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J. Eng. Mater. Technol. 2000;123(4):378-383. doi:10.1115/1.1394202.

An inverse identification technique is proposed based on bending-unbending experiments on anisotropic sheet-metal strips. The initial anisotropy theory of plasticity is extended to include the concept of combined isotropic and nonlinear kinematic hardening. This theory is adopted to characterize the anisotropic hardening due to loading-unloading which occurs in sheet-metals forming processes. To this end, a specific bending-unbending apparatus has been built to provide experimental moment-curvature curves. The constant bending moment applied over the length of the specimen allows one to determine numerically the strain-stress behavior but without Finite Element Analysis. Four constitutive parameters have been identified by an inverse approach performed simultaneously on the bending and tensile tests. Our identification results show that bending-unbending tests are suitable to model quite accurately the constitutive behavior of sheet metals under complex loading paths.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;123(4):384-390. doi:10.1115/1.1395574.

A drawbead model with sheet metal passing through multiple bending-unbending processes was employed in this study to understand the springback phenomenon and to develop a numerical simulation technique for more accurate prediction of the springback process. The deformation process is simulated using an implicit finite element modeling code. The predicted results were compared with the physically measured ones, including clamping and restraining forces, thickness strains, and the curvatures of the deformed sheets. Consideration of the Bauschinger effect and employment of a combined isotropic and kinematic hardening models greatly improve the prediction accuracy. Stress and strain histories under various conditions during the drawing process are studied in detail in an attempt to provide a better basis for comparison for dynamic explicit solutions.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):391-397. doi:10.1115/1.1395021.

The main objective of this paper is to obtain the first few stress-strain loops of sheet metals from reverse loading so that the springback can be simulated accurately. Material parameters are identified by an inverse method within a selected constitutive model that represents the hardening behavior of materials subjected to a cyclic loading. Three-point bending tests are conducted on sheet steels (mild steel and high strength steel). Punch stroke, punch load, bending strain, and bending angle are measured directly during the tests. Bending moments are then computed from these measured data. Bending moments are also calculated based on a constitutive model. Normal anisotropy and nonlinear isotropic/kinematic hardening are considered. Material parameters are identified by minimizing the normalized error between two bending moments. Micro-genetic algorithm is used in the optimization procedure. Stress-strain curves are generated with the material parameters found in this way, which can be used with other plastic models.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):398-402. doi:10.1115/1.1395022.

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 subinterval 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 10,000 thin shell elements, the radial return method takes only 40 percent of the overall computing time by the subinterval integration.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):403-408. doi:10.1115/1.1395575.

Based on the theory of damage mechanics, a viscoplastic constitutive modeling of anisotropic damage for the prediction of forming limit curve (FLC) is developed. The model takes into account the effect of rotation of principal damage coordinates on the deformation and damage behaviors. With the aid of the damage viscoplastic potential, the damage evolution equations are established. Based on a proposed damage criterion for localized necking, the model is employed to predict the FLC of aluminum 6111-T4 sheet alloy. The predicted results agree well with those determined experimentally.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):409-416. doi:10.1115/1.1395023.

The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. 1997, “Approximate Yield Criteria for Anisotropic Porous Ductile Sheet Metals,” Mech. Mater., pp. 213–226. Three fitting parameters are suggested for the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the modified anisotropic Gurson’s yield criterion under uniaxial and equal biaxial tensile loading conditions.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):417-422. doi:10.1115/1.1398083.

A strain-based forming limit criterion is widely used throughout the sheet-metal forming industry to gauge the stability of the deformed material with respect to the development of a localized neck prior to fracture. This criterion is strictly valid only when the strain path is linear throughout the deformation process. There is significant data that shows a strong and complex dependence of the limit criterion on the strain path. Unfortunately, the strain path is never linear in secondary forming and hydro-forming processes. Furthermore, the path is often found to be nonlinear in localized critical areas in the first draw die. Therefore, the conventional practice of using a path-independent strain-based forming limit criterion often leads to erroneous assessments of forming severity. Recently it has been reported that a stress-based forming limit criterion appears to exhibit no strain-path dependencies. Subsequently, it has been suggested that this effect is not real, but is due to the saturation of the stress-strain relation. This paper will review and compare the strain-based and stress-based forming limit criteria, looking at a number of factors that are involved in the definition of the stress-based forming limit, including the role of the stress-strain relation.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):423-429. doi:10.1115/1.1394966.

