Forming Limit Stress Research Articles

Forming limit diagram prediction of 6061 aluminum by GTN damage model

Forming limit diagram (FLD) is one of the formability criteria which is a plot of major strain versus minor strain. In the present study, Gurson-Tvergaard-Needleman (GTN) model is used for FLD prediction of aluminum alloy 6061. Whereas correct selection of GTN parameters’ is effective in the accuracy of this model, anti-inference method and numerical simulation of the uniaxial tensile test is used for identification of GTN parameters. Proper parameters of GTN model is imported to the finite element analysis of Nakazima test for FLD prediction. Whereas FLD is dependent on forming history and strain path, forming limit stress diagram (FLSD) based on the GTN damage model is also used for forming limit prediction in the numerical method. Numerical results for FLD, FLSD and punch’s load-displacement are compared with experimental results. Results show that there is a good agreement between the numerical and experimental results. The main drawback of numerical results for prediction of the right-hand side of FLD which was concluded in other researchers’ studies was solved in the present study by using GTN damage model.

Stress and strain based fracture forming limit curves for advanced high strength steel sheet

In this work, strain based fracture forming limit curve (FFLC) of advanced high strength (AHS) steel grade 980 was determined by means of experimental Nakajima stretch-forming test and tensile tests of samples under shear deformation. During the tests, a digital image correlation (DIC) technique was applied to capture the developed strain histories of deformed samples up to failure. The gathered fracture strains from different stress states were used to construct the FFLC. Subsequently, the FFLC in the strain space was transformed to a principal stress space by using plasticity theories. As a result, the fracture forming limit stress curve (FFLSC) of examined steel was obtained. Furthermore, fracture locus (FL) as a relationship between stress triaxialities and critical plastic strains was determined. Hereby, two anisotropic yield functions, namely, the Hill’48 and Yld89 model were taken into account and their effects on the calculated curves were investigated. To verify the applicability of the obtained limit curves, rectangular cup drawing test and forming tests of so-called Diabolo and mini-tunnel samples were performed. Obviously, the FFLSCs and FLs more accurately described the failure occurrences of 980 steel sheets than the FFLCs. In addition, it was found that the drawing depths predicted by the FLs and the Yld89 yield criterion slightly better agreed with the experimental results than those from the FFLSCs and the Hill’48 model, respectively.

Formability Analysis of Fukui Stretch-Drawing and Square Cup Drawing Using Strain and Stress Based Forming Limit Curves

In this work, the experimental and numerical analyses of Forming Limit Curve (FLC) and Forming Limit Stress Curve (FLSC) for Advanced High Strength Steel (AHSS) sheet, grade JAC780Y, are performed. Initially, the FLC is experimentally determined by means of the Nakazima Stretch forming test. Subsequently, the FLSC of investigated steel was plastically calculated using the experimental FLC data. Different yield criteria including Hill48, and Yld89, are applied to describe plastic flow behavior of the AHS steel and Swift hardening law is taken into account. Hereby, influences of the constitutive yield models on the numerically determined FLSCs are evaluated regarding to those results from the experimental data. The obtained stress based forming limits are affected significantly by the yield criteria. Finally, the experimental and numerical formability analyses of Fukui stretch-drawing and square cup drawing tests are studied through FLC and FLSCs. It is observed that all stress based curves can be used very well to describe material formability of the examined steel compared to the strain based FLC. The strain based FLC depend on forming history and strain paths change. In the other hand, the stress based FLC do not depend on these issue. In this study, it can be concluded that the FLSCs could predict failure more realistically and better than the strain based FLC.

FEA of vertical parts formed with multistage incremental sheet metal forming based on the forming limit stress diagram

Multistage incremental sheet metal forming (MS-ISF) is used to produce sheet metal parts with a large forming angle. Similar to the forming limit diagram (FLD) in stamping, FLD in MS-ISF is not sufficiently reliable due to the effect of loading path. To solve this problem, a method to calculate the forming limit stress diagram (FLSD) from FLD was proposed. Experiments proved that FLSD is a reliable fracture indicator that is unaffected by the loading path in MS-ISF.

