Application of the finite-element method to a design of optimized tool geometry for the O.S.U. formability test

A new, plane-strain, sheet-formability test (the O.S.U. Formability Test, OSUFT) has been recently proposed, and it has shown many improvements over the limiting dome height (LDH) test. However, the prototype tool geometry was initially determined arbitrarily for the experiment so that an enhancement of the tool geometry was made with dual purpose: to design the tool geometry to generate consistent planestrain state up to failure under various lubrication states and different testing materials and, at the same time, to make the testing equipment cost as low as possible so that the test may be readily available for small- and medium-scale stamping companies. The latter demands a compact tool geometry to minimize the required press capacity, while the former requires wider blanks that increase the punch load. Considering these conflicting conditions, computer simulation technique using three-dimensional finite-element method was introduced, rather than performing numerous die tryouts, to design the optimal tool geometry from simulative trial and error. By reducing the size of the entire tool and controlling the width-to-length ratio of the blank, an enhanced tool geometry was found that generates stable plane-strain state up to failure and still features low required load capacity for materials with r-values up to 2.0, friction coefficient ranges of 0.15 to approximately 0.35, and thicknesses up to 1.5 mm. The bending-dominant failure due to smaller radii of the tool was avoided. Comparison of LDH simulation showed that the enhanced configuration of the test will produce more proportional strain path and larger plane-strain area near the predicted failure region. It was also predicted that the testing results will be less sensitive to the lubrication state on the tool surface and the material anisotropy of the sheet, which will contribute to a better repeatability of the test. Experiments revealed that the optimized tool showed significantly less scatter in measurement compared with that of the LDH and the original O.S.U. formability tests.     

Improvements in finite-element simulation for stamping and application to the forming of laser-welded blanks

During stamping-die design, the formability in sheet-metal forming process has been evaluated by the geometrical functions in ‘Die-Face CAD’, which has been developed and improved by Toyota Motor Corporation. When evaluation by these functions is difficult, formability has been estimated by performing experiments using test dies in which the forming defects are similar to those in the actual process.

A numerical method has been developed in order to substitute numerical analysis for experiments using test dies for the accurate prediction of defects in sheet-metal forming. The elastic-plastic FEM with the commercial code ‘JNIKE3D’ has been improved in the areas of: (1) the material constitutive equation; (2) the consideration of the pressure distribution on the blank-holder; and (3) the evaluation of breakage initiation. Using the improved method, the square-cup drawing process and the hemming process have been analyzed. Numerical results for strain, breakage initiation, and hemming deflection were in good agreement with experimental results. The formability of laser-welded blanks and the most efficient process to form them were evaluated also using the improved method.     

Formability prediction of advanced high strength steels using constitutive models characterized by uniaxial and biaxial experiments

Sheet formability, as determined by the limiting dome height (LDH) test, was evaluated for DP and TRIP steel sheet samples. The LDH test was also predicted with finite element (FE) simulations using various constitutive models. Three yield functions, von Mises, Hill's 1948, and Yld2000-2d, were considered to examine the effect of the yield criterion on formability. The anisotropy parameters were determined from different experimental tests and their influences on LDH predictions were analyzed. For Hill's 1948 model, the coefficients were calculated either using the yield stresses or r-values measured in different tension directions. The anisotropy coefficients of the Yld2000-2d were determined using in-plane biaxial test data in addition to the conventional uniaxial test-based data. The stress-strain curves for hardening characterization were measured using uniaxial and bulge tests. The latter provides the flow stress over an extended strain range, compare with uniaxial tension, without showing instability. The constitutive models were implemented in a FE code with a user material subroutine. They were evaluated by comparing the experimental and predicted punch load–displacement and sheet thickness variations after forming in the LDH test. The results for this particular example demonstrated that the non-quadratic yield function and the hardening curve of the bulge test improve the prediction accuracy for sheet forming and formability analyzes significantly.     

Design and analysis of new test method for evaluation of sheet metal formability

A new test method including the tool shape and test procedure was developed to evaluate sheet metal formability using the finite element method (FEM). This method is intended to generate the various modes of deformation and to control the onset of failure independently under each mode so that the forming limit diagram (FLD) achieves a good representation of a wide range of strains.A blank holder force-punch stroke diagram with three failure loci is introduced to define the optimum process condition and the formability index by which each material is quantitatively evaluated. The test procedure of this method consists of three steps: drawing a blank holder force (BHF)-punch stroke diagram, measuring strains from the part stamped at the optimum process condition, and grading the test materials using the formability index. In numerical simulations under optimum process conditions, sheet metals can fail due to multi-mode rupture; this failure leads to a widely balanced strain distribution in the FLD such that strains are developed near the forming limit over a wide range of forming modes.Experiments were conducted on three grades of steel sheets to validate the proposed method. Stamping results yield well-defined strain signatures having a wide range of strain distribution in the FLD in all materials tested. The outcomes of the shape and strain behaviors agree well with the numerical results.     

