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Sheet metals such as advanced high strength steels often exhibit varying degrees of anisotropy due to the existence of preferred orientation of their grain structures from the rolling process. While extensive research has been devoted to characterize and model anisotropic plasticity behavior over the past decades, only recently people began to tackle their anisotropic fracture behavior. The focus of these studies is almost always on the in-plane anisotropy, and ignores out-of-plane fracture behavior. The reasons are two-folds: (1). Sheet metal deformation during a stamping or crash application is mostly thought as in a plane stress state and modeled as such, so there is no need to consider out-of-plane fracture behavior; and (2). It is very challenging to develop experimental techniques to reliably measure out-of-plane fracture strengths for sheet metals with a thickness only about 1 mm. In this paper, we theorize, based on strong empirical evidence, that the fracture strength of a thin sheet metal in out-of-plane shear is inherently weaker than that under in-plane shear, analogous to the interlaminar properties of composite laminates. This weakness is responsible for the so-called “shear fracture” behavior, often observed during the stamping operations of advanced high strength steels when the sheet metal flows around a tight radius. A new double-notched shear specimen with shear plane perpendicular to the thickness direction is carefully designed and tested to accurately measure the out-of-plane shear fracture strength. Simulations are executed to validate the rationality of the out-of-plane shear specimen design. Test results of a DP980 sheet show that the out-of-plane shear fracture strength is indeed about 15% lower than that measured under the in-plane shear condition. A new anisotropic ductile fracture model based on linear transformation of stresses is proposed to account for the out-of-plane fracture strength for AHSS sheets. The model is calibrated with experimental data, and the fracture surface is compared to the isotropic Mohr-Coulomb (M-C) fracture model to illustrate its effectiveness.

Double-Sided Incremental Forming (DSIF) uses two small, independently moving, hemispherical tools on either side of the sheet to form a desired shape by following a predefined tool path. This study was motivated by the observation that the relative tool position of the tools, specified in the tool path generation algorithm, affects the formed geometric accuracy. A methodology for defining the relative tool positioning in the tool path generation algorithm based on local part geometry is proposed using simplified Finite Element Analysis (FEA) and sample physical experiments combined with Gaussian Process modeling techniques. This approach can take into account the mechanics of deformation in DSIF explicitly and physical compliance of the DSIF machine implicitly. Physical experiments were performed to demonstrate the effectiveness of the proposed framework.

Proper friction control during a sheet metal forming process can positively influences the quality of the final product. The effects of textured tooling surface and the rolling direction of the strip surface with respect to the sliding direction, the sliding velocity, and the contact pressure on friction coefficient were investigated in this study with Aluminum 6111-T4 sheet and D2 tool steel. A flat-on-cylindrical setup was used to measure the friction force by pulling a strip sample across a tooling sample. The tool steel has laser-textured micro wedge-shaped dimples. The results showed a reduction in friction coefficient by using a textured tool. In addition, in the tests, the relative motion direction parallel to the sheet rolling direction leads a lowest friction coefficient compared to other orientations.

The path-dependence of the conventional Forming Limit Diagram (FLD) is an important issue for its applications in industry. Great efforts have been made to understand the nature of the path-dependence with both experimental and theoretical approaches, many of them attempting to find a path-independent way for the application of forming limits. In this paper, we focus on the nonlinear strain path effect on forming limit predictions using both isotropic and anisotropic hardening models. The Forming Limit Diagram (FLD), Forming Limit Stress Diagram (FLSD) and Forming Limit Effective Strain Diagram (epFLD) of sheet metals subject to linear and nonlinear strain paths are analyzed and compared using the Marciniak–Kuczynski approach. An anisotropic hardening model based on Yoshida and Uemori development is adopted in this study, and it is coupled with the traditional Hill’48 yield surface. This model is capable of describing the complex Bauschinger phenomenon after the material undergoes the reverse loading process such as the early re-yielding, work-hardening stagnation and permanent softening. Two different scenarios for the change of strain paths are also investigated. In the first scenario, the sheet material is initially loaded with a fixed strain increment ratio, unloaded to the free stress state, and then reloaded with a different strain increment ratio until the forming limit is reached. In the second scenario, the material does not undergo elastic unloading. Instead, the strain path is abruptly changed to a different strain increment ratio and the material undergoes continuous loading until the forming limit is reached. It is found that the work-hardening behavior after the pre-straining and the loading scenario plays an important role in the path dependent behavior of forming limits. Detailed analysis reveals that the M–K approach may have contributed to the significance of path-dependence observed in this study, especially at high pre-strain levels.

