جستجوی مقالات مرتبط با کلیدواژه « constitutive equations » در نشریات گروه « فنی و مهندسی »

The purpose of this research is to investigate the hot working behavior of the cobalt-nickel base superalloy with the chemical composition of Co-22.8Ni-3.4Al-8Cr-17.1W-1.5Ti-2.8Ta-1.5Nb-1.5Mo-0.06C-0.02B (%wt) by performing compression test, providing the constitutive equation and deformation procssing map and determining the safe and unsafe regions of deformation. In this regard, the hot compression test was performed in the temperature range of 1050-1200 degrees Celsius, with a step of 50 degrees Celsius and strain rates of 0.1, 0.01 and 0.001/s up to a strain of 0.7. The evaluation of the constitutive equations governing the hot deformation process of the superalloy showed that the presented model based on the hyperbolic sine equation predicts the experimental results with acceptable accuracy. Using the mentioned equation, the hot deformation activation energy of the investigated alloy in the present study was obtained as 497 kJ/mol. Based on the process in map drawn for the investigated alloy in the present study, at a strain of 0.4, an instability region was observed at a temperature of 1050 degrees Celsius and a strain rate of 0.01 1/s. the extent and intensity of instability region decreased with the increase in deformation temperature. According to the results of the processing map and the constitutive equations, the optimal conditions of deformation of the investigated alloy are in the temperature range of 1150  to 1200  and the strain rate of 0.1 1/s and the temperature range of 1100  to   1200 and the strain rate of 0.1 to 0.001 the peak efficiency of  45% energy consumption.

Duplex stainless steel 2205, famous for its excellent combination of high corrosion resistance and good mechanical properties, is widely used in the industrial fields in different temperature ranges, and can be a suitable alternative to austenitic or ferritic stainless steels. In the present study, the hot compression tests were performed to identify the hot and warm working behavior of duplex 2205 stainless steel and the effect of temperature, strain rate and strain parameters on its flow stress. Cylindrical specimens with a diameter of 8 mm and a height of 12 mm at temperatures of 600, 700, 800, 900, 1000, 1100 °C and strain rates of 0.3, 0.1, 0.01, 0.001 s-1 were compressed to a strain of 0.6. The constitutive equations were used to predict the mechanical behavior and flow stress analysis of this steel, and finally the modified dynamic materials model and strain rate sensitivity(m) maps were used to indicate the best temperature and strain rate ranges for hot and warm working of this alloy. The strain rate sensitivity(m) maps showed the hot and warm stable workability of duplex 2205 stainless steel is in three domains with 800 °C temperature and 0.3 s-1 strain rate, 1050 ˚C temperature and 0.001 s-1 strain rate and 1050 ˚C temperature and 0.001 s-1 strain rate.

The purpose of this paper is to investigate and develop the constitutive equation governing fiber-reinforced dielectric elastomers using finite element software because dielectric elastomers are a class of materials that undergo deformation when subjected to an electric field. As a result, due to this feature and widespread use in artificial muscles, it is very important to study their behavior. In the first step, the stress values are developed and calculated using invariants. Next, due to the nonlinearity of the material behavior, it is necessary to calculate the tangential modulus, which is one of the most important components in the analysis of the finite element model. Finally, according to the results, it is observed that the effect of fiber orientation angle on stress values is inevitable. How the anisotropic material bending rate will increase as the fiber orientation angle increases. Also, increasing the applied voltage, regardless of any orientation of the fibers, is associated with increasing the Kirchhoff stress in the direction shown in the figure.

