Stress-based Forming Limit Diagram 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 Novel Approach for Process and Tool Design During Manufacturing of Industrial Sheet Metal Components

Manufacturing of sheet metal components feeds into several domains such as automotive, aerospace and strategic applications. The optimum process and tool design are crucial in ensuring successful manufacturing of components without developing any defects. The current trend is to do it right the first time during the industrial stamping practice, so that the costly shop floor trials are eliminated or at least minimized. One of the common failures that are observed during manufacturing of industrial sheet metal components is the splitting/cracking. The present work focuses on addressing the design considerations for preventing development of such defects. Traditionally, the strain-based forming limit diagram (FLD) is used to assess if a proposed process and tool design will lead to splitting failures. The approach is to measure or predict the strains that will develop during the stamping process and to infer that splitting failures will occur if these strains are above the FLD. The optimum process and tool design should ensure that the strains developed in the component must be below the FLD. The approach of using the strain-based FLD has serious limitation, as it does not account for the influence of complex strain paths on the forming limit strains. As an alternative, stress-based FLDs have been proposed, which does address the effect of complex strain paths. But, the stress-based FLDs are not intuitive and therefore are not very suitable to use for analysis of industrial sheet metal components. In this work, a novel approach, based on monitoring development of local thickness gradients during manufacturing of sheet metal components, is proposed to assess a given process and tool design for developing splitting/cracking failures. The novel approach is validated for sheets of different metals and thicknesses. The effect of bilinear strains paths on the forming limits is captured and validated using this proposed novel approach. A new approach, based on the novel thickness gradient criteria, is proposed for quantifying the forming severity of industrial sheet metal components.

Influence of anisotropy evolution on strain path independent failure limits

Stress based forming limit diagram (SFLD) and polar effective plastic strain (PEPS FLD) diagram are two techniques reported to be independent of strain path change. Thus, these techniques are capable of predicting failure in pre-strained sheet metal samples. Therefore, in this study evolution in anisotropy properties of sheet metals were considered in terms of evolution in yield shape during conversion of conventional strain based forming limit diagram (FLD) to SFLD and PEPS-FLD. The evolution in anisotropic properties were modelled as a function of effective plastic strain depending on which the anisotropic coefficients of non-quadratic yield model Yld2000-2d were calculated. Further, to analyse the strain path change effect, metal sheets of extra deep drawing quality steels were first deformed under biaxial condition in Marciniak in-plane stretch forming setup. The pre-strained samples were subsequently deformed with hemispherical punch till the necking appears. For failure prediction, finite element modelling of the complete procedure was performed considering evolution in the yield shape. Finally, both the failure criteria were implemented for failure prediction. Implementation of the evolution in yield function in finite element analysis and failure criteria provided better results.

Forming Limit Diagrams of Low-Carbon Steels Obtained Using Digital Image Correlation Technique and Enhanced Formability Predictions Incorporating Microstructural Developments

In the present work, drawing quality (DQ) and interstitial-free (IF) steel sheets were subjected to limiting dome height tests for determining strain-based forming limit diagrams (FLDs) experimentally and effect of dynamic (variable) material properties, such as work hardening ‘n’ and plastic anisotropy ( $$\bar{r}$$ ), on FLDs has been studied and simulated by PAMSTAMP™ finite element software. Dot prints on the steel specimens and an efficient optical strain measurement system GOM™ which works on the digital image correlation technique principle were used to measure limiting strains accurately instead of conventional circle grid analysis technique and strain measurement by traveling microscope. The dynamic (variable) material properties (n) and ( $$\bar{r}$$ ) were estimated by studying the microstructural developments in terms of changes in grain average misorientation and crystallographic texture, respectively, at different strains and strain paths, during deformation. In our proposed work, a novel technique of incorporating dynamic (variable) material properties (n and $$\bar{r}$$ ) in FE simulations was carried out during FLDs predictions. Though marginal but improved predictions in FLDs were observed in both IF and DQ steels. In addition to strain-based FLDs, stress-based FLDs were also determined for both grades. Interestingly, in both cases it was noticed that IF steel had higher formability than DQ steel.