One of the important failure criteria of press operations in industry for forming simulations is the Forming Limit Diagram (FLD). The complex loading effects on FLD, in particular the localized necking phenomenon under stretch-bending condition, have not been fully investigated and well understood. In practical sheet metal applications, the deformation is invariably three dimensional with a combination of stretching and bending. For most sheet materials under these complex loading processes used in industry, strong Bauschinger effect is observed, and the material hardening behavior tends to be anisotropic. This study aims to understand and evaluate such anisotropic hardening effect on the forming limit prediction under stretch-bending condition. The extended through-thickness Marciniak–Kuczynski (M–K) analysis is incorporated with Yoshida–Uemori (YU) two-surface kinematic hardening constitutive model, which has a more accurate description of the reverse loading behavior than that of the conventional isotropic hardening model. The material parameters used in this paper for YU model are calibrated with the experimental data from uniaxial large-strain tension-compression cyclic test. Both the isotropic hardening and YU kinematic hardening models with Hill'48 yield surface are employed in the analysis for the purpose of comparison. The Forming Limit Average Stress Diagram (FLASD) under stretch-bending condition is proposed to extend the understanding of Forming Limit Stress Diagram (FLSD) from in-plane to out-of-plane deformations. The “bending-ratio-dependent” phenomenon in forming limit diagram is predicted and observed in both stress/strain space with the proposed method. It suggests that the individual stress/strain state cannot represent system behavior. Forming limits under stretch-bending is suggested as an occurrence of system instability, not individual material instability. The system behavior of sheet metal deformation is reinforced as critical to the understanding of necking instability in stretch bending processes. The analysis shows that the Bauschinger effect provides positive effect in delaying the necking instability, predicting higher formability for sheet metals under stretch-bending. The insight obtained in this paper provides further understanding of the localized necking phenomenon under stretch-bending condition.

Properly designed micro-scale surface textures can have positive impact on adhesion reduction and lubrication enhancement, which can lead to lower friction and improved performance of a contact interface. The present study aims to utilize this function of textures to reduce the adhesion between a drill and a workpiece. In this study, rectangular surface textures were generated on the margins of drill bits using a diode-pumped Nd:YVO4 picosecond laser with a wavelength of 532 nm. Two designs were created in which the textures covered approximately 10 and 20 % of the margin surface area. Textured drills were tested by drilling a series of holes in a titanium plate while recording cutting forces, and the results were compared with the performance of baseline samples. Thermographic heat profiles and visual inspections of the drills were taken at increments of 5 and 10–15 holes, respectively. The comparison demonstrated an encouraging improvement in drill bit life as judged by the number of holes drilled before failure. Textured drills were found to reduce adhesion of titanium chips on the drill margins. This work has demonstrated the potential of texturing to significantly improve the lifetime of drill bits and similar cutting tools.

The use of advanced high-strength steel (AHSS) has been steadily increasing in vehicle body constructions to enable improved fuel economy and vehicle safety performance. However, the high press loads required for stamping AHSS sheets causes severe chipping and adhesive wear on stamping/blanking die materials. In this study, wear coefficient K is defined for three stages of wearing process, and approximated by pin-on-disc wear experimental results of JIS SKD11 tooling material. The die wear severity index (WSI) is adopted and calculated as an integral of stress and slide speed over time duration. Die wear is then calculated as a multiple of the wear coefficient and WSI. In 2D state, the ABAQUS/UMESHMOTION code has been developed to integrate WSI. Numerical simulation of DP780 flanging predicts that the maximum wear loss occurs at the position where the straight line connects to the circular arc on the 2D die surface. The experimental results for die wear loss demonstrate good agreement with the simulation results.

Incremental Sheet Forming (ISF) is an emerging sheet metal prototyping technology where a part is formed as one or more stylus tools are moving in a pre-determined path and deforming the sheet metal locally while the sheet blank is clamped along its periphery. A deformation analysis of incremental forming process is presented in this paper. The analysis includes the development of an analytical model for strain distributions based on part geometry and tool paths, numerical simulations of the forming process with LS-DYNA, and experimental validation of strain predictions using Digital Image Correlation (DIC) techniques. Three kinds of parts include hyperbolic cone, skew cone and elliptical cone are constructed and used as examples for the study. Analytical, numerical and experimental results are compared, and excellent correlations are found. It is demonstrated that the analytical model developed in this paper is reliable and efficient in the prediction of strain distributions for incremental forming process.

This work proposes a novel Accumulative Double Sided Incremental Forming (ADSIF) strategy in which the forming begins at the location of the deepest feature and gradually shapes up the features by taking advantage of rigid-body motions. Compared to the conventional toolpath used in DSIF and SPIF, this strategy can dramatically improve geometric accuracy, increase formability, form components with desired thickness and create complex components. Furthermore, an examination of the forming forces shows that the dominant forces using this strategy are in the plane of the sheet resulting in a significant improvement in geometric accuracy.

