Behavior Of Sheet Metals Research Articles

Understanding a new wrinkling behavior of annular grooved panel during flexible free incremental sheet forming

Wrinkling behavior of sheet metal by inappropriate process parameters and the resultant variation of thickness and microstructure during incremental sheet forming (ISF) have significant impact on forming stability and geometric profile. The wrinkling-related mechanism is yet to be well understood, which make it difficult to effectively control wrinkling defects during ISF. In the present work, the wrinkling behavior and related mechanism of a typical annular grooved panel are investigated during a novel flexible free ISF process. Experiments demonstrate that during this ISF process, the sheet material sequentially undergoes 4 deformation modes: contacting state under plane strain condition, contracting state with only elastic deflection, thickening state under uniaxial compression condition, and wrinkling state where the circumferential compressive stress exceeds the critical wrinkling stress. The evolution of these deformation modes is dominantly caused by the increasing of edge contraction and circumferential stress, which are induced by the bending moment from the forming tool and auxiliary sheets. Based on the mechanism, an analytical model is developed to predict the wrinkling behavior, by which the corresponded sheet thickness, bending moment, circumferential compressive stress and critical wrinkling stress during the wrinkling process could be comprehensively calculated. Experimental results validate that the analytical model can accurately predict the wrinkling behavior under different process parameters, material properties and auxiliary sheet materials. Through microstructural characterization, numerical simulation and analytical modeling, the influence of process parameter and material property on wrinkling behavior is systematically investigated, along with the variation of sheet thickness and microstructure under different wrinkling modes. This work enhance a deep understanding of wrinkling behavior during ISF process, thereby providing effective methods for process optimization and quality improvement.

A rate-dependent damage mechanics model for predicting plasticity and ductile fracture behavior of sheet metals at high strain rates

Uniaxial tensile tests were performed on H340 steel sheets at different strain rates (10-4 to 103s-1) and temperatures (–30 °C and 280 °C). Oscillation-free forces were measured during high-speed tests at strain rates of up to 1000 s-1 using specimens with different stress states. Material hardening curve, strain rate sensitivity, temperature effects, and Taylor-Quinney coefficient for adiabatic temperature calculations were determined in experiments. Digital image correlation (DIC) technique was employed to measure displacement, deformation, and local strain fields. Meanwhile, the temperature fields of specimen gauge section were measured with a high–speed thermal camera in the uniaxial tensile tests at various strain rates. Damage and fracture-related parameters were calibrated and validated using porosity measurements on SEM micrographs and in combination with finite element (FE) simulations. A rate– and temperature–dependent plasticity and damage mechanics model (e2MBW) was proposed and calibrated to predict the plasticity and fracture behavior of H340 under different loading speeds. The study demonstrated good agreement in the overall experimental and simulated force–displacement responses and local strain evolution across all fracture specimens at loading speeds from 0.005 mm/s to 10000 mm/s.

The Characterization of the Plastic Instability of S235 Thin Steel Sheets by Multiple Regression and Analysis of Variance Methods

In this study, we present a new identification method of parameters characterizing the elastoplastic damage behavior of sheet metal based on analysis of variance. The analysis covered experimental and numerical simulation results using the finite element method of the sheet mild steel bulge test. The identification procedure was validated through a confrontation between numerical simulations and experimental results on several hydroforming applications, such as a free expansion and an expansion in matrix cavities. Results show consistency between experimental observations and numerical predictions of instabilities. Furthermore, the location of risk areas of instability and rupture and the damage level could be quantified. The analysis focused on a set of results combining experimental data and numerical simulations of the bulge test of steel sheets. The identified models were validated thanks to a comparison between numerical simulations and experimental results of a set of forming applications by bulge test. The results show coherence between the experimental observations and the numerical predictions of the instabilities.

Study on the Material Models of the Forming Limit Curves Development for Predicting a Fracture Behavior of AA5754-O in Automotive Parts

