Thickness Strain Distribution Research Articles

Prediction of formability and effects of process parameters on the adhesively bonded composite metallic sheets

The study investigates the deep drawing process for bimetallic sheets formed by bonding dissimilar metals (AA1100 aluminium alloy and C36000 brass) with epoxy-based adhesive. Experimental exploration of process parameters, including blank diameter, stacking sequence, lubrication, and strain rate, was conducted to analyse their impact on load–displacement behaviour and thickness strain distribution. Additionally, the study assessed fracture susceptibility, material flow characteristics (tearing and wrinkling), and the requisite drawing force for the bonded specimens. Results indicate enhanced formability and mechanical properties in bonded sheets compared to individual metal sheets, demonstrating the potential advantages of this approach. The bonded sheets demonstrated improved formability and mechanical properties compared to individual metals. Notably, the maximum drawing force for the bonded sheet (170 mm diameter) significantly increased to 24.2 kN, surpassing individual sheets by 69.85% for AA1100 and 40.54% for C36000. The analysis identified a vulnerable region (12–15 mm from the centre) under maximum risk of failure and consistent deformation patterns in samples with varying diameters and lubrication, providing valuable insights into the behaviour of bonded bimetallic sheets in deep drawing.

Micrometer-size crystalline monolayer MoS2 domains obtained by sulfurization of molybdenum oxide ultrathin films

In this work, the formation of micrometer-size crystalline monolayer (1L) MoS2 flakes with triangular shape and a central multilayer core is obtained by the sulfurization at 800 °C of pre-deposited ultrathin MoOx films (1.2–1.8 nm) on c-sapphire substrates. The thickness uniformity, crystalline quality, doping and strain distribution in the MoS2 flakes as a function of the initial MoOx thickness was evaluated by micro-Raman (μR) mapping. The excellent crystalline quality of the triangular 1L-MoS2 flakes was confirmed by micro-photoluminescence (μPL) maps, showing a very intense peak at ∼1.85 eV, that decreases in the central part, as expected for multilayers MoS2. A biaxial strain of ∼0.38–0.4% was deduced from the μPL data, in perfect agreement with μR results. Our results show how the sulfurization of pre-deposited MoOx films on c-sapphire allows, under proper conditions, to obtain 1L-MoS2 flakes with quality comparable to the one typically reported by the conventional chemical vapour deposition, with important implications for device applications.

Earing prediction of 2090-T3 aluminum-cups using a complete homogenous fourth-order polynomial yield function

AbstractEaring can be described as difference in cup wall height due to planar anisotropy of the sheet metals, and both prediction and minimization of this defect are critical steps of drawing process design to save material and production costs due to additional trimming operations. The finite element (FE) method is a practical design tool in this context. The accuracy of FE analyses is directly dependent on modeling material deformations using an effective plasticity model. In this study, a homogeneous orthotropic fourth-order polynomial stress function is presented and implemented into Ls-Dyna FE software by a user-defined material subroutine to predict the earing evolution of a strongly anisotropic aluminum alloy (AA2090-T3) in cup drawing. Primarily, the parameters of the function were calibrated using test data. The effects of element size, number of through-thickness integration points, and time-step size were investigated separately on the drawn cup’s earing profile and thickness strain distributions. It was observed that mass scaling factor related to time step size has a significant impact on the cup height and profile. Finally, simulations were repeated with optimum parameters to assess the performance of the plasticity model. The yield criterion successfully predicted the cup profile, earing amplitude, and thickness strain distributions.

Enhancement of Accuracy in Multi-Point Stretch Forming: Cushion Stretching

Multi-point stretch forming (MPSF) is one of the flexible manufacturing processes that uses the reconfigurable tools to produce the three-dimensional sheet metal components. An elastic cushion is placed between the tools and sheet surfaces to avoid direct contact and reduce the dimples as well as wrinkles. The cushion is also known to play an important role as it directly affects the component surface characteristics (accuracy and quality) and thickness strain distribution. An attempt made to apply stretching on the cushion resulted in enhancement of accuracy. In the present work, an analytical methodology is proposed to predict the initial thickness of cushion and stretching load necessary to apply on the cushion. FEA of MPSF of the spherical geometry is carried out with and without application of stretching load on the cushion. Results indicate that effective stress and strain distributions are more uniform when the stretching is applied to cushion thickness in certain range. Proposed methodology can be effectively used to determine initial cushion thickness before stretch and stretch load necessary to achieve chosen final cushion thickness to enhance the accuracy of sheet metal components formed using MPSF.