Surface texturing, which fabricates micro dimples or micro channels on the surface of parts, is a growing technique for improving tribological characteristics of materials. Currently, electrical discharge texturing (EDT) technique, one surface texturing method suitable for mass production, is being used to texture aluminum sheets for the applications in automotive industry. It has been widely accepted in industry that EDT improves the forming behavior of aluminum sheets due to better friction behavior. However, how the textures on the surface of sheet metal change the friction behavior has not been investigated. In this paper, the influence of EDT on the friction behavior of aluminum automotive sheet at different contact pressures and sliding speeds is investigated based on both experimental studies and numerical simulations. To fully investigate the tribological behaviors, a flat-on-flat friction test device was built and a numerical code based on mixed lubrication theory was developed. It was found that EDT texturing can reduce the friction coefficient of contacting pair at high contact pressure, however, increase friction coefficient at low contact pressure. Numerical simulations confirmed this finding. Furthermore, the model provides valuable information for the prediction of friction behavior of EDT sheets and helps to optimize processing parameters for various forming processes using EDT aluminum sheets.

A new anisotropic material hardening model is introduced in this study for springback simulation. It is modified from the Mroz multi-yield surface hardening model and incorporated more realistic Bauschinger effect for cyclic loading and anisotropic yield surfaces for sheet metals. The model is targeted for sheet metal forming simulations where the accurate springback predictions are important, and where materials have more rapid hardening characteristics and ability to sustain higher stresses such as so-called advanced high-strength steels (AHSS). The constitutive integration algorithm is derived and it is numerically implemented in the commercial FEA code via a user-material subroutine. The new model is applied to a U-channel forming test with DP600 steel. Experiments are conducted and springback results are compared with numerical prediction to demonstrate the new model’s effectiveness.

Double-sided incremental forming (DSIF) is a relatively new dieless forming process which uses two hemispherical ended tools, one on each side of the sheet, moving along a predefined trajectory to locally deform a peripherally clamped sheet of metal. DSIF provides greater process flexibility, higher formability, and eliminates the tooling cost when compared to conventional sheet forming processes. While DSIF provides much improved geometric accuracy compared to other incremental forming processes, current toolpath planning strategies suffer from long forming times. A novel mixed double-sided incremental forming (MDSIF) toolpath strategy is proposed in the present study. It simultaneously reduces the total forming time by half while preserving the best currently achievable geometric accuracy. The effect of the forming parameters, i.e., of the incremental depth and of tool positioning on the geometric accuracy of the parts formed with MDSIF was investigated and compared to those formed by traditional DSIF strategies.

This paper presents an in-depth experimental and numerical investigation of a split-ring test, which provides a simple yet effective benchmark for correlating forming and springback predictive capabilities with experimental measurements. The experimental procedure consists of deep drawing a circular 6111-T4 aluminum alloy into a cylindrical cup of 55mm depth, crosscutting nine rings each of 5mm wide from the cup, splitting the rings, and measuring their opening displacement, i.e., the springback amount. Experimental data obtained included punch force trajectories, drawn cup profile, thickness distribution after forming, and the ring openings after splitting. A numerical model is built to analyze the process, and both transversely isotropic and fully orthotropic yield criteria are investigated. Simulation results are validated against experimental data. A detailed numerical analysis is also conducted for stress distributions in each ring after each step and their relationship to the total springback amount. Stress and strain signatures suggested that the test is well suited for validating material models, such as anisotropic yield surface models and hardening models.

It is widely accepted that variations in manufacturing processes are inevitable and should be taken into account during analysis and design processes. However, estimating uncertainty propagation in an end-product caused by these variations is a very challenging task, especially when a computationally expensive effort is already needed in deterministic models, such as simulations of sheet metal forming. The focus of this article is on the variance estimation of a system response using sensitivity-based methods. A weighted three-point-based strategy for efficiently and effectively estimating the variance of a system response is proposed. Three first-order derivatives of each variable are used to describe the non-linear behaviour and estimate the variance of a system. A methodology for determining the optimal locations and weights of the three points along each axis is proposed and illustrated for the cases where each variable follows either a normal distribution or a uniform distribution. An extension of th...

