Two-stage Constitutive Model Research Articles

Effects of load and high temperature on uniaxial compressive properties of desert sand concrete

In order to explore the influence of load and high temperature on the uniaxial compressive properties of desert sand concrete (DSC), the axial compressive strength test of desert sand concrete after different loads and temperatures was carried out, and the stress-strain curve was measured. The influence of load level, temperature grade and cooling method on the mass loss rate, ultrasonic velocity and uniaxial compressive performance of desert sand concrete after high temperature was analyzed. The results show that as the temperature increases, the mass loss rate of desert sand concrete gradually increases, the axial compressive strength gradually decreases, the peak strain increases significantly, the stress-strain curve tends to be flat, and the elastic modulus decreases continuously. The "pseudoplastic platform" near the axial compressive strength of the stress-strain curve of desert sand concrete after high temperature is more obvious. Based on the two-stage constitutive model of concrete, the constitutive model of desert sand concrete considering the influence of temperature and load level is established. The research results can provide technical support for the performance evaluation of desert sand concrete after high temperature.

Mechanical properties and constitutive model of cold-formed Q1100 ultra-high strength steel sections at low and elevated temperatures

The Q1100 ultra-high strength steel (UHSS) has broad application prospects in bridges and super high-rise buildings due to its ultra-high strength properties. However, no research has been conducted on the mechanical properties of Q1100 UHSS at low and elevated temperatures. Therefore, an experiment was conducted to examine the low- and elevated-temperature mechanical properties of Q1100 UHSS at the flat and corner regions of cold-formed angle sections. The temperature considered in this study ranged from −80 ℃ to 500 ℃. The failure modes, stress-strain curves, and key mechanical parameters of the flat and corner specimens of Q1100 UHSS at different temperatures were obtained. The experimental results showed that both the flat and corner specimens underwent ductile fracture with obvious necking at different temperatures. The stress-strain curves of all specimens had no yield plateau, showing obvious nonlinear characteristics. The strength properties of Q1100 UHSS at low temperatures were increased by less than 10 %. However, the strength properties of Q1100 UHSS at elevated temperatures were significantly reduced, where the reduction exceeded 60 % at temperatures reaching 500 °C. Notably, the ultimate strength of Q1100 UHSS at 200 °C was about 5 % higher than that at ambient temperature. The cold-forming process significantly reduced the ductile properties of Q1100 UHSS, but improved its strength properties. At low and elevated temperatures, the most significant cold-formed strengthening effects of yield strength, ultimate strength, and elastic modulus occurred at −40 ℃ and 300 ℃, respectively. Moreover, the predictive equations of key mechanical parameters and a two-stage constitutive model were proposed for the Q1100 UHSS flat and corner specimens. The verification results indicated that the proposed predictive equations and constitutive model could accurately predict the mechanical parameters and stress-strain curves of the Q1100 UHSS flat and corner specimens at different temperatures. The experimental results and constitutive model provided a basis for the numerical and theoretical studies on the resistant performance of the cold-formed UHSS structures servicing in low and elevated temperatures, which could be used as the material model.

Bond-slip behaviour between recycled sand concrete and steel bars

The bond-slip behaviour between concrete and steel bars is an important factor that affects the structural bearing capacity, deformation performance, and durability. In order to explore the applicability of recycled sand concrete in reinforced and prestressed concrete structures, this study conducted center pull-out tests on C40 and C60 recycled sand concrete with 50% and 100% replacement ratios of recycled sand, reinforced with plain bars and ribbed bars. The influence of strength grade and recycled sand replacement ratio on the bond performance of recycled sand concrete with steel bars were analysed. A bond-slip constitutive model for recycled sand concrete was established, and finite element analysis were conducted to validate it. The results showed that the bond failure mode of recycled sand concrete with plain bars and ribbed bars were both characterized by steel bar pull-out failure. With the increase of the strength of recycled sand concrete, the bond strength was also increased. However, as the replacement ratio of recycled sand concrete increases, the bond strength first increased and then decreased. The main reason is that when the replacement ratio was 50%, the hydration reaction was sufficient to improve the interfacial bond strength. A formula for calculating the critical anchorage length of steel bars suitable for recycled sand concrete is proposed. A two-stage constitutive model for the bond-slip behaviour of recycled sand concrete was established, and its accuracy was verified through finite element finite element analysis. This study provides a reference for the application of recycled sand concrete in structures.

