True Stress-true Strain Curves Research Articles

Lamellar orientation control of TiAl-based alloy by uniaxial compressive deformation at high-temperature in (α+β) two-phase region

In this study, the orientation of (α+γ) lamellar structure in the TNM alloy (Ti-43.7Al-4 Nb-1Mo-0.1B) is controlled by high-temperature uniaxial compression conducted in the (α+β) two-phase region. The control of the lamellar orientation is focused on a control of α phase orientation because of being decisive for lamellar γ orientation. All true stress-true strain curves indicated the work softening due to dynamic recrystallization. The stress-strain curve behaviors were consistent with microstructure observation. The peak stress increased with a decrease in lamellar colony size. After deformation in the (α + β) two-phase region at 1543 K and 1573 K, where the content of α phase was dominant, a fiber texture with the (0001)α2 plane tilted 35° away from the compression plane was formed by the deformation mechanism of α phase. On the other hand, at 1623 K where the content of β phase was dominant, a double (0001)α2 fiber texture tilted at 35°- 45° and 80°- 90° away from the compression plane was observed. The double (0001)α2 fiber texture is considered to be caused by β→α phase transformation during cooling according to Burgers orientation relationship. Single-step uniaxial compressions conducted at the (α + β) two-phase region at different temperature (1543 K−1623 K) led to an inclination of (0001)α2to compression plane and subsequently lamellar interfaces of one colony unparallel to those of other colonies.

Study on the influence of κ-carbide on the high temperature flow behavior of the medium-Mn lightweight steel: Modeling and characterization

Isothermal compression tests were carried out on the Fe-11Mn-10Al-0.9C medium-Mn lightweight steel in the temperature range from 800 °C to 1100 °C and strain rate range from 0.001 s−1 to 10 s−1 to investigate the influence of κ-carbide on the hot flow behavior. The true stress-true strain curves were analyzed to evaluate the role of κ-carbide on the softening phenomena during straining. It's found flow stress drops more remarkably from the peak point to the end of deformation at low temperature and low strain rate, that condition is favorable for the precipitation of κ-carbide instead of the occurrence of DRX. The activation energy of hot deformation based on the peak stress was calculated as 454.517 kJ mol−1, but this typical strain-compensated Arrhenius-type constitutive equation was found inappropriate to model the flow behavior of the present steel, especially at the low temperature regime. By comparison, a physically-based constitutive model consisting of Bergström's equation (ε<εp) and Kolmogorov-Johnson-Mehl-Avrami's equation (ε>εp) was developed and could predict the flow behavior of the steel accurately. Electron backscattered diffraction (EBSD) analysis revealed the formation of necklace structure at high strain rate and the dynamic recrystallization (DRX) proceeded more adequately with the decrease in strain rate and increase in the deformation temperature. The precipitation of κ-carbides in both austenite grain interior and boundaries (GI and GBs) were enhanced at relatively low deformation temperature (e.g., 800 °C) and greatly improved the peak stress by hindering the dislocation motion. With the increase of deformation, the GB κ-carbide gradually coarsened and induced the decomposition of deformed austenite via the eutectoid reaction (γ→α+κ) at lower strain rate (e.g., 0.001 s−1) due to the sufficient transformation time, consequently leading to the remarkable flow stress softening. The microstructure characterization result was in agreement with variations of parameters (i.e., U, Ω, ρp and nA) with different deformation condition.

Design and validation of a new ring hoop plane strain test for characterizing the anisotropic plastic behavior of tubular materials