Model validation has become an increasingly important issue in the decision-making process for model development, as numerical simulations have widely demonstrated their benefits in reducing development time and cost. Frequently, the trustworthiness of models is inevitably questioned in this competitive and demanding world. By definition, model validation is a means to systematically establish a level of confidence of models. To demonstrate the processes of model validation for simulation-based models, a sheet metal flanging process is used as an example with the objective that is to predict the final geometry, or springback. This forming process involves large deformation of sheet metals, contact between tooling and blanks, and process uncertainties. The corresponding uncertainties in material properties and process conditions are investigated and taken as inputs to the uncertainty propagation, where metamodels, known as a model of the model, are developed to efficiently and effectively compute the total uncertainty/variation of the final configuration. Three model validation techniques (graphical comparison, confidence interval technique, and r2 technique) are applied and examined; furthermore, strength and weakness of each technique are examined. The latter two techniques offer a broader perspective due to the involvement of statistical and uncertainty analyses. The proposed model validation approaches reduce the number of experiments to one for each design point by shifting the evaluation effort to the uncertainty propagation of the simulation model rather than using costly physical experiments.

Fueled by pressures to reduce scrap and tooling costs, the modeling and prediction of springback has become a major focus of interest in sheet metal forming. Finite element codes and packages are being developed or improved but face the demand for higher predictive accuracy which, in turn, requires accurate property data and a more complete understanding of the stresses that are responsible for the elastic part of the springback. In order to provide experimental data for these calculations, synchrotron X-ray diffraction measurements were carried out in order to determine the through-thickness distribution of axial and tangential residual stresses in an Al6022 deep drawn cup. The technique is able to provide true spatial resolutions of 0.05 mm for a strain measurement on a cup with 0.92 mm wall thickness. It is found that both axial and tangential stresses exhibit non-linear gradients through thickness and both exhibit a pronounced dependency on the axial position. The springback measured on a split ring cut from the cup agrees within 3% accuracy with the value predicted from the average of measured through-thickness stresses.

A bifurcation analysis of forming limits for an orthotropic sheet metal is presented in this paper. The approach extends Stören and Rice's (S–R) bifurcation analysis for isotropic materials, with materials following a vertex theory of plasticity at the onset of localized necking. The sheet orthotropy is represented by the Hill’48 yield criterion with three r-values in the rolling (r0), the transverse (r90) and the diagonal direction (r45). The emphasis of the study is on the examination of r-value effect on the sheet metal forming limit, expressed as a combination of the average r-value raverage and the planar anisotropy (Δr). Forming limits under both zero extension assumption and minimum extension assumption as well as necking band orientation evolution are investigated in detail. The comparison between the experimental result and predicted forming limit diagram (FLD) is presented to validate the extended bifurcation analysis. The r-value effect is observed under uniaxial and equal-biaxial loadings. However, no difference is found under plane strain condition in strain-based FLD which is consistent with Hill's theory. The force maximum criterion is also used to analyze FLD for verification.

Numerical simulations have been widely used to assist part and process design. In this paper, deep-drawing processes of an axisymmetric part with a complex geometry are analyzed with the aim of reducing possible forming steps. The existing practice requires a 10-step drawing. Our approach combines a optimization scheme, design rules and numerical tests using the finite-element analysis incorporated with a damage model. As a result, the 10-step drawing is reduced to a 6-step drawing. Additionally, the new process design yields a lower maximum void volume fraction in the sheet, meaning a more formable process and a slightly higher press load.

It is well known in the literature that the isotropic hardening rule in plasticity is not realistic for handling plastic deformation in a simulation of a full sheet metal forming process including springback. An anisotropic hardening rule proposed by Mroz is more realistic. For an accurate computation of the stress increment for a given strain increment by using Mroz’s rule, the conventional sub-interval integration takes excessive computing time. This paper proposes the radial return method to compute such stress increment for saving computing time. Two numerical examples show the efficiency of the proposed method. Even for a sheet model with more than 10000 thin shell elements, the radial return method takes only 40% of the overall computing time by the sub-interval integration.

