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In this research, the deformation of circular metal sandwich panels with vertical tube cores under blast load has been investigated numerically and experimentally. The relationship of energy balance in different components of the structure has been considered. The core tubes are installed in a cross arrangement and vertically with the same height between the upper and lower sheets of the sandwich structure. The amount of energy absorbed by the cores is determined according to their location in the structure and the effect of their number and diameter. The grouping of the desired tests for this research has been done according to the thickness of the sheet 1.2 and 2 mm and with aluminum cores with diameters of 12 and 16 (mm). Numerical simulation has been done in the form of free explosion and by defining the pressure function using the Conwep method in Abaqus software. To validate the numerical results, experimental tests have been carried out with the construction of sandwich structure. In both methods, the maximum lateral displacement of the structure at its center and the displacement in terms of distance from the center of the structure, at cores location have been measured. Increased number of tubes in the core of the structure decreased the maximum rise in the upper layer and decreased the transverse displacement of the lower sheet. Structures with fewer cores and less sheet thickness showed more energy absorption. The average difference between the results of numerical and experimental methods was approximately 11%.

An elaborate numerical study with a validated LS-DYNA® immersed boundary method fluid-solid interaction code is used to characterize the influence of pre-detonation pressure and time duration on plastic deformation of thin steel triangular plates subjected to gaseous detonation. Other objectives of this numerical simulation such as estimation of deflection and stress contour of material at high strain rate are derived based on a strain-rate dependent Johnson-Cook material model. Simulation relies on the modeling of detonation by chemical reaction kinetic and its propagation by Conservative Element Solution Element (CESE) solver. Immersed boundary method is used to simulate the interface motion between the detonating gas and the deforming plate to facilitate the assessment of fluid pressure distribution on the plate surface. The numerical tool relates the pressure distribution and gaseous detonation parameters to the plate macroscopic deformation by employing multi-species reactive Euler’s equations for the gas and Lagrangian equation for plate. Numerical method as an appropriate tool in the evaluation of the deflection profile of the triangular plate shows that deflection decreases by the smaller size of the exposed area of the plate.

In this research, the plastic deformation and failure mechanism of sandwich structures with aluminum face-sheets and waste rubber particles core under low-velocity impact loading have been investigated. The drop hammer testing machine was used to apply the impact load to the sample at seven different energy levels 34.3, 68.6, 102.9, 137.2, 154.3, 171.5, and 205.8 J. To achieve the mentioned energy levels, the weight of the hammer was considered constant and equal to 3.5 kg and the standoff distance of the hammer was changed from 1 to 6.5 m. 10 test samples were considered in two types of layering with and without the core of rubber particles. In this series of experiments, the thickness of aluminum face-sheets was constant at 1 mm and two different thicknesses of 16 and 32 mm were considered for the core. Experimental results showed that, the sandwich panel with 16 mm had a 37 and 18 % smaller deformed area for fall heights of 2 and 3 meters, respectively, due to the less porous space between two aluminum face-sheets. Also, compared to the coreless sandwich structure, the use of a low-mass waste rubber particle cores at low energy levels increased the front sheet perforation diameter by 19 %.

The understanding some characteristics of the influence of an interior gaseous detonation within a confined space on plate deformation is valuable for production purposes. In this study, the center of mass displacement of thin steel triangular plates subjected to acetylene and oxygen mixture detonation loading is investigated theoretically. Empirical modeling is presented to find the relationships between effective parameters in the gas detonation forming process such as mechanical properties of plate, impulse of applied load, plate geometry and strain-rate sensitivity effect and center of mass displacement of the triangular plate. Some important parameters, including plate thickness and yield strength, different triangular clamp sizes were studied to show the exposed area effect on the center of mass displacement. The results from non-dimensional analysis demonstrated a good agreement compared with experimental data and showed that the center of mass displacement decreases greatly with involving thicker plate. Non-dimensional analysis as a profitable tool in the evaluation of the center of mass displacement demonstrates that midpoint deflection was decreased by the smaller size of the exposed area of the plate.

