Forming Limit Criterion Research Articles

An Effective Formability Model of Pearlitic Steel Wires in Multi-stage Drawing Process Based on the Stress-Based Forming Limit Criterion

An Effective Formability Model of Pearlitic Steel Wires in Multi-stage Drawing Process Based on the Stress-Based Forming Limit Criterion

Shear Fracture Criterion of Advanced High-Strength Steel Based on Stress Triaxiality and Equivalent Strain

Abstract Advanced high-strength steel (AHSS) is increasingly used in the automotive industry due to its higher strength and lower weight. The traditional forming limit criterion cannot accurately predict the unique shear fracture of AHSS, so great efforts have been made to develop failure criteria that can predict shear fracture. In this paper, a series of tensile and shear tests for four steel sheets of AHSS are designed, the stress triaxiality and equivalent strain to fracture are solved, and the correlation between them and the performance parameters of steel sheets K and n is studied. In order to study the relationship between stress triaxiality and equivalent strain to fracture in the range of low-stress triaxiality, the Hill'48 orthotropic model and modified Mohr–Coulomb (MMC) fracture model were used to establish tensile and shear fracture models of four dual-phase sheets of steel, simulating and studying the plastic fracture of AHSS. Solving the relevant parameters enriches the stress triaxiality of the four steel types, establishes the relationship between the stress triaxiality and the equivalent strain to fracture, and verifies its correctness through tensile and bending tests and simulations. The results show MMC can accurately predict the fracture of these four dual-phase steels, and the quantitative relationship between stress triaxiality and equivalent strain to fracture of the four dual-phase steels in the low-stress triaxiality range 0–0.3 is similar, which can be established and expressed by the performance parameters of each steel type.

Study on formability and failure modes of steel/CFRP based FMLs consisting of carbon fiber reinforced polymer prepreg and steel sheet

Due to the potential application need of the automotive and transportation industry for Fiber metal laminate parts made of steel sheets and carbon fiber reinforced polymer (i.e., Steel/CFRP based FML parts), the related combined forming process of FML parts has attracted extensive attention in the last decades. In order to design and fabricate the qualified Steel/CFRP based FML auto parts with various plane stress states, it is vital to thoroughly understand the formability and failure modes of Steel/CFRP based FMLs under various forming states and process conditions. Accordingly, in the present work, a series of deep drawing experiments were designed and conducted on Steel/CFRP based FML specimens with various width to embody their special forming features under different stress states. By considering the limit drawing height at fracture for the evaluation indicator of the forming limit of FMLs, authors studied systematically the influence of key process conditions such as lay-up scheme, stamping speed and the number of plies in the carbon fiber reinforced polymer prepreg (i.e.,CFRP prepreg) core on the formability and failure modes of FML specimens with various forming states. The research results are expected to provide a reliable data source for establishing the accurate forming limit criterion of FMLs and optimizing lay-up schemes.

Numerical forming limit prediction for the optimisation of initial blank shape in hot stamping of AA7075

The prediction of failure and optimisation of the initial blank shape of a component formed under the complex thermal and mechanical conditions could not simply rely on its thinning or strain. In contrast, the prediction of forming limit of material as a comprehensive result of temperature, strain rate and loading path is an essential indicator in a non-isothermal hot stamping process. However, it is challenging to implement an advanced forming limit model into conventional finite element (FE) software to simulate the failure of the formed component and thus optimise its initial blank shape. In this work, a unified viscoplastic-Hosford-MK model was developed to post-process the simulated evolutionary thermomechanical characteristics and then numerically predict the forming limit criterion of AA7075 in a hot stamping process, of which results were demonstrated on a dedicated visualiser that independent of FE software. Subsequently, the initial blank shape was optimised by analysing the evolutionary temperature, strain rate and loading path of failure regions. Furthermore, the developed forming limit model and optimised initial blank shape were experimentally verified with an error of less than 10%.

