influence of deformation temperature and strain rate on strain rate sensitivity index and dynamic recrystallization microstructure evolution were studied. The results show that both increasing homogenization temperature and holding time are beneficial for the β-phases to dissolve and alloying elements to diffuse. It is concluded that the proper homogenizing parameter of as-cast AZ80A magnesium alloy is 683 K for 20 h. Both the increase of deformation temperature and the decrease of strain rate are beneficial to the increase of strain rate sensitivity index. The region with an index greater than 0.22 corresponds to dynamic recrystallization softening zone and has good deformation properties.

Deformation behavior and microstructure evolution mechanism of 5vol.% (TiBw + TiCp)/Ti composites during isothermal compression

Isothermal compression tests of as-cast 5vol.% (TiBw + TiCp)/Ti composites were conducted in the deformation temperature ranging from 900 to 1100 °C and strain rate ranging from 0.001 to 1.0 s−1. The thermal deformation behavior and microstructure evolution mechanism of the material are studied to optimize the process parameters. Meanwhile, the flow stress-strain curves were measured. The activation energy decreases with increasing of compression temperature, which is related to the increase of β phase content with the increase of temperature. The constitutive equation was established to characterize the deformation behavior of 5vol.% (TiBw + TiCp)/Ti composites in hot compression. The softening mechanism is mainly dynamic recovery (DRV) and dynamic recrystallization (DRX) in different phase region. Transmission electron microscope (TEM) observation was used to study the effects of reinforcements on microstructural evolution. The results indicate that the reinforcement can prominently promote globularization of α lath in the α + β phase region. In the upper α + β phase region, the reinforcement promotes the formation of some subgrains in the matrix.

Enhancement in Viscoplastic Self-Consistent FLD Prediction Model and Its Application for Austenitic and Ferritic Stainless Steels

The computational algorithm of a crystal-plastic-based FLD predictive model (VPSC-FLD) developed in Jeong et al. (Model Simul Mater Sci Eng, 2016. https://doi.org/10.1088/0965-0393/24/5/055005 ) is enhanced. A real-time monitor process runs while the forming limit diagram is calculated by parallel computation on various strain loading paths. The monitor process enables the CPU workers to communicate with each other so that the unnecessary model runs can be determined and terminated on the fly. Moreover, the advanced numerical algorithm suggested earlier by Schwindt et al. (Int J Plast 73:62–99, 2015. https://doi.org/10.1016/j.ijplas.2015.01.005 ) is implemented to VPSC-FLD. The new numerical algorithm and real-time monitor has improved both the overall computational speed and the efficiency in parallel computation. The enhanced VPSC-FLD model is applied for austenitic and ferritic stainless samples in terms of flow stress–strain curve, R-values, and forming limit diagram. The linearization scheme applied on the local constitutive description is studied to reveal its impacts on various macroscopic properties. It is found that the linearization scheme with the best fit on uniaxial data is not necessary the one that gives the best predictive accuracy on the forming limit prediction.

Determination of the Flow Stress–Strain Curves of Aluminum Alloy and Tantalum Using the Compressive Load–Displacement Curves of a Hat-Type Specimen

The load–displacement curves of an aluminum alloy and tantalum were determined using a hat-type specimen in the compression test. Based on the results of finite element analysis, the employed geometry of the hat-type specimen was found to yield a load–displacement curve that is nearly independent of the friction between the specimen and the platen. The flow stress–strain curves of the alloy and tantalum were modeled using the Ludwik and Voce constitutive laws, respectively; furthermore, simulation of the compression event of the hat-type specimen was performed by assuming appropriate constitutive parameters. The constitutive parameters were varied via an optimization function built in matlab until the simulated load–displacement curves reasonably fit the experimental curve. The optimized constitutive parameters obtained in this way were then used to construct friction-free flow stress–strain curves of the two materials.

