Forming Limit Stress Research Articles

Fracture Prediction of Aluminum Alloy Sheet AA2024-T3 Using Analytical Stress and Experimental Strain Based Failure Criteria

In this work, the fracture prediction of aluminium alloy sheet, grade AA2024-T3 was investigated using the Fracture Forming Limit Curve (FFLC) and Analytical Fracture Forming Limit Stress Curve (FFLSC) as failure criteria. Initially, the FFLC was experimentally achieved by means of the Nakajima Stretch forming test coupled with GOM strain measurement system, providing the Digital Image Correlation (DIC) technique. Subsequently, the analytical FFLSC was plastically computed using experimental FFLC data combination with Swift hardening model and anisotropic Hill’48 yield model for representing anisotropic plastic deformation behaviour on examined sheet. Finally, Fukui stretch drawing and Three point bending tests were conducted both experiment and numerical simulation to evaluate the fracture state and verifying an applicability of obtained FFLC and FFLSC. In the simulation, the ABAQUS 2017 element deletion function was employed for directly implementing the fracture criteria regarding the FFLC and FFLSC. It was concluded that the analytical FFLSC could more realistically predict fracture behaviour better than the FFLC based on strain. In term of percentage error, the analytical FFLSC generated an error less than the FFLC.

Formability prediction of high‐strength steel sheet using experimental, analytical and theoretical analysis based on strain and stress forming limit curves and its application to automotive forming parts

AbstractIn this work, the high‐strength steel (HSS) sheet dual‐phase 440 (DP440) were conducted to establish the forming limit curve (FLC) and analytical forming limit stress curve (FLSC) obtained from experimental forming limit curve. First, the Nakajima stretch forming examination was carried out to obtain forming limit curve of investigated sheet. Afterwards, the theoretical Marciniak–Kuczinsky (M–K) model was developed and calculated to evaluate localized necking limits both in strain and stress spaces combination with anisotropic yield criteria. Then, the analytical forming limit stress curves were plastically calculated by using experimental forming limit curve data combination with Swift hardening model and anisotropic yield criteria namely, Hill’48 and Yld2000‐2d for representing anisotropic plastic deformation behavior on examined steel sheet. Finally, automotive stamping parts were performed in order to verify an applicability of all developed curves. It was observed that the analytical forming limit stress curves could more precisely predict the formability of automotive parts better than the forming limit curve based on strain. Particularly, the one based on Yld2000‐2d predict better than the one based on Hill’48. Simultaneously, the experimental forming limit curve and analytical forming limit stress curve were also evaluated comparing with the theoretical calculated forming limit curve and forming limit stress curve using the Marciniak–Kuczinsky model. It should be noted again that the experimental forming limit curve and analytical forming limit stress curve are the best one. Therefore, the Yld2000‐2d yield function better represented the anisotropic behavior of the high‐strength steel sheet dual‐phase 440 than Hill′ 48 yield function, and can suitable be used for the analysis prediction and design of bumper automotive parts under forming processes.

Assessing the Feasibility of Cold Forming of Automotive Parts from Quenched and Partitioned Martensitic Stainless Steels

Sheet metal forming is among the most widely employed processes in manufacturing. Its economic feasibility relies on many factors, including the mechanical properties of the processed materials, energy efficiency of the metal‐forming processes, and quality of the manufactured parts. This work focuses on developing a computational approach to assess the mechanical behavior of quenched and partitioned (QP) martensitic stainless steels (MSSs) undergoing cold forming, aiming at the serial production of automotive parts. The Johnson–Cook (J–C) constitutive model and forming limit diagram (FLD) are derived and validated for each alloy using the experimental data from tensile and Nakajima tests. From the simulated FLD, a theoretical forming limit stress diagram (FLSD) is calculated. The latter is used as a fracture criterion for the cold‐forming process. Cold stamping of two automotive parts, B‐pillar and tunnel, is modeled using the J–C constitutive model and the FLSD. It is demonstrated that the tunnel can be successfully cold‐formed from all three studied steels. In contrast, extensive cracking is expected during the cold forming of the B‐pillar from all materials. It is envisaged that these computational models can be employed for the assessment of any comparable part manufacturing procedure from the QP MSSs.

Research on Forming Limit Stress Diagram of Advanced High Strength Dual-Phase Steel Sheets.

The Forming Limit Stress Diagram (FLSD) can accurately describe the forming process of high-strength steel. However, obtaining FLSD is relatively difficult. In order to predict fracture in advanced high-strength dual-phase (DP) steels, limit maximum and limit minimum principal strains of sheet were obtained through multiple sets of test and simulation. Two material parameters, strength coefficient K and hardening exponent n are introduced into the FLSD function which is established by the strain-stress transformation function. The function shows that the k-value determines the value of the maximum principal stress, while the n-value affects the curvature of the curve. Verification of correctness by testing and simulation to within 10% accuracy. This paper explores a new approach to FLSD research based on material properties, which can expand the application scope of FLSD.