The response of thin steel plates subjected to gaseous mixture detonation loading is investigated analytically to determine the possible permanent deformation of center of steel plates clamped in triangular clamping frames. Deformation profiles of plates with different thicknesses under various pre-detonation pressures are investigated which shows large plastic deformations with the maximum deformation happening at the center of mass of the triangular plate. By adopting an energy method approach developed earlier for circular plates, and incorporating a newly developed condition, upper bounds are obtained for the center of mass deformation of the triangular plate. Besides, some important parameters, including plate thickness and yield strength were studied to show the exposed area effect on the deformation profile. The results from analytical studies demonstrate a good agreement compared with experiments and show that the center of mass displacement decreases greatly with involving thicker plate and strain rate influence. Energy method as a useful tool reveals that that midpoint deflection was decreased by the smaller size of the exposed area of the plate.

In the present study, the dynamic response of rectangular steel plates under repeated impulsive loading was investigated. In this regard, experiments were performed on three different structures: unstiffened, stiffened with one and two welding lines. To investigate the deformation modes and the failure mechanism of the experimental specimens, dynamic loads in a wide range were applied up to 3 loads by 25, 35, 45, and 50 g charge masses. Experimental observations demonstrate that with increasing charge mass, the Mode Ia and Mode Ib are observed in a higher charge mass and loading repetitions in a higher number. For the unstiffened plate, at the 3rd load with a mass of 25g, a change Mode Ia is observed, however, the same deformation mode occurs for the stiffened plate with a single and two weld lines at the 3rd blast load by 35g and 45 g charge mass, respectively. These observations indicate the effect of the weld line and its numbers on the variation of failure modes. Furthermore, in the numerical modeling section, the Group Method of Data Handling (GMDH) neural network was used to present a mathematical model based on dimensionless numbers to predict the maximum permanent deflection of tested specimens. Good agreement between the proposed model and the corresponding experimental results is obtained and all data points are within the ±10% error range for every two patterns.

In the current research study, the large plastic deformations of similar and dissimilar single- and multi-layered metallic plates with the same areal density under repeated uniform impulsive loading have been investigated. The ballistic pendulum along a 200 mm length standoff blast tube was used to apply the blast load on the specimen. Forty testing specimen in three different layering configurations including single-, double, and triple-layered, and eight different arrangements were considered. For the same loading and experimental condition, 10 g plastic explosive was utilized and the dynamic response of structures was studied up to five consecutive loads. The experimental results indicated large plastic global deformation with thinning happening at the clamped boundary and also tearing for some experiments. The results also represented that the maximum permanent deflections of plates were increased by the number of blast loads and the progressive deflection of the plates at the center was decreased exponentially with increasing the number of blasts. Placing a thick front layer a thin back layer gives better blast performance to the tested specimen against repeated impulsive loading. The obtained result for multi-layered configurations with the same material is completely consistent with those structures made of dissimilar layers.

In this paper, the dynamic response of steel plates under repeated blast loading using a ballistic pendulum system were investigated. In this regard, experiments were performed on three different configurations: unwelded, welded with single and double welding lines. To apply the dynamic load in a wide range, the plastic explosive charge (C4) in different masses of 25, 35, 45, and 50 g were used. Besides, to investigate the behavior of the structure under repeated loading, experiments were tested on up to 3 loads. Experimental observations demonstrate that with increasing charge mass, the large inelastic deformation with necking and tensile tearing around of the boundary were observed in higher charge masses and loading repetitions in higher numbers. For the unwelded plate, at the 3rd load with a charge mass of 25g, a change in the failure mode was observed (large inelastic deformation with necking around part of the boundary), however, for the welded plate with a single weld line, the same deformation mode occurred at the 3rd blast load by the charge mass of 35g. For the welded plate with two weld lines, the same failure mode was observed at the 3rd blast load by the charge mass of 45g. These observations indicate the effect of the weld line and its numbers on the variation of failure modes. The obtained result is one of the main objectives of the present study to show how using welding lines and their arrangements affect the deformation mode and the failure mechanism of steel plates.

GLARE is a kind of fiber-metal composites in which aluminum alloy sheets are used, along with composite laminates with glass reinforcements. In this paper, Glare FMLs were subjected to repeated low-velocity impact loading with an energy of 150 J. Repeated low-velocity impacts were applied using a drop-weight testing machine. To fabricate testing specimens, 2024-T3 aluminum alloy plates with a thickness of 1 mm as the face-sheets as well as the core made of the glass-epoxy composite were used. The epoxy glass laminate used also consisted of five layers of E-type single-sided glass fibers in the epoxy resin. Besides, 99.9% purity silica nanoparticles were added to the base material. To investigate the effect of adding nanoparticles on the behavior of FMLs under repeated low-velocity impacts, silica nanoparticles with a weight percentage of 0 to 4% were added to the matrix of the fabricated samples. The experimental results showed that the sample with 1% nanoparticles had better performance in terms of impact resistance so that after five loads, it was not seriously damaged; however, the perforation phenomenon occurred for samples with 3% and 4% nanoparticles in the second impact load.

