Sharif Digital Repository

Knowing the magnitude of the maximum strain before necking is of utmost importance in the processes of designing sheet metals. Thus, numerous experimental and theoretical efforts have been done to answer these questions. In order to predict allowed strains in biaxial stretching, an experimental diagram was introduced called “Forming Limit Diagram” in which major strain is plotted versus minor strain and if the corresponding point to the strain on the sheet is higher than this diagram, necking will occur. One of the most popular methods of obtaining forming limit diagrams is using a hemispherical rod for shaping sheet, which is named as “Nakazima Test” and then the critical strains are... 

In recent years, two-layer sheets have been used in various industries. In this research, the formability of a two-layer sheet which is made of 1.35 mm steel and 0.45 mm copper sheets has been studied. The two-layer sheet used in this study was made by explosive welding method. In order to investigate the formability of the sheet, forming limit diagram was determined. First, Marciniak-Kuczynski (M-K) model was used. In order to determine forming limit diagram using this method, the two-layer sheet was equated with a single-layer sheet and MATLAB software was used. The two-layer sheet was also modeled in finite element software ABAQUS. In order to determine the forming limit diagram, Nakazima... 

Theoretical studies in the analysis of sheet metal failures are referred to obtain the Forming Limit Diagrams (FLDs). Since extracting the Forming Limit Diagrams experimentally is cost and time consuming, many researches have been accomplished for obtaining these diagrams theoretically. However, in many of these researches, the assumption of plane stress state has been used to obtain the FLD, which is not correct in some processes such as hydroforming because of high level of normal stress. In this study, determination of the forming limit diagram with existence of the normal stress is based on the Marciniak and Kuczynski model. Newton-Raphson method has been used to find the set of... 

The inverse Finite Element method (IFEM) has been used for estimation of the initial length of tube, axial feeding and fluid pressure in tube hydroforming. The already developed IFEM algorithm, which has been used in this work, is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, a technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no try and error process. The solution provides all the components of strain. Using the forming limit diagram (FLD), the components of strain can... 

In designing of sheet metal forming processes, knowledge of the maximum permissible strains in the sheet is of prime importance for the design engineer. Thus, a large amount of experimental and theoretical researches have been carried out to estimate these limiting strains. A renowned and prevalent theoretical method for prediction of forming limits is the Marciniak and Kuczynski model. In this model, it is assumed that a small groove exists in the sheet even before applying the loads; and due to the weakness of this region, necking starts from there. The major problem of the M-K model is requiring of an experimental point to “calibrate” the results. Furthermore, while experiments indicate... 

In designing sheet forming processes, finding out the value of the maximum strain before necking in sheets is extremely important. Therefore, many experimental and theoretical efforts have been carried out in order to answer this question. One of the most well-known and useful theoretical methods in this regard is the Marciniak - Kuczynski method which was introduced in 1967 and is still the topic of many researches. In this model, it is assumed that a groove as a defect primarily exists in the sheet and due to the weakness of this region, necking will initiate. Furthermore, the effects of various parameters such as sensitivity to strain rate, strain path, thickness, three dimensional... 

One of the oldest and most used methods in shaping metals is the formation of metal sheets. In designing the process of printing, it's important to know how much the strain on the sheet prior to slipping is. In order to predict the permissible strains in the two-axis stretch of the sheet, they introduced an empirical diagram called the shape-forming diagram. There are various methods for analyzing the formation of metallic sheets, which can be referred to by M-K method, GTN method, continuous damage mechanics method (CDM). In this research, we have tried to obtain the shape of a metal sheet in various strain paths by studying the method of CDM and modeling the mechanical behavior of the... 

There is a major interest to manufacturers of automobile and aerospace parts towards the tailor-welded blanks (TWBs) to reduce the weight and cost of the parts and improve their performance. In this work, formability of four groups of TWBs (two groups with similar thicknesses and different steels and two groups with similar steels and different thicknesses) are investigated. To produce the TWBs, DX54, E275 and E335 steel sheets were used. The results indicate that the inclined laser beam causes the sample failure from the weld zone in the tensile test. Setting the focal point on the top surface of the sheets results in enhancement of yield strength in comparison to the other positions. ... 

In recent decades, the importance of theoretical and experimental researches on sheet metal forming has been revealed due to its wide-spreading applications. The purpose of these researches is to optimize the forming processes and minimize the existing imperfections. Since classical theories don’t include parameters for describing the dependence of metals behavior on size effects or inhomogeneous plastic deformation effects, gradient theories are considered in many researches. In gradient theories, this dependence is considered by changing the constitutive equations and the existence of higher order of strain gradient in zones with inhomogeneous deformation. By considering the localized and...