Concrete is one of the most widely used building materials in the world and the use of fiber-reinforced concrete (FRC) in structures, to increase its tensile strength and improve its behavior, has been extensively developed in recent decades. It is necessary to determine the constitutive equations of FRCs when the numerical investigation of the behavior of them is running. These equations should be including relations to handle the effect of steel fibers on the behavior of FRC. In this study, the behavior of FRCs with a different percent of steel fiber under triaxial compression, with different values of confining pressure, is experimentally and numerically investigated. Hoek cell is used in triaxial tests. In the numerical simulation, five-parametric constitutive equations with Willam-Warnke (W-W) failure criterion, isotropic hardening/softening function and non-associated plasticity was used and substepping integration method was carried out for integration of constitutive equations. For applying the effect of steel fibers on the failure surface, Kt coefficient was determined from the results of biaxial experimental tests on SFRCs. The constitutive equations are implemented with UMAT subroutine in ABAQUS and specimens are simulated in ABAQUS. By the comparison of the experimental (maximum strength) results and the numerical (stress-strain curve) results, an acceptable agreement was seen between them. Finally, based on the consistency between experimental and numerical results, it was concluded that the numerical model can be used, with enough confidence, to predict the behavior of SFRCs specimens.

The intervertebral discs are of the most important body tissues that provides the required flexibility for the spine during daily activities. Due to the lamellar structure of the Annulus Fibrosus, that surrounds the central part of Nucleus Pulposus, it may show anisotropic behavior in carrying the applied loads. Therefore, this aspect was investigated using the experimental data that were obtained by confined compression relaxation tests on samples in three different directions: Axial, radial and circumferential. To obtain the experimental values of the permeability and aggregate modulus as material parameters, test data in three directions were fit to the constitutive equations that were based on the biphasic relaxation model. The results for the permeability and aggregate modulus in three directions show that the material parameters are almost independent of direction and therefore, it is concluded that AF can be treated as an isotropic material under the compressive loads.

Understanding softening mechanisms of wrought aluminum alloy during hot deformation processes is important in order to control microstructure and to predict flow stress accurately in simulation. In this paper, hot compression tests have been done to study the hot deformation behavior of an A5456 aluminum alloy. The effect of temperature, strain and strain rate on flow behavior of the alloy has been studied as well. For this meaning, several cylindrical samples with respectively 10 and 15 mm in diameter and length have been subjected to the test at 350, 400, 450, 500 and 550 °C, strain rates of 0.001, 0.01, 0.1, 1 s-1 and strain of 0.7. The samples where then immediately quenched in water in order to study the microstructure. Analysis of the strain – strain curves at different deformation conditions show that the flow stress decreases with increasing the test temperature and decreasing the strain rate. Because of high stacking fault energy of aluminum alloy, the dominant softening mechanism in this alloy is dynamic recovery. From experimental results, the equations governing the hot deformation behavior of the material have been determined at peak stress and activation energy of 182 KJ/mol for hot deformation process has been obtained.

The constitutive equations based on the dislocation mechanics are applicable at relatively low temperatures. Nevertheless, considering the diffusion processes is necessary for modeling the hot flow stress. In other words, the softening effects of dynamic recovery and recrystallization should be taken into account. In the present work, a modified Zerilli–Armstrong constitutive equation for predicting the hot flow stress of a microalloyed steel was proposed, in which the effects of hardening and softening phenomena were contemplated. It was shown that the original equation is not able to model the softening part of flow curves related to dynamic recrystallization and it was clarified that the constants of the model should be modified for appropriate consideration of the effects of dynamic recovery. On the other hand, it was found that the hardening and softening stages should be separated and the peak strain can be utilized into the flow stress formula. While retaining the general form of the original Zerilli–Armstrong model, the developed constitutive relation was able to appropriately predict the hot flow stress. Conclusively, this constitutive model can be considered as a simple and viable one for modeling the flow stress of steels.

In this research, industrial hot deformation processes was simulated for 321 austenitic stainless steel using hot compression test with the aim of acquiring technical knowledge and indigenization of stainless steel production. The obtained stress-strain curves showed the common retrieval dynamic behaviour. By microscopic studies, the main restoration mechanism during hot deformation in this steel was diagnosed as dynamic recrystallization, that due to low stacking fault energy of 321 stainless steel, this phenomenon was justified. Then, using diagrams related to real stress, real strain and strain rate, the onset point of dynamic recrystallization was determined under different conditions. Also, using the constitutive equations and Zener-Holloman parameter, hot deformation behaviour of 321 stainless steel was studied and the activation energy of hot deformation for this steel was determined as 422 (Kj/mol).

