Conventional Forming Limit Curve Research Articles

An extended stress-based forming limit diagram focusing on the wrinkling phenomenon and the effect of the normal pressure on clamped surfaces

A novel wrinkling limit representation following the pattern of the conventional forming limit curves (FLCs) and the stress-based forming limit curves (SFLCs) as well as the application of the assumed criterion in finite element modelling are discussed in this manuscript. FLCs can partially refer to the wrinkling potential in the area left to the uniaxial tension line, but just like the SFLCs, cannot characterize the limits of the material behavior in a deeper sense, if negative in-plane stress and normal pressure act together on the sheet. This study predicts the wrinkling risk of clamped surfaces with a stress-based criterion through solving the analytical equations of the critical compressive stress causing wrinkling, and the corresponding blank holder pressure. The critical values were calculated based on the Wang and Cao’s theory using Hill48 anisotropic yield function coupled with the Swift hardening law. The results draw a novel wrinkling limit curve representation methodology, in which the minor stress responsible for wrinkling and its ratio to the major stress are distinguished in the function of the applied blank holder pressure. The applicability of the calculated curves was investigated using finite element simulations, which showed that this method provides the opportunity to quantitatively interpret how close a component is to the wrinkling limit. The calculated wrinkling tendencies were verified by standard cup drawing tests supplemented by round shape error measurements on three different automotive steel sheets. It can be stated that the obtained numerical conditions of wrinkling were fitted to the experiments fairly well.

A general instability framework for ductile metals in complex stress states from diffuse to acute localization

Adoption of stress-based forming limit curves (FLC) and their equivalent strain representations were introduced to overcome the path dependence of the conventional strain-based FLCs. The stress state and its instantaneous magnitude govern formability such that the triaxial stress state, induced through tool contact, can no longer be neglected. The present work reveals that in addition to the composition of the stress state, the boundary conditions of how the stress is applied to the material determine the onset of plastic instability. To this end, the relatively unknown generalized instability model of Hillier, derived from a stable bifurcation of the stress state under neutral stability, is revisited. Analytical solutions for instability in triaxial plane strain loading were derived for boundary conditions of a proportional, constant, or evolving contact pressure that enables critical evaluation of phenomenological plane stress mapping criteria proposed in the literature. As part of this work, the Hillier instability framework is extended to model the localization process under the constraint of quasi-stable plastic flow in arbitrary principal stress states to form the Generalized Incremental Stability Criterion (GISC). It is shown that the Modified Maximum Force Criterion (MMFC) emerges as one of many special cases of the GISC when restricted to plane stress proportional stressing with a prescribed minor load. Finally, the GISC is applied to Marciniak and Nakazima formability tests of a DP980 steel for identification of appropriate boundary conditions.

Fracture Characterisation by Butterfly-Tests and Damage Modelling of Advanced High Strength Steels

Advanced High Strength Steels (AHSS) are widely used in today's automotive structures for lightweight design purposes. FE simulation is commonly used for the design of forming processes in automotive industry. Therefore, besides the description of the plastic flow behaviour, also the definition of forming limits in order to efficiently exploit the forming potential of a material is required. AHSS are prone for crack appearances without prior indication by thinning, like exemplary shear fracture on tight radii and edge-fracture, which can not be predicted by conventional Forming Limit Curve (FLC). Stress based damage models are able to do this. However, the parameterisation of such models has not yet been standardised. In this study a butterfly specimen geometry, which was developed at the Institute for Forming Technology and Machines (IFUM), was used for a stress state dependent fracture characterisation. The fracture behaviour of two AHSS, CP800 and DP1000, at varied stress states between pure shear and uniaxial loading was characterised by an experimental-numerical approach. For variation of the stress state, the specimen orientation relative to the force direction of the uniaxial testing machine was orientated at different angles. In this way, the relevant displacement until fracture initiation was determined experimentally. Subsequently, the experimental tests have been numerically reproduced giving information about the strain and stress evolution in the crack impact area of the specimen for the experimentally identified fracture initiation. With the help of this testing procedure, two different stress-based damage models, Modified Mohr-Coulomb (MMC) and CrachFEM, were parameterised and compared.