Effects of Temperature on Deep Drawing of an Aluminum Alloy for Different Yield Criteria and Hardening Models

In this study, the influences of temperature variation in deep drawing process are investigatedby changing the temperatures of the whole blank, a part of the blank, the punch and die fordifferent yield criteria and hardening models. Von-Mises criterion with isotropic, kinematic and combinedhardening and, Hill48 and Yld2003 yield criteria with isotropic hardening are considered toform the constitutive relations. Circular, square and complex shaped parts made of AA5754 materialare used in the numerical analyses. The local heating simulations are conducted for circular blanksand the drawability of the parts are evaluated by using the Johnson-Cook failure criteria. Hot formingand quenching and local heating analyses are also carried out for a complex shaped part. The resultsobtained by the finite element analyses for different constitutive equations are compared with eachother and experimental results according to thickness strain distribution, punch force variation andrim shape of the deformed blanks.

Effect of natural aging time on anisotropic plasticity and fracture limit of Al7075 alloy

Numerical approaches for fracture modeling have been proposed for various metallic materials, including high-strength steels and aluminum alloys. However, the quantitative relationship between the Portevin–Le Chatelier (PLC) effect and the fracture initiation has not been yet fully explored, considering the influence of the natural aging time (NA) on the material deformation behavior. To address this gap, this study investigated the PLC effect on the anisotropic plasticity and fracture limit of Al7075 alloy according to the natural aging time. Aging behavior and PLC effects are experimentally evaluated through uniaxial tensile and fracture tests using the 3D digital image correlation method. The natural aging-dependent PLC effect is tracked in the visualization of the strain rate map and thickness strain distributions with plastic deformation. Variations in the anisotropic plasticity are captured using Barlat’s YLD2000‐2d anisotropic yield function at different natural aging times, and fracture envelopes that cover general 3D stress states are identified based on the Lou–Huh ductile fracture criterion. A natural aging-dependent fracture modeling approach is proposed to predict the influence of natural aging on the fracture limit transition. Finally, the strain- and stress-based fracture forming limit diagrams, including their corresponding magnitude of the stress vector, are represented. The results reveal that no general trend for the natural aging-dependent fracture limit based on the strain metric is observed, whereas the fracture limit based on the stress metric tends to increase with natural aging in various loading conditions.

Numerical and experimental studies of the formability of the low carbon steel (11008-AISI) by using hydromechanical deep drawing

The hydromechanical deep drawing process (HDD) is one of the low-cost forming processes with a high accuracy of the product dimensions compared to the other forming processes. This work aims to investigate the foamability of the low carbon steel (11008-AISI) by using hydromechanical deep drawing for two sheet thicknesses (0.5 and 0.7) mm numerically using the finite element method and experimentally. The final product of the process was a cylindrical cup of (40) mm outer diameter for both sheets. Different forming pressure values (0, 0.8 and 1.5) N/mm2 ware tested to predict the optimum fluid pressures and blank holder forming, (the optimum fluid pressure is 1.5 N/mm2). It was found that the required fluid pressure is increased with increase of sheet thickness, and also that the required press pressure is increased with the increase of sheet thickness. The numerical simulation was successfully achieved the modeling of hydromechanical low carbon steel deep drawing (11008-AISI) with a maximum deviation (7 percent) of compared to the experimental finding in predicting (thickness distribution and strain distribution). Also, it was found the blank holder force values hance a significant effect in a voiding the wrinkling and to avoid the product rupture.

Experimental and numerical studies on the formability of AA5754 and AA6082 thin sheets in nonisothermal warm redrawing process

The present work demonstrates a comparative investigation of the nonisothermal warm forward redrawing behavior of AA5754-H22 and AA6082-O sheets. The design and development of a new warm forward redrawing process was demonstrated. The complete redrawing was obtained by keeping the redrawing die and binder at 200 °C and cooling punch near to room temperature using water circulation. This process improved the thickness and surface strain distribution in redrawn cups without the onset of strain localization at the bottom corner. A thermomechanical finite element (FE) model of the nonisothermal warm redrawing process was developed applying the temperature-dependent Barlat-89 yield criterion and the Cowper–Symonds strain rate sensitive hardening model. The FE model reasonably predicted the part depth, earing development, thickness distribution, and surface strain evolution of the redrawn cups. The evolution of temperature distribution within the redrawing cup during the process was captured from FE simulations, and its role in the improvement in redrawing depth was demonstrated. Furthermore, the post-forming characterization of redrawn cup wall was also evaluated by microhardness and ring hoop tensile tests. It was found that the hardness, hoop tensile strength, and energy absorption capacity of AA5754-H22 cups were better than AA6082-O cups.

