A Dynamic Constitutive Model and Simulation of Braided CFRP under High-Speed Tensile Loading

In this study, a dynamic constitutive model for woven-carbon-fiber-reinforced plastics (CFRP) is formulated by combining dynamic tensile test data and fitting curves and incorporating variation rules established for the modulus of elasticity, strength, and fracture strain with respect to the strain rate. The dynamic constitutive model is then implemented with finite element software. The accuracy and applicability of the dynamic constitutive model are evaluated by comparing the numerically predicted load–displacement curves and strain distributions with the test data. The stress distribution, failure factor, modulus, and strength of the material under dynamic tension are also explored. The results show that the response simulated with the dynamic constitutive model is in good agreement with the experimental results. The strain is uniformly distributed during the elastic phase compared with the DIC strain field. Subsequently, it becomes nonuniform when stress exceeds 600 MPa. Then, the brittle fracture occurs. With the increase in the strain rate, the input modulus decreased, and the tensile strength increased. When the displacement was 0.13 mm, the simulation model was damaged at a low strain rate, and the stress value was 837.8 MPa. When it reached the high strain rate of 800 s⁻¹, no failure occurred, and the maximum stress value was 432.5 MPa. For the same specimen, the strain rate was the smallest on both clamped ends, and the modulus and strength were large at the ends and small in the middle. The fitting curve derived from the test data was completely input into the dynamic constitutive model to better capture the dynamic change in the material properties.     

Thermodynamic Restrictions in Linear Viscoelasticity

The thermodynamic consistency of linear viscoelastic models is investigated. First, the classical Boltzmann law of stress–strain is considered. The kernel (Boltzmann function) is shown to be consistent only if the half-range sine transform is negative definite. The existence of free-energy functionals is shown to place further restrictions. Next, the Boltzmann function is examined in the unbounded power law form. The consistency is found to hold if the stress functional involves the strain history, not the strain–rate history. The stress is next taken to be given by a fractional order derivative of the strain. In addition to the constitutive equations involving strain–rate histories, finding a free-energy functional, consistent with the second law, seems to be an open problem.     

Hot Deformation Behavior and Microstructural Evolution Based on the Processing Map of Dual-Phase Mg-Li Based Alloy

The deformation behavior of the as-extruded Mg-Li-Al-Zn-Si alloy was studied by conducting a hot compression test, with a temperature range of 180–330 °C and a strain rate range of 0.01–10 s⁻¹. The constitutive relationship of flow stress, temperature, and strain rate was expressed by the Zener–Hollomon parameter and included the Arrhenius term. By considering the effect of strain on the material constants, the flow stress at 240–330 °C could be precisely predicted with the constitutive equation (incorporating the influence of strain). A processing map was established at the strain of 0.7. The unsafe domains that are characterized by uneven microstructures were detected at low temperatures (<230 °C) or high temperatures (>280 °C), with high strain rates (>1 s⁻¹). The optimum hot deformation region was obtained at a medium temperature (270–300 °C), with a peak power dissipation efficiency of 0.44. The microstructural evolution in different domains is investigated. The unstable domains are characterized by a non-uniform flow behavior and uneven microstructure. The observation showed that the dynamic recrystallization (DRX) process could easily occur at the safe domain with high power dissipation efficiency. For the α-phase, some features of continuous dynamic recrystallization can be found. The triple points serve as prominent nucleation sites for the β-phase DRX grains and the growth in the grains was carried out by subgrain boundary migration. The microstructure exhibits characteristics of discontinuous dynamic recrystallization.     