R-adapted arbitrary lagrangian-eulerian finite-element method in metal-forming simulation

In this article, mesh adaptation techniques have been used with the arbitrary Lagrangian-Eulerian finite-element method for analysis of metal-forming problems. The r-method of node relocation has been found suitable for this purpose and is driven by errors based on effective plastic strain. Two forming simulations for elastic-viscoplastic materials have been executed under plane-strain conditions, and the effect of mesh adaptation has been studied.     

Formability evaluation for hot-rolled HB780 steel sheet based on 3-D non-quadratic yield function

A common practice to evaluate formability in the typical sheet metal forming process is to measure hardening behavior and a forming limit diagram as separate material properties, and perform numerical forming simulations utilizing various yield functions. The measured forming limit diagram is applied as the failure criterion. However, the performance of material properties such as hardening behavior and yield functions in predicting strain localization in the simple tension and forming limit diagram tests is seldom validated before their application to forming simulation. In this study, a new numerical formability evaluation procedure was proposed, in which not only hardening behavior but also measured forming limit data were employed in characterizing the input data for the hardening behavior and the yield function. Besides, strain localization was directly monitored to determine failure without employing any forming limit criterion. The new procedure was applied for rather thick advanced high strength hot-rolled steel sheet so that 3-D continuum elements were utilized along with 3-D non-quadratic Hosford and quadratic Hill yield functions.     

Investigations Into the Influence of Weld Zone on Formability of Fiber Laser-Welded Advanced High Strength Steel

In this study, two different dual phase steel grades DP980 and DP600, and IFHS steel sheets were laser welded by a 2-kW fiber laser. The weld quality of these three different LWBs was assessed with the help of microstructure, micro-hardness and transverse tensile tests. Tensile testing of longitudinal and miniature samples was performed to evaluate the mechanical properties of the weld zone. Formability of parent materials and LWBs were assessed in bi-axial stretch forming condition by Erichsen cupping test. To validate the weld zone properties, 3-D finite element models of Erichsen cupping test of LWBs was developed, and the failures in the deformed cups were predicted using two theoretical forming limit diagrams. It was observed that hardness of the fusion zone and HAZ in laser welded DP600 and IFHS steels was more compared to the respective parent metal. However, 29% reduction in hardness was observed at the outer HAZ of DP980 steel weldments due to tempering of martensite. Reduction of formability was observed for all the LWBs with two distinct failure patterns, and the maximum reduction in formability was observed in the case of DP980 LWBs. The presence of the soft zone is detrimental in forming of welded DP steels.     

Prediction of spring-back and side-wall curl in 2-D draw bending

Accurate prediction of spring-back is essential for the design of tools used in automotive sheet-stamping operations. The 2-D draw bending operation presents a complex form of spring-back occurring in sheet-metal forming since the sheet undergoes stretching, bending and unbending deformations. These three sets of deformation can create complex stress-strain states in the sheet which result in the formation of side-wall curls after the sheet is allowed to unload. Accurate prediction of the side-wall curl requires using finite-element shell models which can account for curvature and stress variation through the thickness caused by bending and unbending of sheet. Since such models are generally computationally intense, an alternative and efficient method of predicting side-wall curls is desirable. This paper describes a novel and robust method for predicting spring-back and side-wall curls in 2-D draw bending operations, using moment-curvature relationships derived for sheets undergoing plane-strain stretching, bending and unbending deformations. This model makes use of the membrane finite-element solution to calculate spring-back. The accuracy of the model is verified by comparison with finite element (ABAQUS) and experimental results.     

Comparison of formability of steel strips, which are used for deep drawing of stampings

The paper concerns evaluation and comparison of formability of steel strips, which are used in Czech Republic for production of intricate deep stampings. The properties of sheet-metal which have the principal influence upon the success of deep drawing or strech-forming are described. Two methods used for determination of strain-hardening exponent are compared. It is concluded, that the method according to SN 42 0436 is suitable for approximation of stress-strain curve of given sheet-metal only from point of view of functional values. The values of strain-hardening exponent, calculated by the method using maximum uniform elongation, are more strongly correlated with pure stretchability than are the values of it, calculated by the method according to SN 42 0436.     