On the Effect of Through-Thickness Integration for the Blank Thickness and Ear Formation in Cup Drawing FE Analysis

Various numerical parameters such as element size, mesh topology, element formulations effect the prediction accuracy of sheet metal forming simulations and wrong selection of these parameters can lead to inaccurate predictions. Therefore, selection of proper numerical parameters is crucial for obtaining of realistic results from finite element (FE) analyses. In the present work, influence of the number of through-thickness integration points from the numerical parameters was investigated on the cup drawing simulation. Highly anisotropic AA 2090-T3 aluminum alloy was selected as test material and the anisotropic behavior of the material was defined with Barlat 91 yield criterion. Firstly, cup drawing model was created with implicit code Marc and then FE analyses were performed with five, seven and nine layers to investigate the effect of number of through-thickness integration points. The computed earing profiles and thickness strain distributions were compared with measurements. Comparisons showed that it effects the maximum cup height and thickness strain distribution along the rolling direction.

Effect of plastic anisotropy and Portevin-Le Chatelier bands on hole-expansion in AA7075 sheets in -T6 and -W tempers

Influence of tempers on the hole-expansion formability of an AA7075 aluminum sheet is investigated for -T6 (as-received) and -W tempers (super saturated by the solution heat treatment followed by water quenching). The hole is prepared by end-milling, to limit the effects of hole preparation on the results and instead highlight the effects of material behavior. A flat-headed punch is used to expand the hole, and digital image correlation captures the strain fields throughout the experiment. The results present that the hole can expand by 70 % more in -W compared to -T6 temper with the lower forming force. In contrast, thickness strain distribution around the hole shows a similar pattern in both tempers except the observation of Portevin-Le Chatelier (PLC) effect in -W temper, which causing the inhomogeneous deformation. In parallel, the numerical simulation of the hole-expansion is performed using a user material subroutine implemented for the elasto-plastic material behavior, including plastic anisotropy, of both tempers. The predictions on the thickness strain variation and average level show good agreement with the experiment for -T6 temper, but less so for -W temper. This is shown to be the effect of PLC bands on the deformation: the material in -T6 temper is mainly governed by plastic anisotropy, but -W temper shows combined effect of plastic anisotropy and PLC bands. Nevertheless, the reasonable predictions of both tempers verify that the numerical framework established in this study can be used for preliminary, computationally-efficient virtual process design with a practical purpose, despite omitting the explicit physics of the PLC effect.

Blank thinning predictions of an aluminum alloy in hole expansion process using finite element method

The main objective of this study is to accurately predict the thinning behavior of AA6016-O aluminum alloy in the hole expansion test. In order to perform this aim, three yield functions, namely isotropic von Mises, quadratic Hill48 and non-quadratic Yld91, are considered and their prediction capabilities are evaluated in this study. Firstly, finite element (FE) model of hole expansion test is created by implicit FE software Marc, then FE simulations are performed with each yield criterion. In order to assess prediction capabilities of these yield criteria, thickness strain distributions along the three directions of the sheet (rolling, diagonal and transversal) and punch force–displacement curves are investigated. The results predicted from FE analyses are compared with experimental results. From the comparisons, it is observed that Yld91 yield criterion could successfully predict the thickness strain distributions along the rolling and transverse directions, whereas the other two criteria could only predict the thickness strain distributions along the diagonal direction. On the other hand, it is determined that punch force–displacement curves predicted from three models are identical and these predictions are overestimated compared to experimental data.