A physically based constitutive model considering dynamic recrystallization of ERNiCrMo-3 alloy

ERNiCrMo-3 alloy is widely used in the welding of nickel-based alloys. This study investigated the hot deformation and discontinuous dynamic recrystallization (DRX) behavior of ERNiCrMo-3 alloy through hot compression tests at deformation temperatures ranging from 990 °C to 1170 °C and strain rates ranging from 0.01 to 10 s−1. Experimental results showed that under conditions of elevated temperatures and lower strain rates, discontinuous dynamic recrystallization was prone to occur upon reaching critical strain, and the distribution of carbide and nitride particles within the alloy matrix affects recrystallization nucleation and grain boundary migration. A two-stage constitutive model was established based on classical dislocation density theory and DRX kinetics. Comparison between predicted and experimental data demonstrated a strong agreement, highlighting the accuracy and utility of the proposed constitutive model.

High-temperature mechanical properties of constructional 6082-T6 aluminum alloy extrusion

The application of constructional aluminum alloys is snowballing owing to their high strength-to-density ratio, easy workability, corrosion resistance (high recycling), and good metallic texture. A macro-level understanding of material properties is not sufficiently comprehensive and quantitative to address all fire safety issues, particularly the effect of post high-temperature and creep. In this study, a systematic experimental investigation was conducted on 6082-T6 aluminum alloy extrusion at high temperatures, post high temperatures, and creep (ambient stress ratio: 0.944–0.026). The results showed that the material exhibits no safety reserve at high temperatures over 200 °C; further, at post high temperatures, the strength of the material is reduced at approximately 200 °C after a short-time thermal exposure. The rupture critical stress ratio αcr-Zone corresponding to a creep rupture time of 4.0 h decreases in an anti-S shape with an increase in temperature. Moreover, the strength of the material after exposure to a temperature of 350 °C for 1.0 h was nearly zero; therefore, 160 °C was suggested as the starting temperature of the thermal exposure effect. Additionally, more attention should be paid to the influence of the deteriorating role of creep on the overall structural fire-resistant bearing capacity under long-duration fires. Finally, a new-form reduction factor model of key mechanical property indexes, a two-stage constitutive model using the fast simulated annealing method, and a strain rate prediction model of Creep Stage II were proposed.

A Two-Stage Constitutive Model and Microstructure Evolution Simulation of a Nickel-Based Superalloy during High Temperature Deformation

A Two-Stage Constitutive Model and Microstructure Evolution Simulation of a Nickel-Based Superalloy during High Temperature Deformation

A Two-Stage Constitutive Model for Ti2AlNb Alloy Based on Asymptote Approach and Temperature-Corrected Stress

The flow behavior of Ti2AlNb-based alloy is critical to the research of hot forming due to its high sensitivity to the temperature and strain rate. The hot compression tests were conducted by using a Gleeble thermo-mechanical simulator in the temperature range of 950-1080 °C with strain rate from 0.001 to 10 s−1. The flow curves were modified firstly by taking into account the interface friction. In order to neutralize the thermal effect caused by high-speed deformation, the influence of strain rate on the deformation-induced temperature rise was evaluated, and the true temperature was obtained based on the collected stress–strain data. It was found that, under certain strain and strain rate, the true stress varied with the true temperature in an ‘inverted S’ format. Therefore, an ‘inverted S’ relation was adopted to calculate the flow stress at the given temperature. After the correction of flow stress, the constitutive model including the parabolic equation and modified Arrhenius equation in asymptotic form was established, and the discontinuous yielding and normal yielding behaviors were depicted, respectively. The constitutive model was integrated into the software DEFORM, by which the accuracy and predictability were verified.

Physical-Based Constitutive Modeling of Hot Deformation in a Hot-Extruded Powder Metallurgy Nickel-Based Superalloy

For simulating the hot deformation behavior of a powder metallurgy nickel-base superalloy during isothermal forging, the hot compression tests were performed in the temperatures of 1020-1110 °C with the strain rates from 10−3 to 1 s−1. The thermoplastic deformation and dynamic recrystallization (DRX) behavior of the superalloy during thermocompression were systematically studied. It can be shown that the flow stress of the superalloy exhibits apparent characteristics of DRX. A relationship indicating the dependency of flow stress on deforming temperature and strain rates is built through introducing the Z parameter. The work-hardening rate (θ) curves of the superalloy at various deformation conditions are obtained, and the values of θ are found to decrease with decreasing Z parameter, i.e., decreasing strain rates and increasing deforming temperature. There exists a power exponential relationship between critical strain ec and Z parameter. Combining the experimental data, a two-stage constitutive model on the basis of the Estrin–Mecking constitutive model and the DRX kinetic model is set up to model the flow stress of the superalloy. The flow stresses obtained from the established model are well consistence with the measured values.