The accurate characterization of the plastic behavior of tubular materials is challenging due to the difficulties in acquiring proper specimens for mechanical testing. In this study, we propose a novel testing technique, namely the ring hoop plane strain Test (RHPST), as a supplementary test for characterizing materials experiencing distinct strain paths compared to standard uniaxial tensile tests. To design a suitable ring specimen’s geometry that satisfies the necessary plane strain conditions, we developed a meta-modelling approach merging response surface method (RSM) and the finite element method (FEM). Experimental tests are conducted on RHPST specimens, and 3D digital image correlation (DIC) technique is used to monitor the strain fields within the specimen's gauge section. However, observations indicate the presence of edge effects on the gauge specimen. These edge effects significantly influence and limit the homogeneity of the plane strain field. To tackle this limitation, a correction procedure is developed for separating the authentic plane strain area, constituting approximately 78% of the RHPST specimen's width. Furthermore, we successfully fabricated a novel grooved ring specimen (GRHPST), which exhibits a wider region of the plane strain state encompassing up to 90% of the gauge width, while minimizing the impact of edge effects. The true stress-true strain curve obtained from the GRHPST specimen exhibits exceptional agreement with the curve predicted using the Hill48 yield criterion. Notably, no additional corrections are required for the measured true stress-true strain curve, thereby affirming the efficacy of the GRHPST specimen as an adept test for characterizing the anisotropic plastic behavior of AA6063 tubes.

Dynamic compression intrinsic relationship of W-Ni-Fe-Mn alloys based on J-C modeling

Dynamic compression tests were performed on the sample alloys by using a detached Hopkinson compression bar with a diameter of 14.5 mm caliber for the kinetic behavior of W-Ni-Fe alloy and W-Ni-Fe-Mn alloy materials in the erosion process. The true stress-true strain curves of the two sample alloys were fitted based on the JC eigenstructure model, and the eigenstructure relationships of the two alloys were finally obtained. The obtained constitutive equations were then used to dynamically compress the specimens by using LS-DYNA dynamics software, and the simulated true stress-strain curves of the two alloys at various strain rates agreed well with the experimentally obtained curves, allowing them to be used for simulation calculations under impact loading. When compared toW-Ni-Fe alloys, the dynamic mechanical characteristics of alloys with Mn addition are greatly improved.

Strain-rate sensitivity analysis of microwave processed polypropylene-carbon nanotube composites

The study investigates the strain rate sensitivity of microwave-processed polypropylene nanocomposites containing a 10% volume fraction of multi-walled carbon nanotubes (MWCNTs), synthesized using a domestic microwave applicator (DMA). Through experimental analysis under various loading conditions including tensile, flexural, and multistep relaxation loads, the mechanical strength of these nanocomposites is assessed alongside destructive testing and scanning electron microscopy (SEM) results. Mathematical models are proposed to elucidate the mechanical response under different strain rate loadings. The nanocomposite exhibits elastoplastic behavior, with maximum elongation observed at a strain rate of 3 mm/min. During uniaxial tension tests, the ultimate strength increases significantly from 5.74 MPa at 1.52 mm/min to 13.8 MPa and 15.7 MPa at 1 mm/min and 2 mm/min respectively during multistep relaxation tests. The true stress-true strain curve follows a power law of strain hardening under high strain rate tensile tests. Flexural tests reveal maximum flexural strength and modulus at a strain rate of 1.25 mm/min, with elongation peaking at 1.50 mm/min. Mechanical properties, including modulus and ultimate strength, show an increasing trend with strain rate until a limiting value is reached, beyond which thermal softening occurs. SEM fractography illustrates the random and spatial distribution of CNTs at low strain rates, whereas agglomeration and CNT pull-out are observed at higher strain rates. This comprehensive analysis sheds light on the intricate mechanical behavior of microwave-processed polypropylene nanocomposites, offering insights into their potential applications and optimization strategies.

Hot deformation characteristic of TC21 titanium alloy with lamellar microstructure

