فهرست مطالب ramin hashemi

Extraction of mechanical properties, including plastic and fracture properties, of sheet metal under quasi-static and dynamic states is one of the fundamental issues in crashworthiness studies. According to standards, samples with various geometries can be employed to extract dynamic and quasi-static mechanical properties. Given the dependence of the yield behavior results and fracture strain on the geometry of the test specimen, it is essential for a specimen used under dynamic conditions to have maximum compatibility with quasi-static uniaxial tension test specimens and to be usable in both conditions. Therefore, in the present study, various geometries were initially designed and evaluated to determine plastic behavior. The effect of geometric parameters on the results of uniaxial tension tests was evaluated, and a suitable specimen for extracting dynamic and quasi-static mechanical properties was presented. Additionally, based on the results of quasi-static and dynamic uniaxial tension tests on the selected specimen at strain rates of 0.01/s to 30/s, the sensitivity of the plastic behavior to strain rate was determined. Furthermore, through the calibration of the coefficients of the Johnson-Cook constitutive model, strain rate-dependent plastic behavior was determined within the desired range and strain rates beyond that.

The wires used in the wire EDM process are of great importance in this new machining process as the cutting agent of the workpiece. Factors such as the diameter of these wires, their material, and their manufacturing method make their production simply not possible. In the upcoming research, a widely used type of Chinese wire in the domestic industry has been selected, examined, and analyzed. In the early stages of the research, the Chinese wire sample was elementally analyzed and its compounds were extracted, then it was subjected to a tensile test and its mechanical properties were also extracted. In the next steps, the wire was made with the aim of making a Chinese model by two methods of casting and extrusion and was again subjected to chemical analysis and tensile test. Also, in the final stage, all the wires made on the wire EDM machine were put under the same parameters and conditions and tested on a piece of work. The important innovation of the current research is in making wire EDM wire by extrusion method for mass production inside the country. The manufactured wire sample has up to 80% more strength than Chinese wire and is also 10 times softer than that, which increases the strength and softness of the wire leading to greater resistance of the wire and reducing the possibility of its tearing during machining operations.

Composites of continuous fibers have higher mechanical performance than short fibers, which is why they are produced and used significantly in the aviation industry. One of the new methods of joining composites is ultrasonic welding. In this process, by applying high power (100 to 2000 watts) and high frequency (15 to 100 kHz) vibrations to the joint of two parts, heat is generated in the joint and causes the two parts to stick together. In this research, the parameters of the ultrasonic welding of polyamide 6 glass composite, the effect of the interlayer film, and the direction of the fibers on the strength of the connection have been investigated. Ultimately, the ultrasonic welding connection has been compared with the adhesive bond. In examining the connection as an edge-to-edge connection, the samples were cut according to ASTM D5868 standard and subjected to a tensile-shear test after ultrasonic welding. Considering the average input parameters for time, pressure, and power, it was observed that using a pure polymer film layer as the interlayer film increases the welding strength. By changing the direction of the fibers of all layers by 90 degrees, the welding strength decreased a little. The amount of polymer and fiber protrusion increased, and the appearance quality decreased. In comparing the welding connection with the adhesive bond, the value of the welding strength was higher than the strength of the adhesive connection. Also, the time spent on the welding connection was much less than on the adhesive bonding.

This paper aims to examine the influences of heat treatment on forming limit diagrams and mechanical properties of aluminum alloy AA6061 sheets with thicknesses of 1.5 mm. The uniaxial tensile and the micro-hardness tests are employed to specify the mechanical properties and their variations. The Nakazima test is performed to characterize the strain forming limits of this aluminum alloy. Comparison between the results of micro-hardness and forming limit diagrams indicates that by increasing the temperature up to the peaked ageing temperature, the strength of the alloy is increased, but the forming limits are decreased, and after the peaked aged in over the aged state, the strength is decreased and the forming limits are increased. The peaked-aging is touched in this specific alloy after 4 hours heat treatment at 180 oC.