Forming limit analysis of AA5052 sheet under bilinear strain path by designing a novel large-scale gripping fixture

The combined strain paths have significant effects on the formability on the sheet metal. In this work, aiming at a widely-used AA5052-O sheet metal, the uniaxial tension and the Nakazima tests were conducted on the large-scale specimens subjected to the pre-tension deformation. First, a novel gripping fixture was designed and manufactured to achieve the uniform pre-strains of the large specimen. Then, two types of strain paths of the tension - tension and tension - bulging were implemented to reveal the evolutions of the mechanical properties and forming limit curves (FLCs), respectively. Moreover, the forming limit stress curves (FLSCs), which are more insensitive to the changes of strain paths, are calculated from the experimental FLCs to improve the prediction accuracy of finite element (FE) simulations. Compared to the conventional necking criterion of path transition and the FLC criterion, the FLSC criterion can effectively enhance the simulation precision in the biaxial tension region.

Discussion on failure criteria of orthogonally biaxial stress field

Some components which constitute a part of the boundary in nuclear plants are very important from the viewpoint of protection of radioactive material propagation. Especially, it is a serious matter if the function as the boundary is maintained or not in the case of severe accident (SA). In this paper the characteristics of FLD (Forming Limit Diagram) as the failure criteria is studied compared with the rule of ASME Code and the applicability to the boundaries of structures is discussed. Furthermore, the prospect of the application of FLSC (Forming Limit Stress Curve) to structural components including loading hysteresis is referred.

Cryogenic formability of a solution-treated aluminum alloy sheet at low temperatures

• A newly-designed digital image correlation (DIC) testing device at cryogenic temperatures was developed. • The cryogenic FLDs and FLSDs of the solution-treated Al-Cu-Mn alloy sheet were experimentally obtained. • The cryogenic FLD and FLSD ductile fracture models were determined to predict the drawing limits of the Al-Cu-Mn alloy sheet. In this paper, the analysis of the necking and limit strains of a solution-treated aluminum alloy sheet at extreme low temperatures is performed using a newly-designed test apparatus equipped with the digital image correlation (DIC) device. The forming limit diagram (FLD) and forming limit stress diagram (FLSD) ductile fracture models were used to predict the drawing limit and fracture resistance capacity of an Al-Cu-Mn alloy sheet under complex stress at room temperature (RT) and -160 °C. It was found that the FLD 0 value at -196 °C increased to 0.32 as compared to 0.23 at RT. The Al-Cu-Mn alloy sheets at -160 °C and -196 °C were found to have significantly higher limit strains than those at RT. The drawing height and limit major strain at the round corner of the cryogenic deep-drawn cups were found to be increased by 21.3 % and 9.7 %, respectively, as compared to those at RT. Moreover, a larger necking amount and higher fracture resistance of the Al-Cu-Mn alloy sheet could be achieved during cryogenic deformations. The obtained cryogenic FLDs and FLSDs can be used to accurately predict the damage evolution and failure occurrence for the forming of complex-shaped aluminum alloy components at low temperatures.

Investigation on the forming limit diagram of AA5754-O alloy by considering strain hardening model, strain path, and through-thickness normal stress

This study clarified the effects of the chosen hardening model, through-thickness normal stress, and non-linear strain path on the precision of forming limit diagram (FLD). The Marciniak-Kuczynski (M-K) instability theory was employed to calculate the FLD of AA5754-O based on the different hardening models. Swift, Voce, modified Voce, Kim-Tuan, and modified Kim-Tuan hardening models were adopted to predict the forming limits, and their constant parameters were presented. Predicted FLDs indicate that modified Kim-Tuan has a better agreement with experimental data than other models. After that the influences of through-thickness normal stress on the forming limit diagram were examined. The three-dimensional stress state was converted to plane-stress condition according to the assumption that hydrostatic stress is ineffective on the plastic deformation. The results show that formability improves when normal stress increases. However, the effect of the normal stress on FLD for various hardening models is different. Due to the complexity of sheet metal forming, the strain path of the material may change during the deformation process. The results indicated that strain path has a significant effect on the FLD, and the path dependence of the forming limit stress diagram (FLSD) will be examined in detail. Finally, the forming limits were computed to analyze the effect of the normal stress on the non-linear loading path deformation. It was observed that by increasing the amount of pre-strain, the effect of the normal stress on the formability will diminish. Moreover, results showed that normal stress will affect the path dependence of the FLSD.