The hot deformation characteristic of TC21 titanium alloy with lamellar microstructure was investigated with the help of isothermal compression tests in the temperature and strain rate ranges of 760–920 ℃ and 0.001–10 s−1. The principal feature of true stress-true strain curves is flow softening. The flow softening extent increases with decreasing strain rate, but has no obvious relationship with temperature. Based on processing map and microstructure observation, the regime of flow instability was determined to be about 760–855 ℃, 0.01–10 s−1 with flow instability phenomena including macrocrack and adiabatic shear band. The preferable parameters for forging were in the temperature and strain rate ranges of (760–850 ℃, 0.001–0.005 s−1) and (850–920 ℃, 0.001–0.01 s−1), where the microstructure with higher globularization fraction can be achieved. In terms of Arrhenius kinetic rate equation, the activation energies were determined to be 400.635 and 734.430 kJ·mol−1 in the strain rate ranges of 0.001–0.01 s−1 and 0.1–10 s−1, respectively. TEM analysis showed that different activation energies correspond to different deformation modes, resulting in different globularization mechanisms. In the strain rate range of 0.001–0.01 s−1, the deformation is characterized by dislocation motion. The globularization mechanism involves the formation of groove, localized shear and subgrain in α lamellae, followed by β phase penetrating α lamellae along groove, shear interface and subgrain boundary. In the strain rate range of 0.1–10 s−1, the deformation is characterized by twinning besides dislocation motion. The globularization mechanism involves the formation of the twins of α phase and β phase penetrating α lamellae along the twinned region.

Flow behaviors and microstructural evolutions of nickel-based ODS superalloys during hot deformation

The hot deformation behaviors of nickel-based oxide dispersion strengthened (ODS) superalloys fabricated by mechanical alloying (MA) and hot extrusion (HEX) were investigated, the hot compression tests were performed to obtain true stress-true strain curves, the influence of strain rate and temperature connected with the microstructure evolution was analyzed, and the processing map and microstructure proposed at different strain levels was used to select its hot working parameters. The results illustrated that hot working conditions, especially the temperature, strongly influenced the grain structure. Specifically, deforming under high temperatures and low strain rate conditions enhances dynamic softening via dynamic recovery (DRV), dynamic recrystallization (DRX), and grain growth to consume the stored strain energy. In addition, the size and morphology of nanoparticles are not significantly changed before and after deformation, the nanoparticles and the matrix still maintain a good interface combination, and no interfacial mismatch such as nanosvoids between the nanoparticle and matrix is detected due to their outstanding interfacial binding ability and excellent ductility of matrix.

Dynamic compressive property of extruded VW75-Ti (wt.%) alloy under high strain rates

The dynamic compressive properties of extruded VW75 and VW75+Ti alloys were investigated by using a split Hopkinson pressure bar (SHPB) at 25°C under high strain rates of 1, 600-2, 700 s-1 in the present work, and the microstructure evolution after deformation was inspected by OM, SEM, and EBSD. The results demonstrated that the maximum stress value rises with the escalating strain rate in the course of impact, and the true stress-true strain curves of the two alloys exhibit strain strengthening and positive strain effect. The addition of Ti particles refines alloy grains, increases fracture strength, and decreases the twinning ratio.

Memory effect of spider major ampullate gland silk in loading-unloading cycles and the structural connotations

Spider silk is repeatedly stretched while performing biological functions. There is a close relationship between the shape change of the fibre materials and their mechanical properties. However, the effect of the deformation and interval time on the structure and tensile behaviour properties of spider silk after repeatedly stretching by given strain value has been rarely reported. Here we found that spider major ampullate gland silk (MAS) can revert its tensile behaviour independent of its previous loading history via intervals of approximately 8 s to 5 min with constant and increased elongation, respectively, after being subjected to yield and hardening regions. The true stress-true strain curve beyond a given value of true strain is independent from the previous loading history of the sample. Even after longer intervals (≥1 h), MAS can reproduce the last tensile behaviour via one stretched. Despite recognizing the development of irreversible deformations in the material when tested in air, the reversible change in tensile behaviour outside the spider silk's elastic region has rarely been observed before. MAS has at least one proper ground state that allows it to present good shape and mechanical behaviour memory in terms of longitudinal stretching, functioning as a new strategy to achieve certain tensile properties. The analysis of the true stress–true strain curves was performed from a series of loading‒unloading tests to evaluate the evolution of those mechanical parameters with the cycle number. The elastic modulus measured in the loading steps increases monotonously with increasing values of true strain reached in the cycles. In contrast, a marginal variation is found in the values of the yield stress measured in the different cycles. The memory and variation in the mechanical behaviour and performance of MAS can be accounted for through the irreversible and reversible deformation micromechanisms and its combination in which the viscoelasticity of the material plays a leading role. These findings may be helpful to guide the biomimetic design of novel fibre materials such as spider silk gut via artificially stretching spider silk glands.

