Sharif Digital Repository

In this paper, considering the problems of common finite element (FE) codes that consider simple constitutive equations, a developed FE code that considers a new constitutive model is used to simulate the behavior of copper sheets under severe plastic deformation (SPD). The new proposed constitutive model, that considers dislocation densities in cell interiors and cell walls of material as true internal state variables, can investigate all stages of flow stress evolution of material during large plastic deformations and also can explain the effects of strain rate magnitude on the mechanical response of material, during room temperature SPD. The proposed FE analysis is used to investigate the... 

In this study, empirical constitutive relations of materials with different crystalline structures through severe plastic deformation are introduced. Here, for each material, an optimized empirical relation is chosen by fitting some empirical relations on the results achieved from a dislocation- based constitutive model. In this work, four modes of empirical relations are fitted on the results of modified Estrin-Toth-Molinari-Brechet constitutive model for four materials with different crystalline structures (Al, Cu, Ta, and Zr). The obtained relations for the materials can be usable in commercial finite element codes  

By coupling a kinetic dislocation model and Monte Carlo algorithm, the recrystallized microstructure of severely deformed Oxygen Free High Conductivity Copper (OFHC) is predicted at different strains imposed by Equal-Channel- Angular-Pressing (ECAP) and annealing temperatures. From a flow field model, the strain rate distribution during the ECAP of the material in a curved die is calculated. Then using the kinetic dislocation model, the total dislocation density and correspondingly the stored energy after each ECAP pass is estimated. Utilizing the Monte Carlo algorithm and the stored energy, the recrystallized microstructure is predicted. The results show that the recrystallized grain size... 

A hybrid algorithm based on the finite element method, Monte Carlo model, and Hall-Petch relationship is utilized to predict the mechanical properties of the rods after cold forging at different degrees of deformations and heat treatments at different temperatures and times. The results show that the flow stress and hardness of the rods after forging and those of the forged rods after the heat treatments are decreased from their center to surface. However, with increasing the temperature and time of the heat treatment the flow stress and hardness are decreased, their effects are not considerable. In addition, the distribution of the mechanical properties of the forged rods after the heat... 

In this research, an algorithm based on the Q-state Potts model is presented for modeling the austenite to ferrite transformation. In the algorithm, it is possible to exactly track boundary migration of the phase formed during transformation. In the algorithm, effects of changes in chemical free energy, strain free energy and interfacial energies of austenite-austenite, ferrite-ferrite and austenite-ferrite during transformation are considered. From the algorithm, the kinetics of transformation and mean ferrite grain size for different cooling rates are calculated. It is found that there is a good agreement between the calculated and experimental results  

For microstructure modeling of copper wire after wire drawing process and annealing, an algorithm based on the Upper Bound Method and Potts Model is developed. In the algorithm, the Upper Bound Method is utilized to calculate the stored energy distribution in the drawn wire and then the stored energy is used in the Potts Model to obtain the grain size distribution of the drawn wire after annealing. The microstructure modeling is carried out at different deformation and annealing conditions. In all of the conditions, the fine and coarse grains are achieved at the surface and center of the wire, respectively. Also, the grain size of the drawn wire after annealing is decreased with increasing... 

The Monte Carlo simulation is utilized to model the nano-scale grain growth of two nanocrystalline materials, Pd81Zr19 and RuAl. In this regard, the relationship between the real time and the time unit of simulation, i.e. Monte Carlo step (MCS), is determined. The results of modeling show that with increasing time of heating, the grain sizes of both nano-crystalline materials increased as in the case of conventional materials. Moreover, it is found that for both nano-crystalline materials the relationship between the real time and MCS is in power law form, which is linear for the conventional materials. © Indian Academy of Sciences  

Through tearing test, the absorbed energy of a low carbon steel and an Al-Mg alloy sheets are compared. The tests are carried out quasi-statically using the wedge tools with different angles. Also, the effects of the inclination angle of sheet to vertical and angle between normal to sheet and edge of wedge are investigated on the energy absorption of both the steel and aluminum alloy. The results show that with increasing the later angles, the absorbed energy is decreased and with increasing the wedge angle, the energy is increased. Comparing the absorbed energy of the sheets with the same thicknesses, it is found that the energy absorption of the steel is higher than that of the aluminum... 

Utilizing the differential scanning calorimetry (DSC) and Vickers hardness tests, the relationship between the stored energy and indentation hardness of copper after compression test is achieved experimentally. Three dislocation models are utilized to develop the relationships between the stored energy and hardness for justifying the experimental relationship. The relationships show that the stored energy is increased by increasing the hardness, non-linearly. By comparing the models' results with the experimental data, the validity of each model at different ranges of hardness is determined. © 2008 Springer Science+Business Media, LLC  

A Monte Carlo model on the basis of hardness input is developed to predict the annealing microstructure of deformed specimens in tensile, compression, and tensile + compression tests. From experimental value of hardness, the stored energy of the deformed specimens is calculated and entered into the Monte Carlo model. The consistency between the simulation results and experimental data shows that the developed model based on hardness input can be more practical since the effect of different deformation states is considered for estimating of stored energy. © 2008 Elsevier B.V. All rights reserved  

A study on the redundant deformation factor in wire drawing process of an austenitic 304 stainless steel is carried out. Utilizing the upper bound methods based on the trapezoidal and spherical velocity fields, the redundant deformation factors in different deformation conditions are calculated and the achieved results are compared with the results of the FEM and superposition method presented by other researchers. From the results it is concluded that when Δ values are lower than 5, the redundant deformation factors calculated from the spherical and trapezoidal velocity fields with angle β of 80-90° are valid. Also, the results of the trapezoidal velocity field with angle β of 90° are the... 