Analysis of the pre-straining effects on the limit strains of interstitial-free steel: experiments and elasto-plastic modeling of strain and stress-based forming limit curves

In this work, the limit strains under as-received and pre-strained conditions of an interstitial-free steel sheet were investigated by mechanical tests and numerical modeling. An original testing procedure was proposed to reproduce two equivalent pre-straining amounts under equibiaxial stretching (EB-PS) and uniaxial tension (UT-PS) deformation modes. The limit strains were defined from Nakajima’s hemispherical punch tests using digital image analysis according to the ISO 12004:2 standard. The plastic behavior of the interstitial-free steel sheet was evaluated by uniaxial tensile, disk compression, and hydraulic bulge tests. Moreover, an elasto-plastic framework based on the Marciniak–Kuczynski (M–K) model is proposed to forecast both the strain-based and stress-based forming limits. The parameters of the Yld-2000-2d yield criterion were identified using the plastic anisotropy coefficients with the flow-stress values determined from two distinct amounts of plastic-work per unit volume. For both deformation modes and pre-straining levels defined by the von Mises effective plastic-strain (4.8% and 9.0% EB-PS; 5.0% and 10% UT-PS), the transformed polar effective plastic-strain (PEPS) and forming limit stress (FLSC) results shown to be more strain-path insensitive than the conventional strain-based forming limit curve (FLC). The proposed elasto-plastic M–K model successfully forecasted the linear strain-path limit strains defined using the FLC, PEPS, and FLSC representations. The M–K model also provided quite conservative predictions for the pre-strained PEPS and FLSC. The Yld-2000-2d parameters identified using the flow-stress values defined from an upper-level of the plastic-work per unit volume proved to be the best choice in the present M–K modeling framework.

Development of Stress- and Strain-Based Fracture Forming Limit Curves of Sheet Aluminium-Alloy AA2024-T3 through Various Approaches

In this work, four fracture criteria—namely, Fracture Forming Limit Curve (FFLC), Fracture Forming Limit Stress Curve (FFLSC), Fracture Locus (FL) and Fracture Locus Embedded with Bao-Wierzbicki Ductile Damage Criterion (BW-FL)—are comparatively deployed to forecast breakage of deformed AA2024-T3 sheet aluminium-alloy. An FFLC can be experimentally formed by conducting a set of Nakajima stretch-forming based tests. To obtain an FFLSC, such an FFLC drawn in the strain space has to be entirely mapped onto the stress space. This can computationally be accomplished with the help of those well-known plasticity-relevant models like the Hill’48 anisotropic yield criterion and the Swift hardening law. Likewise, both BW-FL and FL in terms of stress triaxialities and critical plastic strains can mathematically be derived from the FFLC incorporated with the Hill’48 anisotropic yield criterion. Hole expansion and tree-point bending tests are carefully carried out both experimentally and simulatively to verify those four generated fracture limits. The more innovative FFLSC and FL demonstrate more accurate prediction on rupture of AA2024-T3 sheet aluminium-alloy than the conventional FFLC. The BW-FL however performs the worst.

Material Modeling in High Strain Range and Forming Limit Analysis for 6000 Series Aluminum Alloy Sheet

This study investigates the effects of material modeling in high strain range on the forming limit analysis of a 6000-series alloy sheet 6016-T4. A servo-controlled tension-internal pressure testing machine was used to measure the multiaxial plastic deformation behavior in a strain range from initial yield to fracture. Tubular specimens were fabricated with a weld line thicker than the sheet thickness to prevent fracture from occurring in the weld zone. Proportional loading in the first quadrant of the principal stress space was applied to the 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. Moreover, forming limit strains were measured using a flat-headed punch stretching test (PST). From the multiaxial tube expansion test (MTET) data, although a differential hardening effect was observed, appropriate coefficients including the exponent of the Yld2000-2d yield function (Barlat et al, 2003) were determined and employed in the Marcińiak-Kuczyski (1967) forming limit analysis (M-K analysis). The calculated forming limit strains in the vicinity of equibiaxial tension were smaller than the measured ones. The M-K analysis predicted that the forming limit strain in the vicinity of equibiaxial tension becomes minimum when the inclination angle of the localized neck from the rolling direction (RD) is 45° (diagonal direction; DD) while the experimental fracture direction was the RD. With the additional MTET, the plastic deformation behavior in the DD was measured and compared with that calculated from the material model. The reason of the discrepancy in the fracture direction between the experiment and the M-K approach is discussed.