A Constitutive Model for Cemented Tailings Backfill Under Uniaxial Compression

Constitutive model is the foundation describing the mechanical properties of materials. Cemented tailings backfill (CTB) plays an important role in goaf filling. However, a universally applicable constitutive model for CTB has not been proposed yet. In this paper, a two-stage constitutive model of CTB under uniaxial compression was established, based on the Weibull distribution density function, the strain equivalence principle and the damage mechanics theory. Eight groups of CTB samples with a diameter of 50 mm and a height of 100 mm prepared with different solid contents (70-78 wt%) and cement-sand ratios (1/4-1/10) were subjected to uniaxial compression tests to verify the validity of the theoretical model. The compared results showed that the predictions of the proposed constitutive model agreed well with the experimental results. The following conclusions were also obtained: (i) Solid content and cement-sand ratio had a significant effect on the basic mechanical parameters of the CTB samples, especially at the peak stress; (ii) The constitutive model of CTB was similar to that of the ordinary cement mortar M5, but with obvious residual stress; (iii) The failure mode of the CTB specimens under uniaxial compression was mainly tensile failure. The results presented in this paper contribute to a better understanding of the uniaxial compression characteristics of CTB and lay an important foundation for future research.

Tensile properties and strain hardening mechanism of Cr-Mn-Si-Ni alloyed ultra-strength steel at different temperatures and strain rates

To reveal the relationship between the microstructural morphologies, tensile behaviors, and strain hardening mechanism of Cr-Mn-Si-Ni alloyed ultra-strength steel, uniaxial tensile tests of a Cr-Mn-Si-Ni alloyed steel were conducted at room temperature (RT) and elevated temperatures with different strain rates in this study. When the tensile test was carried out at RT, increased strain rate led to increased dislocation density of the tensed Cr-Mn-Si-Ni alloyed steel specimen and resulted in increased value of yield strength. Because the dislocation entanglement and strain hardening of tensed Cr-Mn-Si-Ni alloyed steel were inhibited by increased strain rate, decreased value of ultimate strength was measured. During tensile test at RT, the dislocations rearranged and transformed to low-angle grain boundaries and high-angle grain boundaries sequentially. Above microstructural evolution resulted in microstructural refinement of Cr-Mn-Si-Ni alloyed steel. The strain hardening of Cr-Mn-Si-Ni alloyed steel during tensile test at RT was divided into four stages according to the calculated values of strain hardening rate. The microstructural evolution behaviors including accumulation of dislocations, generation and transformation of slips took place in different stages of strain hardening were affected significantly by the strain rate. Based on the true stress-true strain curves, the effects of the tensile temperature and strain rate on the values of the yield strain, fracture strain, yield strength, and ultimate strength of Cr-Mn-Si-Ni alloyed steel tensed under different experimental conditions were studied. A two-stage constitutive model of Cr-Mn-Si-Ni alloyed steel associated with dislocation density was established based on the experimental results.

Constitutive behavior and hot workability of multi-direction forged T2 copper during hot compression deformation

The hot deformation behavior of a multi-direction forged (MDFed) T2 copper was investigated by the isothermal compression test at deformation temperatures between 673 and 1173 K and strain rates between 0.001 and 10 s− 1. The results reveal that the deformation characteristics of the flow stress are sensitive to the hot deformation parameters. The deformation activation energy of the MDFed copper under the test conditions was calculated as 195.601 kJ/mol. The constitutive behavior was described by a two-stage constitutive model, which is based on the stress–dislocation relation and kinetics of dynamic recrystallization (DRX). Based on the dynamic material model, the three-dimensional (3D) processing maps were established to identify the instability regions and optimal hot processing parameters. It is found that DRX occurred in all the stability and instability regions, and the optimal processing conditions are in the temperature range of 923–1023 K and strain rate range of 0.1–1 s− 1, which indicates a feature of incomplete DRX. Moreover, the grains overgrew at high deformation temperatures and low strain rates, resulting in a poor workability for the MDFed copper.