The forming limit curve (FLC) is commonly used to predict the formability behavior of sheet metal after the forming process. In this research, the forming limit curve generated from the Materials Model was applied to analyze and predict the fracture behavior of the fuel tank workpiece, a motorcycle part made of AA5754-O material, using the deep drawing process simulated by the finite element method. The research involved a comparison with actual cracks that occur in the automotive industry after molding. To determine the mechanical properties of the AA5754-O material for use in the forming limit curve, a specimen with a thickness of 1.5 mm was subjected to a tensile strength test, providing the necessary input for the mechanical properties in the forming limit curve based on the Keeler-Beizer equation. The forming limit curve is a correlation graph between major strain and minor strain. When the FLC is created from the Materials Model, it is utilized in conjunction with deep drawing drag simulation in the PAM-STAMP program to predict the fracture point. The accuracy of the mathematically generated FLC in predicting fracture behavior was verified after the deep drawing process. The study found that the FLC based on the Keeler-Beizer equation can accurately predict the cracking behavior of AA5754-O sheet metal, enabling identification of the fracture location during the deep drawing process. One advantage of creating the FLC from the material models is its compatibility with the same material but with different workpiece shapes, allowing its use in conjunction with molding simulations using various programs. This approach saves costs associated with testing to obtain the FLC.

Integrating multiple samples into full-field optimization of yield criteria

Describing the anisotropic yielding behavior of sheet metal requires the determination of a yield criterion along with its model parameters. A method often used for this task is inverse full-field optimization. The method is typically combined with either multiaxial experiments or complex-shaped specimens to cover various stress states, over which the parameters of the yield criterion are optimized. This study investigates the feasibility of replacing the complex experiments with multiple simpler ones simultaneously. As material, the aluminum alloy AA6014-T4 is used. The yield criterion considered is YLD2000 2D, assuming both the associated and non-associated flow rules. Firstly, it is demonstrated through identifiability analysis that the model parameters, although often attempted in the literature, cannot be uniquely identified using only conventional experiments if non-associated flow is assumed. Secondly, it is shown that parameter identifiability in the latter case is achieved by combining multiple specimen geometries and orientations to rolling direction simultaneously. Thirdly, it is quantitatively shown that the use of multiple specimens simultaneously generally enhances the identifiability of model parameters due to an increase in the aggregated stress heterogeneity. Furthermore, the result indicates that while the full-field optimization of yield criteria assuming the associated flow rule can rely on force–displacement or direction of plastic strain increment alone, yield criteria assuming the non-associated flow rule require both. All yield criteria are benchmarked based on the strain distribution of Nakazima experiments, demonstrating comparable or higher accuracy compared to conventionally derived models.

Key performance indicators for heterogeneous mechanical tests

Characterizing sheet metal behavior is crucial for accurately simulating sheet metal forming processes. Typically, material parameters are obtained through quasi-homogeneous mechanical tests, which makes the mechanical testing task expensive and time-consuming. However, newly proposed mechanical testing approaches, known as heterogeneous tests, are outperforming quasi-homogeneous mechanical tests. Full-field measurement techniques, such as Digital Image Correlation, are used to extract this information. Despite several proposed test designs, selecting the best one to characterize a specific complex material behavior remains challenging. This work aims to apply Key Performance Indicators (KPIs) in a robust and straightforward way to rank mechanical tests, based on their potential to improve the material behavior characterization procedure. Scalar indicators are suggested to quantitatively evaluate important features of each test, from the diversity of strain states to the test’s sensitivity to the material model parameters. Additionally, measurement errors associated with Digital Image Correlation are taken into account via a numerical procedure. For validation purposes, five recently developed advanced mechanical tests are chosen to be analyzed. The performance of each test is evaluated numerically, leading to an overall ranking of these heterogeneous mechanical tests.

Study on formability and microstructure evolution of hot deep drawing manufactured 7005 aluminum alloy sheet metal

The hot deep drawing process with an in-die heating system was proposed on the forming of 7005 aluminum alloy to improve the formability due to the limitation of ductility during severe plastic deformation at room temperature. The feasibility of hot deep drawing AA7005 sheet (only 0.8 mm) was investigated and evaluated by Swift cup tests from RT to 450 °C. The priority of main process parameters, namely temperature, blank holder force, and stamping speed, on sheet metal forming limit were discussed by analysis of range and variance. Experimental results indicated that elevating the temperature could fundamentally improve the deep drawing performance of the alloy, which is manifested by the revolutionary change in sheet metal behavior — from the failure of deformation at lower temperatures (RT-200 °C) to achieving a limiting drawing ratio of 2.19 at 450 °C. The optimal process parameters under HDD conditions are given as drawing temperature of 400 °C∼450 °C, BHF of 3 kN, and punch speed of 15–20 %. The thickness variation increases with rising temperature corresponding to the formability enhancement during the process within acceptable limits. DRV and DRX are the flow softening mechanism under the high temperature and large strain in HDD process obtained from the analysis of microstructure and texture evolution. The elongation and rotation of grains further substantiated the interrelationship between drawing performance and microstructure evolution. Improving the deep drawing performance through HDD process can provide practical guidance for the application of AA7005 sheet metal.