In the last few years, researchers have been interested in the fabrication of laminated composite sheets. In this research, mechanical properties and fracture toughness of three-layer aluminum-magnesium-aluminum composite sheet produced by cold-rolling bonding method were investigated. Mechanical properties and fracture cross-sections of the specimens were studied by uniaxial tensile test, hardness test and scanning electron microscopy, respectively. It was observed that the tensile strength of composite specimens was higher than that of aluminum and the microhardness and fracture toughness values were increased compared to the initial specimens. High applied cold work can be the main reason for the increase in hardness and fracture toughness, and the reason for the decrease in composite strength over magnesium is the creation of plastic instability in the magnesium reinforcer due to the high strain.The results of scanning electron microscopy also show that the fracture mechanism is for the soft aluminum layer and for the crisp magnesium and the surface of the fracture cross section in the aluminum layer has a shallower and smaller micropores, indicating shear ductile fracture.

Decoupling the uplink and downlink user association improves the throughput of heterogeneous networks (HetNets) and balances the traffic load of macro- and small- base stations. Recently, fiber-wireless HetNets (FiWi-HetNets) have been considered as viable solutions for access networks. To improve the accuracy of user association and resource allocation algorithms in FiWi-HetNets, the capacity limitation of various backhaul technologies must be considered. In this paper, we investigate the backhaul-aware decoupled uplink/downlink (UL/DL) user association, subcarrier allocation, and power control optimization problem in FiWi-HetNets. In our system model, fiber and millimeter wave (mmWave) links are used as backhaul of base stations, and the backhaul capacity limitation and minimum required transmission rate ($R_{min}$) are modeled in the optimization problem. As the formulated optimization problem is non-convex, we present a heuristic algorithm to divide the main problem into two sub-problems that are solved iteratively. The proposed algorithms are evaluated through exhaustive simulations. The results indicate that decoupling UL/DL user association improves the sum rate of FiWi-HetNets. Besides, we evaluate the effect of backhaul capacity limitation and $R_{min}$ on the sum rate of FiWi-HetNets. The effect of upgrading fiber backhaul technology is also investigated to evaluate the role of fiber backhaul on the sum rate of the radio access network.

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.

Aluminum foils have been extensively used in packaging and household applications to protect foods and pharmaceutical products from environmental effects. In recent years, sever plastic deformation processes have been highly regarded due to the production of ultra-fine-grained metal materials. The high applicability of nanostructures, due to their unique physical and mechanical properties, reveals the importance of investigations on new forming methods. Accumulative roll bonding (ARB) process is one of the best and most practical methods for forming metal sheets, which mechanism is the plastic deformation of material through the passage between two or more rollers. In this investigation, thin aluminum foils with a thickness of two hundred microns were produced using accumulative roll bonding method in five passes without lubricant or additional heat treatment between passes and at ambient temperature. To investigate the mechanical properties, uniaxial tensile test and microhardness test were used, and to investigate the microstructure and fracture surface area, scanning electron microscopy was used. The ultimate tensile strength at the end of the fifth ARB pass reached 393 MPa, about 5.9 times larger than of the initial sample. Also, compared to the previous research, the obtained strength was highest due to the lower thickness of the layers and the penetration of surface oxides into the metal matrix during preparation. Furthermore, by increasing the number of accumulative roll bonding passes, the thickness of the layers decreases and the bonding quality between layers is improved. Investigation on tensile fracture surface after five passes exhibits ductile failure mechanism.

Forming limit diagram is one of the most applicable methods for prediction of plastic instability in sheet metal forming that temperature and strain rate is among factors effecting on the FLD. In this paper, the effects of temperature and strain rate at quasi-static condition on the true stress-true strain curve and forming limit curve of AA3104 aluminum are analytically investigated using Marciniak-Kuckzynski method and Johnson-cook model. The stress-strain response of numerical results validation using the Ludwik model is performed with experimental results. Theoretical results show a good agreement with experimental results. Then, according to the stress-strain curves obtained based on the Ludwik equation, Johnson-Cook coefficients are calculated for AA3104 and the true stress-true strain respond and forming limit diagram are produced for different temperatures 50°C، 300°C and 400°C and several t strain rates 〖10〗^(-5)، 〖10〗^(-4)and 〖10〗^(-3) s^(-1). The stress-strain curve decreases with increasing temperature and increases with increasing strain rate. Also the FLD increases with increasing temperature and decreases with increasing strain rate. The results exhibit a positive sensitivity of temperature on the limit strain due to the thermal softening and the negative strain rate sensitivity on the FLD AA3104 due to the behavior of crystallographic structure of the material