Experimental study on the formability of AA6016 sheets pre-strained by rolling

The effects of prestrain by rolling on the formability of AA6016 sheets in the biaxial stretching region are studied in this paper. An experimental program including formability experiments has been carried out for as-received and prestrained sheets. Forming limit strains are determined by the digital image correlation technique and then mapped into stress space using an anisotropic plasticity model in order to assess the path-independence of forming limit stresses. Different diagrams for description of formability such as the traditional strain-based forming limit diagram (FLD), the forming limit stress diagram (FLSD) and various equivalent plastic strain based (EPS-based) diagrams are applied in order to study the effect of prestrain. It is shown that prestrain by rolling has the same effect on the forming limit strains as prestrain by plane strain tension. Furthermore, the forming limits of the virgin material nearly coincide with the forming limits of the prestrained material in the FLSD and EPS-based diagrams, serving as a conservative estimate for the prestrained material. Due to the roping phenomenon, the material displays significant anisotropy in forming limit strains. At the same time, the presence of roping does not affect the path-independence of the forming limits in the FLSD and EPS-based diagrams.

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.

Fracture Prediction for High-strength Steel Sheet Subjected to Draw-bending Using Forming Limit Stress Criterion

A fracture criterion for sheet metals subjected to draw-bending is investigated using the concept of the forming limit stress criterion. The test material used is a 1.0-mm-thick high- strength steel sheet with a tensile strength of 590MPa. The specimen undergoes bendingunbending under tension when passing over the die profile. The drawing speed was set to 5-100 mm • s-1. The magnitude of true stress σDB when a specimen fractured has been precisely determined. Moreover, multiaxial tube expansion tests of the test material are performed to measure the forming limit stress σPT of the test material under plane-strain tension. It is found that σDB is larger than σPT by 2.8-6.3%. Therefore, it is concluded that the forming limit stress criterion is effective as a fracture criterion in draw-bending.

Elasto-Plastic Modeling of the Limit Strains in Metallic Sheets

In this work, the model of Marciniak and Kuczynski, hereafter referred to as the M-K model, was extended to account for the elastic strains to forecast the Forming Limit Curve (FLC) of metallic sheets. The return mapping algorithm is adopted where an elastic predictor step is performed with the generalized Hooke’s law and the plastic correction step is performed assuming the isotropic work-hardening together with the associated flow rule. The current M-K model predicted quite well both experimental and rigid-plastic results obtained for an IF steel sheet. Also, the principal stresses predicted by the elasto-plastic M-K model provided a good agreement with the experimental Forming Limit Stress Diagram (FLSD) of a Bake-Hardening steel sheet. Therefore, the elastic strains should be taken into account in the modeling of limit strains in metallic sheets, especially in the case of advanced high strength steels for which the Young modulus decreases with the plastic strain.

Forming limit prediction for two-stage aluminum alloy sheet forming process considering the effect of normal stress

Purpose – The purpose of this paper is to analyze theoretically the influence of normal stress on the formability of aluminum alloy sheets in non-linear strain paths. Design/methodology/approach – Four loading modes of non-linear strain paths are investigated in detail to consider the effect of normal stress on formability of aluminum alloy sheets. Findings – Results show that the influence of normal stress in the first stage can be ignored. However, the normal stress in the second stage enhances the formability of aluminum alloy sheets obviously. Besides, the normal stress in the second stage is found to have larger effect on forming limit stress than that in the first stage. Research limitations/implications – Maybe more experiment data should be obtained to support the theoretical findings. Originality/value – This current study provides a better understanding of normal stress effect on the formability of aluminum alloy sheets in non-linear strain paths. Since the reacting stage of normal stress play important roles in normal stress effect on the formability of aluminum alloy sheets, the insight obtained in this paper will help to judge the instability of aluminum alloy sheets in complex forming processes with normal stress reacting on the sheet or tube.

Forming limit prediction using a self-consistent crystal plasticity framework: a case study for body-centered cubic materials

A rate-dependent self-consistent crystal plasticity model was incorporated with the Marciniak–Kuczyński model in order to study the effects of anisotropy on the forming limits of BCC materials. The computational speed of the model was improved by a factor of 24 when running the simulations for several strain paths in parallel. This speed-up enabled a comprehensive investigation of the forming limits of various BCC textures, such as , , , and fibers and a uniform (random) texture. These simulations demonstrate that the crystallographic texture has significant (both positive and negative) effects on the resulting forming limit diagrams. For example, the fiber texture, which is often sought through thermo-mechanical processing due to a high r-value, had the highest forming limit in the balanced biaxial strain path but the lowest forming limit under the plane strain path among the textures under consideration. A systematic investigation based on the results produced by the current model, referred to as ‘VPSC-FLD’, suggests that the r-value does not serve as a good measure of forming limit strain. However, model predictions show a degree of correlation between the r-value and the forming limit stress.