Study on the influence of the yield surface shape in the hole expansion test

The hole expansion test has become popular since it allows to study the formability of metallic sheets, in particular the onset of necking in stretch flanging areas. The accurate prediction of strain localization and consequent fracture requires a proper description of the plastic behavior, particularly the anisotropic yield function. In the context of strain localization prediction, the yield criterion adopted plays an important role, particularly when using an associated flow rule, since the direction of the plastic strain tensor is modelled by the normal to the yield surface. In this work, the parameters of an advanced yield criterion are calibrated considering a wide set of experimental data, which includes results from uniaxial and biaxial tension tests. This enables establishing yield surfaces with similar shape in the plane defined by the stress components in the rolling and transverse directions and a null shear component in the same plane. However, their shape changes slightly when considering non-null values for that shear component. The numerical simulations of the hole expansion test demonstrate the impact of these slight differences on the thickness strain distribution and, consequently, in the instant and location of the necking.

Formability prediction of the Al1050/SS304 sandwich composite sheet by using a numerical and experimental approach

ABSTRACT The present study investigates the formability of the Aluminium (Al1050)/Steel (SS304) bimetallic sandwich composite sheet. The formability was predicted by generating the forming limit diagram (FLD) by using the experimental approach. The recorded strain distribution in terms of major and minor strain by using the digital correlation method was utilised for the generation of FLD. The failure in the utilised Al1050/SS304 sandwich composite sheet for the deep drawing of the cup was detected by recording the thickness strain distribution by using a numerical and experimental approach. The calculated thickness strain distribution in the deep drawn Al1050/SS304 sandwich composite cup was integrated with the strain non-uniformity index (SNI) approach for identifying defects such as thinning and thickening. The contribution of the individual sandwiched metal sheet on such kind of defects was also explored. The results signify that the prediction of the formability and identification of defects such as tearing and wrinkling for the deep drawn Al1050/SS304 sandwich composite cup can be performed precisely.

Mechanism of magnetic field condition on deformation behavior of sheet metal using a property-adjustable flexible-die

To provide intelligent control options during sheet metal forming process, magnetorheological (MR) fluid has been applied as a property-adjustable flexible-die. However, the mechanism of the magnetic field effect on the sheet deformation behavior is not clear yet. In this paper, to clarify the deformation mechanism, the bulging behavior of thin-walled Al1060-O sheet was systematically investigated through experiment and numerical simulation. Special attention was paid to the effect of magnetic field on loading curve, bulge dome height, and thickness strain distribution. Results showed that the maximum bulging force increased obviously with the increase of magnetic flux density. The bulge dome height and thickness strain were influenced by magnetic field condition and magnetic particle content synthetically. Appropriate magnetic field condition and magnetic particle content can improve formability. However, excessive magnetic flux intensity and magnetic particle volume fraction, for example, B = 0.20 T and φ = 46%, would lead to premature rupture. Finite element analysis was adopted to assist in explaining the bulging behavior. Detailed analysis indicated that the flow stress variations caused by magnetic field affect the stress states, velocity distribution of MR fluid, and sheet/MR fluid contact condition, further leading to different stress and strain distribution of sheet metal. Finally it causes the great difference in specimen geometry and wall thickness distribution.

Investigation on changing loading path in sheet metal forming by applying a property-adjustable flexible-die

In sheet metal forming operations, the loading path is a significant process parameter, which greatly influences material flow and part quality. In this paper, an innovative method was proposed to change the loading path by using a property-adjustable flexible-die (MR fluid) in sheet forming process. Experimental and numerical simulations on free bulging process of Al 1060-O sheet using a MR fluid under two different magnetic field changing types were carried out. Results showed that the loading curves were changed noticeably by varying the magnetic flux density in the working area during the bulging test. The differences of configuration, velocity, stress distribution and thickness strain distribution of forming parts indicate that the loading path change has a great effect on the deformation behavior. It provides a new method to change the loading path in near real-time during the forming process, which brings potential application for intelligent control of sheet metal forming.

Equivalent Stiffness Methods for Free Vibration and Bending of Bimodular Composite Laminated Thick Curved Beam

In this research work an attempt has been made to analyzed the bending and free vibration behavior of bimodular composite material laminated thick curved beam based on first order shear deformation theory (FSDT). The effect of coupling parameter is more severe in bimodular laminated beam as compare to unimodular laminated beam. Therefore, equivalent stiffness methods (VS and RC) are used to incorporate the effect of all the coupling parameters. In the present analysis uniformly distributed load in transverse direction is considered. Hamilton’s principle is applied to elaborate governing equations from energy functional, and the equations are solved by analytical method. The position of neutral axis, transverse deflection, through the thickness strain distribution and frequencies for positive and negative side bending are presented for different bimodular composite material laminated curved beam. The results are presented for different stacking sequence and geometric parameter of the beam. The non-dimensional neutral surface location, positive and negative side bending deflections and positive and negative half cycle frequencies are having same magnitude for [00]4 or [00/900]s laminated curved beam of Material 1 (Aramid Rubber), and for Material 2 (Polyester Rubber) they are not same.