Characterisation of out-of-plane shear behaviour of anisotropic sheet materials based on indentation plastometry

This paper presents a new methodology for characterising the out-of-plane plastic anisotropy behaviour of sheet metal, based on indentation testing. Conventionally, advanced yield criteria are used to describe plastic anisotropy, requiring multiple in-plane mechanical tests (such as uniaxial and biaxial tests) to calibrate a model. However, in certain forming applications (e.g. blanking, ironing and incremental forming), the influence of mechanical behaviour through thickness cannot be ignored, necessitating the characterisation of out-of-plane material behaviour. To do this, a 3D plastic anisotropy model must be used and calibrated for the out-of-plane shear parameters, which can be difficult to determine. Researchers often assume an isotropic case or equal shear parameters for in-plane and out-of-plane behaviour. More advanced calibrations involve the crystal plasticity model. In this work, we propose a two-stage calibration procedure. In the first stage, we calibrate the in-plane parameters of the YLD2004–18p yield function conventionally. In the second stage, after fixing the in-plane parameters, we determine the remaining out-of-plane shear parameters based on the results of the ball indentation test. We show for the first time that out-of-plane shear parameters can be determined from a macro-mechanical test for a 2.42 mm thick cold-rolled AA5754-H22 series aluminium sheet.

A Novel High-Speed Bulge Test to Identify the Large Deformation Behavior of Sheet Metals

A Novel High-Speed Bulge Test to Identify the Large Deformation Behavior of Sheet Metals

Deformation and Springback Behavior of Sheet Metal With Convex-Shaped Surfaces in Heat-Assisted Incremental Bending Process Based on Minimum Energy Method

Abstract Three-dimensional sheet metal forming is one of the biggest challenges in the shipbuilding industry. The forming quality of the traditionally applied line heating method depends entirely on the skills of the technicians. Moreover, this approach is inefficient and error-prone. This calls for a need to develop new forming technologies that are easy to control and more efficient. In this paper, a novel forming method called heat-assisted incremental bending is presented. The minimum energy loading path of bidirectional curvature sheet along the direction of Gaussian curvature is adapted to deform the sheet metals with a convex shape surface. Besides, the auxiliary heating method and the auxiliary supporting are exclusively included in the forming process to improve the formability and accuracy. In this study, the convex-shaped sheet metal with large curvature is obtained along the two loading trajectories in two principal curvature directions, respectively. Results proved that using the minimum energy loading trajectory and including the auxiliary supports and heating can reduce the forming force to the greatest extent and effectively reduce the number of stamping points, thus improving the sheet metal forming efficiency and forming accuracy.

On the identification of material hardening for anisotropic sheets via bulge tests

The hydraulic bulge test provides a useful tool to characterize the mechanical behavior of sheet metal under nearly equibiaxial loading, such as the material hardening response. However, the kinematic relationships during bulge tests of anisotropic sheets are still less understood and need further clarification. To this end, extensive numerical simulations of bulge tests are first performed, covering different die geometries and materials that exhibit distinct hardening features and Hill48 anisotropy. Based on the general scaling laws of the kinematic relationships, the numerical results are then used to establish an analytical model that explicitly relates the dome height, apex strain, and radii of curvatures in terms of the die ratio, material hardening parameter, and anisotropy. In addition, the general extraction procedure, which incorporates the analytical model to obtain the hardening responses of anisotropic sheets, is also provided. Finally, the effectiveness of the analytical model is confirmed based on representative results of AA6061 and DP600 sheet experiments and supplementary numerical simulations. The proposed model is expected to help facilitate the application of bulge tests in characterizing the plasticity and forming behavior of anisotropic sheet materials.