Hot Deformation Behavior and Simulation of Hot-Rolled Damage Process for Fine-Grained Pure Tungsten at Elevated Temperatures

Fine-grained pure tungsten fabricated by a sol drying reduction low-temperature sintering method and hot isothermal compression tests were performed by using the Gleeble 3800 thermo mechanical simulator at deformation temperatures from 1273 K to 1473 K and strain rates from 0.001 s⁻¹ to 1 s⁻¹. In addition, the constitutive equation was established by least square method combined with the Zerilli–Armstrong model, and the hot deformation behavior was discussed. Moreover, based on constitutive equation, the influence of the rolling process and its parameters on temperature, strain, density and rolling force in the hot rolling process was investigated at elevated temperature by the finite element model (FEM). Furthermore, the form of rolling damage and its formation mechanism were analyzed. Results showed the grains of pure tungsten are dense, irregular polyhedral spherical and very fine, and the average grain size is about 5.22 μm. At a high strain rate, the flow stress increases rapidly with the increase in strain, while the stress–strain curve shows a flattening trend in the tested strain rate range with increasing temperature, and no flow stress peak exists, showing obvious dynamic recovery characteristics. Furthermore, the FEM simulation showed that compared with the rolling temperature, the reduction has a greater influence on the temperature, stress–strain field and its distribution. There are three kinds of damage in the hot rolling process: transverse cracks, longitudinal cracks and side cracks, which are attributed to the competition between additional stress caused by uneven deformation and material strength. Moreover, the control method of hot rolling defects had been preliminarily proposed. These results should be of relevance for the optimum design of the hot rolling process of pure tungsten.     

Random Forest Approach in Modeling the Flow Stress of 304 Stainless Steel during Deformation at 700 °C–900 °C

The alloy 304 stainless steel is used in a wide variety of industrial applications. It is frequently applied in tough environments, such as those involving high temperatures, low temperatures, and corrosive environments. Hence, research on the flow stress behavior of the alloy during deformation under tough environments is critically important to achieving the maximum effectiveness in the application of the alloy. This research presents a study on the flow stress of 304 stainless steel during hot deformation at the temperatures of 700 °C–900 °C under the strain rates ranging from 0.0002/s–0.02/s. For this study, hot tensile experiments are conducted, and the flow stress variations of the alloy are studied with respect to the variations in the strain rate and temperature. Next, the stress behavior was modeled by the traditional Arrhenius-type constitutive equation and random forest algorithm. Then, the flow stresses predicted by different methods were studied by comparing errors. The results showed that the flow stress was modeled more accurately by the random forest algorithm.     

Dynamic Deformation Behavior and Fracture Characteristics of a near α TA31 Titanium Alloy at High Strain Rates

The quasi-static and dynamic impact compression tests of the TA31 titanium alloy were conducted at the strain rates from 0.001 s⁻¹ to 4000 s⁻¹ and deformation temperatures from 293 K to 773 K, and the TA31 titanium alloy showed typical elastic-plastic characteristics. In the initial stage of compression (elastic deformation), the stress and strain are proportional, and the stress–strain curve is a straight line. In the plastic deformation stage, the flow stress decreases significantly with the increase of deformation temperature, while the strain rate has no significant effect on the flow stress during dynamic compression. A constitutive model has been established to predict the flow stress, and the relative error is 2.32%. It is shown by observing the microstructure that when the deformation temperature is 293 °C, and the strain rate reaches 1600 s⁻¹, a shear band with an angle of about 45° to the axial direction of the specimen appears, and the severe shear deformation makes the α phase in the shear band fibrous and contains high-density dislocations. The formation process of the shear band and its influence on fracture are analyzed and discussed.     

Nonlinear Models of Thermo-Viscoelastic Materials

The paper develops a general scheme for viscoelastic materials, where the constitutive properties are described by means of measures of strain, stress, heat flux, and their time derivatives. The constitutive functions are required to be consistent with the second law of thermodynamics. Indeed, a new view is associated with the second law: the non-negative expression of the entropy production is set equal to a further constitutive function. The introduction of the entropy production as a constitutive function allows for a much wider range of models. Within this range, a scheme to obtain nonlinear models of thermo-viscoelastic materials subject to large deformations is established. Notably, the Kelvin–Voigt, Maxwell, Burgers, and Oldroyd-B viscoelastic models, along with the Maxwell–Cattaneo heat conduction, are obtained as special cases. The scheme allows also for modelling the visco-plastic materials, such as the Prandtl–Reuss work-hardening function and the Bingham–Norton fluid.     