A simplified stress-based forming limit criterion for advanced high strength steel (AHSS)

A methodology for stress-based forming limit analysis has been developed for advanced high strength steel (AHSS). It was proposed that localized necking occurs when a critical normal stress condition is met. Using a basic, isotropic material model (von Mises, power law hardening), the criterion was applied to various 980 Class AHSS. In most cases the simplified criterion adequately described the experimental strain-based forming limit curve (FLC). For AHSS with substantial volume fractions of metastable austenite, a more sophisticated material model and/or an adapted failure criterion will be required. A strong linear relationship was found between the critical normal stress and the measured true stress at maximum load in tension. This empirical functionality applies over a large range of strength levels and may form the basis for a methodology by which FLCs may be estimated from standard tension tests. Finally, in the context of the proposed failure criterion, the effects of work hardening behavior on the “shape” of the strain-based FLC are explored.

Identification of forming limit curve at fracture in incremental sheet forming

Computer-aided manufacturing technology is widely used in the sheet-forming industry to predict forming performance. Strain-based forming limit criterion is popularly used for this purpose. In incremental sheet forming, the forming limit curve at fracture (FLCF) is a line from the equi-biaxial strain-point to plane strain-point and is high in comparison with those in conventional press forming methods. This study aims to empirically define the FLCF, specifically the equi-biaxial strain at fracture which has yet to be experimentally defined. In addition, to confirm the experimental measurement results, the finite element simulation by ABAQUS/Explicit was performed wherein the fitted flow curve of the large-strain range, accompanied with non-associated flow rule yield behaviour, demonstrates good agreement with the experiment. A new stress-strain equation is thus introduced to describe the flow curve in a large-strain range.

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.

Forming-induced Gloss Reduction of Coil Coated Sheets for White Goods

In the household appliance industry piecework coating of body components has been successively substituted by usage of coil-coated sheets. For components with low strains or components not visible for the customer and therefore with no requirements concerning the visual impression these organic-coated materials bear a proper possibility for cost savings. But besides that, for high quality household appliances there are high visual requirements on the front panels. Already the gloss reduction of the coating layer due to higher strains restricts the application for front panels in most cases. From an economic point of view the application of coil-coated sheets even for these components is highly demanded. For an acceptable substitution the resulting paintwork properties after the forming process should be able to forecast within numerical simulations. Therefore the forming-induced gloss reduction of the respective coated material has to be determined in a proper manner.This paper deals with analyses concerning the forming-induced and strain-state-depending gloss reduction of a coil-coated material commercially used for white goods components. The investigations include measurements of strains and gloss by using an in situ approach. For that purpose, material specimens are formed using a modified experimental setup referring to the Marciniak-Test (ISO 12004-2). A fundamental advantage of the in situ measurements is a minor demand of experiments together with a high resolution of the measured variables. In conclusion, based on the experimental results a conceivable forming limit criterion is defined and integrated in an exemplarily simulation model. The front panel of a front-loading washing machine is used as a practice-oriented application example. Using of the pursued approach improper gloss reductions on the formed panel can be predicted within forming simulation.

Prediction and Experimental Validation of Forming Limit Curve of a Quenched and Partitioned Steel

Forming limit curve (FLC) is an effective tool to evaluate the formability of sheet metals. An accurate FLC prediction for a sheet metal is beneficial to its engineering application. A quenched and partitioned steel, known as QP980, is one of the 3rd generation advanced high strength steels and is composed of martensite, ferrite and a considerable amount of retained austenite (RA). Martensite transformation from RA induced by deformation, namely, transformation induced plasticity (TRIP), promotes the capability of work hardening and consequently formability. Nakazima tests were carried out to obtain the experimental forming limit strains with the aid of digital image correlation techniques. Scanning electron microscopy (SEM) was employed to examine the fracture morphologies of Nakazima specimens of the QP980 steel. The observed dimple pattern indicated that tensile stress was the predominant factor which led to failure of QP980 specimens. Therefore, maximum tensile stress criterion (MTSC) was adopted as the forming limit criterion. To predict the FLC of QP980 steel, Von-Mises yield criterion and power hardening law were adopted according to the tested mechanical properties of QP980 steel. Results were compared with those derived from other three representative instability theories, e. g. Hill criterion, Storen-Rice vertex theory and Bressan-Williams model, which shows that the MTSC based FLC is in better agreement with the experimental results.