Forming limit diagrams (FLD) have been widely used as a powerful tool for predicting sheet metal forming failure in the industry. The common assumption for forming limits is that the deformation is limited to in-plane loading and through-thickness bending effects are negligible. In practical sheet metal applications, however, a sheet metal blank normally undergoes a combination of stretching, bending, and unbending, so the deformation is invariably three-dimensional. To understand the localized necking phenomenon under this condition, a new extended Marciniak–Kuczynski (M–K) model is proposed in this paper, which combines the FLD theoretical model with finite element analysis to predict the forming limits after a sheet metal undergoes under continuous-bending-under-tension (CBT) loading. In this hybrid approach, a finite element model is constructed to simulate the CBT process. The deformation variables after the sheet metal reaches steady state are then extracted from the simulation. They are carried over as the initial condition of the extended M–K analysis for forming limit predictions. The obtained results from proposed model are compared with experimental data from Yoshida et al. (2005, “Fracture Limits of Sheet Metals Under Stretch Bending,” Int. J. Mech. Sci., 47(12), pp. 1885–1986) under plane strain deformation mode and the Hutchinson and Neale's (1978(a), “Sheet Necking—II: Time-Independent Behavior,” Mech. Sheet Metal Forming, pp. 127–150) M–K model under in-plane deformation assumption. Several cases are studied, and the results under the CBT loading condition show that the forming limits of post-die-entry material largely depends on the strain, stress, and hardening distributions through the thickness direction. Reduced forming limits are observed for small die radius case. Furthermore, the proposed M–K analysis provides a new understanding of the FLD after this complex bending-unbending-stretching loading condition, which also can be used to evaluate the real process design of sheet metal stamping, especially when the ratio of die entry radii to the metal thickness becomes small.

Since the forming limit diagram (FLD) was introduced by Keeler, etc., five decades ago, it has been intensively studied by researchers and engineers. Most work has focused on the in-plane deformation which is considered as the dominant mode of the majority forming processes. However the effect of out-of-plane deformation becomes important in the accurate prediction of formability when thick sheet metals and/or smaller forming radii are encountered. Recent research on the stretch-bending induced FLD (BFLD) has been inconclusive. Some studies indicated that the bending effect will enhance a sheet metal's formability while others suggested otherwise. In this paper, we present an in-depth study of the through-thickness bending effect on the forming limits. The Marciniak–Kuczynski (M–K) analysis is extended to include bending, and models based on both flow theory and deformation theory of plasticity are proposed. The study is limited to the right-hand-side of FLD where the bending is along the major stretch direction. The radial return method is adopted as the framework to integrate constitutive equations. The results show that the bending process decreases the sheet metal formability with the flow-theory based model, while the opposite is true if the deformation theory based analysis is adopted. A detailed examination of the deformation histories from those two models reveals that the loading–unloading-reverse loading process during stretch-bending holds the key to the understanding of the conflicting results. The insight gained from the proposed FLD prediction model in this paper provides a new understanding of how the bending process affects the FLD, which can be used to predict and explain the localized necking phenomenon under the stretch-bending condition.

The objectives of this project are to establish the scientific bases, engineering technologies and energy/emission impact of a novel dieless forming process, Double side Incremental Forming (DSIF), and to explore the effectiveness of its hybrid variation, Electrical-Assisted Double Side Incremental Forming (EADSIF), on increasing the formability of metallic sheets. The scope of this project includes: (1) the analysis of environmental performance of the proposed new process as compared to conventional sheet metal forming processes; (2) the experimental investigation of the process capabilities of DSIF and EADSIF via the self-designed and newly established lab-scale EADSIF equipment; (3) the development of the essential software in executing the new proposed process, i.e., the toolpath generation algorithms; and finally (4) the exploration of the electricity effect on material deformation. The major accomplishments, findings and conclusions obtained through this one and a half years exploratory project are: (1) The first industrial medium-size-scale DSIF machine using two hexapods, capable of handling a sheet area up to 675 mm x 675 mm, was successfully completed at Ford. (2) The lab-scale of the DSIF machine was designed, fabricated and assembled to form a workpiece up to 250 mm x 250 mm. (3) Parts with arbitrary freeform double-curvatures using the genetic, not geometric-specific tooling were successfully formed using both machines. (4) The methodology of the life cycle analysis of DSIF was developed and energy consumption was measured and compared to conventional forming processes. It was found that the DSIF process can achieve 40% to 90% saving when the number of parts produced is less than 50. Sensitivity analysis was performed and showed that even at very large number of produced parts (greater than 2000), incremental forming saves at least 5% of the energy used in conventional forming. (5) It was proposed to use the offset between the two universal tools in DSIF to actively create a squeezing effect on sheet metal and therefore, increase the geometric accuracy. The idea was confirmed through both experimental and numerical validations. (6) A novel toolpath strategy, i.e., the so-called In-to-out toolpath or accumulative toolpath, was proposed to further increase formability and geometric accuracy compared to the SPIF configuration. A dimensional form accuracy of 1 mm can be achieved using the new strategy. (7) The effect of electricity on magnesium alloy was experimentally investigated. It was found that the formability has a ridge with respect to the applied current density and pulse duration. This finding implies that there are multiple choices of process parameters that are workable depending on the desired microstructure. The above results demonstrated that DSIF/EADSIF is a promising forming technology that can create impacts in revolutionizing how the prototyping and small volume production of sheet metals will be fabricated, i.e., it can (1) eliminate the need of casting and machining of drawing dies; (2) tailor material utilization to function requirement therefore achieving a light weight product; (3) reduce the amount of sheet metal scraps; and (4) shorten the engineering and manufacturing time for sheet metal parts from the current 8 {approx} 25 weeks to less than 1 week after the technology is fully developed. DSIF/EADSIF can be implemented in aerospace, automotive and appliance industries, or be used for producing personalized and point-of-use products in medical industry. Our analysis has shown that once developed, verified and demonstrated, the implementation and growth of DSIF will increase U.S. manufacturing competitiveness, advance machine tool and software industries, and create opportunities for emerging clean energy and low-carbon economy with estimated energy savings of 11 TBtu and CO2 reduction of 1 million tons per year. The work has been disseminated into three (3) journal articles and two (2) provisional patent submissions. A new company has been spun off from this research group aiming to commercialize the technology. A team, consisted of Northwestern Kellogg Business school students and Northwestern McCormick Engineering school graduate students, has independently examined business facts and business models, and has assisted in developing go-to-market strategy. One of the key recommendations for utilizing the full potential of this work is to demonstrate the DSIF/EADSIF concept in a true large-scale industrial setup, i.e., being able to form sheet size of 1.5 m x 1.5 m, where technical challenges, such as machine design, shape compensation, dynamic effect on geometrical accuracy, need to be further explored.