Subregional flexible-die control in magnetorheological pressure forming

Magnetorheological pressure forming (MRPF) has shown great flexibility in process control by adjusting the mechanical property of MR fluid. However, the regulation of flexible-die property at present is holistic. In this paper, MRPF based on subregional flexible-die control was proposed, which makes the MR fluid show different force transfer characteristics to meet the requirements of flexible-die performance in different areas. Two kinds of non-uniform magnetic fields were established using the combination of coil and iron core groups based on the measurement and finite element simulations. The MRPF experiments of the Al1060-O sheet using the holistic and subregional flexible-die control methods were conducted. The effects of subregional flexible-die control on loading curve, strain distribution, configuration, wall thickness thinning rate, and fracture characteristics were analyzed. Compared with the case that the specimen ellipticity changes little under the central-dominated magnetic field (CMF), the ellipticity gradually decreases under the fringing-dominated magnetic field (FMF) with the increase of the current. The fracture modes can be divided into three types, and the fracture position transfers from the center of the specimen to the circle of R10mm and then to the die fillet area. The influence mechanism of subregional flexible-die control on sheet deformation behavior and fracture mode is further clarified. The non-uniform distribution of cavity pressure and friction conditions caused by the magnetorheological effect is the main factor affecting the stress states and final deformation behavior of sheet metal. This study provides a new path for intelligent control in sheet metal forming of complex thin-walled parts.

On capturing rate-dependent anisotropic behavior of sheet metal forming using a viscoplastic computational framework

Manufacturing of metal sheets—of critical importance in the automotive, aerospace, and railway industries; is notoriously prone to uncertainty and inaccuracy driven by the lack of control in responding to anisotropic behavior developed during a rate-dependent forming process. Various expensive efforts have been made to evaluate these complex behaviors largely based on trial-and-error approaches, implying a high-fidelity predictive numerical tool is inevitable to promote a cost-effective solution. In this work, a high fidelity anisotropic-viscoplastic constitutive model framework based on Hill 48 yield function, isotropic hardening, and Cowper-Symonds viscoplasticity is developed to investigate the rate-dependent anisotropic behavior of sheet metals. This model is holistically implemented as a user-defined material subroutine (VUMAT) in ABAQUS software. The quality of numerical results is evaluated through comparison with experimental works. In the quasi-static and dynamic tensile test, the stress-strain curves obtained from numerical simulation using the developed constitutive model are in excellent agreement with experimental results. Furthermore, numerical simulation of cup drawing test using the developed constitutive model can accurately predict the earing height compared to experimental results. In addition, some novel relationships in terms of plastic rate-dependent anisotropic behavior of sheet metal forming are successfully established through the extended use of the validated numerical model.

Error Estimation of the 3D Reconstruction of a Displacement Field from DIC Measurements

To enable an accurate simulation of manufacturing processes, it is essential to characterise and model the mechanical behaviour of sheet metals up to large deformations. However, after the onset of necking, deformation becomes highly heterogeneous and the stress is triaxial. By combining full-field measurements and inverse methods, it is possible to calibrate the mechanical behaviour beyond necking. A possibility is to use the virtual fields method, by extending its formulation to a fully three-dimensional approach. However, measuring deformation in the bulk of the material is still a challenge. To address this limitation, a volume reconstruction method able to estimate the deformation inside the specimen was proposed and successfully validated. The aim of this work is to estimate the error of the volume reconstruction method by using a simulated tensile test and the measurement chain associated with a virtual stereo-DIC setup composed of four cameras. A three-dimensional finite element model is used to deform synthetically generated images. The DIC field maps obtained with different setup configurations and DIC settings are used to estimate the error by comparing the reconstructed volume with the reference finite element model. Results show that the impact of conditions and DIC settings on the reconstructed volume is low.

Characterization of elasto-plastic transition of sheet metal by using large-scale four-point bending test

The elastic properties of a material do play an important role in the spring back behaviour of sheet metal and have a dominant influence on the depth of where the bending tool has to go. In industry, the elastic behaviour is often approximated to a pure linear behaviour defined by two coefficients: Young’s modulus (E) and yield stress (Re). This modelling hypotheses result in geometrical errors in the angle and flange lengths of bended part. In order to better determine material behaviour at very small strains, a large-scale four-point bending test machine is presented in this study. Generating pure bending and measuring the residual radius allow observation of the transition between elastic and plastic deformation behaviour. By deforming the test beam in the supposed pure elastic area, it appears that the pure elasticity behaviour of the material is indeed non-existent. Plastic strains can be detected as soon as the very first bending of the sample, at very low equivalent stress well under usual accepted elastic yield stresses. Perspectives are addressed in order to solve this difficulty, which hinders the possibility of correctly simulating the bending process, particularly with regard to tight geometry requirements.