Influence of Pre-Stretching Levels on the Forming Limit Strain and Stress Curves of High Strength Steel Sheet

In this work, Forming Limit Curves (FLCs) of the conventional and pre-stretched High Strength Steel (HSS) sheet grade 440 (SCGA440-45) were investigated. The conventional forming limit curve was experimentally determined by using the Nakajima stretching test. Subsequently, the non-linear strain path FLCs were precisely developed through the Nakajima stretching test after the specimens were pre-stretched in biaxial direction up to several levels on the Marciniak In-plane stretching test. The gained non-linear strain path FLCs were compared with the conventional FLC.Additionally, the experimental Forming Limit Stress Curve (FLSCs) were calculated using the experimental FLC and non-linear strain path FLCs data from investigated steel sheet. The yield criterion Hill’48 was employed in combination with the Swift strain hardening law to describe anisotropic deformation and plastic flow behavior of the HSS sheet, respectively. Hereby, the influence of pre-stretching levels on the experimentally determined the FLCs and FLSCs were examined. The results prove a significant influence of the pre-stretching levels on the both FLCs and FLSCs of the investigated HSS sheet. For a low pre-stretching in biaxial loading the FLCs demonstrated a reduced formability and the FLSCs exhibited the limited stress levels depending on the experimental FLC data.

Analysis of the failure of H240LA steel sheets subjected to stretch-bending conditions

Industrial sheet metal forming processes with certain complexity involve intrinsically non-linear strain paths, abrupt changes in the local strain ratio (β) due to successive stages during the manufacturing operation and/or the existence of strain/stress gradients through the sheet thickness due to the simultaneous action of stretching and bending. Under these situations, both the use of classical failure criteria assuming a uniform strain/stress distribution across the sheet thickness and the use of strain-path dependent metrics, such as the conventional FLC (Forming Limit Curve), for assessing sheet formability are highly questionable. In this work a failure model for stretch-bending which combines both the use of a path-independent formability diagram, based on the polar equivalent plastic strain curve (epFLC), along with different rules to account for the influence of the stress/strain gradient across the sheet thickness, particularly the Mid-Plane Rule (MPR), Concave-Side Rule (CSR) and Convex-Side Rule (CxSR), is explored. Their capabilities to predict failure by necking in a series of stretch-bending tests over H204LA steel sheets of 1.2 mm thickness are discussed in the light of experimental results. To this end, a 3D calibrated numerical model was used to precisely describe the realistic distribution of stresses/strains across the sheet thickness.

Application of an advanced necking criterion for nonlinear strain paths to a complex sheet metal forming component

For meeting time, cost and quality targets in industrial sheet metal forming processes, correct formability prediction in a very early project stage has become a crucial factor. It is well known that the conventional Forming Limit Curve (FLC), which is most commonly used for this purpose, is only valid for linear strain paths. Yet, in most industrial sheet metal components, the occurring strain paths are nonlinear. Due to this fact, most users apply a safety margin of 10 to 20% when using the Forming Limit Diagram for formability prediction resulting in higher process robustness, but also increasing component weight and material costs in production. Reasons for the broad application of the FLC in industry is the simple experimental determination of the curve as well as the easy implementation in finite element post-processing. In this paper, an advanced failure criterion for nonlinear strain paths is presented and applied to a deep drawn door inner part. The investigated deep drawing specimen was manufactured using the aluminium alloy AA6014 T4 and the dual phase steel DP600. The sheet thickness was chosen to be closely to 1.0 mm. The calibration procedure of the criterion for arbitrary sheet materials is based purely on uniaxial tensile test data. Experiments for the calibration of the model as well as the application of the criterion to an experimental stamping part will be explained in the paper. Finally, a comparison of the newly presented model with conventional formability evaluation using standard FLC will be given.