A mathematical analysis of failure developments for tubular hydroforming under combined internal pressure and end feeding is presented in this paper. Under considerations are two distinct failure modes, namely, the bursting and the wrinkling. Bursting is an instability phenomenon where the tube can’t sustain any increased tensile loading. Splitting usually follows due to extreme deformations in the bursting area. Wrinkling is due to high compression load, which deteriorates the quality of the final product. The deformation theory of plasticity is utilized in this study and the material anisotropy is accounted for in the constitutive model. The governing equations for the onset of both failure modes are established. The results are presented as Hydroforming Failure Diagram in the End Feed—Internal Pressure space. A parametric study of the failure criteria for a variety of materials and process parameters is performed. It is shown that the material anisotropy plays a significant role. The results provide guidelines for product designers and process engineers for the avoidance of failure during hydroforming. The validity and applicability of current study are also discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):430-435. doi:10.1115/1.1395018.

Thin-walled tube bending has found many of its applications in the automobile and aerospace industries. This paper presents an energy approach to provide the minimum bending radius, which does not yield wrinkling in the bending process, as a function of tube and tooling geometry and material properties. A doubly-curved sheet model is established following the deformation theory. This approach provides a predictive tool in designing/optimizing the tooling parameters in tube bending.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):436-441. doi:10.1115/1.1396348.

In this paper, the occurrence of recoil and surface warp during the flat surface-straight edge hemming process is investigated. A general-purpose finite element code ABAQUS/Standard is used to simulate the hemming operations. Reverse bending and springback are the fundamental mechanisms that cause surface warp and recoil. Recoil and warp are not independent. One parameter, final equivalent warp, is used to represent both. Pre-hemming target ending position is proposed based on the minimization of the final equivalent warp. The influence of the geometrical and process parameters on recoil and warp are also discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):442-446. doi:10.1115/1.1396351.

A brief review of the literature on wrinkling in deep drawing processes is presented. It is noted that, while there is a large body of literature related to thin sheet, only one study related to thick sheet or plate has been identified. Finite element based models are used to investigate the effect of initial tooling imperfections on the initiation of wrinkling in deep drawing of thick sheet. Two sorts of tooling imperfections, punch displacement and blank tilting, are considered. The simulation results are compared qualitatively to the experimental forming operation. It is confirmed that tooling imperfections, in particular blank tilting, are an important type of imperfection governing the wrinkling behavior of the blank in deep drawing process.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):447-455. doi:10.1115/1.1395578.

This paper studies the effects of some modeling parameters on the accuracy of finite element simulation in sheet-metal forming. A simple stepdie, which simulates binder forming, is used. In this two-dimensional case, a flat blank is bent into an S-shape, which has an exact solution. Four modeling parameters are studied. They are: die close speed, die gap, mass damping, and width of blank. One significant finding of this study reveals that in calculations using explicit finite elements, the simulation speed should be selected with care. The dynamic effects may be prevalent if the simulation speed is too fast. Numerical errors may accumulate and renders the results erroneous if it is too slow.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):456-461. doi:10.1115/1.1395019.

A study on the prediction of springback angle is presented, with focus on the straight flanging operation. The objective of this work is to evaluate the reliability of different methods of prediction. An experiment of straight flanging operation is conducted. Major prediction approaches such as analytical model, numerical simulation using the Finite Element Method (FEM) and the Meshfree Method using the Reproducing Kernel Particle Methods (RKPM) are discussed. A set of sample problems is computed and comparisons are made with the experiment. The numerical analysis shows that the prediction from the 3D meshfree contact code matches well with the data from the FEM 2D solid model. A material property described by the kinematic hardening law provides a better prediction of springback than the isotropic hardening law.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):462-467. doi:10.1115/1.1396349.

A stabilized conforming (SC) nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in collocation meshfree methods. The gradient matrix associated with strain smoothing satisfies the integration constraint (IC) of linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for history-dependent problems are introduced. Applications to metal forming analysis are presented, with the results demonstrating a significant improvement in computational efficiency without loss of accuracy.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):468-475. doi:10.1115/1.1398082.