Numerical simulation of Eulerian fluid Lagrangian solid interaction incorporating H2-O2 mixture gas detonation plate forming by employing conservative element and solution element immersed boundary method in LS-DYNA software is proposed in this paper. The detonation mechanism includes 7 species and 16 reactions. The chemical reaction mechanism and detonation wave propagation of Eulerian solver and dynamic plastic response of mild steel thin plate of Lagrangian solver are discussed thoroughly. The Johnson-Cook phenomenological material model with failure criterion is used to provide accurate predictions of dynamic response and failure state of detonation loaded steel plates taking into account material strain-rate sensitivity and non-linearities. The 2D numerical model is validated by comparing the simulation results with experimental data for thickness strain. The simulated pressure-time history of combustion cylinder, von Mises stress and deflection pattern of plate are also represented. Furthermore, a series of numerical simulation was carried out to determine the effect of the magnitude of internal detonation pressure on plate, taking into account different combustion cylinder longitudinal capacities, pre-detonation pressures and ignition point locations. Results show that an increase of pre-detonation pressure is conducive to increase the value of maximum detonation pressure while decreasing the combustion duration. Moreover, combustion cylinder with higher longitudinal capacity is more powerful to deform the plate.

In this paper, experimental and regression analysis of the effective parameters in the free and die forming of circular metallic plates using gas mixture detonation were investigated. In the experimental section, steel, aluminum, and brass plates in different thicknesses were used. To better evaluate the experimental results, the condition of the same areal density was used to compare the results of steel, aluminum, and brass plates under the same loading conditions. In the regression analysis section, the Design-Expert software package and response surface methodology were used. The effect of parameters measured in experimental tests including the pressure of Oxygen, the pressure of Acetylene, plate thickness and die apex angle on the deflection of circular plates were investigated simultaneously. To find a significant model, the confidence level of 95% was considered in the analysis. Experimental results showed that using a die with an apex angle of 60° leads to the decrease of the maximum permanent deflection. On the other hand, using aluminum and brass plates in the die forming resulted in a more reduction of permanent deflection in comparison with free forming. The results of the regression analysis show that the predicted values of the model are in good agreement with the experimental data and the presented model is suitable. Optimal conditions for the minimum deflection of the circular plates under explosive loading were also presented. The pressure of Oxygen and the die apex angle has the highest effect and the least effect on the forming of circular metallic plates.

In the current research, the plastic behavior of circular plates under dynamic loading was investigated. In the experimental section, a ballistic pendulum apparatus and aluminum alloy plates were used. To investigate the deformation profile and the failure pattern of the specimens, dynamic loads were applied in a wide range from 6.49 to 24.69 Ns. To test the behavior under successive loading, each experiment was continued up to 5 loadings. Experimental observations indicate a large plastic deformation of the structure along with the thinning of the test specimens at fully clamped boundaries and the rupture of some in the same area. The results showed that with increasing the number of explosions and the charge mass, the maximum deflection increases, but the progressive deflection decreases exponentially. In the modeling section, some closed-form relations were proposed using the dimensional analysis approach to predict the maximum permanent deflection plates. In these relations, the effect of various parameters such as the plate geometry, inertia of the applied load, and strain rate sensitivity of material was considered. Comparing the results of the model with the experimental results showed that there is a very good agreement between the experimental results and the predictions of the model.