Development of the Johnson-Cook flow stress and damage parameters for the impact response of polycarbonate: Experimental and numerical approach

The Johnson and Cook (JC) flow stress and damage model parameters of a polycarbonate (PC) plate were determined by the mechanical tests and numerical simulations of the tests. The experimental tests included quasi-static and high strain rate tension and compression, quasi-static notched-specimen tension, quasi-static indentation (QSI), low velocity impact (LVI) and projectile impact (PI). Initially, five different quasi-static flow stress-strain equations were extracted from the experimental and numerical tests. The flow stress equation determined from the experimental average true stress-true strain curve well agreed with the effective stress-strain obtained from the quasi-static numerical tension test. The numerical QSI force-displacement curve based on the experimental average true stress-true strain equation was further shown to be very similar to that of the experiment. The LVI and PI test simulations were then continued with the experimental average true stress-true strain equation using five different flow stress-strain rate relations: JC, Huh and Kang (HK), Allen-Rule and Jones (ARJ), Cowper-Symonds (CS) and the nonlinear rate approach (NLA). The rate sensitivity parameters of these relations were extracted from the quasi-static and high strain rate tests. The LVI test simulations using the stress-strain rate relations exhibited force-displacement curves higher than those of the experiments. The detected almost no strain rate sensitivity in the LVI tests was ascribed to low strain rate dependency of the flow stress at these intermediate strain rates and large strains involved. On the other side, all the stress-strain rate relations investigated nearly predicted the experimental damage types: dishing at 100 and 140 m s−1 and petalling at 160 m s−1, except the CS relation which predicted the fracture of the plate at 140 m s−1. The experimental average projectile exit velocity at 160 m s−1 was further well predicted by the used stress-strain rate relations while the experimental average petal thicknesses were under estimated by the models. The absorbed energy at 160 m s−1 PI test was determined 1.6 times that of the QSI test, which proved an increased energy absorption capability of the tested PC at the investigated impact velocities.

Real-time measurement of minimum cross-sectional area and radius of curvature of miniature plate specimens using a high-speed laser profiler for calculating true stress-true strain curves

True stress-true strain curves are fundamental for designing and analyzing structures such as fusion reactors. These curves are typically obtained by conducting tensile tests on round bar specimens. However, due to material dimension limitations, plate specimens are sometimes used instead of round bar specimens. Obtaining true stress-true strain curves experimentally from plate specimens can be challenging. To address this challenge, this study aims to obtain true stress-true strain curves of miniature plate specimens using both analytical and experimental methods. The analytical method involved inverse finite element method (FEM), while the experimental method utilized real-time measurement of the minimum cross-sectional area and radius of curvature of a miniature plate specimen with a high-speed laser profiler. Comparing the true stresses obtained from the analytical and experimental methods, we found that the difference was typically within 5%. These findings suggest that inverse FEM and laser profilometry are effective methods for determining the true stress-true strain of miniature plate specimens.

Variation in the Elastic Modulus and Increased Energy Dissipation Induced by Cyclic Straining of Argiope bruennichi Major Ampullate Gland Silk

The trends exhibited by the parameters that describe the mechanical behaviour of major ampullate gland silk fibers spun by Argiope bruennichi spiders is explored by performing a series of loading-unloading tests at increasing values of strain, and by the subsequent analysis of the true stress-true strain curves obtained from these cycles. The elastic modulus, yields stress, energy absorbed, and energy dissipated in each cycle are computed in order to evaluate the evolution of these mechanical parameters with this cyclic straining. The elastic modulus is observed to increase steadily under these loading conditions, while only a moderate variation is found in the yield stress. It is also observed that a significant proportion of the energy initially absorbed in each cycle is not only dissipated, but that the material may recover partially from the associated irreversible deformation. This variation in the mechanical performance of spider silk is accounted for through a combination of irreversible and reversible deformation micromechanisms in which the viscoelasticity of the material plays a leading role.