Establishment of a two-stage constitutive model based on dislocation density theory for as-forged SA508 Gr.3Cl.1

The high-temperature deformation behavior of the SA508 Gr.3Cl.1 steel was investigated by the uniaxial isothermal compression tests at the deformation temperature from 1223 K to 1473 K and strain rate from 0.001s−1 to 1 s−1, which were carried out using Gleeble-1500 thermo-mechanical simulator. Based on the experimental data, the material parameters and active energy of hot deformation were determined according to the regression analysis method. The critical strain of dynamic recrystallization (DRX) was confirmed by simplified P-J method. Furthermore, the constitutive model for work hardening-dynamic recovery (WH-DRV) stage and DRX stage was established based on dislocation density theory and the kinetics of DRX. Finally, the flow stress calculated using the established model and experiment data was compared and the results showed that it is enough accurate to predict the flow stress during hot deformation for SA508 Gr.3Cl.1. Thus, the model will be beneficial for the accuracy of simulation by Finite Element Method (FEM) method.

High-temperature deformation mechanisms and physical-based constitutive modeling of ultra-supercritical rotor steel

This study presents an investigation that characterizes the evolution of the dynamically recrystallized structure and flow behavior of FB2 rotor steel during hot deformation in the temperature range from 900 °C to 1200 °C at strain rates from 0.001s−1 to 0.1s−1 using Gleeble-3500 thermo-simulation machine. Dynamic recrystallization (DRX) plays a key role in softening mechanism for hot deformed FB2 rotor steel. The fraction of LABs greatly increases with the decrease of deformation temperature. Low angle boundaries (LABs) always have higher local misorientation angle, which means the lower deformation temperature is capable of providing not enough driven force for the migration of LABs and thereby decelerates the DRX process to consume the dislocations. Furthermore, the critical stress and critical strain for initiation of DRX are calculated by setting the second derivative of the third order polynomial. Based on the classical stress–dislocation relation and the kinetics of dynamic recrystallization, a two-stage constitutive model is developed to predict the flow stress of FB2 steel. Comparisons between the predicted and measured flow stress indicate that the established physically-based constitutive model can accurately characterize the hot deformations for the studied steel.

Compressive ratcheting and creep of non-asbestos fibre composite considering temperature effect

Compressive ratcheting response and creep of non-asbestos fibre composite are tested based on a designed compression–compression clamp for plate-shape specimens. The influences of temperature, stress amplitude and stress rate are discussed in detail. A two-stage constitutive model is developed to describe the compression-resilience relationship of non-asbestos fibre composite. Results present that a crescent-shaped stress–strain relationship of non-asbestos fibre composite is observed under repeated compression, and the proposed two-stage constitutive model can predict the compression-resilience curve for the first cycle very well under various temperatures and stress rates. Additionally, the ratcheting strain of non-asbestos fibre composite obviously enhances with increasing the temperature. However, it has a little change when the stress rate and stress amplitude are varied based on the experimental data. The ratcheting strain rate per cycle reduces promptly during about the first 75 cycles, and it is always less than 1 × 10−4 per cycle during the subsequent cycles and tends to shakedown. Moreover, the ratcheting strain with small stress amplitude is very close to the creep deformation at the same testing time and peak stress under different temperatures. This indicates that the ratcheting strain of non-asbestos fibre composite under fatigue loads with small stress amplitude can be evaluated equivalently by the corresponding creep deformation with high precision.

Microstructure Evolution and Flow Stress Model of a 20Mn5 Hollow Steel Ingot during Hot Compression.

20Mn5 steel is widely used in the manufacture of heavy hydro-generator shaft due to its good performance of strength, toughness and wear resistance. However, the hot deformation and recrystallization behaviors of 20Mn5 steel compressed under high temperature were not studied. In this study, the hot compression experiments under temperatures of 850–1200 °C and strain rates of 0.01/s–1/s are conducted using Gleeble thermal and mechanical simulation machine. And the flow stress curves and microstructure after hot compression are obtained. Effects of temperature and strain rate on microstructure are analyzed. Based on the classical stress-dislocation relation 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 hollow steel ingot.

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.