A microstructure based modelling of high strength steel sheet under stretch-bending

In the automotive industry, advanced high strength (AHS) steel sheets are widely used for various structural and safety parts in car body. Such AHS steels exhibit complex microstructures containing different phase constituents. The yield and tensile strength of these steel sheets are significantly increased, but the formability is very restricted due to earlier occurred local damages. Their fracture behaviours are thus strongly governed by the microstructure characteristics and interplays between various phases. Besides, the forming processes of AHS parts mostly showed a non-linear strain history, for which the conventional forming limit curve (FLC) could not be properly applied. In this work, stretch-bending tests were carried out for the AHS steel sheet grade 980 after subjected to different pre-strains. FE simulations on the micro-scale of the forming experiments were performed by using 2D representative volume element (RVE) model, which was generated from the real microstructure of examined steel. Hereby, local crack occurrences in the microstructure of steel were described. Furthermore, the FE results by using isotropic and kinematic hardening law were compared. Finally, the bending limits of steel grade 980 after varying pre-strains were predicted.

Predicting shear fracture of aluminum 6016-T4 during deep drawing: Combining Yld-2000 plasticity with Hosford–Coulomb fracture model

Shear fracture cannot be predicted with conventional forming limit curves even though it often limits the formability of modern engineering materials. To circumvent the need of a special set of ductile fracture experiments in addition to standard forming experiments, a hybrid experimental–numerical procedure is proposed to identify the three material parameters of the Hosford–Coulomb fracture initiation model from the same experiments that are used to identify the forming limit curve. To increase the reliability of the model identification, a cup drawing experiment is proposed to characterize the fracture response of out-of-plane shear loading. Uniaxial tension, bulge, Nakazima and drawing experiments are performed on specimens extracted from 1 mm thick aluminum 6016-T4 sheets. The anisotropic Yld2000 plasticity model with self-similar Swift-Voce hardening is identified to describe the large deformation response. The loading paths to fracture for stress states ranging from pure shear to equi-biaxial tension are obtained from detailed numerical simulations of all forming experiments. The identified material parameters of the Hosford–Coulomb model reveal that the fracture response of the aluminum 6016-T4 alloy is highly Lode angle dependent. Aside from identifying the anisotropic plasticity, the forming limit curve and the stress-state dependent fracture model, the deep drawing of a complex three-dimensional part with a triangular-shaped die is performed experimentally and simulated to validate the models at the structural level.

Bending Limit Curves in Sheet Metal Bending Evaluation

Bending and hemming process are used in automotive industries for assembling the car body panel.The main failure mechanism under bending loads is the intercrystalline fracture. This is due to the fact that the Forming Limit Curve (FLC) describes first occurrence of membrane instability and no material failure in consequence of an intercrystalline fracture at bending.The FLC fails to predict the formability in hemming processes since difference in failure mechanism. A new failure criterion, the so-called Bending Limit Curve (BLC) has been developed. In this work, the left hand side BLCs are experimentally determined for Advanced High Strength Steel grade DP1000, Stainless Steel grade SUS430 and Deep Drawing Steel grade SPCC having a thickness of 1.0 mm. The influence of various bending radii and level of pre-strain on the bending strains are investigated and discussed by using the Three Point Bending Test. Bendability of investigated materials are evaluated by using optical strain measurement system GOM-Aramis to determine maximal achievable bending strain on the specimens. The developed left hand side BLCs were found to be higher level than conventional FLCs. The bigger bending radius established lower bending limit strain. The higher bending strain was obtained from the higher pre strain level.

Modeling of the ductile fracture during the sheet forming of aluminum alloy considering non-associated constitutive characteristic

This research was aimed to predict the ductile fracture for aluminum alloy 5083-O sheet using a phenomenological Modified Mohr-Coulomb fracture (MMC) criterion. The plasticity anisotropy of sheet was described by a non-associated constitutive relationship whose yield function and plastic potential function were represented by two different Hill’48 functions. The parameters of Hill’48 functions were calibrated on the basis of yield stresses and Lankford r-values, respectively. The loading paths of critical points for six specimens were utilized to calibrate the parameters of MMC fracture model. The determined non-associated constitutive relationship and MMC fracture model were validated to be able to predict the tension-dominated fracture mode of a modified compact-tension (MCT) specimen as well as shear-dominated fracture of a simple shear specimen. Besides, the fracture forming limit curve expressed by major strain and minor strain was derived directly from the MMC fracture model and its advantages were evaluated by comparing it with the conventional forming limit curve.