Stress-based forming limit diagrams (SFLD) considering strain rate effect and ductile damage phenomenon

Abstract Although drawing forming limit diagrams is a suitable tool for analyzing material formability, it can only be used when loading is proportional. In other words, when the ratio between main strains stays unaffected during the formation process. Since forming limit diagrams are strictly dependent on strain path, the significance of the limit increases. As the path of the strain changes in a formation process, the forming limit diagrams and therefore the designer's decision changes as well. In order to eliminate this issue, stress-based forming limit diagrams (SFLD) which are independent from the strain path are gaining attention. This paper gives an efficient method to determine the SFLDs and can accurately predict the location for the onset of failure, including strain rate calculations. Furthermore, introducing a damage function based on a simple continuum damage mechanics is dependent on the stress state (Triaxiality and Lode parameters). As a characterization parameter, elastic modulus is eventually chosen to measure the ductile damage in the process of plastic deformation of the material. Furthermore, a UMAT subroutine is developed in finite element simulation by ABAQUS according to original formulations, in order to analyze and link the related essential models. To examine the accuracy of the results from the present simulative study and compare with the experimental results, applicability is considered. Forming limit tests are also performed for St 13 sheets measuring the FLD and then transforming to SFLD. It should be noted that the rule of these simulative SFLDs is in good agreement with the experimental points. Results revealed that the level of the stress-based forming limit diagram for the material St 13 increases with enhancing the strain rate.

Improvement in Accuracy of Failure Prediction in Sheet Hydroforming of Square Cups Using Stress-Based Forming Limit Diagram

Prediction of failure in sheet metal forming processes accurately is very important for successful production and optimization of parameters. A major problem of conventional strain-based forming limit diagrams (FLDs) is their inability to predict failure accurately in processes such as sheet hydroforming where there is a change in strain path and mode of deformation. In the present work, a stress-based forming limit diagram has been developed for AA 5182 alloy sheets modifying the analytical procedure, proposed by Stoughton, to determine forming limits in stress space from failure strains incorporating anisotropy using Balart’s yield criterion. The developed stress-based FLD has been used to predict failure in sheet hydroforming of square cups. Results are compared with Hill’s quadratic yield criterion. Significant difference has been found in failure prediction between strain-based and stress-based criteria when they are applied to sheet hydroforming. A change in strain path has been observed at the critical corner regions in hydroforming of square cups due to initial drawing and then biaxial stretching during calibration. The experimental validation clearly showed that accuracy in failure prediction can be improved in sheet hydroforming by using a stress-based forming limit diagram.

A comparative study of the extended forming limit diagrams considering strain path, through-thickness normal and shear stress

The substitute presentations of the conventional forming limit diagram (FLD) are stress-based forming limit diagram (FLSD), extended stress forming limit diagram (XSFLD), and polar effective plastic strain forming limit diagram (PEPS-FLD). These diagrams have already been proposed as alternative criteria to the conventional FLD for predicting forming limits in processes that sheet does not experience proportional or in-plane loading conditions. The present study provides a complete comparison of different forms of forming limit diagrams. For this purpose, FLD and extended FLDs are predicted based on the modified Marciniak and Kuczynski (M-K) model with Yld2011 anisotropic yield function while various factors that cause a change in the FLD of a specific alloy including initial imperfection coefficient (f0), non-linear strain path, through-thickness normal and shear stresses are considered. The results indicate that all forms of extended diagrams are independent of strain path and the diagrams in stress space (i.e., FLSD and XSFLD) are less sensitive to the strain path than PEPS-FLD. In this regard, the main weakness of XSFLD, especially on the right-hand side, is that the safety margin cannot be visualized easily. By increasing the initial imperfection coefficient, the level of all forms of diagram increases. However, the effect of through thickness stresses on different diagrams is not the same. Increase in normal and shear stresses results in a downward shift in FLSD and an upward shift in other types of forming limit diagrams.

A Study on Infrared Local Heat Treatment for AA5083 to Improve Formability and Automotive Part Forming

Automotive industries are increasingly employing aluminum alloys for auto parts to reduce vehicle weight. However, the low formability of aluminum alloys has been an obstacle to their application. To resolve the formability problem, some studies involving heat treatments under laboratory conditions have been reported. However, for industrial applications, the heat treatment sequence, heating energy efficiency, and a commercial part test should be studied. This work shows an infrared (IR) local heat treatment, heating only small areas where the heat treatment is required, for an aluminum alloy to improve the formability with a reduction of heating energy. The experiment shows that the formability drastically increases when the aluminum alloy is heat treated between two forming stages, referred to as intermediate heat treatment. The microstructures of the test pieces are evaluated to identify the cause of the increase in the formability. For an industrial application, an aluminum tailgate, which cannot be manufactured without heat treatment, was successfully manufactured by the IR local heat treatment with a reduction of energy. A simulation was also conducted with a stress-based forming limit diagram, which is not affected by the strain path and heat treatment histories. The simulation gives a good prediction of the formability improvement.