Shell-element formulations in LS-DYNA3D: their use in the modelling of sheet-metal forming

Recent developments in finite-element (FE) analysis include the generation of an increasing number of element formulations. With the burgeoning use of FE simulations for sheet-metal forming, these elements are being applied to finite-strain problems.

This paper examines the cost-benefit relationship of the seven four-noded shell elements currently included in the LS-DYNA3D element library for sheet-metal forming. In order to assess the relative merits of the shell formulations, the Numisheet 93 square benchmark problem was solved using each of the shell formulations. Strain predictions, drawing force, and the relative cpu times are presented. Conclusions are drawn about the cpu cost-effectiveness of the available shell elements.     

Theoretical and numerical study of strain rate influence on AA5083 formability

With the application of new forming techniques (hydroforming, incremental forming), it is necessary to improve the characterization of the formability of materials and in particular the influence of strain rate. This paper begins with the characterization of material behavior of an aluminum alloy 5083 at high temperatures. To describe its visco-plastic behavior, Swift’s hardening law is used and the corresponding parameter values are identified. Then, two different approaches are introduced to construct FLDs (forming limit diagrams) of this alloy sheet and evaluate the effect of the rate sensitivity index on its formability. The first one is theoretical (the M-K model), and an algorithm is developed to calculate the limit strains by this model. In the second approach, the Marciniak test is simulated with the commercially available finite-element program ABAQUS. Based on FEM results, different failure criteria are discussed and an appropriate one is chosen to determine the onset of localized necking. With the material behavior data corresponding to AA5083 at 150 °C, parametric studies are carried out to evaluate the effect of the strain rate sensitivity index. The comparison of results by these two approaches shows the same tendency that an improvement of the formability with increasing strain rate sensitivity is observed. Finally, by consideration of the compensating effects of the strain hardening and rate sensitivity indices, the FLDs of this sheet at 150, 240 and 300 °C are determined and compared. Results show that the formability of AA5083 seems not to be improved up to a certain temperature (between 240 and 300 °C), above this temperature, the formability is greatly enhanced.     

Microstructures,Forming Limit and Failure Analyses of Inconel 718 Sheets for Fabrication of Aerospace Components

Recently, aerospace industries have shown increasing interest in forming limits of Inconel 718 sheet metals, which can be utilised in designing tools and selection of process parameters for successful fabrication of components. In the present work, stress-strain response with failure strains was evaluated by uniaxial tensile tests in different orientations, and two-stage work-hardening behavior was observed. In spite of highly preferred texture, tensile properties showed minor variations in different orientations due to the random distribution of nanoprecipitates. The forming limit strains were evaluated by deforming specimens in seven different strain paths using limiting dome height (LDH) test facility. Mostly, the specimens failed without prior indication of localized necking. Thus, fracture forming limit diagram (FFLD) was evaluated, and bending correction was imposed due to the use of sub-size hemispherical punch. The failure strains of FFLD were converted into major-minor stress space (σ-FFLD) and effective plastic strain-stress triaxiality space (ηEPS-FFLD) as failure criteria to avoid the strain path dependence. Moreover, FE model was developed, and the LDH, strain distribution and failure location were predicted successfully using above-mentioned failure criteria with two stages of work hardening. Fractographs were correlated with the fracture behavior and formability of sheet metal.     

Investigation on ductile fracture in fine-blanking process by finite element method

In order to continuously analyze the whole fine-blanking process.from the geginning of the operation up to the total rupture of the sheet-metal,without computational divergence, a 3-D rigid visco-plastic finite-element method based on Gurson void model was developed.The void volume fraction was introduced into the finite element method to document the ductile fracture of the sheet-metal.A formulation of variation of the rigid visco-plastic material was presented according to the virtual work theory in which both the effects of equivalent stress and hydrostatic pressure in the deformation process were considered.The crack initiation of the sheet was predicted and the crack propagation was geometrically fulfilled in the simulation by separating the nodes according to the stress state.Furthermore.the influences of different state-variables on the deformation process were also studied.     