A two-stage constitutive model of X12CrMoWVNbN10-1-1 steel during elevated temperature

In order to clarify the competition between work hardening (WH) caused by dislocation movements and the dynamic softening result from dynamic recovery (DRV) and dynamic recrystallization (DRX), a new two-stage flow stress model of X12CrMoWVNbN10-1-1 (X12) ferrite heat-resistant steel was established to describe the whole hot deformation behavior. And the parameters were determined by the experimental data operated on a Gleeble-3800 thermo- mechanical simulation. In this constitutive model, a single internal variable dislocation density evolution model is used to describe the influence of WH and DRV to flow stress. The DRX kinetic dynamic model can express accurately the contribution of DRX to the decline of flow stress, which was established on the Avrami equation. Furthermore, The established new model was compared with Fields-Bachofen (F-B) model and experimental data. The results indicate the new two-stage flow stress model can more accurately represent the hot deformation behavior of X12 ferrite heat-resistant steel, and the average error is only 0.0995.

Constitutive Model Based on Dynamic Recrystallization Behavior during Thermal Deformation of a Nickel-Based Superalloy

The thermal deformation and dynamic recrystallization (DRX) behavior of a nickel-based superalloy were investigated by the thermal compression test. The experimental results show that the process parameters have great influence on the flow stress of the superalloy. In addition, there is an inflection point on the DRX softening stage of the work-hardening rate versus stress curve. DRX under the conditions of higher temperatures and lower strain rates easily occurs when the strain reaches a critical level. Based on the classical dislocation density theory and the DRX kinetics models, a two-stage constitutive model considering the effect of work hardening-dynamic recovery and DRX is developed for the superalloy. Comparisons between the predicted and experimental data indicate that the values predicted by the proposed constitutive model are in good agreement with the experimental results.

A physically-based constitutive model for SA508-III steel: Modeling and experimental verification

Due to its good toughness and high weldability, SA508-III steel has been widely used in the components manufacturing of reactor pressure vessels (RPV) and steam generators (SG). In this study, the hot deformation behaviors of SA508-III steel are investigated by isothermal hot compression tests with forming temperature of (950–1250)°C and strain rate of (0.001–0.1)s−1, and the corresponding flow stress curves are obtained. According to the experimental results, quantitative analysis of work hardening and dynamic softening behaviors is presented. The critical stress and critical strain for initiation of dynamic recrystallization are calculated by setting the second derivative of the third order polynomial. Based on the classical stress–dislocation relation and the kinetics of dynamic recrystallization, a two-stage constitutive model is developed to predict the flow stress of SA508-III steel. Comparisons between the predicted and measured flow stress indicate that the established physically-based constitutive model can accurately characterize the hot deformations for the steel. Furthermore, a successful numerical simulation of the industrial upsetting process is carried out by implementing the developed constitutive model into a commercial software, which evidences that the physically-based constitutive model is practical and promising to promote industrial forging process for nuclear components.

Nonlinear analysis of axially loaded circular concrete-filled stainless steel tubular short columns

Experiments show that the ultimate compressive strength of stainless steel is much higher than its tensile strength. The full-range two-stage constitutive model for stainless steels assumes that stainless steels follow the same stress–strain behavior in compression and tension, which may underestimate the compressive strength of stainless steel tubes. This paper presents a fiber element model incorporating the recently developed full-range three-stage stress–strain relationships based on experimentally observed behavior for stainless steels for the nonlinear analysis of circular concrete-filled stainless steel tubular (CFSST) short columns under axial compression. The fiber element model accounts for the concrete confinement effects provided by the stainless steel tube. Comparisons of computer solutions with experimental results published in the literature are made to examine the accuracy of the fiber element model and material constitutive models for stainless steels. Parametric studies are conducted to study the effects of various parameters on the behavior of circular CFSST short columns. A design model based on Liang and Fragomeni's design formula is proposed for circular CFSST short columns and validated against results obtained by experiments, fiber element analyses, ACI-318 codes and Eurocode 4. The fiber element model incorporating the three-stage stress–strain relationships for stainless steels is shown to simulate well the axial load–strain behavior of circular CFSST short columns. The proposed design model gives good predictions of the experimental and numerical ultimate axial loads of CFSST columns. It appears that ACI-318 codes and Eurocode 4 significantly underestimate the ultimate axial strengths of CFSST short columns.