This paper dealing with an experimental study, numerical simulation, and mathematical modeling of the dynamic response of single-layered and double-layered circular plates under localized impulsive loading. In the experimental section, six experiments were conducted on double-layered configurations made of copper-aluminum plates (2mm+2mm) under different loading conditions. ABAQUS commercial software via a user-defined FORTRAN subroutine was used to develop a numerical model. The Johnson-Cook thermo-viscoplastic constitutive law, as well as the Johnson-Cook damage model, was used in the model. The numerical simulations were verified using the conducted experiments in this study and those in the literature. It has been shown that simulations correctly reproduce the deformation mechanisms of structures during the loading process. Furthermore, a rigorous parametric study was conducted on double-layered metallic plates made of five different layering configurations including aluminum-aluminum, steel-steel, steel-aluminum, copper-aluminum, and copper-steel plates. Two and four different plate radiuses and charge diameters were considered. After conducting the parametric study, an empirical model based on new dimensionless numbers was developed to predict the maximum transverse deflection of plates. Very good overall agreement was obtained between the results of numerical simulations and empirical predictions.

In this paper, the experimental study and regression analysis of the dynamic response of metal plates under impulsive loading are investigated. For this purpose, in the experimental section, 86 experiments were performed on metal plates under different conditions. The plates were made of steel, copper and aluminum in a circular shape. The effect of the measured parameters in the experimental tests such as plate thickness, loading impulse, charge mass, and standoff distance on the circular plates deflection were evaluated simultaneously using the Design-Expert software package and response surface methodology. In this study, the material of the plates is considered as an independent qualitative parameter. In order to find a significant model, the confidence level of 95% was considered in the analysis. In this study, the value of R2 and R_adj^2 was 0.9746 and 0.9673, respectively. The results show that the predicted values of the models are in good agreement with the experimental tests and the presented models are suitable. Optimal conditions for the minimum deflection of the circular plates under impulsive loading were also presented. The impulse loading has the highest effect and the mass of the charge has the least effect on the plate deflection.

In the current study, an experimental study and modeling of the penetration behavior of single-layered and multi-layered targets made of either aluminum alloy or mild steel or a combination of these materials impacted by a spherical projectile were introduced. For conducting 66 experiments, eight different layering configurations consist of monolithic aluminum and steel plates with the thickness of 2 mm and 3mm, double-layered aluminum and steel plates with a total thickness of 2 mm, triple-layered aluminum, and steel plates with the total thickness of 3 mm, and triple mixed layered plates of Aluminum-Steel-Aluminum and Steel-Aluminum-Steel configurations with the total thickness of 3 mm were considered under various impact velocities of 42 to 158 m/s. The impact velocity and maximum permanent deflection of specimens were measured in all experiments. In the numerical modeling section, the group method of data handling neural network was used to present a mathematical model based on dimensionless numbers to predict the maximum permanent deflection of monolithic and multi-layered metallic plates under the rigid projectile impact. To increase the prediction capability of the proposed neural network for this process, the experimental data were divided into two training and prediction sets. The results showed that good agreement between the proposed model and the corresponding experimental results is obtained and 94% of data points are within the ±10% error range.

In the current research study, the large plastic deformation and failure mechanism of sandwich structures with aluminum facesheets and pumice core under low-velocity impact loading have been investigated. The drop hammer testing machine was used to apply the impact load on the specimen at seven different energy levels 34.3, 68.6, 102.9, 137.2, 171.5, 205.8, and 223 J. To achieve the mentioned energy levels, the weight of the impactor was considered constant and equal to 3.5 kg and the standoff distance of the hammer was changed from 1 to 6.5 m. 16 experimental samples were considered in two types of layering with and without pumice core. Also, in this series of experiments, the thickness of facesheets was fixed and two different thicknesses of 16 and 32 mm were considered for the core. Experimental results showed that at all energy levels, the sandwich panel with 16 mm pumice core shows a smaller deformed area due to the shorter porous space between two facesheets. Also, at low energy levels, the thickness of the pumice core does not play a key role in improving the impact resistance of the structure. Compared to the coreless sandwich structure, the use of a very low-mass pumice core can prevent the plastic deformation of the rear facesheet, and the 16 mm thickness of the pumice core can even prevent the front surface from petalling.

A single-stage gas detonation apparatus was used for the free forming of metallic-polymeric structures. In the experimental section, to improve the performance of aluminum plates under gas mixture detonation loading, a layer of polyurea material was sprayed onto the back surface of the metallic plate. In order to investigate the effect of the thickness of the metallic and polymeric layers on the dynamic response of the structure, aluminum plates with different thicknesses of 1, 1.5, 2 and 2.5 mm, as well as polyurea coatings with different thicknesses of 3, 4, 5 and 6 mm, were used. Experimental results showed that spraying the polyurea coating onto the back surface of aluminum plates can significantly reduce the maximum permanent deflection of the structure and also prevent the rupture of the aluminum specimens. In the numerical modeling section, the Group Method of Data Handling (GMDH) neural network was used to present a mathematical model based on dimensionless numbers to predict the maximum permanent deflection of metallic-polymeric structures under impulsive loading. In order to increase the prediction capability of the proposed neural network for this process, the experimental data were divided into two training and prediction sets. The results showed that good agreement between the proposed model and the corresponding experimental results is obtained and all data points are within the ±10% error range.