Fracture-based forming limit criteria for anisotropic materials in sheet metal forming

This paper is concerned with modeling of fracture-based forming limit criteria for anisotropic materials in sheet metal forming to predict the sudden fracture in complicated forming processes. The Lou–Huh ductile fracture criterion is modified using the Hill's 48 anisotropic yield function instead of the von Mises isotropic yield function to take account of the influence of anisotropy on the equivalent plastic strain at the onset of fracture. For the derivation of an anisotropic ductile fracture criterion, the principal stresses (σ1,σ2,σ3) are expressed in terms of the stress triaxiality, the Lode parameter, and the equivalent stress (ηH,LP,σ¯H) based on the Hill's 48 yield function. Three different kinds of fracture-based forming limit criteria are suggested and investigated with an assumption that the stress state is under the plane stress condition with proportional loading. To determine the parameters of the model proposed, the two-dimensional digital image correlation (2D-DIC) method is utilized to measure the strain histories on the surface of three different types of specimens during deformation and the measurement results are investigated to identify the anisotropy effect on the equivalent plastic strain at the onset of fracture. This paper also discusses about a scaling method for a strain-based fracture forming limit criterion in order to capture the onset of fracture using a single forming limit curve for an anisotropic material. From the comparison of various forming limit criteria suggested, it is concluded that a polar effective plastic strain-based (PEPS) fracture forming limit diagram (FFLD) is suitable for prediction of the sudden fracture in AHSS sheets in complicated sheet metal forming processes on the basis of its path independence and simplicity of measuring strains in real forming processes.

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.

Stress based prediction of formability and failure in incremental sheet forming

A strain-based forming limit criterion is widely used in sheet-metal forming industry to predict necking. However, this criterion is usually valid when the strain path is linear throughout the deformation process [1]. Strain path in incremental sheet forming is often found to be severely nonlinear throughout the deformation history. Therefore, the practice of using a strain-based forming limit criterion often leads to erroneous assessments of formability and failure prediction. On the other hands, stress-based forming limit is insensitive against any changes in the strain path and hence it is first used to model the necking limit in incremental sheet forming. The stress-based forming limit is also combined with the fracture limit based on maximum shear stress criterion to show necking and fracture together. A derivation for a general mapping method from strain-based FLC to stress-based FLC using a non-quadratic yield function has been made. Simulation model is evaluated for a single point incremental forming using AA 6022-T43, and checked the accuracy against experiments. By using the path-independent necking and fracture limits, it is able to explain the deformation mechanism successfully in incremental sheet forming. The proposed model has given a good scientific basis for the development of ISF under nonlinear strain path and its usability over conventional sheet forming process as well.

Forming limit criterion for ductile anisotropic sheets as a material property and its deformation path insensitivity, Part II: Boundary value problems

In the common industrial thin sheet metal forming process at room temperature, in which in-homogenous deformation under the plane stress condition is typically the case, sheets are so ductile that sheet forming more often fails after abruptly severe strain localization, especially in the thinning mode. In such a case, measuring the fracture property might be impractical and an alternative criterion to measure sheet proneness to abruptly severe strain localization according to deformation modes, often dubbed as the forming limit criterion, replaces the fracture criterion to account for formability of the sheet, assuming that the criterion is applicable as a material property. However, severe strain localization is a mathematical consequence (of the boundary value problem) of the principle of linear momentum and the constitutive law; therefore not a part of material properties in principle, regardless of its sensitivity to deformation path. Nonetheless, the assumed applicability of the forming limit criterion as a material property in approximation for room temperature forming under the plane stress condition was partially validated in Part II in view of regular and modified hemispherical dome stretching and circular cup drawing tests, while its deformation path insensitive formulae were theoretically justified in Part I by examining the isotropic hardening formulation of rigid-plasticity and also theoretical forming limit models including the Considère (1885), Dorn (1947) and Hill (1952) models as well as the M–K (1967) model.