Investigations on fracture curves in strain and stress space for advanced high strength steel forming

Conventional forming limit curves (FLCs) are inappropriate for describing formability for advanced high strength (AHS) steel sheets, since such steel grades experience fracture without localized necking occurrence. The aim of this work was to develop a fracture curve (FC) for the AHS steel grade DP980. The FC was determined by means of the Nakajima stretch forming test and tensile tests of various sample geometries, by which shear fracture governed. An optical strain measurement system was used to capture strain histories of deformed samples up to failure. From these results, fracture strains were gathered and plotted in a strain space. Subsequently, the strain based curve was transformed to space between stress triaxiality and plastic strain. Hereby, effects of anisotropic yield function, namely, the Hill’48 model on obtained stress fracture loci were investigated. In order to verify applicability of the determined limit curves, a Mini-tunnel part was pressed and simulated. It was found that the stress based FC do predict failure of the DP980 steel sheet more accurately than the strain based F C.

EXPERIMENTAL FLC DETERMINATION OF HIGH STRENGTH STEEL SHEET METAL

To assess formability in sheet forming, experimentally determined Forming Limit Curves (FLC) are often used. These conventional FLCs represent the forming limits (i.e. onset of necking) of a sheet material subjected to in-plane deformation or almost in-plane deformation. A widely used approach to experimentally determine the onset of necking of sheet material subjected to in-plane and almost in-plane deformation is formulated in ISO 12004. The aim of this work is to investigate limit strains for deep drawing quality sheet metal of HX180BD with nominal thickness 0.6 mm. The FLC curve has been measured by implementation of Nakajima test on universal testing machine Erichsen 145-60. The Nakajima test has been measured according to EN ISO 12004-2. Limit strains have been measured using 3D photogrammetric system ARAMIS by GOM. Forming limit curve was evaluated both the section method and the time dependent technique. The resulting experimental FLC curves were compared. With the time based method for the determination of FLC a greater strain values was achieved.

Curvature Based Forming Limit Prediction of High-Strength Steel Components with Superimposed Stretching and Bending in the Deep Drawing Process

The state of deformation in deep drawing operations is characterized by superimposed stretching and bending (i.e. stretch-bending). Bending effects, especially for Advanced High Strength Steels (AHSS) are known to influence the material formability. Traditional formability measures such as the Forming Limit Curve (FLC) fail to reliably predict stretch-bending formability. Consequently, to ensure an efficient and economical use of AHSS in the industrial application, current research work is focusing on the reliable numerical prediction of stretch-bending formability of AHSS sheets.Within this work, a phenomenological concept to predict the forming limit (e.g. the onset of necking) in deep drawing processes taking bending effects into account is presented. The proposed concept is based on curvature-dependent (i.e. regarding the principle curvatures κ1 and κ2 of the stretch-bend (convex) sheet surface) forming limit surfaces representing the probability of failure and is calibrated with experimental results from stretch-bending tests and conventional forming test such as a Nakazima test. The results of the phenomenological forming limit criterion are promising and show a more accurate prediction of the drawing depth at failure than the conventional FLC approach. The method contributes also to a probabilistic view on the forming limit of deep drawing parts.

Establishing a new Forming Limit Curve for a flax fibre reinforced polypropylene composite through stretch forming experiments

In developing an understanding of the failure in natural fibre reinforced polymer composites, the failure limits of this class of the material system are required. It is found that the conventional Forming Limit Curve is not suitable to predict the failure initiated in the natural fibre composite as principal strains cannot differentiate the strain on the flax fibres and the polypropylene matrix. This study proposes a new Forming Limit Curve for the composite which expresses limiting fibre strain as a function of forming mode depicted by the ratio of minor strain to major strain. The new Forming Limit Curve, along with the Maximum Strain failure criterion have been successfully implemented in FEA simulations, and numerical simulations suggest that the former is more accurate. The current work provides an innovative method to predict the onset of failure in natural fibre composites, which can be applied in composite forming and structural design.