Application of Equivalent Stiffness to Consider Coupling Effects in Bimodular Beam

In bimodular material (different elastic properties in tension and compression) beam, shear-extension, twisting-stretching, bending-twisting coupling are present irrespective of stacking sequence, ply-angle unlike unimodular materials. The presence of these coupling parameters can affect transverse deflection when beam is subjected to pure bending. In this paper an attempt is made to take consideration of these coupling by implementing equivalent stiffness methods along with classical beam theory. The objective is to find out the effects of these couplings on transverse deflections, neutral surface positions and on stress and strain distribution throughout the thickness of the beam. Transverse deflection, neutral surface position, through the thickness stress and strain distribution are obtained for simply supported and clamped-clamped boundary conditions. The analysis shows that results obtained for neutral surface position, positive and negative half cycle frequencies, transverse deflection and even strain, strain distribution through the thickness by considering the coupling parameters are different from the results obatained by neglecting the couplings.

Binder force effect on stretch flange forming of aluminum alloy

ABSTRACTThe present research investigates the effect of binder force in flanging of aluminum alloy sheets. FEM simulation of stretch flange forming is realized for zero, constant, and fixed binder forces. The finite element simulation is carried out to evaluate strain (circumferential and radial), flange thickness, position of commencement, and extension of cracks due to variation of binder force. The investigations reveal that the binder force has a significant effect on punch load, flange thickness (percentage thinning), circumferential and radial strain distribution, and commencement and extension of edge cracks. The results of FEM simulation are validated with results obtained by experimentation, and an excellent agreement is obtained.

Numerical simulation study on multi-pass non-axisymmetric spinning of cylindrical parts with oblique flange

A non-axisymmetric cylinder with an oblique flange has broad application prospects. Spinning is the main production process for this kind of workpiece. Finite element modeling is a necessary method to study some key problems that are difficult to be solved merely through experiments, such as the strain and stress fields in the development of this spinning technology. In this study, the spinning process of a non-axisymmetric oblique flange cylindrical part was established and simulated using ABAQUS/explicit software. The credibility of the simulation result was validated through an experiment. The influence of the axial roller feed along the cylinder wall on the distribution of wall thickness and stress and strain during the forming process was analyzed. The change in stress field and strain field with time was analyzed, and the quantitative relationship between forming conditions and forming results was described. Furthermore, the forming principle of the flange was analyzed. It would be beneficial for flange forming to reduce the increasing distance of the cylinder wall in the 180° direction (parameter c) and the vertical distance from the closest point to the spindle as the roller returns back in the 180° direction (parameter d), to a certain extent. Hence, a workpiece with an ideal appearance was obtained. By comparing the wall thickness distribution, the design and optimization of the roller path were once again verified to be reasonable.

Equal channel angular sheet extrusion (ECASE) as a precursor of heterogeneity in an AA6063-T6 alloy

We study the deformation inducing heterogeneity in an aluminum alloy 6063-T6 in the form of a sheet processed at room temperature by equal channel angular sheet extrusion (ECASE) up to a maximum equivalent strain of 1.86 following route C. The through thickness strain distribution showed higher strains in the edge vicinities than in the sheet core. The texture was heterogeneous between the edges and the sheet core with a strong cube component in the initial deformation stages, and a rolling texture with the S component in the sheet edges. Different microstructural characteristics, like grain size, average misorientation, and fraction of high angle grain boundaries (HAGB), decreased by increasing the deformation. The geometrically necessary dislocation (GND) calculations corroborated the existence of a heterogeneous microstructure along the sheet thickness, giving rise to gradients of plastic deformation which allowed to obtain a good strength-ductility relationship. It was demonstrated that ECASE process was a good alternative to produce heterogeneous microstructures. The material heterogeneity was found not to be randomly distributed across the sheet thickness but rather showing higher dislocation concentration and bigger grain size reductions in the edge’s vicinities than in its middle zone.