Forming limit criterion for ductile anisotropic sheets as a material property and its deformation path insensitivity. Part I: Deformation path insensitive formula based on theoretical models

In the common industrial thin sheet metal forming process at room temperature, in which in-homogenous deformation under the plane stress condition is typically the case, sheets are so ductile that sheet forming more often fails after abruptly severe strain localization, especially in the thinning mode. In such a case, measuring the fracture property might be impractical and an alternative criterion to measure sheet proneness to abruptly severe strain localization according to deformation modes, often dubbed as the forming limit criterion, replaces the fracture criterion to account for formability of the sheet, assuming that the criterion is applicable as a material property. However, severe strain localization is a mathematical consequence (of the boundary value problem) of the principle of linear momentum and the constitutive law; therefore not a part of material properties in principle, regardless of its sensitivity to deformation path. Nonetheless, the assumed applicability of the forming limit criterion as a material property in approximation for room temperature forming under the plane stress condition was partially validated in Part II in view of regular and modified hemispherical dome stretching and circular cup drawing tests, while its deformation path insensitive formulae were theoretically justified in Part I by examining the isotropic hardening formulation of rigid-plasticity and also theoretical forming limit models including the Considère (1885), Dorn and Thomsen (1947) and Hill (1952) models as well as the M–K (1967) model.

Comparative analysis between stress- and strain-based forming limit diagrams for aluminum alloy sheet 1060

The forming limit diagram (FLD) and forming limit stress diagram (FLSD) of aluminium alloy 1060 under linear and nonlinear strain paths are investigated. The calculation of FLSD is based on experimental FLD using the method proposed by Stoughton. Different from the FLD that varies with the strain path, the FLSD is not sensitive to the strain path. Therefore, FLSD is convenient as a forming limit criterion for multi-stage sheet forming. The influences of the material's yield criteria on FLSD are also discussed by comparison of the Hill's 48, Hill's 79 and Hosford non-quadratic criterion. The impacts of material hardening laws (Voce and Swift models) on translation of FLD and FLSD are analyzed. The Voce hardening law and the Hosford yield criterion are appropriate for the FLSD calculation of the aluminium alloy 1060. The stress calculation program and display interfaces of FLD and FLSD are developed on MATLAB, where the strain data can be input from experiment measurement or FEM calculations.

A practical method to evaluate the forming severity of tubular hydroformed parts

In view of the prevalence of non-linear strain paths that develop in parts that are formed in multiple stages, such as bent and hydroformed structural components, the conventional forming limit curve (FLC) cannot be used to assess the forming severity of this manufacturing process. A path-independent stress-based forming limit criterion has been shown to be far more suitable to evaluate such parts, and this paper shows how this failure criterion can be effectively used to evaluate tubular hydroformed parts “on the shop floor”. Knowing the strain history in a given location of a part, a shifted FLC can be computed from the stress-FLC and used to determine the safety margin at this location. This methodology was used to evaluate the forming severity of an automotive instrument panel beam. It was found that this approach is user-friendly and provides a significant improvement in the ability to assess process robustness and product quality compared to the conventional method. The FLCs obtained using the proposed method were found to be in good agreement with those predicted with an MK-based calculation code. Finally, it is shown that a numerical simulation of the entire forming process is recommended to confirm the estimated strain path in critical locations and improve the accuracy of the method.