成形限界応力を用いた軟鋼板および高強度鋼板の曲げ曲げ戻し割れ予測

成形限界応力を用いた軟鋼板および高強度鋼板の曲げ曲げ戻し割れ予測

An approach to predicting the forming limit stress components from mechanical properties

Forming limit curves (FLCs) are used to determine the amount of deformation that can be applied to a sheet metal before the onset of a localized neck. Most FLCs are shown in strain space, and stress-based FLCs have advantages because they are often strain-path independent. The current study develops a method to calculate a stress-based forming limit curve. The necessary data for this calculation can be obtained from a uniaxial tensile test. The calculations depend on the Z parameter, which can be considered to be the point of instability during a tensile test. With the use of the Keeler–Brazier equation, the effective stress in plane strain at the forming limit is shown to be a function of the Z parameter and thickness. Data from 4 experimental studies are shown to be consistent with this function. With the generally accepted observation that the left side of the strain-based FLC is a line with slope of –1 and an appropriate constitutive model for the stress-strain behavior of the material, the stress-based FLC corresponding to the left side of the strain-based FLC can be calculated. Comparison of the calculated stress-based FLC for three steels with the stress-based FLC determined directly from the strain-based FLC shows good agreement. The calculated stress-based FLC is 15–20MPa below the data generated directly from the strain-based FLC.

Fracture Prediction for Ultralow Carbon Steel Sheet Subjected to Draw-Bending Using Forming Limit Stress Criterion

A fracture criterion for sheet metals subjected to draw-bending is investigated using the concept of forming limit stress criterion. The test material used is a 1.0-mm-thick ultralow carbon steel sheet. Draw-bending experiment of a wide specimen is performed for a die profile radius of 4mm. A specimen undergoes bending-unbending under tension when passing over the die profile radius. The drawing speed was set to 5mm/s. The magnitude of true stress when a specimen fractured has been precisely determined from the measured data of a drawing force and the cross sectional area of the draw-bent specimen after fracture. Moreover, multiaxial tube expansion tests of the test material are performed to measure the forming limit stress of the test material under plane strain tension. It is found that the is larger than by approximately 10 %. Therefore, it is concluded that the forming limit stress criterion is effective as a fracture criterion for a mild steel sheet subjected to draw-bending.

Effect of Equivalent Stress-Strain Relation and Differential Hardening on Accuracy of Forming Limit Analyses

Multiaxial tube expansion tests (MTETs) were performed to measure the multiaxial plastic deformation behavior of a cold rolled interstitial-free (IF) steel sheet for a range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to tubular specimens using an electrical, closed-loop servo-control system for an axial force and an internal pressure. Tubular specimens with an inner diameter of 44.6 mm were fabricated from a cold rolled IF steel sheet with a thickness of 0.7 mm by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit strains and forming limit stresses of the as-received sheet sample, in addition to the contours of plastic work and the directions of the plastic strain rates. It was found that the shapes of the measured work contours changed with increasing plastic work. The observed differential hardening behavior was approximated by changing the material parameters and the exponent of the Yld2000-2d yield function (Barlat et al, 2003) as functions of the reference plastic strain. The hydraulic bulge tests were also conducted to measure the forming limit strain and forming limit stress for equibiaxial tension and to determine the equivalent stress-equivalent plastic strain relation for a larger strain range. The forming limit curve and forming limit stress curve were calculated using the Marciniak-Kuczyński-type approach. The calculated results were in fair agreement with the measurement.

Strain path dependence of the FLC0 formability parameter in an interstitial free steel

This work aims at studying the influence of the strain path upon the FLC0 formability parameter, the root of the forming limit curves (FLC). The investigation was conducted in an interstitial free (IF) quality steel. The FLC0 parameter was evaluated in an intrinsic tensile test in near plane strain (NPS) condition, but following two strain paths. The first one being a uniaxial (proportional) path up to initial necking. The second (non-proportional) path corresponded to applying 15 % nominal plastic strain in one direction (near plane strain) followed by a second deformation applied in the orthogonal direction up to the rupture of the samples. A reduction in the limit strains corresponding to FLC0 in the non-proportional test has been observed. The forming limit stress curves (FLSC) and the critical values FLSD0 are also related to these trajectories. A simulation using finite element method (FEM) has been applied to analyze the evolution of stress and strain during the two paths, and the results have been found consistent for both proportional and non-proportional paths. Texture and surface roughness evolution of the sheet were also measured and related to the applied strain paths.