Design of new anti-buckling fixture for cyclic tension-compression testing of sheet metal

The currently available anti-buckling fixtures for uniaxial tension-compression testing of sheet metal could not fulfill the requirements and standards. In this study, a unique system of the anti-buckling fixtures to enable getting accurate and repeatable isotropic and kinematic behavior of sheet metal was designed. The front surface of the specimen was fully supported during the initial position, tension, and compression and free from any buckling. Because using acrylic blocks, has a greater level of optical clarity, there was the possibility to measure the deformation on the front surface of the specimen using a digital image correlation system. The special pusher vice with compressed spring was attached to the fixture to avoid misalignment and calculating supplementary forces related to uniaxial direction. Furthermore, the new fixture was simple, flexible, and suitable for any universal testing machine.

Explicit Analysis of Sheet Metal Forming Processes Using Solid-Shell Elements

To simulate sheet metal forming processes precisely, an in-house dynamic explicit code was developed to apply a new solid-shell element to sheet metal forming analyses, with a corotational coordinate system utilized to simplify the nonlinearity and to integrate the element with anisotropic constitutive laws. The enhancing parameter of the solid-shell element, implemented to circumvent the volumetric and thickness locking phenomena, was condensed into an explicit form. To avoid the rank deficiency, a modified physical stabilization involving the B-bar method and reconstruction of transverse shear components was adopted. For computational efficiency of the solid-shell element in numerical applications, an adaptive mesh subdivision scheme was developed, with element geometry and contact condition taken as subdivision criteria. To accurately capture the anisotropic behavior of sheet metals, material models with three different anisotropic yield functions were incorporated. Several numerical examples were carried out to validate the accuracy of the proposed element and the efficiency of the adaptive mesh subdivision.

Hybrid fitting-numerical method for determining strain-hardening behavior of sheet metals

The uniaxial tensile test is well-established for experimentally identifying the stress–strain relationship for sheet metals. Conventionally, true stress–strain data obtained from the test are used to identify the hardening law's parameters using the curve-fitting method. Extrapolation using the identified hardening law describes the stress–strain relationship at large strains; however, it varies widely, depending on the selection of hardening models and their identified parameters. This study presents a hybrid method incorporating the curve-fitting method and inverse finite element analysis to identify the Kim–Tuan hardening model's parameters over large strain ranges. Here, the curve-fitting method enforces the identified hardening law's accuracy in the pre-necking range. Simultaneously, the inverse finite element analysis method maintains the goodness of the post-necking prediction. The proposed method is used to calibrate hardening laws for DP780 and AA6016-T651 sheet metals subjected to uniaxial tensile tests at room and warm temperatures, respectively. The calibrated hardening laws capture the force–displacement curves of both materials well, validating the ability of the presented method in practice.

Study on the wrinkling behavior of perforated metallic plates using uniaxial tensile tests

The Yoshida buckling test (YBT) is a commonly used method to evaluate the wrinkling behavior of sheet metals; however, it is difficult to reflect the actual in-plane stresses in many sheet forming processes owing to the limited variation in the stress state. Furthermore, the test is impracticable for some low-ductility materials because fracture typically occurs before wrinkling. This paper proposes an approach for examining the wrinkling properties of sheet metals using uniaxial tension of plates with a central cut-out; a relevant wrinkling model is established using stress analysis of a finite perforated plate and an energy method. The results show that the typical stress distribution modes around the central hole before wrinkling are biaxial compression in the top/bottom domains and biaxial tension in the lateral domains, and the mode changes with the hole size and tensile displacement. The ratio of transverse to axial stresses increases with the diameter/width ratio; this leads to a larger influence of transverse nonuniform compressive stress, consequently decreasing the critical wrinkling stress. The wrinkling tendency in perforated sheets is more sensitive than that in a conventional YBT specimen; thus, it can be used to capture the subtle distortion of wrinkling for low-ductility materials. A second wrinkling phenomenon that occurred in plates with large holes under a large tensile displacement was observed and addressed.

Comparative analysis of forming limit diagram of Al 5052-H32 and Al 6063 T5

Formability of a material is found to be one of the important characteristic of a sheet metal to know the variation of the major and minor strain of a sheet metal, using this value one can predict the forming limit diagram of sheet metal, forming limit diagram gives the behavior of sheet metals under various loads and also helps in the prediction of breakage or necking of the material under specific load and velocity of the punch. Current study is mainly focused on obtaining the forming limit diagram of two different aluminium alloys like Al-5052 H32 and Al-6063 T5 using numerical analysis software PAMSTAMP and the results obtained are validated by conducting experiments, there is a good agreement of results between the experimental and numerical values. The forming limit diagram of the mentioned alloys helps in manufacturing of automobile and electric vehicle parts.