汽车底盘横梁拉伸时压边力与摩擦润滑条件的数值分析

建立了汽车横梁拉伸的有限元模型,通过数值模拟与实验对比分析,在此基础上讨论了压边力与摩擦润滑条件对板料拉伸过程的影响。     

A comparative estimation of the forming load in the deep drawing process

The deep drawing process is one of the important sheet-metal forming processes. Using this operation, many parts are manufactured in various industries. In this paper, different methods of analysis such as analytical, numerical and experimental techniques are employed to estimate the required drawing force for a typical component. With this regard, the numerical simulations were conducted using the finite-element (FE) method. In these simulations, the effects of the element type on the forming load and the variation of the thickness strain were studied. Moreover, the influences of the friction coefficient on the load–displacement curve of the process and maximum drawing force were quantitatively investigated for both the analytical and FE methods. A die set including a blankholder was designed to carry out the experiments on a 600 kN Instron testing machine. Different analytical relationships suggested by different researchers were also used to calculate the maximum drawing force. The results obtained from these methods together with the numerical results were compared with the experimental findings. Based on this comparison, it was concluded that Siebel’s formula predicts more accurate results, compared with other analytical relationships. It was also found that this formula is more sensitive to the friction coefficient than the finite-element simulations. On the other hand, the shell elements are more suitable than four-node solid elements for the numerical analyses because the relevant FE predictions present much better agreement with the experimental results.     

Logistic regression analysis for experimental determination of forming limit diagrams

The forming limit diagram (FLD) is probably the most common representation of sheet metal formability and can be defined as the locus of the principal planar strains where failure is most likely to occur. Experimental determination of the FLD consists in performing a set of formability tests on a sheet metal blank, where a regular grid has been previously etched. After each test, the deformation of the grid is measured and the relative strains computed. Strains observed closely at the fracture location are related to as ‘failed’ points, while strains observed on the sound areas of the specimens are labelled as ‘safe’ points. Starting from a set of experimental tests, the FLD should be empirically determined through a statistical analysis of collected data. In fact, statistical approaches (such as linear regression) are required to properly account for the internal randomness of failure occurrence. Linear regression, as well as most of the other empirical approaches in the scientific literature, takes into account only information related to the safe points.This paper proposes a different approach, the logistic regression, for the empirical determination of FLDs. Logistic regression allows to directly derive the probability of an event (e.g. the failure) as a function of different predictor variables (both the principal planar strains). Therefore, by using logistic regression, the process designer can directly associate the failure probability to the scrapping costs, in order to economically evaluate a new sheet metal forming operation.Logistic regression allows the determination of the FLD by including information concerning both safe and failed points.     

Finite-element analysis for high-temperature deformation of bulk metallic glasses in a supercooled liquid region based on the free volume constitutive model

A constitutive relation based on the free volume model was developed to describe the strain-rate-dependent deformation behavior of bulk metallic glasses (BMG) at temperatures within the supercooled liquid region (SLR). Validity of the present approach has consequently been assessed by comparing the numerical results obtained from finite-element analyses with the experimental results previously obtained from compression tests of Vitreloy-1 BMG alloy. Finite-element-method simulations combined with free volume constitutive relations were found to reproduce well the plastic deformation behavior of Vitreloy-1 alloy, exhibiting a Newtonian viscous flow without stress overshoot and also a non-Newtonian viscous flow with stress overshoot at temperatures within the SLR. The present approach appears to provide a powerful means of understanding plastic deformation behavior in relation to localized and uniform deformation and also of making reliable formability estimations of BMG alloys.     

A new approach for evaluating sheet metal forming based on sheet drawing test. Application to TRIP 700 steel

Sheet formability has usually been evaluated by experimental tests that act under different conditions to those the material is subjected to during industrial processing. The different variables acting on the process are not split up sufficiently to be separately analysed. In this work, a new approach to evaluate formability in pure shear deformation has been developed. For this purpose, a new apparatus has been devised to do drawing tests to thin sheets which permits the calculation of deformation work as a function of the drawing strain. Moreover, the coefficient of friction under high pressure values can be modelled. One application to TRIP 700 steel and the friction results have been considered up to an apparent pressure of 1900 MPa. Deformation work has been analysed and inhomogeneity deformation has been evaluated in terms of redundant work as a function of the geometry of the die. The obtained results agree with the theory of plasticity and demonstrate the utility of the methodology presented herein.     

Deep drawing of square cups with magnesium alloy AZ31 sheets

The square cup drawing of magnesium alloy AZ31 (aluminum 3%, zinc 1%) sheets was studied by both the experimental approach and the finite element analysis. The mechanical properties of AZ31 sheets at various forming temperatures were first obtained from the tensile tests and the forming limit tests. The test results indicate that AZ31 sheets exhibit poor formability at room temperature, but the formability could be improved significantly at elevated temperatures up to 200 °C. The test results were then employed in the finite element simulations to investigate the effects of process parameters, such as punch and die corner radii, and forming temperature, on the formability of square cup drawing with AZ31 sheets. In order to validate the finite element analysis, the deep drawing of square cups of AZ31 sheets at elevated temperatures was also performed. The experimental data show a good agreement with the simulation results, and the optimal forming temperature, punch radius and die corner radius were then determined for the square cup drawing of AZ31 sheets.