Different constitutive models are used to model the hot deformation flow curves of different materials. In this research, the hot deformation flow stress of API X65 pipeline steel was modeled using the exponential law equation with strain dependent constants. The results of this model were compared with the results of a model which has recently been developed based on a power function of Zener-Hollomon parameter and a third order polynomial function of strain to power of m (m is a constant)). Root mean square error (RMSE) criterion was used for this purpose. It was found that the he exponential law equation with strain dependent constants has a better performance (lower RMSE) to model the hot deformation flow curves of API X65 pipeline steel. The results can be used further for mathematical simulation of hot deformation processes.

Hot deformation of an extruded Mg–10Li–1Zn alloy was studied by compression testing in the temperatures range of 250- 450 ˚C and strain rates of 0.001–0.1 s−1. During the hot compressive deformation of the Mg-10Li-1Zn alloy, flow stress curves reach a maximum value and then reach a steady state which is indicative of the occurrence of dynamic recrystallization. Because of the activation of softening mechanisms at higher temperatures and lower strain rates, this phenomenon is more pronounced at lower temperatures and higher strain rate.
The flow stress of the Mg–10Li–1Zn alloy at elevated temperatures was modeled via an Arrhenius-type constitutive equation. The values for the activation energy of about
103 kJ mol–1 and the power-law stress exponents in the range of 5.2–6.0 obtained from the Arrhenius-type model indicate that the dominant mechanism during hot deformation of the Mg–10Li–1Zn alloy is dislocation climb which is controlled by the lattice
self-diffusion of Li atoms.

In this article constitutive equations on dynamic behavior of off- axis polymer matrix composites in different strain rates were investigated. Using the Hill Anisotropy and assumptions governing in fiber composites, a model was developed to express the dynamic behavior of polymer matrix composites. Using the flow rules and effective stress and assumptions in fiber composites like non plastic behavior of composites in fiber direction, the Hill parameters were omitted and reduced to one namely a_66 parameter. This model was called2D one- Parameter Plastic Model (also it can be developed for 3D composite layers). This model was developed for off axis composites as well. For each composite with different fiber directions, effective stress- effective strain was introduced. With choosing the right value for parameter a_66 by try and error, all the stress- strain curves were collapsed in to one single curve. Using this model and the experimental static and quasi- static results gathered from different authors (in range of〖 0.01s〗^(-1)), a viscoplastic model was obtained which can predict the polymer composite respond both in static and high strain rate tests (between 400 s^(-1) and 700s^(-1)). Constant parameters in high strain rates in this model were calculated through extrapolating the data in the static test rang. The accuracy of this model was investigated and approved by Split Hopkinson Pressure Bar test. The results showed that the visco plastic model can predict the dynamic respond of composite fibers in high strain rates very well.

Subsurface rocks (by their nature) are filled with cracks and pores which are saturated with one or more fluid phases (water، air، oil، etc.). These fluids have a significant influence on the mechanical behavior of a rock mass. Closing the state of the stress to failure surface and pore pressure effect on the rock deformation are among these influences of pore fluids. To account for these effects، one should investigate the rock mass response in an elastic medium with porosity. Therefore، poroelastic theory should be used. In poroelastic medium the governing equations، stress-strain and strain-displacement relations are affected by pore pressure and reciprocal effects of displacements and pore pressure. In this paper، firstly the constitutive equations and other required relations for describing a poroelastic medium are presented. Then the coupled effect of pore pressure and displacements is removed by using a potential method. Differential equations of time-dependent and time-independent are solved for a point force and point source which gives Green’s functions. Resulted Green’s functions can be used in any suitable numerical method such as boundary element method to investigate the response of rock mass to poroelastic effects.