The equal channel angular rolling (ECAR) process is one of the methods of severe plastic deformation that is considered to obtain ultrafine-grain materials (UFG.( In this study, the effect of temperature on the mechanical properties of 5083 aluminum alloy was investigated in this process. Equal channel angular rolling process was performed at the temperatures 25℃ (room temperature), and 200 and 300℃. The equal channel angular rolling was used as a lubricant. The evaluation of mechanical properties and fracture mode of the samples was assessed using uniaxial tensile test, micro-hardness test and scanning electron microscope (SEM). The results revealed that by increasing number of ECAR passes at a specific temperature, yield strength, ultimate tensile strength and micro-hardness increased in which that increasing rate is more higher at the initial passes than the last ones, while the elongation decreased, contrarily. Study of the mechanical properties of the samples after applying the ECAR process in a specified pass at different temperatures showed that by increasing the temperature, the yield strength, ultimate tensile strength and micro-hardness of samples decreased in comparison with the samples processed in the ambient temperature. However, the elongation was improved. As a quantitatively results, at the end of the third pass at 300°C, the yield strength and micro-hardness of the samples decreased by 14.8% and 8.5%, respectively, in comparison with the samples processed in the ambient temperature, and the elongation increased by 22.2%.

In the present study, for the first time the Young's modulus, anisotropy coefficient and elastic and plastic parameters of multi-layered Al/Br/Al composite produced by cold roll bonding process were assessed by digital image correlation method. The digital image correlation (DIC) is a relatively new method used to measure strain fields to determine various parameters such as anisotropy and Young's modulus for many materials and alloys. Structure, mechanical properties, elastic and plastic parameters are determined by optical microscopy (OM), micro-hardness measurements and tensile tests equipped by 2D DIC system. Using longitudinal and transverse strains from DIC and plasticity theory thickness strain, anisotropy coefficient and other elastic and plastic parameters were calculated. The results showed that mechanical properties were improved compared to the primary samples, so that the yield strength and ultimate tensile strength of the composite were more than five times the original aluminum, and microhardness of both layers of aluminum and brass improved more than two times due to cold working caused by increasing the dislocation density during rolling. The value of the calculated elastic modulus was obtained 77.8GPa by digital image correlation method, which are little difference from the values obtained from theoretical relationships based on the volume of the composite materials. Also, the anisotropy coefficient during the tensile test, after the initial oscillation increased to the necking point, then decreased and a little before the failure point fixed.

In this paper, we propose to use discretized version of the so-called Enhanced Gaussian Noise (EGN) model to estimate the non-linearity effects of fiber on the performance of optical coherent and uncompensated transmission (CUT) systems. By computing the power of non-linear interference noise and considering optical amplifier noise, we obtain the signal-to-noise (SNR) ratio and achievable rate of CUT. To allocate power of each CUT channel, we consider two optimization problems with the objectives of maximizing minimum SNR margin and achievable rate. We show that by using the discretized EGN model, the complexity of the introduced optimization problems is reduced compared with the existing optimization problems developed based on the so-called discretized Gaussian Noise (GN) model. In addition, the optimization based on the disctretized EGN model leads to a better SNR and achievable rate. We validate our analytical results with simulations and experimental results. We simulate a five-channel coherent system on OptiSystem software, where a close agreement is observed between optimizations and simulations. Furthermore, we measured SNR of commercial 100Gbps coherent transmitter over 300 km single-mode fiber (SMF) and non-zero dispersion shifted fiber (NZDSF), by considering single-channel and three-channel coherent systems. We observe there are performance gaps between experimental and analytical results, which is mainly due to other sources of noise such as transmitter imperfection noise, thermal noise, and shot noise, in experiments. By including these sources of noise in the analytical model, the gaps between analytical and experimental results are reduced.