Single point incremental forming (SPIF) is plagued by an unavoidable and unintended bending in the region of the sheet between the current tool position and the fixture. The effect is a deformation of the region of the sheet in between the formed area and the fixture as well as deformation of the already formed portion of the wall, leading to significant geometric inaccuracy in SPIF. Double sided incremental forming (DSIF) uses two tools, one on each side of the sheet to form the sheet into the desired shape. This work explores the capabilities of DSIF in terms of improving the geometric accuracy as compared to SPIF by using a novel toolpath strategy in which the sheet is locally squeezed between the two tools. Experiments and simulations are performed to show that this strategy can improve the geometric accuracy of the component significantly by causing the deformation to be stabilized into a local region around the contact point of the forming tool. At the same time an examination of the forming forces indicates that after a certain amount of deformation by using this strategy a loss of contact occurs between the bottom tool and the sheet. The effects of this loss of contact of the bottom tool on the geometric accuracy and potential strategies, in order to avoid this loss of contact, are also discussed.

Single Point Incremental Forming (SPIF) is plagued by an unavoidable and unintended bending in the region of the sheet between the current tool position and the fixture, which leads to significant geometric inaccuracies. Double Sided Incremental Forming (DSIF) uses two tools, one on each side of the sheet to form the sheet into the desired shape. This work explores the capabilities of DSIF in terms of improving the geometric accuracy as compared to SPIF by using a novel toolpath strategy in which the sheet is locally squeezed between the two tools. Experiments and simulations are performed to show that this strategy can improve the geometric accuracy of the component significantly. An examination of the forming forces indicates that after a certain amount of deformation using this strategy a loss of contact occurs between the bottom tool and the sheet. The effects of this on the geometric accuracy are discussed as well.

This paper presents an analytical and numerical study of deformation analysis for multistage incremental sheet forming processes, with a truncated conical part is used as an example. Unlike in the single-pass incremental forming where the sheet deformation is dominantly plane strain in the axial direction when forming a conical part, the sheet is also deformed in the circumferential direction when it is incrementally formed subsequently. Ideal deformation kinetics is assumed in the analytical derivations of strain distributions, which should be valid as long as the increment in deformation from one stage to the next is small. Numerical simulations with LS-DYNA are also conducted in an effort to understand the fundamental deformation mechanics of multistage incremental forming. The simulation result for a five-stage incremental forming process is presented. It is also used to correlate the analytical solution. An improved analytical equation for strain distributions is derived, which compares favorably with simulation results.Copyright © 2010 by ASME

High strength steels (HSSs) are one of the light-weight sheet metals well suited for reducing vehicle weight due to their higher strength-to-weight ratio. However, HSS tend to have bigger variations in their mechanical properties due to more complex rolling techniques involved in the steel-making process. Such uncertainties, when combined with variations in the process parameters such as friction and blank holder force, pose a significant challenge in maintaining the robustness of HSS sheet metal stamping. The paper presents a systematic and robust approach, combining the power of the finite element method and stochastic statistics to decrease the sensitivity of HSS stamping in the presence of above-mentioned uncertainties. First, the statistical distribution of sheet metal properties of selected HSS is characterized from a material sampling database. Then a separate interval adaptive response surface methodology (RSM) is applied in modeling sheet metal stamping. The new method significantly improves the model accuracy when compared with the conventional RSM within a single interval. Finally, the Monte Carlo method is employed to simulate the stochastic response of material/process variations to stamping quality and to provide optimal process parameter designs to reduce the sensitivity of these effects. The experiment with the obtained optimal process design demonstrates the improvements of stamping robustness using small-batch experiments.