In this paper, a series of experiments were conducted aluminum plates to investigate the large plastic deformation of single, double, and triple-layered plates under repeated uniform loading up to five times. In order to perform experiments, plates were mounted onto a ballistic pendulum. Generally, the tested plates represented large plastic deformation of dome-like shape along with thinning or tearing occurring at the boundary due to the uniform impulsive loading. The experimental results showed that the maximum permanent delfection of single- and multi-layered plates increases by the increase of mass charge and number of blasts. Furthermore, the progressive deflection was decreased exponentially because the test plate material undergoes work hardening after each blast load. The results also indicated that triple-layered plates made of similar materials may have a better blast performance compared to double-layered at the first low-impulse blast but their resistance decreases as the number of blast increases. However, this trend was not observed for high-impulse blasts and multi-layered plates have a different behavior.

In the current study, an experimental investigation and modelling of the large plastic deformation of single-layered and multi-layered metallic targets made of either aluminum alloy or mild steel or a combination of these materials impacted by a rigid spherical projectile were presented. To conduct experiments, eight different layering configurations were considered under various impact velocities from 42 to 158 m/s. Also, the modeling of this process was employed by the Adaptive Neuro-Fuzzy Inference System using a multi-objective design of the genetic algorithm by dividing data into two parts, training and prediction sets. To improve the ability of the system, the genetic algorithm was used for the optimal design of Gaussian membership function parameters in the antecedent part, and the singular value decomposition method was employed for calculation of linear coefficient vectors in the consequent part. The procedure of optimal designing and modeling was performed by considering three membership functions for each of the three experimental inputs. The accuracy of proposed model was assessed by the coefficient of determination and root-mean-square error for training and prediction data sets.

In this paper, a non-dimensional analysis approach has been used to propose two empirical equations based on dimensionless numbers to predict the maximum transverse permanent deflection-thickness ratio of single-layered quadrangular plates under uniformly and locally distributed dynamic loading. In the presented dimensionless numbers, the effect of plate geometry, the impulse of the applied load, the mechanical properties of the plate, the strain-rate sensitivity, and the loading radius have been considered. To validate the empirical models, eight series of conducted experiments and 267 data points in the state of the art over the past forty years have been used. The obtained results show good agreement between the model prediction results and the experimental values so that in the total of 117 experimental data for uniform loading, 94% (110 data) and 98% (115 data) of the data points were distributed in the ±10% and ±20% error range, respectively. Besides, in the total of 150 experimental data for localized loading, 83% (124 data) and 97% (146 data) of data points were distributed in these two ranges, respectively. The results also showed that assuming the material constants as variables based on the plate thickness, in the Cooper-Symonds constitutive equation improves the prediction accuracy of the empirical models so that only 6% and 12% of the data for uniform and localized loading respectively, are not within the 10% error range.

The aim of this study is investigating the center of mass deflection to thickness ratio of triangular plates using the GMDH-type neural networks and comparing it with results of laboratory tests performed on a narrow triangular plate using water-hammer apparatus. Also, the study focuses on the overall deformation, strain and impact transmission. Dimensionless input variables are used to investigate the center of mass deflection of triangular plate with changing variables. A simpler polynomial expression is derived using GMDH-type neural network and dimensionless number. The vector of coefficients of quadratic sub-expressions involved in GMDH-type networks is obtained by Singular Value Decomposition (SVD) method. SVD can improve the proficiency of GMDH-type networks to model the intricate process of deformation of triangular plates. Obtaining results by applying a GMDH model and comparing them with actual data indicates good agreement between model output and experimental data. The advantages of this approach are in the simplification of computation and convenient application to parametric study for impact behavior.