On Characteristics of Ferritic Steel Determined during the Uniaxial Tensile Test

Tensile uniaxial test is typically used to determine the strength and plasticity of a material. Nominal (engineering) stress-strain relationship is suitable for determining properties when elastic strain dominates (e.g., yield strength, Young’s modulus). For loading conditions where plastic deformation is significant (in front of a crack tip or in a neck), the use of true stress and strain values and the relationship between them are required. Under these conditions, the dependence between the true values of stresses and strains should be treated as a characteristic—a constitutive relationship of the material. This article presents several methodologies to develop a constitutive relationship for S355 steel from tensile test data. The constitutive relationship developed was incorporated into a finite element analysis of the tension test and verified with the measured tensile test data. The method of the constitutive relationship defining takes into account the impact of high plastic strain, the triaxiality stress factor, Lode coefficient, and material weakness due to the formation of microvoids, which leads to obtained correctly results by FEM (finite elements method) calculation. The different variants of constitutive relationships were applied to the FEM loading simulation of the three-point bending SENB (single edge notched bend) specimen to evaluate their applicability to the calculation of mechanical fields in the presence of a crack.     

Deformation Behavior and Constitutive Model of 34CrNi3Mo during Thermo-Mechanical Deformation Process

With higher creep strength and heat resistance, 34CrNi3Mo has been widely used in the production of engine rotors, steam turbine impellers, and turbine blades. To investigate the hot deformation behaviors of 34CrNi3Mo steel, hot compressive tests were conducted on a Gleeble-3500 thermomechanical simulator, under the temperature range of 1073 K–1373 K and strain rate ranges of 0.1 s⁻¹–20 s⁻¹. The results show that the flow stress of 34CrNi3Mo steel under high temperatures is greatly influenced by the deformation temperature and strain rate, and it is the result of the interaction between strain hardening, dynamic recovery, and recrystallization. Under the same deformation rate, as the deformation temperature increases, the softening effect of dynamic recrystallization and dynamic recovery gradually increases, and the flow stress gradually decreases. Under the same deformation temperature, with the increase of strain rate, the influence of strain hardening on 34CrNi3Mo steel is gradually in power, and the flow stress gradually increases. To predict the flow stress of 34CrNi3Mo steel accurately, a modified Arrhenius-type constitutive model considering the effects of strain, temperature, and strain rate at the same time was made based on the experiment data. On this basis, the evolution law of deformation activation and instability characteristics of 34CrNi3Mo steel were investigated, and the processing map of 34CrNi3Mo steel was established. The formability of 34CrNi3Mo steel under high temperature deformation was revealed, which provided a theoretical foundation of the equation of reasonable hot working process.     

Thermal Processing Map and Microstructure Evolution of Inconel 625 Alloy Sheet Based on Plane Strain Compression Deformation

Plane strain compression tests were used to study the deformation behavior of an Inconel 625 alloy sheet at various temperatures and strain rates. The peak stress was selected to establish the constitutive equation, and the processing maps under different strains were drawn. The results show that the effective stress–strain curve of Inconel 625 has typical dynamic recrystallization (DRX) characteristics. With the increasing deformation temperature and the decreasing strain rate, the softening effect is significantly enhanced. The parameters of the constitutive equation are calculated, and the average error of the constitutive equation is 5.68%. Through the analysis of the processing map, a deformation temperature of 950–960 °C with a strain rate of 0.007–0.05 s⁻¹ were determined as the unstable region, and obvious local plastic-rheological zones were found in the unstable region. The optimum deformation condition was found to be 1020–1060 °C/0.005–0.03 s⁻¹. Through electron backscattered diffraction (EBSD) characterization, it was found that both the increase of temperature and the decrease of strain rate significantly promote the recrystallization process. At a low strain rate, the main recrystallization mechanism is discontinuous dynamic recrystallization (DDRX). It is expected that the above results can provide references for the optimization of the rolling process and microstructure control of an Inconel 625 alloy sheet.     