In the past two decades, the development of layered composites as well as their manufacturing methods has become a fascinating subject for researchers. The CRB is a solid-state welding to create a bonding between a wide ranges of metals using a simple rolling. In this study, the multi-layered Al5052/MgAZ31B composite was produced by CRB and its formability was studied. Rolling operations were performed by applying a 70% reduction in room temperature. The formability of Al/Mg composite was carried out using stretch test with semi-circular punch in different loading and the forming limit diagram was drawn. FLDs are the most practical method for obtaining sheet formability, which determines the strain before necking and fracture. In addition to formability, mechanical properties and fracture surface of Al/Mg were also studied using a tensile test, microhardness, optical and scanning electron microscopy. Due to low formability of magnesium and the production of Al/Mg composite at room temperature, the surfaces of the FLD is desirable due to the lack of separation between the aluminum/magnesium interfaces and the compensation tightness of magnesium with high formability of aluminum. Also, the results of mechanical properties showed that strength and microhardness of Al/Mg composite compare to initial aluminum improved 149.5% and 80%, respectively, due to the cold working and increasing density of dislocations. The images of the fracture surfaces showed that the aluminum before and after rolling had a ductile fracture with different size, number of dimples that after the rolling the size and depth of the dimples decreased.

One of the most important factors affecting the mechanical, physical and chemical properties of metals, are crystal structure and grain size. Ultrafine metals with an average grain size of 1000-100nm and nanostructured metals have an average grain size of less than 100nm. Ultrafine and nanostructured materials are known as a new generation of metal products, which have remarkably mechanical and physical properties in comparison to coarse-grained metals. In the last two decades, due to good properties such as high strength, high ductility and toughness, good corrosion resistance and high superplasticity properties, these materials have been considered by many researchers. In recent years, many methods have been proposed for severe plastic deformation and are now being developed and expanded. In these processes, in spite of the high hydrostatic pressure and the unaltered dimensions of the sample during the process, it is possible to apply very high strains, which results in the desired mechanical properties and ultrafine grained and nanostructured materials. The accumulative roll bonding process is one of the methods of SPD. ARB process is simple, extensive use, low-cost, industrially capability method that can produce ultrafine and nanostructured metals. In this research, light metals such as aluminum, magnesium and titanium and also extremely used metal such as copper and steel are discussed. Also, mechanical properties, fractography and microstructural properties of ultrafine and nanostructured metals produced by ARB are compared with initial samples and the mechanisms governing of ARB process that cause changes in mechanical and microstructural properties are analyzed.

Metal matrix composites are relatively low-weight materials comprising of reinforcing elements in their structure which tend to improve the hardness, abrasion resistance as well as well as fatigue resistance of the material. One of the metal matrix composites with significant mechanical features is titanium metal matrix composite (Ti-MMC) which can be considered as an alternative to nickel based superalloys in the wide range of applications in numerous manufacturing sectors, including automotive, and aerospace. Despite significant features aforementioned, due to high manufacturing costs and the presence of reinforcing elements in metal matrices, machining and machinability of Ti-MMCs is a complex subject. Knowing that limited studies are available on machining Ti-MMC under various lubrication modes and lubrication rates, adequate knowledge on the effects of cutting parameters and lubrication modes on machinability attributes of Ti-MMCs is a delicate subject. Therefore, the first aim of this work is to present the effects of cutting parameters, including lubrication modes and lubrication rate on machinability attributes, including surface quality. Furthermore, the Fast Fourier transform (FFT) will be used to evaluate the effects of cutting parameters on the frequency domain of recorded cutting forces.

Metal matrix composites are bunch of materials that have wide range of uses such as construction, abrasion, and heat. This type of composite exhibits better dimension than the base metal such as temperature applications, strength, rigidity, thermal conductivity, wear resistance, creep resistance and stability. In this study, the methods of producing aluminum composite reinforced with ceramic particles, especially the processes of sever plastic deformation, have been investigated. The main focus of this research is to study the microstructure, mechanical properties and mechanisms governing this type of composite produced by two ARB and cross CARB methods. The results of the research showed that in the initial passes of the processed composites there is no proper distribution of reinforcing particles but by increasing the number of passes, the particle distribution is improved and the reinforcing particles are distributed in longitudinal and transverse directions. Tensile strength and microhardness have the same trend which they gradually increased with increasing strain rates and improvement of particle distribution but elongation at first decreased in the initial passes due to the inappropriate distribution of the particles, porosity and cluster particles, and then improved with the elimination of these imperfections and distribution. However, the mechanical and microstructural properties of the CARB method are more favorable. Also, the governing mechanisms for microstructure modification in produced composites by rolling processes are the formation of the Orowan loop, role of reinforcing particles, difference in the coefficient of thermal expansion of the matrix and reinforcement, and so on.