Microstructure and Macroscopic Characteristics of Powder Superalloy under Different Plastic Deformation Process Parameters

Through the uniaxial compression deformation test, this work focuses on analyzing the microstructure evolution of the alloy in the two stages of dynamic softening and strain hardening in the true stress-true strain curve during hot deformation, including grain size, local misorientation and The interaction of its relative mobility, and through the grain boundary orientation difference and grain orientation, explained the dynamic softening mechanism and strain hardening phenomenon, so as to find the microstructure-determining characteristic parameters of the dynamic recrystallization nucleation and core growth of the alloy and its evolution.

Grain Size Evolution of Nickel-Based Superalloys after Hot Deformation

In this work, the uniaxial compression deformation test of nickel-based powder superalloys was carried out in a vacuum isothermal adiabatic environment using the Thermocmaster-Z thermal processing simulation test machine. The evolution of the microstructure in the two stages of dynamic softening and strain hardening in the true stress-true strain curve in the process, including the interaction of grain size, local misorientation and their relative mobility. During most of the plastic deformation time, the flow stress is gradually increased, that is, the strain hardening dominates, while in the remaining plastic deformation process parameters, dynamic softening dominates. Under different plastic deformation process parameters, The average grain size fluctuates to a certain extent under the condition of partial strain values, but the final evolution law is gradually decreasing, while the final trend of the average local misorientation is increasing.

The Spider Silk Standardization Initiative (S3I): A powerful tool to harness biological variability and to systematize the characterization of major ampullate silk fibers spun by spiders from suburban Sydney, Australia

The true stress-true strain curves of 11 Australian spider species from the Entelegynae lineage were tensile tested and classified based on the values of the alignment parameter, α*, in the framework of the Spider Silk Standardization Initiative (S3I). The application of the S3I methodology allowed the determination of the alignment parameter in all cases, and were found to range between α* = 0.03 and α* = 0.65. These data, in combination with previous results on other species included in the Initiative, were exploited to illustrate the potential of this approach by testing two simple hypotheses on the distribution of the alignment parameter throughout the lineage: (1) whether a uniform distribution may be compatible with the values obtained from the studied species, and (2) whether any trend may be established between the distribution of the α* parameter and phylogeny. In this regard, the lowest values of the α* parameter are found in some representatives of the Araneidae group, and larger values seem to be found as the evolutionary distance from this group increases. However, a significant number of outliers to this apparent general trend in terms of the values of the α* parameter are described.

Development of Automatic Stress Correction System for Triaxial Stress State after Necking Initiation in True Stress-True Strain Curves and Application to Polycarbonate

Development of Automatic Stress Correction System for Triaxial Stress State after Necking Initiation in True Stress-True Strain Curves and Application to Polycarbonate

Constitutive Model of TNM Alloy Using Arrhenius-Type Model and Artificial Neural Network Model

TNM alloys are frequently employed in automotive and aeronautical applications. Hot compression experiments on a Gleeble-3800 testing apparatus were conducted at a range of temperatures (1150°C–1250°C) and strain rates (0.001s-1 - 1s-1) to investigate the high temperature deformation behavior of TNM alloys. The complex deformation mechanisms of TNM alloys at various temperatures and strain rates were studied using the experimentally discovered true stress-true strain curves. The constitutive relationships between deformation parameters and flow stresses were constructed using two methods, Arrhenius model and neural network model respectively. The results demonstrated that the correlation coefficient R and root mean square error (RSME) achieved by BPNN are, respectively, 0.9982 and 4.7784, and are notably better than those anticipated by the Arrhenius-type model. In terms of the distribution of relative errors, the BPNN findings are similarly more concentrated, and the bulk of them fall inside the 10% range. Therefore, the BP neural network is a useful tool for forecasting the elevated temperature flow behavior of TNM alloys.