Developing a proper local formability failure criterion is the key to the successful prediction of the local formability of Advanced High Strength Steels (AHSS) in computer simulations. Shear fracture, which refers to the fracture occurred in the die radius when a sheet metal is drawn over a small die radius, often occurs earlier than predicted by the conventional forming limit curve (FLC). As shown in a previous study using a laboratory Stretch-Forming Simulator (SFS), shear fracture depends not only on the radius-to-thickness (R/T) ratio but also on the tension/stretch level applied to the sheet during stretching or drawing. In the SFS test, a flat sheet is first clamped at the both ends then gradually is wrapped around the die radius as the punch moves downward. This process simulates the early stage of stamping when a sheet metal is initially stretched or drawn over a die/punch radius. However, shear fracture may not occur in this stage if the stretch/tension level is not high enough. In this study, the Bending under Tension (BUT) tester is used to evaluate shear fracture occurring in the later stage of stamping, after the sheet metal is totally wrapped around the die radius. It is demonstrated that shear fracture does occur in this deformation mode when a sufficient tension level is applied. Effects of forming conditions, such as forming speeds and lubrication on shear fracture, are also investigated. When compared to the results from the SFS, the data points failing at the die radius tangent point agree very well. It is observed that all data points above the tangent point failure line show shear fracture, while data points below this line show tensile failure (localized necking) regardless of the test methods used. This indicates that the tangent point fracture line can be used as the shear fracture failure limit. This failure criterion can be used in a computer simulation to simulate the shear fracture phenomenon in the entire deformation process involved in a sheet metal stretching or drawing over a die radius.Copyright © 2009 by ASME

A new anisotropic material hardening model is introduced in this study for springback simulation. It is modified from the Mroz multi-yield surface hardening model and incorporated more realistic Bauschinger effect for cyclic loading and anisotropic yield surfaces for sheet metals. The model is targeted for sheet metal forming simulations where the accurate springback predictions are important, and where materials have more rapid hardening characteristics and ability to sustain higher stresses such as so-called Advanced High-Strength Steels (AHSS). The constitutive integration algorithm is derived and it is numerically implemented in the commercial FEA code via a user-material subroutine. The new model is applied to a U-channel forming test with DP600 steel. Experiments are conducted and springback results are compared with numerical prediction to demonstrate the new model’s effectiveness.

Experimental procedures and results of a benchmark test for springback are reported and a complete suite of obtained data is provided for the validation of forming and springback simulation software. The test is usually referred as the Slit-Ring test where a cylindrical cup is first formed by deep drawing and then a ring is cut from the mid-section of the cup. The opening of the ring upon slitting releases the residual stresses in the formed cup and provides a valuable set of easy-to-measure, easy-to-characterize springback data. The test represents a realistic deep draw stamping operation with stretching and bending deformation, and is highly repeatable in a laboratory environment. In this study, six different automotive materials are evaluated. They included one aluminum alloy (AA6022-T4), one deep drawing quality and special killed (DQSK) mild steel, one bake hardenable (BH) medium strength steel, a conventional high-strength low-alloy (HSLA) steel, and two advanced high-strength steels (AHSS) represented by one dual-phase (DP) steel, and one TRansformation Induced Plasticity (TRIP) steel. A particularly interesting aspect of this experiment is the direct measurement of residual stresses by diffractive stress analysis in collaboration with NIST Center for Neutron Research, and is believed to be the first application of this technique to sheet metal forming. Complete material data and experimental results are documented, including punch force trajectories, amount of draw-in, ring opening displacement, axial and hoop stresses before and after the rings were slit. The data is ideal for the evaluation and improvement of current forming and springback simulation capabilities. Efforts for the correlation of simulation with the obtained experimental data are underway and will be reported in follow-up studies.

Prediction of springback has become a major focus in sheet metal forming. Validation of finite element codes that are being developed to predict springback require accurate property data and a more complete understanding of the residual stresses that are involved. To provide experimental data for these calculations, neutron and synchrotron X-ray diffraction measurements were carried out to determine the through-thickness distribution of axial and hoop (or tangential) residual stresses in deep-drawn steel and aluminum cups. The techniques are able to provide true spatial resolutions as low as 0.05 mm for a strain measurement on cups with {le} 1 mm wall thickness. It was found that the stresses exhibit non-linear gradients through the thickness that also depend on the axial position.