In this paper, Forming Limit curves (FLCs) of AA3105 aluminum alloy sheet were obtained at four different temperatures using the Nakazima test. A novel approach based on the Nakazima test was applied to fabricate the experimental setup for determining forming limit diagrams (FLDs) at elevated temperatures. First, the Nakazima-die-set was manufactured, and a thermal system was prepared for increasing sheet and die’s temperature; then AA3105 samples were tested at four different temperatures experimentally. Moreover, the ABAQUS finite element software was employed. Three different criterions including the 2nd order of derivatives for major strain, equivalent plastic strain, and thickness strain were applied to estimate the onset of localized necking. The numerical results were verified by experiment. Both the experimental and finite element method results illustrated that the level of the forming limit diagram for the aluminum sheets improved by increasing its temperature. The forming limit improvement was not equal in every strain paths.

One of the most important studies in tube hydroforming process is optimization of loading paths. The primary purpose of this research is to maximize formability by detecting the optimal forming parameters. The most significant settings in the prosperity of tube hydroforming process, are internal pressure and end axial feed (i.e., load path). In this paper, a finite element analysis was performed for a double-layered tube hydroforming process using the ABAQUS/Explicit software. Then, the finite element model has been verified with published experimental data. Using design of experiments (DOE) working with the Taguchi method, 32 loading paths are designed for optimization. All 32 loading paths are modelled using the finite element method in ABAQUS/Explicit and the magnitudes of bulge height and the total thickness of tubes at the branch tip are obtained in each loading path. The regression analysis is carried out to estimate the tubes formability and obtain objective functions that are bulge height and the total thickness of tubes at the protrusion peak as functions of loading parameters (internal pressure and axial feed). For solving the multi-objective optimization problem, the non-dominated sorting genetic algorithm II (NSGA-II) is utilized and the optimum results were obtained from the Pareto optimal front. Finally, the optimized loading path was applied to the finite element model and better formability (3.4% increase in the bulge height) has been achieved in the results.

Ultrasonic energy is used for applying severe plastic deformation on metal surfaces. In the present work, the effect of ultrasonic vibration on the formability, microhardness and microstructural properties of St14 steel sheet has been investigated. To be precise, a semi-hemispherical-head forming tool had shaped the specimens until the necking started to happen. Conventional as well as the ultrasonic-assisted biaxial stretch forming test has been performed on St14 steel sheets and obtained data has been used to compare the hardness and microstructure of the specimen with and without superimposing the ultrasonic vibration. It was observed that the hardness of the samples which have been shaped by applying ultrasonic vibrations to the tool with an amplitude of 15µm at 20.5 kHz increased significantly in compared with the samples which have been shaped without using ultrasonic vibration, revealing the efficiency of the ultrasonic operation in increasing the hardness.

In this article, the effect of different yield functions on prediction of forming limit curve (FLC) for aluminum sheet is studied. Due to importance of FLC in sheet metal forming, concentration on effective parameters must be considered exactly in order to have better theoretical prediction comparing experimental results. Yield function is one of the factors which are improved by adding new coefficients that follows the behaviour of material with good approximation, so applying different yield functions can change shape and level of FLCs. In this study the yield criteria which are used in determination of forming limit curves, are Hill48, Hosford, BBC2008, Soare2008, Plunkett2008 and YLD2011. The YLD2011 yield function is more appropriate than the other yield function for prediction of the FLD of aluminum alloy. The well-known Marciniak-Kuczynski (M-K) theory and voce hardening law have also been used. To verify the numerical results, the obtained results have been compared with available experimental data.

An enhanced unfolding Inverse Finite Element Method (IFEM) has been 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 have also been considered to improve the accuracy and capability of the proposed IFEM. The extended strain-based forming limit diagram based on the Marciniak and Kuczynski (M-K) model has been computed and used to predict the onset of necking during sheet processing. The EFLD is built based on equivalent plastic strains and material flow direction at the end of forming. This new forming limit diagram is much less strain path dependent than the conventional forming limit diagram. Furthermore, the use and interpretation of this new diagram are easier than the stress-based forming limit diagram. Finally, two applied examples have been presented to demonstrate the capability of the proposed approach.