Forming limit diagram of tubular hydroformed parts considering the through-thickness compressive normal stress

In this study, the effect of a compressive normal stress has been considered in the determination of forming limit diagrams and forming limit stress diagrams to predict neck initiation failure in tube hydroforming of T-shaped parts. Computation of the forming limit diagrams and FLSDs is based on the generalized Marciniak and Kuczynski method to consider the existence of through-thickness compressive normal stress. The proposed forming limit diagrams and FLSDs were used in conjunction with ABAQUS/EXPLICIT finite element simulations to predict the onset of necking in tube hydroforming of T-shaped part. The amount of calibration pressure and axial feeding required to produce an acceptable part in finite element method was compared to published experimental data, and a satisfactory agreement between the FEM and test results has been achieved. Therefore, the present approach can be used as a reliable criterion to design tube hydroforming processes and reduce the number of costly trials.

Formability prediction of AL7020 with experimental and numerical failure criteria

The formability of aluminum alloy sheet metal is a key issue in its design, analysis and operation of manufacturing processes. The conventional forming limit diagram (FLD) which evaluates the principal strains at failure is often used to quantify the formability limits. Due to the sensitivity of the FLD to the strain paths, the forming limit stress diagram (FLSD) based on principal stresses is shown to be more efficient. In contrast, a fully coupled behavior-damage models are recently proposed, which allow to predict the strain localization and the failure occurrence based on appropriates fully coupled constitutive equations describing the main physical phenomena involved. In this work a fully coupled constitutive equations taking into account the mixed nonlinear isotropic and kinematic hardenings fully coupled with the isotropic ductile damage is used. The microcracks closure is added to affect the equivalent plastic strain at fracture in a large range of stress states. Various tests are conducted to test the formability of aluminum alloy AL7020. The three different methods (FLD, FLSD and the fully coupled model) are identified and validated separately. With the help of Nakazima tests and cross-section deep drawing tests, the quality of the three failure criteria for AL7020 are compared and demonstrated with the investigations of the simulation results.

Forming Limit Analyses of 590 MPa High Strength Steel Sheet Using Differential Work Hardening Model

A servo-controlled tension-internal pressure testing machine with an optical 3D deformation analysis system (ARAMIS®, GOM) was used to measure the multiaxial plastic deformation behavior of a 590MPa high strength steel sheet for a range of strain from initial yield to fracture. Tubular specimens were fabricated from the sheet sample by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit curve (FLC) and forming limit stress curve (FLSC), in addition to the contours of plastic work and the directions of plastic strain rates. It was found that the shapes of the measured work contours changed with the increase of work hardening (plastic work). The observed differential work hardening (DWH) behavior was approximated by changing the material parameters and the exponent of the Yld2000-2d yield function (Barlat et al, 2003) as a function of the equivalent plastic strain. The FLC and FLSC calculated using the Marciniak-Kuczyński-type (M-K) approach with the DWH model were in good agreement with the measurement.

A pragmatic approach to accommodate in-plane anisotropy in forming limit diagrams

The traditionally used forming limit diagram (FLD), a locus of limit strain states under different linear strain paths is usually determined from the blanks along the rolling direction. The effect of in-plane anisotropy on the forming limit diagram is neglected for engineering applications. However, the in-plane anisotropy effect is significant when the FLD is used to estimate forming limit stress diagram (FLSD). The available models to account for the in-plane anisotropy are reviewed and their limitations are discussed. A simpler and more pragmatic approach to account for the in-plane anisotropy in forming limit diagrams is proposed. The new method calculates the change in the plane strain limit using constitutive models of plasticity theory. The orientation specific FLD is then calculated by interpolating between the limit strains along the uniaxial, plane and biaxial strain paths. The proposed methodology is discussed by comparing the experimental FLDs for three different grades of low carbon steels and an aluminum alloy. The calculation of FLSD using the predicted anisotropic FLD, assuming Hill48 yield criterion is illustrated for one of the materials.

Analysis of necking in tube hydroforming by means of extended forming limit stress diagram

In this paper, an extended forming limit stress diagram (EFLSD) was applied to predict neck initiation failure in tube hydroforming of metal bellows. The proposed EFLSD was used in conjunction with ABAQUS/ EXPLICIT finite element simulations to predict the onset of necking in tube hydroforming of metal bellows. The amount of calibration pressure and axial feeding required to produce an acceptable part in finite element method (FEM) were compared with the published experimental data and a satisfactory agreement between the FEM and published test results was achieved. Therefore, the present approach can be used as a reliable criterion for designing metal bellows hydroforming processes and reducing the number of costly trials.