Hot Deformation Behavior and Processing Map of Cast 5052 Aluminum Alloy

Hot deformation behavior of cast 5052 aluminum alloy was investigated at the temperature between 300°C and 500°C and the strain rate range from 0.01 s-1 to 10 s-1 by hot compression tests. The constitutive model was established through the flow stress–strain curves, the activation energy was 207 kJ/mol, and the correlation coefficient for linear regression of constitutive model was 0.98. The processing map was established to optimize the deformation parameters, such as the optimize deformation parameters with 0.6 strain was at 420℃-480℃ and 0.01 s-1-0.223 s-1.

Effects of Heterogeneous Microstructures on the Strain Hardening Behaviors of Ferrite-Martensite Dual Phase Steel

The complex strain hardening behaviors of dual phase (DP) steel are subjected to the heterogeneous microstructures. The current work aims to predict the strain hardening behaviors of ferrite-martensite DP steel, focusing on the effects of heterogeneous microstructure on mechanical properties. The flow stress of material was calculated based on the dislocation-based work-hardening model with considering the multi-boundaries hardening. The ferrite-martensite phase boundary percent and grain shape factor were selected as the heterogeneous feature parameters, which were introduced into the new proposed model. The theoretical calculated stress-strain responses were verified with experimental results using the tensile test. The model with the boundary strengthening consideration has more accurate results. The parameter effects of ferrite-ferrite boundary (FFB) spacing, ferrite-martensite boundary (FMB) percent, and grain shape factor on the flow stress-strain curve were researched.

Formability predictions and measurement of 316L stainless steel using self-consistent crystal plasticity

A viscoplastic self-consistent (VPSC) crystal plasticity model was used to describe the mechanical behavior of a 316L stainless steel sample. Mechanical anisotropy of the 316L stainless steel was evidenced in the experimental results collected from the uniaxial tension tests along various directions. EBSD images were obtained from the as-received sample, and a representative population of discrete orientations was created to account for the initial crystallographic texture in the model. The hardening parameters were identified by using the flow stress-strain curve obtained from a bulge test. The model-predicted and experimental flow-stress curves and R-values were compared in order to estimate the adequacy of the VPSC model to describe the anisotropic behaviour of the 316L stainless steel sample. Furthermore, the crystal plasticity model, in conjunction with the Marciniak-Kuczyński approach, was used to predict forming limit diagram. The model was validated by comparing with the experimental flow stress curves from uniaxial tension and bulge tests. The predictive accuracy on forming limit diagram was also estimated by comparing with the experimental forming limit strains obtained through Nakajima tests.

An optimized constitutive model for reproducing flow stress–strain relationships of anisotropic materials

Due to the strong anisotropic property of the advanced metal materials used in automobile, aviation, and aerospace, experimental flow stress–strain relations including different stress states are necessary to provide the information of anisotropic hardening and plastic flow for constructing a constitutive model. Therefore, reasonably reproducing the experimental stress–strain relations is the most fundamental work to substitute adequate flow stress–strain curves into the constitutive equation at the same time. However, accurate and stable regression results are difficult to obtain through the current regression models such as power exponent, second-order function model, fourth-order function model, and so forth. In this paper, an optimized model named as a least square quadratic regression model (ordinary least square model) was proposed based on the most useful second-order function model. The significant difference is that all experimental points are used to reproduce the experimental stress–strain relations in ordinary least square model in place of only three experimental points adopted in second-order function model, which results in good regression accuracy. Through comparison, it is found that the regression results by power function are poor with regard to some experimental results, and the results reproduced by second-order function model or fourth-order function model are very sensitive to the experimental points selected to do the regression. The sum of squares for error (SSE) increases sharply when the selected points are unreasonable. In addition, for second-order function and fourth-order function models, only limited experimental points are adopted to do the regression, the best regression accuracy cannot be obtained even if the selected points are reasonable. In contrast, SSE of the regression curve by ordinary least square model reduces to less than 50% of the best regressed result by second-order function model, the yielding behavior and variable strain increment ratio of the anisotropic materials can be reflected more accurately. This is very important for accurately describing the plastic flow behaviors of anisotropic materials.