Strain Localization of Orthotropic Elasto–Plastic Cohesive–Frictional Materials: Analytical Results and Numerical Verification

Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.     

Hot Deformation Behaviour and Constitutive Equation of Mg-9Gd-4Y-2Zn-0.5Zr Alloy

The thermal deformation behaviour of Mg-9Gd-4Y-2Zn-0.5Zr alloy at temperatures of 360–480 °C, strain rates of 0.001–1 s⁻¹ and a maximum deformation degree of 60% was investigated in uniaxial hot compression experiments on a Gleeble 3800 thermomechanical simulator. A constitutive equation suitable for plastic deformation was constructed from the Arrhenius equation. The experimental results indicate that due to work hardening, the flow stress of the alloy rapidly reached peak stress with increased strain in the initial deformation stage and then began to decrease and stabilize, indicating that the deformation behaviour of the alloy conformed to steady-state rheological characteristics. The average deformation activation energy of this alloy was Q = 223.334 kJ·mol⁻¹. Moreover, a processing map based on material dynamic modelling was established, and the law describing the influence of the machining parameters on deformation was obtained. The experimental results indicate that the effects of deformation temperature, strain rate and strain magnitude on the peak dissipation efficiency factor and instability range were highly significant. With the increase in the strain variable, the flow instability range increased gradually, but the coefficient of the peak power dissipation rate decreased gradually. The optimum deformation temperature and strain rate of this alloy during hot working were 400–480 °C and 0.001–0.01 s⁻¹, respectively.     

An Incremental Mori-Tanaka Homogenization Scheme for Finite Strain Thermoelastoplasticity of MMCs

The present paper aims at computational simulations of particle reinforced Metal Matrix Composites as well as parts and specimens made thereof. An incremental Mori-Tanaka approach with isotropization of the matrix tangent operator is adopted. It is extended to account for large strains by means of co-rotational Cauchy stresses and logarithmic strains and is implemented into Finite Element Method software as constitutive material law. Periodic unit cell predictions in the finite strain regime are used to verify the analytical approach with respect to non-proportional loading scenarios and assumptions concerning finite strain localization. The response of parts made of Metal Matrix Composites is predicted by a multiscale approach based on these two micromechanical methods. Results for the mesoscopic stress and strain fields as well as the microfields are presented to demonstrate to capabilities of the developed methods.     

Elastoplastic Model Framework for Saturated Soils Subjected to a Freeze–Thaw Cycle Based on Generalized Plasticity Theory

The failures of soil slopes during the construction of high-speed railway caused by the soil after the freeze–thaw (F–T) cycle and the subsequent threat to construction safety are critical issues. An appropriate constitutive model for soils accurately describing the deformation characteristics of soil slopes after the F–T cycle is very important. Few constitutive models of soils incorporate the F–T cycle, and the associated flow rule has always been employed in previous models, which results in an overestimation of the deformation of soil exposed to the F–T cycle. Generalized plasticity theory is widely used to predict the performance of geotechnical materials and is especially well adapted to deal with this type of generalized cyclic loading (such as a freeze–thaw cycle), and it overcomes the shortcomings of the associated flow rule that causes larger shear deformation. To this end, an elastoplastic model framework based on generalized plasticity theory with double yield surfaces for saturated soils subjected to F–T cycles was developed. Two types of plastic deformation mechanisms, i.e., plastic volumetric compression and plastic shear, were considered in this elastoplastic model. It was found that this model can accurately predict the mechanical behavior and deformation characteristics of saturated soils after F–T cycles.     