Application of an Extended Stress-Based Forming Limit Curve to Predict Necking in Stretch Flange Forming

An extension of the stress-based forming limit curve (FLC) advanced by Stoughton (2000, “A General Forming Limit Criterion for Sheet Metal Forming,” Int. J. Mech. Sci., 42, pp. 1–27) is presented in this work. With the as-received strain-based FLCs and stress-strain curves for 1.6-mm-thick AA5754 and 1-mm-thick AA5182 aluminum alloy, stress-based FLCs are obtained. These curves are then transformed into extended stress-based forming limit curves (XSFLCs), which consist of the invariants, effective stress, and mean stress. By way of application, stretch flange forming of these aluminum alloy sheets is considered. The AA5754 stretch flange displays a circumferential crack during failure, whereas the AA5182 stretch flange fails through a radial crack at the edge of the cutout. It is shown that the necking predictions obtained using the strain- and stress-based FLCs in conjunction with shell element computations are inconsistent when compared with the experimental results. By comparing the results of the shell element computations with those in which the mesh comprises eight-noded solid elements, it is demonstrated that the plane stress approximation is not valid. The XSFLC is then used with results from the solid-element computations to predict the punch depths at the onset of necking. Furthermore, it is shown that the predictions of failure location and failure mode obtained using the XSFLC are in accord with the differences observed between the two alloys/gauges.

Bursting failure prediction in tube hydroforming using FLSD

In tube hydroforming, circular components are hydrobulged or hydroformed from tubular blanks with internal pressure and simultaneous axial loading. Thus the tube can be fed into the deformation zone during the bulge operation allowing more expansion and less thinning without any defects such as wrinkling, buckling, and bursting. By contrast with the buckling and the wrinkling, the bursting is generally classified as an irrecoverable failure mode. Hence in order to obtain the sound hydroformed products, it is necessary to predict the bursting behavior and to analyze the effects of process parameters on this failure condition in hydroforming processes. In this study, a forming limit stress diagram (FLSD) is constructed by plotting the calculated principal stresses based on the local necking criterion. Using the theoretical FLSD, we carry out the numerical prediction of bursting failure in a hydroforming process, which usually has non-linear strain path. Finite element analyses are carried out to find out the state of stresses during simple hydroforming operation, in which the FLSD is utilized as the forming limit criterion for assessment of the initiation of necking, and influences of the material parameters on the formability are investigated. In addition, the numerical results obtained from the FEM combined with the FLSD are confirmed with a series of bulge tests in view of bursting pressure and show a good agreement. Consequently, it is shown that the theoretical and numerical approach to bursting failure prediction proposed in this paper will provide a feasible method to satisfy the increasing practical demands for assessment of the forming severity in hydroforming processes.

Analytical and numerical analysis of sheet metal instability using a stress based criterion

Strain based Keeler–Goodwin diagrams are widely used in forming processes to predict onset of local necking. Plastic instability is determined once the forming limit strain is exceeded. Use of these diagrams requires proportional strain paths, which is not necessarily the case in sheet metal forming operations. In many forming processes, the strain path changes during deformation. This may change the forming limit curve significantly. In the paper, a stress based forming limit criterion is adopted to deal with strain path non-linearities. Comparisons with earlier published work on forming limits are made through analytical considerations. Furthermore, the criterion is implemented into the finite element code LS-DYNA and verified numerically against results from large scale bulge tests.

Development and Application of the Finite Element Analysis Program of the Stress-Based Forming Limit Criterion for Sheet Metal Forming

In order to solve the problem existed in the numerical simulation of sheet metal forming for its use the strain-based forming limit diagram as criterion, which has the flaw of dependence on the strain paths, this paper develops the finite element analysis program based on the stress forming limit criterion applicable to the blank plastic forming technique, which follows the stress-strain transformation relationship when the sheet metal is undergoing plastic deformation, chooses Hill’s quadratic normal anisotropic criterion as computational model and selects the commercial finite element code Dynaform as its development environment. Also it be analyzed the finite element numerical simulation results of two deep drawing parts by the developed program module and realizes the prediction of sheet metal forming limit adopting the FLSD as criterion. The stress-based forming limit criterion for the developed program provides a new means to analyze the forming limit for the multistage sheet metal forming.