A methodology for determination of extended strain-based forming limit curve considering the effects of strain path and normal stress

In this paper, an approach based on the modified Marciniak-Kuczynski (M-K) method for computation of an extended strain-based forming limit curve (FLC) is presented. An extended strain-based FLC is built based on equivalent plastic strains and material flow direction at the end of forming. This curve has some advantages in comparison with other necking criteria such as the traditional FLC and also the stress-based FLC. This new criterion is much less strain path dependent than the conventional FLC. Furthermore, the use and interpretation of this new curve is easier than the stress-based FLC. The effect of strain path on the predicted extended strain-based FLC is reexamined. For this purpose, two types of pre-straining on the sheet metal have been imposed. Moreover, the plane stress state assumption is not adopted in the current study. The verifications of the theoretical FLCs are performed by using some available published experimental data.

Edge cracking mechanism in two dual-phase advanced high strength steels

Abstract One of the manufacturing issues restricting the applications of advanced high-strength steels is edge cracking during forming. Computer simulations using the conventional forming limit curve (FLC) as a failure criterion often fail to predict edge cracking. A new failure criterion is needed to assess the edge stretchability in simulations and applications, subsequently understanding the fracture mechanism in the microstructural scale is a prerequisite. In this study, the edge fracture mechanisms of two selected dual-phase steels (designated as DP980 and IBF980) with identical chemistry but different edge cracking behaviors are studied by controlled edge tension tests and scanning electron microscopy (SEM). The results show that the edge cracking behaviors are essentially fractures propagated from pre-existing microcracks introduced by the shearing process. The dominant edge fracture mechanism is decohesion between the martensite and ferrite phases. This study employs the interfacial strength between ferrite and martensite as an index to predict the material edge cracking resistance. The interfacial strength is calculated to be 1070 MPa for IBF980 and 854 MPa for DP980 using void-nucleation models. This result indicates that IBF980 has a higher resistance to edge cracking and subsequently a higher local formability, which is consistent with the higher hole expansion ratio values observed. Refining the martensite particle size and minimizing banded martensite structures are effective approaches to increase the local formability.

Analysis of the extended stress-based forming limit curve considering the effects of strain path and through-thickness normal stress

In this study, an approach based on the modified Marciniak–Kuczynski (M–K) method for computation of an extended stress-based forming limit curve (FLC) is presented. The extended stress-based FLC is built based on equivalent plastic stress versus mean stress. This curve has some advantages in comparison with the conventional FLC. This new criterion is much more strain path independent than the conventional FLC. The effect of strain path on the predicted extended stress-based FLC is reexamined. For this purpose, two types of pre-straining on the sheet metal have been loaded. Moreover, the plane stress state assumption is not adopted in the current study. The influence of a through-thickness compressive normal stress is also investigated theoretically. The verifications of the theoretical FLCs are performed by using some available published experimental data.

Deformation Scenarios of Combined Stretching and Bending in Complex Shaped Deep Drawing Parts