Forming limit curves analysis of aluminum alloy considering the through-thickness normal stress, anisotropic yield functions and strain rate

Based on three anisotropic yield functions including Karafillis–Boyce (K–B), Yld96 and Yld2011, directional normalized uniaxial yield stresses, directional r-value and forming limit curve (FLC) for AA3104-H19 aluminum alloy under plane stress condition are numerically investigated in this article. Moreover, considering the through-thickness normal stress effect the forming limit diagram (FLD), stress-based forming limit diagram (FLSD) and extended forming limit stress diagram (XFLSD) is also studied theoretically based on Yld2011 yield criterion and modified Marciniak–Kuczynski (M–K) model. The nonlinear equations set are solved through employing Newton–Raphson numerical method to calculate limiting strains. The anisotropic plastic behavior and FLC of AA3104-H19 predicted by Yld2011 yield criterion are in good agreement with experimental data and are more accurate than those of K–B and Yld96 yield functions. In addition, according to FLD, the formability of sheet metal increases by applying the through-thickness normal stress. The effects of strain rate at quasi-static condition and temperature are theoretically investigated on the FLD of AA3104 aluminum alloy. The positive temperature sensitivity and negative strain rate sensitivity are observed of FLD of AA3104.

A REVIEW ON FORMABILITY PREDICTION AND CONISTITUVE DAMAGE MODELS OF SHEET FORMING OF MAGNESIUM ALLOYS

In recent years, the demand for using magnesium (Mg) alloys has significantly increased in several industrial fields. Due to their favorable strength/weight ratio thus Mg alloy demonstrating a valid replacement for aluminum alloys and High Strength Steels particularly for the production of lightweight parts in aerospace and automotive industries. However the formability of Mg at cold forming conditions is significantly poor and determination of the material formability need special testing procedures and understanding of material failure mechanism. FLD is commonly used to characterize the formability of materials and the key feature of FLD is the forming limit curve (FLC). This paper provides a review on the determination of strain-based and stress-based forming limit diagrams is introduced in this paper. In addition, the constitutive damage models for predicting and characterizing the forming limits of magnesium alloy sheet metals under a wide range of forming conditions at both industrial and scientific level.

Modeling of forming limit for multilayer sheets based on strain-rate potentials

In order to evaluate the forming limits of planar anisotropic multilayer sheet materials, the Marciniak–Kuczynski (M−K) model was formulated based on the strain-rate potential. A common practice to predict the forming limits of sheet materials has been based on yield stress potentials defined in the stress field. As an alternative, a method based on plastic stain-rate potentials, which are especially convenient to apply for rigid-viscoplasticity, was considered in this work. The formulation based on the strain-rate potential facilitates the modeling of forming limits for multilayer sheet materials because the number of unknown variables is significantly reduced by assuming the iso-strain condition for each layer without delamination. As for the strain-rate potential, Srp2003-2d, which is the pseudo-conjugate of the yield stress potential Yld2000-2d, was applied along with Hill's 1948 strain-rate potential for comparison. In the approach proposed, rigid-viscoplasticity was formulated according to the incremental deformation theory based on the minimum plastic work path. The rotation of anisotropic symmetry axes in the groove region was also properly accounted for in the formulation. For verification purposes, the predicted forming limit criteria such as the strain-based forming limit diagram (FLD), the stress-based forming limit diagram (FLSD) and the effective strain-based forming limit diagram (x-EPS) were experimentally validated for a monolithic aluminum alloy (AA5182-O) sheet and a three-layer AA5182-O/polypropylene/AA5182-O (AA/PP/AA) sandwich sheet, which confirmed good agreement. In addition, the path-sensitivity of the strain-based FLD and the path-insensitivity of the FLSD and x-EPS were numerically proven based on the M−K model for the three-layer sandwich sheet. Finally, the M−K model was compared with a maximum force model most recently developed.