Constitutive Model and Recrystallization Mechanism of Mg-8.7Gd-4.18Y-0.42Zr Magnesium Alloy during Hot Deformation

The hot deformation behavior of Mg-8.7Gd-4.18Y-0.42Zr alloy was investigated by uniaxial hot compression tests at 300–475 °C with strain rates of 0.002–10 s⁻¹. The average activation energy was calculated as 227.67 KJ/mol and a constitutive relation based on the Arrhenius equation was established in this study. The results show that Mg-8.7Gd-4.18Y-0.42Zr magnesium alloy is a strain rate and temperature-sensitive material. When the temperature is constant, the flow stress increases with the increase of strain rate, while when the strain rate is stable, the flow stress decreases with the increase of temperature. DRX is the main softening mechanism of the alloy, including continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). Meanwhile, the DRX grains nucleate preferentially at the twin intersections in the parent grains under the deformation condition below 300 °C and gradually expand outward with the increase of strain. When the compression temperature is above 400 °C, DRX grains nucleate preferentially at the original grain boundary and then gradually expand inward with the increase of strain. The optimum deformation conditions of the studied alloy are performed at 400–450 °C and 0.002–0.02 s⁻¹ by a comprehensive comparison of the hot processing map, microstructure refinement, and formability.     

Theoretical Analysis and Experimental Verification of the Stress and Strain of Axially Compressed Steel-Reinforced Concrete Columns under Long-Term Loads

The objective of this study is to provide a theoretical method to accurately calculate the stress and strain of steel-reinforced concrete (SRC) columns under long-term axial compression. First, considering the cross-sectional stress redistribution and the influence of each stress increment in the process, the theoretical formula of stress and strain under long-term loading was deduced. Then, the stress and strain calculation program of SRC columns under long-term axial compression was programmed by using object-oriented Visual C++ language. Finally, an experimental study on the long-term deformation performance of SRC axial compression columns was performed to validate the accuracy of the proposed theoretical method. By comparing the calculated results with the experimental results, the influence of steel bars on the long-term stress and strain of SRC columns under axial compression was analyzed and the corresponding long-term stress–strain variation law was studied. Results show that the changing trend of the long-term strain of plain concrete (PC) and SRC with loading time is basically the same, increasing rapidly in the first 270 days and gradually tending to be stable beyond 270 days. After 750 days, the maximum difference in the total strain between the PC columns and SRC columns reaches 26.60%, and the steel bars have a strong influence on the long-term strain of the concrete columns. The errors between the measured values of the two SRC columns, and the calculated results are 2.96% and 5.78%, respectively. Therefore, the derived stress–strain calculation formula and calculation program of SRC columns under long-term loads are accurate and reliable. When the loading time is 750 days, the tensile stress increment of 1.92 MPa and a compressive stress increment of 168.26 MPa are produced in concrete and steel bars. The long-term stress of concrete columns is markedly influenced by steel bars. In the first three years, the stress and strain of the concrete and steel bars develop rapidly and then gradually slow down.     

High Temperature Behaviors of a Casting Nickel-Based Superalloy Used for 815 °C

The hot deformation behaviors of the SJTU-1 alloy, the high-throughput scanned casting Nickel-based superalloy, was investigated by compression test in the temperature range of 900 to 1200 °C and strain rate range of 0.1–0.001 s⁻¹. The hot processing map has been constructed with the instability zone. At the beginning of hot deformation, the flow stress moves rapidly to the peak value with the increased strain rates. Meanwhile, the peak stress is decreased with the increased temperature at the same strain rates. However, the peak stress shows the same tendency with the strain rates at the same temperature. The optimum hot deformation condition was determined in the temperature range of 1000–1075 °C, and the strain rate range of 0.005–0.1 s⁻¹. The microstructure investigation indicates the strain rate significantly affects the characteristics of the microstructure. The deformation constitutive equation has also been discussed as well.     