Dynamic mechanical properties of FGH4097 powder alloy and the applications of its constitutive model

As a typical multiphase alloy, FGH4097 has good lasting strength (thermal stability and thermal fatigue properties), excellent wear resistance and heat resistance. It has been widely used in aerospace and other hot-end parts manufacturing fields. Most of the existing researches on the mechanical properties of FGH4097 alloy are carried out at low strain rate. There is no effective research on high temperature dynamic mechanical properties of FGH4097. Through the impact compression test of FGH4097 under different strain rates and different temperature conditions by the split Hopkinson compression bar equipment, the corresponding true stress-true strain curve was obtained, the strain rate sensitivity and temperature sensitivity of the material were analyzed. The specific heat capacity of FGH4097 alloy at different temperatures was measured by a laser thermal conductivity meter, and the adiabatic temperature rise of the alloy at different temperatures and strain rates was studied. The isothermal true stress-strain curve of the alloy was obtained by calculating the thermal softening coefficient. Two constitutive equations, Johnson-Cook and Power-Law, were introduced to fit and characterize the dynamic mechanical properties of FGH4097 alloy at different strain rates and temperatures, and the corresponding material constitutive models were obtained. Comparing the fitting accuracy of the two models, it is found that the fitting accuracy of the Power-Law model is higher, with an average error of less than 8%. The cutting simulation of FGH4097 alloy was carried out by AdvantEdge software, and the effects of strain and strain rate on the machinability of FGH4097 alloy were investigated.

Hot deformation characteristics and dynamic recrystallization of biomedical CoCrWCu alloy

In order to explore the dynamic recrystallization of biomedical CoCrW-2Cu alloy, the hot deformation behavior was investigated by isothermal compression tests. True stress-true strain curves showed that the true stress increased with increasing strain rate or decreasing deformation temperature. Meanwhile, obvious dynamic softening was observed. The constitutive equation and processing maps were constructed to elucidate the relationship between true stress and deformation parameter. The phase component and microstructure were investigated to reveal the relationship between microstructure evolution and deformation condition, which was beneficial to the optimization of the hot deformation parameter. The variation of deformation condition has a limited influence on the phase component. The strain rate has a significant influence on the extent of recrystallization. An obviously discontinuous dynamic recrystallization (DDRX) process was occurred in this study. Furthermore, the extent of dynamic recrystallization (DRX) of sample deformed at 1100 °C/0.01 s -1 was the highest. Negative value of efficiency of power dissipation could be found in the top left corner of processing maps, while high value of efficiency of power dissipation was observed in the region with high temperature and low strain rate. The processing maps predicted that the optimized deformation parameters were 1100~1150 °C and 0.01~0.1 s -1 .

High-temperature deformation behavior and processing maps of a novel AlNbTi3VZr1.5 refractory high entropy alloy

High-temperature deformation behaviors of a nonequiatomic novel AlNbTi 3 VZr 1.5 refractory high entropy alloy were studied. Hot compression tests were carried out at different temperatures ranging from 1100 to 1250 ℃ and various strain rates from 0.001 to 1 s −1 . The true stress-true strain curves indicated obvious sharp drops in the flow stress after reaching peak stress. This may be caused by either dislocation unlocking from a substitutional solute atmosphere or destroying short-range ordered structures. Flow stress analysis was investigated by introducing the Arrhenius constitutive relation. The apparent activation energy ( Q ) for high-temperature deformation was calculated to be 228.1 kJ/mol. The processing maps show that the best processing window was determined at 1200–1250 °C and 10 −0.75 to 1 s −1 . Detailed microstructure evolution characterization with EBSD analysis shows that the occurrence of discontinuous dynamic recrystallization along grain boundaries is the main softening mechanism of the AlNbTi 3 VZr 1.5 RHEA during the hot compression deformation. The size and volume percentage of dynamically recrystallized grains increase as the Z parameter decreases. • The high-temperature behavior of novel AlNbTi 3 VZr 1.5 refractory high entropy alloy is investigated. • The apparent activation energy was 228.1 kJ/mol. • The best processing window is determined at 1200–1250 °C and 10–0.75–1 s −1 . • Discontinuous dynamic recrystallization along grain boundaries is the main softening mechanism of the AlNbTi 3 VZr 1.5 RHEA during the hot compression deformation.