A different approach to estimate the process parameters in tube hydroforming

An enhanced unfolding inverse finite element method (IFEM) has been used together with an extended strain-based forming limit diagram (FLD) to develop a fast approach to predict the feasibility of tube hydroforming process of concept part and determine where the failure or defects can occur. In tube hydroforming, the inverse IFEM has been used for estimating the initial length of tube, axial feeding and fluid pressure. The already developed IFEM algorithm used in this study is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, in this article a modeling technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no trial and error process. In addition, the solution provides all the components of strain. Using the extended strain-based forming limit diagram, the components of strain can lead us to measure the potentials for failures during the deformation. The extended strain-based FLD based on the Marciniak and Kuczynski (M-K) model has been computed and used to predict the onset of necking during tube hydroforming. The extended strain-based FLD is built based on equivalent plastic strains and material flow direction at the end of forming. This new forming limit diagram is much less strain path dependent than the conventional forming limit diagram. Furthermore, the use and interpretation of this new diagram is easier than the stress-based forming limit diagram. The results of analysis for free bulging and square bulging have been compared with some published experimental data and the results obtained by conventional commercial software. The results indicate that the fluid pressure estimated by this method is 2.7 % greater than the results obtained by the experiment in the square bulging sample. In addition, the fluid pressure estimated in the free bulge sample is 5.6 % greater than the experimental results.

Theoretical analysis of strain- and stress-based forming limit diagrams

Forming limit diagram is extensively used in the analysis of sheet metal forming to define the limit of deformation of materials without necking or fracture. This article contributes in construction of strain- and stress-based forming limit diagrams by theoretical analysis of several available instability criteria, including bifurcation analysis of diffuse and through-thickness neck formation, shear stress-based criteria onset of through-thickness necking, and so on, and comparative studies among different available theories are done with earlier published work on forming limit in different literatures. The scope of Tresca criterion in forming limit diagram is also investigated in this article. It is found that apart from stress-based forming limit diagram, conventional failure criterion equivalent failure strain versus triaxiality (η) plot is also strain path independent.

The strain gradient approach to predict necking in tube hydroforming

A stress-based forming limit diagram for necking prediction which is based on the strain gradient theory of plasticity in conjunction with the M–K model has been represented and used in tube hydroforming. In this study, the finite element model for bulge forming of straight tube has been constructed and verified with published experimental data. The adaptive simulation technique is based on the ability to detect the onset and growth of defects (e.g., wrinkling, and bursting) and to promptly readjust the loading paths. Thus, a suitable load path has been obtained by applying Adaptive Simulation Method in ANSYS Parametric Design Language (APDL).

Forming limit analysis for two-stage forming of 5182-O aluminum sheet with intermediate annealing

Stress-based forming limit diagrams for a two-stage forming technique with an intermediate annealing step were generated for aluminum alloy 5182-O with a new experimental/theoretical methodology. It was demonstrated that unlike strain-based forming limits, stress-based forming limits are independent of pre-strain levels, pre-strain paths and annealing conditions, and converge to a single forming limit curve that is close to the stress forming limit of the as-received material. For this purpose, AA5182-O specimens were pre-strained to various levels in uniaxial, plane strain, and equibiaxial tension; smaller shapes were extracted, annealed, and tested in limiting dome height (LDH) tests. Strain fields for the forming limit diagrams were measured with stereo digital image correlation during each LDH test, where the onset of localized necking was identified to construct the forming limits. In the calculation of stress-based forming limit curves, only the as-received material properties were required, while the effects of pre-strain and annealing were accounted for with a calculated constant “effective plastic strain.” An analytical method is described to develop a new experimental/theoretical methodology effectively predicting the pre-strain and annealing effects. This enables reliable prediction of formability in multi-stage forming processes interrupted by annealing treatment employed to recover additional stretchability in critical areas of a formed part.

Effect of Element Types on Failure Prediction Using a Stress-Based Forming Limit Curve

Strain-based forming limit diagrams (FLDs) are the traditional tool used to characterize the formability of materials for sheet metal forming processes. However, this failure criterion exhibits a significant strain path dependence. Alternatively, stress-based FLDs have been proposed and shown to be less sensitive to the deformation path. The stress-based failure criterion can be conveniently implemented in numerical simulations. However, for reliable numerical modeling, the sensitivity of the models to the selection of discretization parameters, in particular, the element type must be assessed. In this paper, Marciniak tests have been numerically simulated to investigate failure prediction using three different element types (shell, solid, and solid-shell). Seven different specimen geometries were modeled in order to vary the loading paths. The results show that despite differences in stress calculation assumptions, shell, solid, and solid-shell elements do not provide differences in failure prediction when a stress-based failure criterion is used.