Mechanical Characterization of the Elastoplastic Response of a C11000-H2 Copper Sheet

This work presents an elastoplastic characterization of a rolled {"type":"entrez-nucleotide","attrs":{"text":"C11000","term_id":"1536071"}}C11000-H2 99.90% pure copper sheet considering the orthotropic non-associated Hill-48 criterion together with a modified Voce hardening law. One of the main features of this material is the necking formation at small strains levels causing the early development of non-homogeneous stress and strain patterns in the tested samples. Due to this fact, a robust inverse calibration approach, based on an experimental–analytical–numerical iterative predictor–corrector methodology, is proposed to obtain the constitutive material parameters. This fitting procedure, which uses tensile test measurements where the strains are obtained via digital image correlation (DIC), consists of three steps aimed at, respectively, determining (a) the parameters of the hardening model, (b) a first prediction of the Hill-48 parameters based on the Lankford coefficients and, (c) corrected parameters of the yield and flow potential functions that minimize the experimental–numerical error of the material response. Finally, this study shows that the mechanical characterization carried out in this context is capable of adequately predicting the behavior of the material in the bulge test.     

Comparison of Constitutive Models and Microstructure Evolution of GW103K Magnesium Alloy during Hot Deformation

The characteristics of constitutive behavior and microstructure evolution of GW103K magnesium alloy were investigated via hot compression tests at a strain rate of 0.001–1 s⁻¹ and a temperature of 623–773 K. The rheological stress of GW103K alloy decreased with increasing temperature or decreasing strain rate during hot deformation. Three models including the Johnson Cook (JC) model, the strain-compensated Arrhenius (SCA) model and back-propagation neural networks (BPNN) were applied to describe the constitutive relationships. Subsequently, the predictability and precision of the models were compared by evaluating the correlation coefficient (R), root mean square errors (RMSE), and relative errors (RE). Compared with the JC and SCA models, the BPNN model was more efficient and had higher prediction accuracy in describing flow stress behavior. Furthermore, EBSD maps confirmed that magnesium alloy easily causes dynamic recrystallization (DRX) during hot deformation. The volume fraction and size of DRX grains increased with decreasing strain rate and/or increasing temperature.     

Investigating Optimal Confinement Behaviour of Low-Strength Concrete through Quantitative and Analytical Approaches

Reinforced concrete is used worldwide in the construction industry. In past eras, extensive research has been conducted and has clearly shown the performance of stress–strain behaviour and ductility design for high-, standard-, and normal-strength concrete (NSC) in axial compression. Limited research has been conducted on the experimental and analytical investigation of low-strength concrete (LSC) confinement behaviour under axial compression and relative ductility. Meanwhile, analytical equations are not investigated experimentally for the confinement behaviour of LSC by transverse reinforcement. The current study experimentally investigates the concrete confinement behaviour under axial compression and relative ductility of NSC and LSC using volumetric transverse reinforcement (VTR), and comparison with several analytical models such as Mander, Kent, and Park, and Saatcioglu. In this study, a total of 44 reinforced-column specimens at a length of 18 in with a cross-section of 7 in × 7 in were used for uniaxial monotonic loading of NSC and LSC. Three columns of each set were confined with 2 in, 4 in, 6 in, and 8 in c/c lateral ties spacing. The experimental results show that the central concrete stresses are significantly affected by decreasing the spacing between the transverse steel. In the case of the LSC, the core stresses are double the central stress of NSC. However, increasing the VTR, the capacity and the ductility of NSC and LSC increases. Reducing the spacing between the ties from 8 in to 2 in center to center can affect the concrete column’s strength by 60% in LSC, but 25% in the NSC. The VTR and the spacing between the ties greatly affected the LSC compared to NSC. It was found that the relative ductility of the confined column samples was almost twice that of the unrestrained column samples. Regarding different models, the Manders model best represents the performance before the ultimate strength, whereas Kent and Park represents post-peak behaviour.