The sensitivity method is employed in this work in order to find initial blank shapes which result in desired shapes after deformation. By assuming the final deformation shape be the drawn cup with uniform trimming allowance at the flange, the corresponding initial blank which gives the desired final shape after deformation has been found. With the aid of a well-known dynamic explicit analysis code PAM-STAMP, shape sensitivity has been obtained. To get the shape sensitivity numerically, a couple of deformation processes have been analyzed. Drawings of trapezoidal cup, oil pan, and Audi front door panel, the benchmark test problem of Numisheet ’99, have been chosen as the examples. In every case the optimal blank shape has been obtained after only a few modifications without a predetermined deformation path. With the predicted optimal blank, both computer simulation and experiment are performed. Excellent agreements are obtained between simulation and experiment in every case. Through this investigation, the sensitivity method is found to be very effective in the design of arbitrary shaped drawing processes.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):476-481. doi:10.1115/1.1395579.

Process optimization is carried out to determine process parameters which satisfy the given design requirements and constraint conditions in sheet-metal forming processes. The scheme incorporates with a rigid-plastic finite element method for calculation of the final shape and the strain distribution. The optimization scheme adopts a direct differentiation method or a response surface methodology in order to seek for the optimum condition of process parameters. The algorithm developed is applied to design of the draw-bead force and the die shapes in deep drawing processes. Results show that design of process parameters is well performed to increase the amount of strain for increasing the strength or to decrease the amount of strain for preventing fracture by tearing. The present algorithm also enhances the stable optimum solution with small number of iterations for optimization.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):482-488. doi:10.1115/1.1395020.

In stamping, operating costs are dominated by raw material costs, which can typically reach 75 percent of total costs in a stamping facility. In this paper, material utilization efficiency is modeled by considering two primary sources of scrap: material cut away from the exterior of each blank on the strip and off-cuts of unusable narrow strips generated when wide master coils are slit into strips for subsequent stamping. Based on these, layout optimization techniques for minimizing raw material usage are described that predict the optimal blank orientation on the strip and the optimum slitting width for the strip. In addition, methods are given for determining optimal common strip widths for multiple parts, both for dependent and independent demand. These algorithms are ideally suited for incorporation into die design CAE systems.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):489-495. doi:10.1115/1.1395576.

Tooling cost is a major contributor to the total cost of small-lot production of sheet metal components. Within the framework of an academic/industrial/government partnership devoted to the development of a reconfigurable tool for stretch forming, we have implemented a Finite Element-based procedure to determine optimal die shape. In the reconfigurable forming tool (Hardt, D. E. et al., 1993, “A CAD Driven Flexible Forming System for Three-Dimensional Sheet Metal Parts,” Sheet Metal and Stamping Symp., Int. Congress and Exp., Detroit, MI, SAE Technical Paper Series 930282, pp. 69–76.), the die surface is created by the ends of an array of square pins, which can be individually repositioned by computer driven servo-mechanisms. An interpolating polymer layer is interposed between the part and the die surface to attain a smooth pressure distribution. The objective of the die design algorithm is to determine optimal positions for the pin array, which will result in the desired part shape. The proposed “spring-forward” method was originally developed for matched-die forming (Karafillis, A. P., and Boyce, M. C., 1992, “Tooling Design in Sheet Metal Forming using Springback Calculations,” Int. J. Mech. Sci., Vol. 34, pp. 113–131.; Karafillis, A. P., and Boyce, M. C., 1996, “Tooling And Binder Design for Sheet Metal Forming Processes Compensating Springback Error,” Int. J. Tools Manufac., Vol. 36, pp. 503–526.) and it is here extended and adapted to the reconfigurable tool geometry and stretch forming loading conditions. An essential prerequisite to the implementation of the die design procedure is the availability of an accurate FE model of the entire forming operation. The particular nature of the discrete die and issues related to the behavior of the interpolating layer introduce additional challenges. We have first simulated the process using a model that reproduces, as closely as possible, the actual geometry of the discrete tool. In order to optimize the delicate balance between model accuracy and computational requirements, we have then used the information gathered from the detailed analyses to develop an equivalent die model. An automated algorithm to construct the equivalent die model based on the discrete tool geometry (pin-positions) is integrated with the spring-forward method, to generate an iterative die design procedure that can be easily interfaced with the reconfiguring tool. The success of the proposed procedure in selecting an optimal die configuration is confirmed by comparison with experimental results.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):496-503. doi:10.1115/1.1397780.

