Sharif Digital Repository

The inverse solution is helpful to determine the drawability of a part and drawing parameters at the initial design stage. The usual inverse algorithms consider the drawing process that occurs in one step and therefore they are not able to analyze the processes which need more than one drawing step. Therefore, multistep inverse solution has been used for such problems. The multistep inverse solution deals with finding the initial guesses of nodal positions on intermediate stages and solving inverse equations between two consecutive steps. In this paper, a new mapping method has been developed to find the initial nodal positions on intermediate stages and the unfolding technique has been... 

In this research, numerical optimization of the rear part of a gas turbine, consisting of a single stage axial turbine is carried out. Automated aerodynamic shape optimization is performed by coupling a CFD flow simulation code with the Genetic Algorithm. An effective multi-point optimization method to improve efficiency and/or pressure ratio of the axial turbine is performed. Some variations of optimization parameters such as lean and sweep angels of stator and rotor blades are accomplished. Furthermore, during the optimization process, three-dimensional and turbulent flow field is numerically investigated using a compressible Navier-Stokes solver. The gas turbine experimental... 

The linear unfolding inverse finite element method (IFEM) has been modified and enhanced by implementing large deformation relations. The method is helpful to predict forming severity of the part that should be deep drawn as well as its blank shape and strain distribution in preliminary design stage. The approach deals with minimization of potential energy and large deformation relations with membrane elements. To reduce the computation time, the part is unfolded properly on the flat sheet and treated as 2D problem. Moreover, the nonlinear stress-strain relationship of plastic material properties has been considered to increase the accuracy of the results. An experiment set up has been... 

A stress-based forming limit diagram for necking prediction which is based on the strain gradient theory of plasticity in conjunction with the M-K model has been represented and used in tube hydroforming. In this study, the finite element model for bulge forming of straight tube has been constructed and verified with published experimental data. The adaptive simulation technique is based on the ability to detect the onset and growth of defects (e.g., wrinkling, and bursting) and to promptly readjust the loading paths. Thus, a suitable load path has been obtained by applying Adaptive Simulation Method in ANSYS Parametric Design Language (APDL)  

Major forming limit prediction models and calibration methods are reviewed briefly and their advantages and disadvantages are discussed. Two modified Marciniak-Kuczynski (M-K) models and one modified NADDRG (Keeler-Brazier) model are also presented which have some advantages over conventional models. In the first modified M-K model, material non-homogeneity has been substituted for geometrical non-homogeneity to reduce the sensitivity of the traditional model to variations of the initial non-homogeneity. Using this important advantage, a semi-empirical relation is proposed to predict the value of the initial material non-homogeneity. In the second modified M-K model, the conventional... 

To determine the curvature of the exit profile in the extrusion process of non-symmetrical flat dies, the dead metal zone profile was predicted using the energy minimization method. The dead zone is a natural non-linear die for the process and it is pragmatic to use this non-linear die to estimate the value of the exit profile curvature and the required bearing length for reducing this deviation. The velocity field is calculated based on Hermite cubic spline and some additional assumptions. In non-symmetrical dies the entrance section of the deformation region is not flat. Considering this fact, axial velocity decreases with increasing the distance to die center line which is in agreement... 

A nonlinear inverse finite element method is developed for estimation of initial blank shape and strain distribution in final shape. This method often based on implicit static algorithms, causes sometimes convergence problems because of strong nonlinearities. In order to avoid the converging problems, especially in the quasi vertical walls, an appropriate initial guess is introduced. By using this initial guess, the number of iterations in the nonlinear numerical solution is decreased, solution speed is significantly increased and complicated geometries can be analyzed by this method with good accuracy. Application to a Srail part shows good agreement between commercially available finite... 

The major problem in determining the forming limit diagram (FLD) with the Marciniak-Kuczynski (M-K) model is the necessity of an experimental point in order to find the initial inhomogeneity coefficient and calibrate the diagram. The purpose of the present work is to eliminate this requirement. To do this, the usual assumption of geometrical inhomogeneity has been replaced with material inhomogeneity and it has been shown that the sensitivity of the diagram to variations of the inhomogeneity factor is reduced greatly with the new assumption. Using this advantage and collecting enough experimental data for different materials, an empirical law in terms of sheet thickness has been proposed... 

The main drawback of the method proposed by Marciniak and Kuczynski for prediction of the limit strains in sheet metal forming processes is requirement of an experimental point of the forming limit curve (FLC) in order to calibrate the curve. The purpose of this work is to introduce a new method to calibrate the FLC using the M-K model in which no experimental data is needed. To achieve this goal, many experimental FLCs were collected from the literature and the values of the initial inhomogeneity factors were determined for them with trial and error aproach. Using these data, an empirical law was developed to predict the value of inhomogeneity factor. The resultant curves show good... 

In this study, a general methodology has been developed to design the proper bearing in order to eliminate the curvature of the final product in extrusion process. Three smooth curved (advanced-surface) dies with non-symmetric T-shaped sections and different off-centricities have been studied. For each die, the proper bearing has been designed and physical and numerical modeling have been performed to validate the design. The design procedure is as follows: A formulation, based on Bezier curves, has been used to determine the exit velocity profile. Since the result of Bezier method is different from the actual velocity profile, the Chitkara corrective function has been modified and applied... 