Abstract. Bending effects, especially for Advanced High Strength Steels (AHSS), are known to influence the material formability when stretching and bending is combined in sheet forming. Traditional formability measures (e.g. the conventional forming limit curve (FLC)) fail to reliably predict formability when bending is added. Consequently, in order to take full advantage of the available forming potential of AHSS sheets in industrial applications and to ensure a reliable failure assessment at the same time, current research is focusing on the experimental characterization and modeling of the influence of bending effects on the AHSS sheets formability in forming scenarios of combined stretching and bending. It is expected that aside parameters such as bending radius or strain ratio, individual deformation scenarios of combined stretching and bending may affect the material formability too. Due to tool geometry and the resulting material flow in deep drawing various complex scenarios of combined stretching and bending can occur. For example, a material element is subjected to a complex deformation history of in-plane stretching with subsequent stretch-bending over a cylindrical tool contour, followed by unbending under tension. Another material element of the same drawing part presumably starts also with in-plane stretching but is consequently stretch-bent over a doubly curved tool geometry. Consequently, comprehensive knowledge on the stretch-bending deformation scenarios prevailing in deep drawing is crucial for a more reliable formability assessment. This work aims to identify and characterize the stretch-bending deformation scenarios to occur in different complex deep drawing parts (i.e. B-pillar, cross-die test) and small scale tests (i.e. Angular Stretch-Bend Test (ASBT)). For this reason, this investigation uses an innovative approach recently developed by some of the authors and published elsewhere to categorize the stretch-bending scenarios in industrial deep drawing processes. The approach consists of a stretch-bending categorization schema and a procedure to categorize the forming scenarios in deep drawing parts using data of finite element (FE) simulations. Results of the categorization can directly be plotted on the FE mesh of the deep drawing part (i.e. map type plot of deformation scenarios). The categorization approach mentioned uses results of conventional shell-type FE forming simulation and is therefore applicable in an industrial environment. The FE forming simulation results of the parts selected were analyzed using the stretch-bending categorization approach to identify which stretch-bending scenarios occur in deep drawing parts, to quantify which scenarios to prevail and to show that the conventional ASBT does not represent all the relevant deformation scenarios that prevail in typical deep drawing parts. Furthermore, with the use of experimental observations from real part forming, the stretch-bending scenarios which are the most critical (i.e. the scenarios under which failure occurs) in forming the cross-die geometry are identified. Results of these analysis are presented and discussed in detail.

Development of a new failure prediction criterion in sheet metal forming

In industrial try-out processes in sheet metal forming usually the forming limit curve is used as failure criterion in order to describe the onset of localized necking. Forming limits, however, are strain-path dependent. Up to today many different approaches how the strain-path dependent behavior of the forming limit curve can be avoided have been published. Best known are the approaches based on forming limit stress curves published by Arrieux, and the approach of Muschenborn published in 1975. An overview over existing failure criteria is given in this contribution. The failure criterion forming limit stress curve as well as several failure criteria based on Muschenborn’s approach will be evaluated with newly recorded experimental data on forming limit curves for non-proportional loading. A new approach, that is in contrast to the two mentioned approaches not based on assumptions but on experimental observations, is presented herein. The suggested approach is presented as failure surface where strains above the surface indicate the onset of localized necking. The failure surface is given as function of the loading mode and the level of effective pre-stretching. Different suggestions how to use and simplify the new approach are given in this paper. The prediction accuracy of the addressed approaches as well as of the newly suggested approach is evaluated by transforming the data of the approaches back into the conventional forming limit curve for several non-linear strain paths. The comparison of the described approaches shows that forming limits for non-proportional loading can be well-predicted with the suggested approach.

On the use of effective limit strains to evaluate the forming severity of sheet metal parts after nonlinear loading

The conventional forming limit curve (FLC) is significantly strain path-dependent and therefore is not valid for formability evaluation of sheet metal parts that undergo nonlinear loading paths during the forming process. The stress-based forming limit curve (SFLC) is path-independent for all but very large prestrains and is a promising tool for formability evaluation. The SFLC is an ideal failure criterion for virtual forming simulations but it cannot be easily used on the shop floor as there is no straightforward experimental method to measure stresses in stamped parts. This paper presents a theoretical basis for predicting the effective limit strain curve (ELSC) using the Marciniak and Kuczynski (MK) analysis (Int J Mech Sci 9:609–620, 1967, Int J Mech Sci 15:789–805, 1973). Since the in-plane strain components are sufficient to calculate the effective strain, the ELSC can easily be determined from strains measured in the stamping plant, and therefore it is a better alternative to the SFLC for formability evaluation. This model was validated using experimental data for AISI-1012 steel (Molaei 1999) and AA-2008-T4 aluminum alloys Graf and Hosford (Metall Trans 24A:2503–2512, 1993). Predicted results showed that, similar to SFLC, the ELSC remains practically unchanged for a significant range of prestrain values under various bilinear loading paths, but some strain-path dependence can be observed for significant magnitudes of the effective prestrain (ee ≥ 0.37 for AISI-1012 steel and ee ≥ 0.25 for AA-2008-T4 aluminum).