As more Advanced High‐Strength Steels (AHSS) are heavily used for automotive body structures and closures panels, accurate springback prediction for these components becomes more challenging because of their rapid hardening characteristics and ability to sustain even higher stresses. In this paper, a modified Mroz hardening model is proposed to capture realistic Bauschinger effect at reverse loading, such as when material passes through die radii or drawbead during sheet metal forming process. This model accounts for material anisotropic yield surface and nonlinear isotropic/kinematic hardening behavior. Material tension/compression test data are used to accurately represent Bauschinger effect. The effectiveness of the model is demonstrated by comparison of numerical and experimental springback results for a DP600 straight U‐channel test.

One of the principal foundations of mathematical theory of conventional plasticity for rate-independent metals is that there exists a well-defined yield surface in stress space for any material point under deformation. A material point can undergo further plastic deformation if the applied stresses are beyond current yield surface which is generally referred as 'plastic loading'. On the other hand, if the applied stress state falls within or on the yield surface, the metal will deform elastically only and is said to be undergoing 'elastic unloading'. Although it has been always recognized throughout the history of development of plasticity theory that there is indeed inelastic deformation accompanying elastic unloading, which leads to metal's hysteresis behavior, its effects were thought to be negligible and were largely ignored in the mathematical treatment.Recently there have been renewed interests in the study of unloading behavior of sheet metals upon large plastic deformation and its implications on springback prediction. Springback is essentially an elastic recovery process of a formed sheet metal blank when it is released from the forming dies. Its magnitude depends on the stress states and compliances of the deformed sheet metal if no further plastic loading occurs during the relaxation process. Therefore themore » accurate determination of material compliances during springback and its effective incorporation into simulation software are important aspects for springback calculation. Some of the studies suggest that the unloading curve might deviate from linearity, and suggestions were made that a reduced elastic modulus be used for springback simulation.The aim of this study is NOT to take a position on the debate of whether elastic moduli are changed during sheet metal forming process. Instead we propose an approach of modeling observed psuedoelastic behavior within the context of mathematical theory of plasticity, where elastic moduli are treated to be constant. In the context of this investigation we refer psuedoelastic behavior in the most general sense as any deviation from linearity in the unloading curve. The non-linearity leads to a hysteresis loop upon reloading. The approach is based on the non-conventional theory with a vanishing elastic region as advanced by Dafalias and Popov. The treatment is purely phenomenological where we don't distinguish between macroscopic plasticity and micro-plasticity. The macroscopic uniaxial stress-strain curve is used to define effective plastic response in the same manner as classical plasticity theory except that the nonlinearity during unloading and reloading are incorporated into plasticity. It is shown that such models can be easily formulated within the context of elastoplasticity without violating any physical mechanisms of deformation. Springback for a plane strain bending model is used to demonstrate the potential effect if such a model is applied.« less

Forming Limit Diagram (FLD) has been proved to be a powerful tool for assessing necking failures in sheet metal forming analysis for majority of stamping operations over the last three decades. However, experimental evidence and theoretical analysis suggest that its applications are limited to linear or almost linear strain paths during its deformation history. Abrupt changes or even gradual deviations from linear strain‐paths will shift forming limit curves from their original values, a situation that occurs in vast majority of sequential stamping operations such as where the drawing process is followed by flanging and re‐strike processes. Various forming limit models have been put forward recently to provide remedies for the problem, noticeably stress‐based and strain gradient‐based forming limit criteria. This study presents an alternative path‐independent forming limit criterion. Instead of traditional Forming Limit Diagrams (FLD) which are constructed in terms of major ‐ minor principal strains throu...

The aim of this study is to develop an analytical solution to the deformation profile of hydroforming pre-bend process, which will be in turn fed into finite element simulation code for subsequent hydroforming simulation. The conventional approach of using FEM to simulate pre-bending is extremely time consuming in terms of both CAE work and computer running, and can not meet the cycle time required for product development and manufacturing. This is part of a series work for pre-bend modeling, with the focus here on the practice without the use of an inner mandrel, and the tube is free to ovalize during the process. Since only a portion of the tube is undergoing the bending operation, the ovalization magnitude of the tube cross-section is not longitudinally uniform due to the end constraints provided by the undeformed portion of the tube. A large deformation elastoplastic analysis is presented, with the anisotropic plastic behavior of the tube sheet accounted for through the constitutive model. Deformation modes associated with tube ovalization and beam bending are analyzed. The actual deformation is determined by minimizing the total work done during the bending process. Numerical examples are presented for a series of tube geometries and bending curvature to illustrate the proposed approach.