Hot Deformation Behavior and a Two-Stage Constitutive Model of 20Mn5 Solid Steel Ingot during Hot Compression.

20Mn5 steel is widely used in the manufacture of heavy hydro-generator shaft forging due to its strength, toughness, and wear resistance. However, the hot deformation and recrystallization behaviors of 20Mn5 steel compressed under a high temperature were not studied. For this article, hot compression experiments under temperatures of 850–1200 °C and strain rates of 0.01 s−1–1 s−1 were conducted using a Gleeble-1500D thermo-mechanical simulator. Flow stress-strain curves and microstructure after hot compression were obtained. Effects of temperature and strain rate on microstructure are analyzed. Based on the classical stress-dislocation relationship and the kinetics of dynamic recrystallization, a two-stage constitutive model is developed to predict the flow stress of 20Mn5 steel. Comparisons between experimental flow stress and predicted flow stress show that the predicted flow stress values are in good agreement with the experimental flow stress values, which indicates that the proposed constitutive model is reliable and can be used for numerical simulation of hot forging of 20Mn5 solid steel ingot.

Dynamic Recrystallization Behavior and Corrosion Resistance of a Dual-Phase Mg-Li Alloy

The hot deformation and dynamic recrystallization behavior of the dual-phase Mg-9Li-3Al-2Sr-2Y alloy had been investigated using a compression test. The typical dual-phase structure was observed, and average of grain size of as-homogenized alloy is about 110 µm. It mainly contains β-Li, α-Mg, Al4Sr and Al2Y phases. The dynamic recrystallization (DRX) kinetic was established based on an Avrami type equation. The onset of the DRX process occurred before the peak of the stress–strain flow curves. It shows that the DRX volume fraction increases with increasing deformation temperature or decreasing strain rate. The microstructure evolution during the hot compression at various temperatures and strain rates had been investigated. The DRX grain size became larger with the increasing testing temperature or decreasing strain rate because the higher temperature or lower strain rate can improve the migration of DRX grain boundaries. The fully recrystallized microstructure can be achieved in a small strain due to the dispersed island-shape α-Mg phases, continuous the Al4Sr phases and spheroidal Al2Y particles, which can accelerate the nucleation. The continuous Al4Sr phases along the grain boundaries are very helpful for enhancing the corrosion resistance of the duplex structured Mg-Li alloy, which can prevent the pitting corrosion and filiform corrosion.

High-temperature deformation behavior of a beta Ti–3.0Al–3.5Cr–2.0Fe–0.1B alloy

The high-temperature deformation behavior of a beta Ti–3.0Al–3.5Cr–2.0Fe–0.1B alloy was investigated by a Gleeble-1500D thermal simulator. The height reduction was 50%, corresponding to a true strain of 0.693. The strain rate ranging from 0.01 to 10.00 s−1 and the deformation temperature ranging from 800 to 950 °C were considered. The flow stress and the apparent activation energy for deformation, along with the constitutive equation, were used to analyze the behavior of the Ti–3.0Al–3.5Cr–2.0Fe–0.1B alloy. The processing map was established. The effect of strain rate on the microstructure at 850 °C was evaluated. The flow stress–strain curves indicated that the peak flow stresses increased along with an increase in the strain rate and decreased as the deformation temperature increased. Based on the true stress–true strain curves, the constitutive equation was established and followed as the $$\dot{\varepsilon } = 6.58 \times 10^{10} \left[ {{ \sinh }\left( {0.0113\sigma } \right)} \right]^{3.44} { \exp }\left( { - 245481.3/RT} \right)$$ . The processing map exhibited the “unsafe” region at the strain rate of 10 s−1 and the temperature of 850 °C, and the rest region was “safe”. The deformation microstructure demonstrated that both dynamic recovery (DRV) and dynamic recrystallization (DRX) existed during deformation. At the lower strain rate of 0.01 s−1, the main deformation mechanism was the DRV, and the DRX was the dominant deformation mechanism at the higher strain rate of 1.00 s−1.