In the present study, deformation pattern in impact spot welded plates with flat and spherical-nosed projectiles using gas mixture detonation set up has been investigated and compared with numerical simulations. The steel plate with a thickness of 4mm was considered as a base plate and steel plates with 1, 2, and 3mm thicknesses were selected as flyer plates and were under direct contact with flat- and spherical-nosed metallic projectiles with a mass of 650 and 1300 gram, respectively. The average velocity of the projectiles was 600 meters per second. The ABAQUS finite element software was used to investigate the high-velocity impact of projectiles on steel sheets. The Johnson-Cook (J-C) model was utilized to describe the behavior of metals. The deformation of plates during the impact spot welding process has been simulated. Comparing the plate deformation pattern in numerical simulation and experimental results found that the numerical model predicted well the deformation of plates during the projectile impact spot welding process. The stress wave propagation on the flyer plates also was studied numerically. The results show that the waves start from the center and progress to the corners of the plate. The values of the equivalent plastic strain (PEEQ) and shear stress pattern for flyers and target plates have investigated as a measure of the quality of welding.

In present study, the experimental investigation and regression analysis of the large plastic deformation of square and rectangular plates subjected to extreme dynamic loading with uniform and localized distribution were discussed. In the experimental section, 5 experiments were conducted on mild steel plates with different thicknesses. To perform the regression analysis and multi-objective optimization, Design-Expert software in conjunction with the response surface methodology were exerted. Subsequently, the effect of parameters such as the thickness of the plate, the impulse of applied load, the mechanical properties of the plate, the loading radius, and the ratio of width to length of the plate on the maximum deflection of quadrangular plates was simultaneously investigated. Two separate analyses based on statistical analysis and ANOVA were performed for each type of uniform and localized loading. The values obtained for the coefficient of determination (R2) of two types of uniform and localized loading showed that the models have a good prediction ability of the experimental results and it can be used to evaluate the plastic deformation of the quadrangular plates. Subsequently, the optimal conditions for each effective parameter including yield stress and width to length ratio were determined with respect to considering the minimum values for central deflection and plate thickness simultaneously. The multi-objective optimization results were compared to the experimental results of the present study.

One of the main objectives of impact mechanics is the design of a structure resistant to explosion by introducing a structure with a special design pattern while maintaining its lightweight conditions. In this study, the plastic deformation and failure pattern of quadrangular metallic plates under localized impulsive loading were investigated due to the lack of experimental, analytical, and numerical results in the field of deformation of multilayer structures under impulsive loading. In this series of experiments, 26 double-layered metallic plates with different layering arrangements of steel-steel and steel-aluminum in different thicknesses were fabricated and designed. To apply the localized impulsive load, a ballistic pendulum system was used without using standoff distance blast tubes. A thick layer of polyester foam was used to prevent explosive debris. Steel plates in different thicknesses of 1, 2, and 2.5mm, and aluminum plates in different thicknesses of 1 and 2mm in 5 different layering configurations were used. In the experimental study, parameters such as impulse, central permanent deflection, and longitudinal strains in x and y directions were measured. The results showed that the use of aluminum plate as a backing layer reduces the explosive performance of the double-layered mixed configurations of steel-aluminum plates under localized impulsive loading.

In the last decade, the gas mixture detonation forming (GDF) method has been introduced as a novel and alternative method instead of other high-velocity forming (HVF) methods such as explosive method. Due to the lack of research in this field, the present study investigates the free and die forming of circular metallic plates under gas mixture detonation loading. In this series of experiments, steel plates with thicknesses of 1, 2, and 3mm, aluminum plates with a thickness of 3mm, and brass plates with a thickness of 1mm were used. Furthermore, the test specimens were loaded in the impulse range of 4.12 to 54.68N·s. For better comparison, the same areal density condition was considered to compare the results of steel, aluminum, and brass plates under the same loading conditions. Experimental results showed that using a die with an apex angle of 60° leads to the decrease of the maximum permanent deflection by 14.8, 20.2, and 21.4% in 1, 2, and 3mm steel plates, respectively. Under the same loading and areal density conditions, for free forming, the use of aluminum and brass plates lead to increasing the maximum permanent deflection by 19.4 and 13.1% compared to the steel sample, respectively. However, in die forming, these values were 5 and 2%, respectively. Also, the comparison of the results for aluminum and brass plates shows that the using die forming reduces the maximum permanent deflection of the specimen by 12.1 and 10.6%.