Sharif Digital Repository

In spite of the fact that the experimental results indicate the significant effect of strain rate on forming limits of sheets, this effect is neglected in all theoretical methods of prediction of Forming Limit Diagrams (FLDs). The purpose of this paper is to modify the most renowned theoretical method of determination of FLDs (e.g., M-K model) so as to enable it to take into account the effect of strain rate. To achieve this aim, the traditional assumption of preexistence of an initial geometrical inhomogeneity in the sheet has been replaced with the assumption of a preexisting "material" inhomogeneity. It has been shown that using this assumption, the strain rate would not be omitted from... 

The influence of sheet thickness on sheet metal forming limits is a controversial issue; while some investigations indicate the considerable influence of thickness on forming limit diagrams (FLDs), others suggest that it is of negligible importance. In the present work, it has been demonstrated that if the thickness-reduction process is chosen so as not to alter the micro structure of the material, the forming limits do not change with variations of thickness. A material which has extensive usage in sheet metal forming processes of automotive industry (St14) has been provided. The initial thickness of the sheet is 1.5mm and using grinding process (which does not alter the microstructure) the... 

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... 

In this study, the effect of a compressive normal stress has been considered in the determination of forming limit diagrams and forming limit stress diagrams to predict neck initiation failure in tube hydroforming of T-shaped parts. Computation of the forming limit diagrams and FLSDs is based on the generalized Marciniak and Kuczynski method to consider the existence of through-thickness compressive normal stress. The proposed forming limit diagrams and FLSDs were used in conjunction with ABAQUS/EXPLICIT finite element simulations to predict the onset of necking in tube hydroforming of T-shaped part. The amount of calibration pressure and axial feeding required to produce an acceptable part... 

Forming limit diagram is often used as a criterion to predict necking initiation in sheet metal forming processes. In this study, the forming limit diagram was obtained through the inclusion of the Marciniak–Kaczynski model in the Nakazima out-of-plane test finite element model and also a flat model. The effect of bending on the forming limit diagram was investigated numerically and experimentally. Data required for this simulation were determined through a simple tension test in three directions. After comparing the results of the flat and Nakazima finite element models with the experimental results, the forming limit diagram computed by the Nakazima finite element model was more convenient... 

In this study, the effect of through-thickness shear (TTS) stress has been examined on the prediction of forming limit diagrams (FLDs). Determination of the FLD is based on the Marciniak–Kuczynski (M–K) model with some modifications on the stress states for consideration of the TTS stress effects. For solving the equations, the Newton–Raphson method has been used. Furthermore, the Nakazima test has been simulated to investigate the stress state which occurs in the sheet during the test. Results showed that the formability of sheet metal could be better as the through-thickness stress increased. Also, implementation of TTS stress in the present model, the corresponding FLD has better... 

In this study, the effect of through-thickness shear (TTS) stress has been examined on the prediction of forming limit diagrams (FLDs). Determination of the FLD is based on the Marciniak–Kuczynski (M–K) model with some modifications on the stress states for consideration of the TTS stress effects. For solving the equations, the Newton–Raphson method has been used. Furthermore, the Nakazima test has been simulated to investigate the stress state which occurs in the sheet during the test. Results showed that the formability of sheet metal could be better as the through-thickness stress increased. Also, implementation of TTS stress in the present model, the corresponding FLD has better... 

In this study, the effect of through-thickness shear (TTS) stress has been examined on the prediction of forming limit diagrams (FLDs). Determination of the FLD is based on the Marciniak–Kuczynski (M–K) model with some modifications on the stress states for consideration of the TTS stress effects. For solving the equations, the Newton–Raphson method has been used. Furthermore, the Nakazima test has been simulated to investigate the stress state which occurs in the sheet during the test. Results showed that the formability of sheet metal could be better as the through-thickness stress increased. Also, implementation of TTS stress in the present model, the corresponding FLD has better... 

Tailored welded blanks (TWBs) technology can give the important possibilities to obtain components in the automobile industry. Friction stir welding (FSW) is a joining approach, which can adhere parts well with desired properties in weld zone. In this article, the main aim is investigation the effect of weld zone orientation on forming limit diagram (FLD) of the TWBs using experimental and finite element model. Three TWBs are produced FSW with three different orientations of weld zones including 00, 450 and 900 against major stress direction. The microstructure of the weld zones is divided and then observed via metallography procedures. Tensile tests are carried out to determine the... 

The main objective of this study is to predict the deformation behavior, strain localization, and forming limits of ferrite-pearlite steels by incorporating the contributions of the microstructural characteristics and mechanical properties of the underlying microstructure. A realistic microstructure-based micromechanical approach in the framework of the crystal plasticity (CP) model was carried out using the periodic representative volume element (RVE) generated from the scanning electron microscopy (SEM) image. The homogenized stress–strain curve of the realistic RVE was validated with the experimental data with an error of less than 6.71% at large strains. Afterward, the initial... 

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... 

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... 

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... 

Metal forming processes are widely used in industrial productions, automobile bodies, food industries, oil refineries, and liquid and gas transmission systems. Analyzing these processes is very important to reduce wastes and optimize the processes. Study of some main factors such as physical and mechanical properties of material and its formability, die geometry, die material, lubrication and pressing speed has been the topic of many research projects. In this paper, forming limit diagrams (FLDs) for LC and ULC steels and the effect of different parameters like the work-hardening exponent, n, and the plastic strain ratio, r, on these diagrams have been evaluated and simulated using... 

The forming limit stress diagram (FLSD) has been reported as being much less path dependent and much more favourable than the forming limit diagram (FLD) in representing forming limits in the numerical simulation of sheet metal forming processes. Therefore, the purpose of this study was to develop a methodology for the prediction of the forming limits both in strain and stress forms. All simulations are based on strain gradient theory of plasticity in conjunction with the Marciniak-Kuczynski (M-K) approach. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. The...