Z. Cedric Xia

Approaches for model validation: Methodology and illustration on a sheet metal flanging process

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 r 2 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.

Improvement of Geometric Accuracy in Incremental Forming by Using a Squeezing Toolpath Strategy With Two Forming Tools

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.

Analysis of an axisymmetric deep-drawn part forming using reduced forming steps

Abstract 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.

Probabilistic Design in a Sheet Metal Stamping Process under Failure Analysis

Sheet metal stamping processes have been widely implemented in many industries due to its repeatability and productivity. In general, the simulations for a sheet metal forming process involve nonlinearity, complex material behavior and tool‐material interaction. Instabilities in terms of tearing and wrinkling are major concerns in many sheet metal stamping processes. In this work, a sheet metal stamping process of a mild steel for a wheelhouse used in automobile industry is studied by using an explicit nonlinear finite element code and incorporating failure analysis (tearing and wrinkling) and design under uncertainty. Margins of tearing and wrinkling are quantitatively defined via stress‐based criteria for system‐level design. The forming process utilizes drawbeads instead of using the blank holder force to restrain the blank. The main parameters of interest in this work are friction conditions, drawbead configurations, sheet metal properties, and numerical errors. A robust design model is created to con...

Forming Limits of a Sheet Metal After Continuous-Bending-Under-Tension Loading

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 Neales (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.

A Mixed Double-Sided Incremental Forming Toolpath Strategy for Improved Geometric Accuracy

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.

Experimental Study on Shear Fracture of Advanced High Strength Steels: Part II

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

A weighted three-point-based methodology for variance estimation

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 the weighted three-point-based strategy is introduced to take into account the interaction between parameters. In addition, an extension is given for mean estimation of the system response without requiring more data. The considerable improvement in accuracy compared with the traditional first-order approximation is demonstrated in a number of test problems. The proposed method requires significantly less computational effort than the Monte Carlo method.

Deformation Analysis of Multi-Stage Incremental Sheet Forming

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

An Engineering Approach to Improve the Stamping Robustness of High Strength Steels

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.