In recent years, different SPD methods have been attention of researchers to produce metal matrix multi-layered composite and to achieve good mechanical properties and microstructure. Among SPD methods, CARB process is inspired by ARB which has the ability to produce metal composites with better mechanical and microstructural properties. In this investigation, for the first time, aluminum composite matrix consisting of 5% pure nickel powder was produced by CARB in eight pass. Microstructure and mechanical properties of produced composite were evaluated in the different cycles of CARB process by optic and scanning electron microscopy, elemental analysis, uni-axial tensile test, microhardness, respectively. Results of microstructure showed that the bonding between the layers in the first passes is weak and there is a porosity in structure but by increasing the passes and after 8 pass, in produced composite, distribution of nickel powders and oxide layers has better than previous cycles, and porosity reduced. By increasing the number of CARB passes, tensile strength and microhardness increased continuously. The reason for this increase is due to the governing mechanisms in the process of SPD, and the nickel powder did not contribute much to this increase. Also, the amount of elongation after a severe drop in the initial sandwich, increased by increasing the pass until the end of the eighth cycle, continuously with a low increase rate. The tensile strength and microhardness increased 3.88 and 2.5 times, respectively, compared to the annealed sample

Nowadays due to water shortage, the use of treated wastewater as sustainable solution has been considered by industrial units; especially in industrial cooling units and boilers. However the use of treated wastewater also has its own problems such as corrosion of metal parts that they are often made of carbon steel. Therefore different methods such as coating have been considered by the industrial user of treated wastewater in order to reduce corrosion. So in this study, SiO2/TiO2 Ceramic Nano composite coatings was put on Carbon Steel plates by Sol-Gel method and by dipping process for 100 seconds and microstructure and properties of produced ceramic coatings were investigated. The results showed that ceramic Nano composite coatings improved corrosion properties of Carbon Steel. In order to improve the properties and performance of the coating, the molar ratio of components and factors affecting performance of coating were evaluated till optimum coating with Nano structure and highest level of corrosion protection is provided. To evaluate the performance of coatings for corrosion protection, polarization curves and to determine the surface morphology, scanning electron microscope was used. In order to study the bonds type and functional groups in the optimal sol, infrared spectrum was used. The optimum corrosion protection coatings were studied in 3.5% sodium chloride solution. The results showed that the ceramic optimal deposited coating provides effective protection for the surface of Carbon Steel against corrosion in 3.5% sodium chloride solution.

In the new sheet metal forming process as incremental sheet forming and spinning forming, this is not perfectly true in Marciniak-Kuczyinski model to assume that sheet deformation occurs in the plane-stress state indispose there are normal compressive stress and through-thickness stress. In this type of forming processes, the obtained limit strains refer to improving the sheet forming. However, in researches the effects of through-thickness shear stresses, also known as out-of-plane shear, has been studied less. The generalized forming limit diagram is a great curve that includes all six components of the stress tensor. In this paper, the effect of normal comprehensive and through-thickness shear stresses on the limit strain AA6011 aluminum sheet using a modified M-K and the anisotropic Yield function, Hill 48 and by using numerical solutions of nonlinear equations, Newton-Raphson method. The first the forming limit diagram was drawn with the assumption that the through-thickness shear stresses and then the effects of normal comprehensive stress and through-thickness shear stress on the limit strains were proved and the generalized forming limit curves were obtained. The results show that forming limits can be increased significantly by both normal compressive stress and through-thickness shear stresses. Also, the effects of normal stress on increasing the formability of sheet compared with the effects of through-thickness shear stress is greater.

In the present study, Al/Cu layered composite was produced through CRB method at room temperature, without lubricant and via using laboratory rolling machine by applying 60% reduction in thickness. Also mechanical properties, fracturgraphi and microstructure investigated through uniaxial tensile test, microharsness, scanning electron and optiv microscope. Results of carried out tests, showed the value of tensile strength and microhardness for Al/Cu layered composite compared to initial Al 5052 and pure Cu, increased that the main cause of this increase is applied high strain and cold working. Value of tensile strength for Al/Cu layered composite received 415 MPa that compared to initial Al 5052 and pure Cu 48% and 140% enhanced, respectively. Also microhardness calculated for each layers of composite individually and for Al and Cu increased 14% and 83% respectively. Results of SEM demonstrated that ductile fracture mechanism govern for Al/Cu composite such as initial samples, but the difference is that dimples for composite layers shallower and smaller compared to initial samples.