A simplified efficient finite element method called the inverse approach (IA) has been developed to estimate initial blank and strain distribution in sheet metal forming. This algorithm is an inverse method since the position of points in final shape is known and their corresponding position in the initial blank should be determined. This approach deals with the geometric compatibility of finite elements, plastic deformation theory, and virtual work principle. This method often based on implicit static algorithms, sometimes causes convergence problems because of strong nonlinearities. This paper introduces an initial guess to speed up the convergence of Newton- Raphson solution. The... 

The goal of this study is to evaluate the effects of proportional loading, plane stress, and constant thickness assumptions on hydro-mechanical deep drawing (HDD) by developing analytical models. The main model includes no simplifying assumption, and then each of the mentioned assumptions is considered in a specific model. The interrelationships between geometrical and mechanical variables are obtained in the finite difference form based on the incremental strain theory, thereby being solved by Broyden algorithm. Published experimental and FE results are used for evaluation of the results obtained in the present work. The results of models under proportional loading, plane stress, and... 

Crystallographic texture considerably affects the formability of crystalline materials. In this paper, the effects of BCC ideal rolling fibers—including α, ε, η, γ, and ξ fibers—on the sheet formability are numerically studied. The simulations are based on the numerical procedure developed by the authors in [1] in which a rate dependent crystal plasticity model along with the power law hardening are employed in a user material subroutine to model the behavior of crystalline materials. In order to determine FLD—in a M-K type approach—second-order derivative of sheet thickness variations with respect to time is used as necking criterion. The calculated FLDs of the fibers are compared with each... 

In this study, a methodology has been presented for radial positioning of the die holes in multi-hole extrusion of non-symmetric sections. The objective of radial positioning is to minimize exit profile curvature. For this purpose, a two-hole die with non-symmetric T-shaped holes has been investigated. A kinematically admissible velocity field at deformation zone has been developed. The deformation region includes the dead metal zone (DMZ) which is assumed to be linear. The DMZ length was obtained by energy minimization through the upper bound method. To predict the exit profile curvature a deviation function has been suggested. Using the proposed function, the velocity field has been used... 

In this paper, a less studied factor in the asymmetrical rolling process of sheets, namely the rolls horizontal displacement, is investigated using an analytical approach based on the slab method analysis. The presented method is capable of computing the force and torque of the process under different asymmetrical factors such as the rolls horizontal displacement, the interface friction inequality, and the rolls speed mismatch. A formula is presented to predict the outgoing sheet curvature induced by the rolls horizontal displacement. The results can be potentially used in producing curved sheets of various shapes by the asymmetrical rolling process. The analytical model is compared with a... 

Ideal orientations are one of the material characteristics of the applied mode of deformation. The transfer of material texture to orientations near specific ideal orientations can improve the mechanical properties of the material. In this paper, we focus on the determination of ideal orientations of BCC crystals under the equibiaxial tension mode of deformation. To do this, an Euler space scanning method based on a crystal plasticity approach is presented. In this method some initial orientations which are evenly spaced in the Euler space are selected and their evolutions into the ideal orientations are tracked. The loading is applied incrementally until all of the lattice spin components... 

This article presents a crystal plasticity methodology to evaluate the AA1050 sheet formability. In order to determine the orientation distribution of the crystals, initial texture of the material is measured through X-ray diffraction technique. Also, the stress-strain behavior of the material is determined by performing tensile test. In order to simulate the path-dependent crystal plasticity behavior of body-centered cubic crystal structures, a UMAT subroutine that employs the rate-dependent crystal plasticity model along with the power law hardening was developed previously by the authors and linked to the finite element software ABAQUS. This subroutine was further developed to simulate... 

An enhanced unfolding inverse finite element method (IFEM) is used together with an extended strain-based forming limit diagram (EFLD) to develop a fast and reliable approach to predict the feasibility of the deep drawing process of a part and determining where the failure or defects can occur. In the developed unfolding IFEM, the meshed part is properly fold out on the flat sheet and treated as a 2D problem to reduce the computation time. The large deformation relations, nonlinear material behavior and friction conditions in the blank holder zone are also considered to improve the accuracy and capability of the proposed IFEM. The extended strain-based forming limit diagram based on the... 

Material modeling of high strength steels plays an important role in the accurate analysis of autofrettaged tubes. Although, the loading behavior of such materials is nearly elasticperfectly plastic, their unloading behavior due to Bauschinger effect is very complicated. DIN1.6959 steel is frequently used for construction of autofrettaged tubes in some countries such as Germany and Switzerland. In spite of similarity between chemical compositions of this steel with that of A723 steel, due to different material processing, these two steels have an unlikely behavior. In this paper the material behavior of DIN1.6959 was accurately modeled by uniaxial tension-compression test results. Both 6 mm... 

Effects of the grain size on the forming limits of stainless steel 316 L sheets are investigated using crystal plasticity finite element method (CPFEM) by modeling of all grains. For preparing simulation models with different grain morphology, a grain generator code is developed. Using data from metallographic images, texture, and material properties, the developed code can be used for preprocessing of CPFEM. In order to extract mechanical and metallurgical data required for CPFEM, some experiments are carried out on different samples. Moreover, for the purpose of implementing the crystal plasticity formulations, an Abaqus user material subroutine (UMAT) is developed. Concerning the...