Hot Deformation Characterization of Haynes-242

Ni-based super alloys are metallic materials with exceptional combinations of creep and oxidation resistance at high temperatures. Wrought alloys are hot formed at high temperatures and subsequently annealed and aged. The final mechanical properties of the alloys are a combination of the grain size generated during the process and the precipitation state after aging. In fact, precipitation phenomena are complex for these alloys, which contain up to 12 different elements in their compositions. This study deals with the forming characteristics of Haynes 242. Hot forming is easy to carry out as it requires less efforts but it makes material more dynamic in nature. Haynes 242 was deformed at different temperatures and strain rates. The variation of these parameters on the stress strain flow curves were analysed and study has made on the microstructure evolution and recrystallised grain size.

Forming limits of dual phase steels using crystal plasticity in conjunction with MK approach

A viscoplastic self-consistent crystal plasticity model was used to describe the mechanical behavior of two dual phase steel samples DP780 and DP1000. Mechanical anisotropy of these alloys was observed in uniaxial tests conducted along various directions. Additionally, X-ray diffraction was conducted to obtain the averaged crystallographic texture of ferrite and martensite. The hardening parameters were identified by fitting with the flow stress-strain curve obtained from bulge tests. The model-predicted and experimental flow-stress curves and R-values were compared in order to estimate the adequacy of the crystal plasticity model to describe the anisotropic behavior of the dual-phase steel samples. Furthermore, the crystal plasticity model, in conjunction with the Marciniak-Kuczynski approach, was used to predict forming limit diagram. The predictive accuracy was estimated by comparing with the experimental forming limit strains obtained through Nakazima tests. It turned out that several assumptions made in the current study led to somewhat poorer predictive accuracy in comparison with the previous reports, which implies that certain improvements in the model application are required for successful and valid model applications.

A method for determining material's equivalent stress-strain curve with any axisymmetric notched tensile specimens without Bridgman correction

Large deformation analyses of problems such as plastic forming, ductile fracture with finite element method need a full range of material's equivalent stress-strain curve or flow stress-strain curve. The equivalent stress-strain curve determined from the smooth round bar specimen should be corrected after diffuse necking, since tri-axial stress state occurs in the neck. The well-known Bridgman correction method is a candidate, however, it is not accurate as the strain increases. Furthermore, it is impossible to measure the equivalent stress-strain curve of each individual material zone in a weldment with cross weld tensile tests. To cope with these challenges, a correction function and an associated test procedure are proposed in this study. With the proposed procedure, the true stress-strain curve from any axisymmetric notched tensile specimen can be converted to the material's equivalent stress-strain curve accurately and no Bridgman correction is needed. The proposed procedure can be applied to both perfectly plastic and strain hardening materials. The equivalent stress-strain curve of each individual material zone in a weldment can also be measured with the proposed procedure.

Hot deformation behavior of AZ40 magnesium alloy at elevated temperatures

Hot compression tests on AZ40 magnesium alloy were conducted on a Gleeble 1500d hot simulation testing machine in a deformation temperature range of 330 °C-420 °C and a strain rate range of 0.002-2 s-1. Hot deformation behaviors were investigated on the basis of the analysis of the flow stressstrain curves, constitutive equation, and processing map. The stress exponent and apparent activation energy were calculated to be 5.821 and 173.96 kJ/mol, respectively. Deformation twins and cracks located in grain boundaries were generated at 330 °C and 0.02 s-1, which are associated with a high strain rate and a limited number of available slip systems. With increasing temperature and decreasing strain rate, the twins disappeared and the degree of dynamic recrystallization increased. The alloy was completely dynamically recrystallized at 420 °C and 0.002 s-1, with a homogenous grain size of approximately 13.7 μm. The instability domains of the deformation behavior can be recognized by processing maps. By considering the processing maps and characterizing the microstructure, the optimum hot deformation parameters in this experiment were determined to be 420 °C and 0.002 s-1.