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A Forming Limit Diagram (FLD) is a graph which depicts the major strains versus values of the minor strains at the onset of localized necking. Experimental determination of a FLD is usually very time consuming and requires special equipment. Many analytical and numerical models have been developed to overcome these difficulties. The Gurson- Tvergaard- Needlemann (GTN) damage model is a micromechanical model for ductile fracture. This model describes the damage evolution in the microstructure with physical equations, so that crack initiation due to mechanical loading can be predicted. In this work by using the GTN damage model, a failure criterion based on void evolution was examined. The aim is to derive constitutive equations from Gurson's plastic potential function in order to predict the plastic deformation and failure of sheet metals. These equations have been solved by analytical approach. The Forming Limit Diagrams of some alloys which studied in the literatures have been predicted using MATLAB software. The results of analytical approach have been compared with experimental and numerical results of some other researchers and showed good agreement. The effects of GTN model parameters including 〖 f〗_0 〖,f〗_C 〖,f〗_N,f_f , as well as anisotropy coefficient and strain hardening exponent on the FLD and the growth procedure of void volume fraction have been investigated analytically.

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Prediction and prevention of wrinkling are very important in tool design and determining the effective parameters in sheet metal forming processes. In forming metallic cups, wrinkling generally occurs in the two regions of flange and wall. The control of wrinkling in flange area is not so difficult by controlling the blankholder pressure, but it is difficult in the wall region because the sheet is not supported in this area. In this paper, using a geometric method based on numerical simulation, the wrinkling in the wall of the symmetric conical parts in the developed hydrodynamic deep drawing with radial pressure and inward flowing liquid is investigated. In the process, two independent pressure supplies have been used for forming the sheets. Due to the nature of the process, the effects of radial and cavity pressures on wrinkling have been investigated. In addition, the effects of material, initial blank thickness and punch velocity on wrinkling in wall area were investigated. To verify the results of the simulation, several experimental tests have been done on the St13 and copper sheets. Good agreement between the simulation and experimental results shows the reliability of this method in the wrinkling study. It was also demonstrated that increasing the maximum radial pressure or decreasing cavity pressure leads to increasing wrinkling. Additionally, wrinkling was decreased with increasing blank thickness. Moreover, it was shown that wrinkling simulation is much depended on input parameters such as punch velocity and appropriate element size

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The sheet metals formability can be restricted by localized necking and internal cavitation. On the one hand, nucleation and growth of cavities during plastic deformation can increase the inhomogeneity of sheet metal and accelerate the localized necking. On the other hand, localized necking at the intervals between the cavities can lead to accelerate the joining and coalescence of the internal cavities. In this paper an analytical model based on Marciniak-Kuczynski (M-K) model and Gurson plastic potential function in order to exert the internal voids effect on localization necking has been developed. Stowell’s model was used to illustrate void growth behavior during plastic deformation. In order to examine the effect of the voids on localized necking, the void volume fraction was considered in the imperfection factor and the plastic volume constancy principle. The nonlinear system of equations was solved with the modified Newton-Raphson method using MATLAB software. This new analytical method (M-K-Gurson) was used to predict the forming limit diagram (FLD) of IF steel alloy sheets and the results were compared with those of other researchers. The results showed that the M-K-Gurson method predicted the FLD with better agreement comparing with experimental results. Thereafter, the effects of strain hardening exponent, anisotropy coefficients, geometrical imperfection factor, the void volume fraction and the void growth rate parameter on the FLD were investigated.

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Forming Limit Diagrams (FLDs) are very useful measures for safe forming of sheet metals without failure due to necking or fracture under different loading conditions. This paper uses ductile fracture criteria to predict the formability of low carbon steel sheets to evaluate their accuracy in predicting the FLDs. In addition, the fracture forming limit curves (FFLD) and necking forming limit curves (NFLD) for St12 low-carbon steel have been extracted experimentally and numerically. In the experimental procedure, the Nakazima stretching test was used. In the numerical procedure, by defining six phenomenological ductile fracture criteria in ABAQUS / Explicit finite element software, the failure is predicted and compared with the experimental results. These criteria were calibrated using 6 tests namely as In-plane shear, uniaxial tensile test, circle hole test, notched tension test, plane stress test, and Nakazima stretching test. The results showed that the criteria, which include both the stress triaxiality (η) and Lode parameter (L), provide a more accurate prediction of failure. Also to predict necking during numerical simulation of Nakazima test and also to extract the NFLD, three criteria of the second derivative of major strain, the second derivative of thickness strain and the second derivative of equivalent plastic strain have been used.

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In forming conical parts by traditional deep drawing techniques, due to the stress concentration at the contact area between the punch and the workpiece, thinning and rupture occurs on the sheet. There is also a high possibility of wrinkling in the free area of ​​the sheet; where there is no contact between the punch and the sheet. Therefore, new methods have been examined in forming this group of parts. Electromagnetic forming is one of the relatively old methods of high-speed forming that has attracted more attention in recent years. In the present study, the process of pre-forming of aluminum conical parts using electromagnetic force has been discussed numerically and experimentally. First, experiments were carried out by a simple spiral coil and after confirming the validity of the numerical simulations, the effect of electromagnetic force density in radial and axial directions was investigated in different areas of the sheet. Using the obtained results, a new coil was designed and built that has the ability to provide suitable distribution of the force in the radial and axial directions. Reduction in power consumption by up to a quarter, an increase in the amount of radial inward force and the height of the preform formed cone up to 2 times, minimizing the friction force, reduction of the workpiece center thinning by 3% (while increasing the height by 2 times) and elimination of wrinkles in the flange area of the sheet are the advantages of using the new coil compared to the primary coil.

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Today, the industry's need to join dissimilar metals has increased, especially in the automotive and aircraft industries. In this regard, in order to join metals, new methods, called solid state joining, have been used, among which electromagnetic joining is performed with a lower cost and at a higher speed. In this research, firstly, the feasibility of joining copper tubes to composite tubes by electromagnetic method and the quality of the joinit have been studied. Then, the effect of the welding voltage process parameter on the mechanical properties of the strength has been investigated by the ring test. Finally, in order to examine the surface hardness of the welded samples, the Vickers hardness test was performed. The results show that the joining of the copper samples to the composite tubes has been done well. It has been observed that with the increase in voltage, due to the increase in the collision energy of the two tubes, the connection force has increased by about 2 times. In the 8 kV voltage, due to the increase in the impact speed, a more severe plastic deformation has occurred than in other samples which has caused more local deformation of the weld interface and, as a result, an increase in the hardness. The hardness of the interface in this condition was about 8% higher than that of the 5 kV voltage.