The process of stretch forming is used extensively in the aerospace industry to form large sheet panels of mild curvature. This has traditionally been a low precision process requiring considerable hand-working at assembly. However, recent demands for faster, less wasteful production have placed new demands on the accuracy and consistency (quality) of this process. In this paper the various modes of control for this process are examined, from both an analytical and experimental point of view. It is shown clearly that the process is least sensitive to material and machine property variations if controlled to a target level of strain in specific areas of the sheet. This method is compared with the conventional methods of controlling either the force applied to the sheet during stretching or the displacement of the stretch jaws. A series of both lab scale and full production experiments concur with the analytical findings, demonstrating reduced process variation if strain feedback is used. Lab experiments and analysis indicate that far greater reductions are possible if a more precise form of strain control is used. In production trials forming wing leading edges, a manually implemented strain control showed a shape variation reduction of 50 percent over normal factory practice using force control.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):504-510. doi:10.1115/1.1395577.

Aluminum is expected to gain popularity as material for the bodies of the next generation of lighter and more fuel-efficient vehicles. However, its lower formability compared with that of steel tends to create considerable problems. A controllable restraining force caused by adjusting the penetration of drawbeads can improve the formability. This paper describes the effects of temporal variations in drawbead penetration on the strain distribution in a symmetric stamped part. Comparison of the results of numerical simulations with the corresponding experimental results shows that the predictions of strain distribution on the panel are in very good agreement. Furthermore, forming limit diagram analysis indicates that the active drawbead concept is beneficial to the formability of AA 6111-T4.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2000;123(4):511-516. doi:10.1115/1.1396350.

Open die forging is a process in which products are made through repeated, incremental plastic deformations of a workpiece. Typically, the workpiece is held by a manipulator, which can position the workpiece through program control between the dies of a press. The part programs are generated with an empirically derived parameter, called the spread coefficient, whose value is subject to some contention. In this work, we demonstrate how process information can be used in real time to derive the actual spread coefficient for a given workpiece as it is being formed. These measurements and calculations occur in real time, and can be used to regenerate part programs to optimize the forming process, or can be used to adaptively control each incremental deformation of the workpiece.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;123(4):517-523. doi:10.1115/1.1397779.

The forces during wire and tube drawing can be reduced by ultrasonically oscillating dies. It is a major problem of conventional wire and tube drawing to introduce high forces into the forming area. Compared to conventional wire and tube drawing, the forming process limits can be extended by superimposing ultrasonic waves due to decreasing drawing forces. Different techniques can be used to excite the die. One possibility is the variation of the vibration mode. In tube and wire drawing, the dies are usually excited longitudinally. If the vibration direction is parallel to the drawing direction, the main influence will be on the friction between workpiece and die. The Institute for Metal Forming Technology of the University of Stuttgart, Germany started a project to investigate the effect of ultrasonic waves on the tribology and on the formability of the workpiece. The objective of this investigation is to separate the ultrasonic effect on the surface from the volume effects. This paper shows that the reduction of the sliding friction between a longitudinal oscillating die and the workpiece can be explained by the so-called Sliding Friction Vector Effect (SFVE). A statistical evaluation of roughness-measurements makes it possible to show the effect of the ultrasonic vibration on the friction and gives an insight into the operation of the SFVE. The results are compared with wire and tube drawing experiments of copper and Ti-alloys. New tube- and wire-drawing experiments with longitudinally vibrating dies support the theoretical approach. The surface quality of the manufactured workpieces can be improved and the productivity increased.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;123(4):524-529. doi:10.1115/1.1397374.

Free plastic forming of a slender part means that an initially straight bar, clamped at its both ends, is bent and twisted by an appropriate motion of the end supports only. Emphasis is attached on the computer controlled, precise forming of workpieces with prescribed shape. In this paper the design of an appropriate forming machine at the laboratory scale will be presented. Moreover, the forming limits due to replastification of already completed sections of the part will be illustrated geometrically using one or two “cylinders of admissibility.” Finally, the method will be demonstrated by means of actually formed parts.

Commentary by Dr. Valentin Fuster

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