In assessing of the effect of redundant strain factor on the microstructure inhomogeneity of the drawn wire after annealing, the Upper Bound Model based on spherical velocity field and a computer simulation based on Monte Carlo Model are utilized. Using the models, the strain, stored energy due to deformation and grain size distribution of the wires after different deformation and annealing conditions are calculated. From the achieved results the deformation and microstructure inhomogeneity are computed. It is observed that the deformation inhomogeneity as well as microstructure inhomogeneity is increased with increasing the parameter Δ and redundant strain factor. Also, the results show... 

A Monte Carlo model is modified by using Turnbull-Fisher nucleation rate model to simulate the ultra-fine microstructure evolution during annealing of pure copper processed by equal channel angular pressing (ECAP). The simulation is utilized to predict the grain size of pure copper samples at different annealing temperatures and pass numbers of ECAP. Also, in the simulation the constant nucleation rate model is assumed and a good agreement is achieved between the simulation results and experimental data. Thus, it can be concluded that the constant nucleation rate is prevailed during the microstructure evolution. © 2007 Elsevier B.V. All rights reserved  

Modeling of the static recrystallization in deformed copper specimens with different initial grain sizes is carried out based on a previous dislocation-grain size interaction model and a Monte Carlo simulation. From the dislocation-grain size interaction model, the stored energy of the deformed copper is calculated considering the interaction of the dislocations due to the different initial grain sizes. Then, utilizing the stored energy and Monte Carlo simulation the kinetic of recrystallization and recrystallized grain sizes are obtained. The JMAK plots of the modeling results show that, in conditions of 2D modeling and site-saturated nucleation, the Avrami exponent is 2 ± 0.1. The time for... 

To investigate the effect of 3D and 2D deformations on flattened wires, the effective strain fields of flat rolled and sidepressed wires are predicted using the combined finite and slab element method (FSEM) and two-dimensional finite element method (TDFEM), respectively. The validity of the calculated strain fields are verified using the Vickers microhardness test. Utilizing the calculated strain fields, the strain inhomogeneity of the flat rolled and sidepressed wires are investigated. To assess the effects of height to width ratio and frictional condition on the strain inhomogeneity, an inhomogeneity factor (IF) is defined. The results show that for both the flat rolled and sidepressed... 

The deformation inhomogeneity in flattened wire produced by the wire flat rolling process is studied. Utilizing the combined Finite and Slab Element Method (FSEM), the effective strain fields in the flattened wire are calculated at different reductions in height and frictional conditions and compared with experiment. The calculated and experimental results exhibit that the deformation is inhomogeneous and macroscopic shear bands are appeared in the cross section of flattened wire. Using the results of the analysis, it is shown that the deformation inhomogeneity, introduced by an Inhomogeneity Factor (IF), is different on the x-axis and y-axis in the cross section of the flattened wire. By... 

Purpose - The purpose of this paper is to present an assessment of the ability of combined finite and slab element method (FSEM) for analyzing the wire flat rolling process. Design/methodology/approach - Using the FSEM, the effective strain field of flat rolled wire is predicted for different reductions in height and frictional conditions. The validity of the method is assessed by performing the Vickers microhardness measurements on the flattened wire cross section. Also, the creation of macroscopic shear bands in cross section of the flat rolled wire is investigated and confirmed by microhardness and metallographic examinations. Moreover, the lateral spread and width of contact area are... 

In this study a slab analysis is developed to predict the rolling pressure distribution and rolling force in the wire flat rolling process. In the slab analysis the variations of width of contact area between the rolls and wire during rolling is considered. Two differential equations are derived and solved using a modified Eulerian numerical method. The effects of friction coefficient, reduction in height and yield stress of wire on the rolling pressure distribution and rolling force are assessed. It is found that in the flat rolling of wire, there exists a maximum in the pressure distribution similar to that of the strip rolling process. Also, the effects of friction coefficient, reduction... 

In this research the deformation of wire in flat rolling process has been investigated. A theoretical relationship has been developed to relate the reduction in height of wire to the width of contact area between the rolls and wire. This relationship depicts that the width of contact area is proportional to square root of reduction in height of wire. Using that relationship the width of contact area for wires of different diameter have been calculated and compared with the appropriate experimental data after flat rolling. Also, a relationship is developed to assess the effect of reduction in height of wire on the lateral spread in wire flat rolling process. Moreover, the effect of material...