Loading Path Dependence of Forming Limit Diagram of a TRIP800 Steel

In this paper, the microstructure-based finite element modeling method is used in investigating the loading path dependence of formability of transformation induced plasticity (TRIP) steels. For this purpose, the effects of different loading path on the forming limit diagrams (FLD) of TRIP steels are qualitatively examined using the representative volume element (RVE) of a commercial TRIP800 steel. First, the modeling method was introduced, where a combined isotropic/kinematic hardening rule is adopted for the constituent phases in order to rightly describe the cyclic deformation behaviors of TRIP steels during the forming process with combined loading paths which may include the unloading between the two consecutive loadings. Material parameters for the constituent phases remained the same as those in the authors’ previous study [1] except for some adjustments for the martensite phase due to the introduction of the new combined hardening rule. Based on the new material parameters and new hardening rule, the predicted deformation behaviors of the TRIP800 steel show quite similar qualitative trends to those reported in other experimental works. Pseudo-forming limit strain diagrams (Pseudo-FLD) for the TRIP800 steel were, then, obtained for various loading paths. The computational results show that, similar to other single phase materials, the TRIP800 steelmore » shows very sensitive loading path dependence in the strain-based forming limit diagrams (strain-FLD), but does not in the stress-based forming limit diagrams (stress-FLD), and that the phase transformation does not have significant effects on the FLD for the TRIP800 steel. From the observations in this study, the current modeling methods can be used in examining the qualitative trends of FLD of TRIP steels under different loading paths/prestrains.« less

Necking Prediction in Tube Hydroforming by Stress-Based Forming Limit Diagrams

Path-independent stress based forming limit diagrams for anisotropic materials along with the Hill 48 yield function; power law strain hardening and isotropic hardening are derived. Bifurcation analyses via solving equilibrium equations of a pointed vertex on subsequent yield loci are utilized. The presented practical forming limit diagrams (FLSDs) show more acceptable agreements with experimental data compared with those obtained by other methods. A typical neck detection macro in APDL is developed by FEA simulation for a free bulge tube hydroforming to confirm the significant simplicity and straightforwardness of the mentioned FLSD.

A study on fracture behaviour of three different high strength low alloy steel sheets during formation with different strain ratios

This paper deals with the study on fracture behaviour of three different steels, namely, the HSLA, the Micro alloyed and the Carbon–Manganese steels, using stress- and strain-based forming and fracture limit diagrams obtained from the experimentally determined strain values for different strain or stress ratios. With an aim to analyse the fracture behaviour, the strain- and stress-based forming and fracture limit diagrams have been developed for three different steel sheets, namely, the HSLA steel sheet of 1.6 mm thickness, the Micro alloyed steel sheet of 1.2 mm thickness, and the Carbon–Manganese steel sheet of 1.4 mm thickness. The forming and fracture behaviour and size and shape of voids (particularly, the ratio of length to width of voids, ( L/ W)) developed at fracture during the formation of these steels, under different strain ratio conditions, have been correlated with the mechanical properties such as microstructure of steels, minor strain at fracture, and Mohr’s circle shear strains, various combinations of mean strain and effective strain, and material properties, namely, strain hardening exponent ( n)-value, normal anisotropy ( r ¯ ) and the range of localized neckings.

Effect of Yield Criterion on Numerical Simulation Results Using a Stress-Based Failure Criterion

Determining tearing concerns in numerical simulations of sheet metal components is difficult since the traditional failure criterion, which is strain-based, exhibits a strain path dependence. A stress-based, as opposed to a strain-based, failure criterion has been proposed and demonstrated analytically, experimentally in tube forming, and through numerical simulations. The next step in this progression to the acceptance of a stress-based forming limit diagram is to demonstrate how this failure criterion can be used to predict failure of sheet metal parts in numerical simulations. In this paper, numerical simulation results for dome height specimens are presented and compared to experimental data. This procedure was repeated for various yield criteria to examine the effect of this parameter on the ability to predict failure in the numerical simulations. Reasonable agreement was obtained comparing the failure predicted from numerical simulations and those found experimentally, in particular for the yield criterion which has been shown to best characterize the material used in this study.