Review on multi-stage incremental forming process to form vertical walled cup

Using incremental forming, forming of a vertical walled cup was impossible in a single-stage due to the reason that failure is followed by thinning at transition region (in between the wall & base of the cup). However in the recent years, forming of a cup with vertical wall or maximum wall angle compared to Single-stage Single Point Incremental Forming (SPIF) are being done successfully by many researchers using Multi-stage Single Point Incremental Forming (MSPIF) process. The reason behind the implementation of MSPIF process is that the thinning will be postponed even when the maximum wall angle is achieved, with number of intermediate stages during Incremental Forming. In the case of Single-stage Incremental Forming, wall angle beyond a certain limit can’t be obtained due to the reason that thinning will occur suddenly at transition region. In this paper, a review is presented on MSPIF process to form cup with vertical wall or maximum wall angle compared to Single-stage Incremental Forming. In addition, tool path design, different forming strategies, effect of forming direction & strategy, Rigid Body Translation (RBT) during intermediate stages, geometrical accuracy of formed part such as dimensional deviation & step formation at base, Formability using Forming Limit Stress Diagram (FLSD) and Thickness distribution and comparisons of MSPIF process are discussed. Further, works proposed for future to improve the process is also presented in this paper.

A Comparative Study of Forming and Crash Behavior of High Strength Steels

Abstract Advanced high strength (AHS) steel sheets of various grades have been increasingly used in the automotive industries because of their advantageous mechanical properties. High strength and great energy absorption are desired for a structural component design. On the other hand, large formability and strain hardening are necessary for achieving an effective forming process. To apply eligible steel grades, precise understanding of their forming and crash characteristics is needed. In this work, AHS steels with varying strengths, namely grades 780, 980, and 1180, were investigated. First, tensile tests were performed, and mechanical properties, including r-values, of the examined steels were obtained for different loading directions. The forming limit curves (FLCs) and respective forming limit stress curves (FLSCs) were determined by means of a Nakajima forming test and finite element simulation. The cyclic tension-compression tests were conducted to characterize the elastic recovery and Bauschinger effect of steels. Afterward, forming processes of an automotive part were performed, and the forming and springback behaviors of steels were evaluated by using simulations coupled with Hill’48 and Yoshida-Uemori models, determined material parameters, FLCs, and FLSCs. In addition, crashworthiness of steels was numerically studied by means of a crash rectangle profile and simplified side impact pole test. The mechanical, forming, and crash performances of all the investigated AHS steels were evaluated and discussed so that the results can be applied for part design and manufacturing.

Fracture Prediction for Mild Steel Sheet and High-Strength Steel Sheet Subjected to Draw Bending Using Forming Limit Stress Criterion

Abstract A fracture criterion for sheet metal subjected to draw bending is proposed based on the concept of the forming limit stress criterion. An experimental apparatus that is capable of draw bending sheet specimens with forming speeds (approximately 100 mm·s−1) comparable to those for commercial press forming machines was designed and built. The test materials were an ultralow-carbon steel sheet and a high-strength (590 MPa) steel sheet. Specimens underwent bending and unbending under tension when passing over a die. The magnitude of the true stress, σ D B , at which the stretch-drawn specimens fractured was precisely determined from the measured drawing force and the cross-sectional area of the specimen after fracture. Moreover, multiaxial tube expansion tests were performed to measure the forming limit stress, σ P T , for the test materials under plane-strain tension. It is found that σ D B is consistent with σ P T when the strain rate is properly taken into account in evaluating σ P T .

Forming Limit Stress Diagram Prediction of Pure Titanium Sheet Based on GTN Model.

In this paper, the initial values of damage parameters in the Gurson–Tvergaard–Needleman (GTN) model are determined by a microscopic test combined with empirical formulas, and the final accurate values are determined by finite element reverse calibration. The original void volume fraction (f0), the volume fraction of potential nucleated voids (fN), the critical void volume fraction (fc), the void volume fraction at the final failure (fF) of material are assigned as 0.006, 0.001, 0.03, 0.06 according to the simulation results, respectively. The hemispherical punch stretching test of commercially pure titanium (TA1) sheet is simulated by a plastic constitutive formula derived from the GTN model. The stress and strain are obtained at the last loading step before crack. The forming limit diagram (FLD) and the forming limit stress diagram (FLSD) of the TA1 sheet under plastic forming conditions are plotted, which are in good agreement with the FLD obtained by the hemispherical punch stretching test and the FLSD obtained by the conversion between stress and strain during the sheet forming process. The results show that the GTN model determined by the finite element reverse calibration method can be used to predict the forming limit of the TA1 sheet metal.

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.

Impact of strain rate sensitivity on the identification of the material parameters scattering and on the formability of zinc sheet

The mechanical behavior of zinc alloys drastically depends on strain rate and temperature, which are not constant during forming processes. During the production of zinc sheets, the slight variations of the industrial equipment parameters induce different local thermomechanical conditions. These variations could be stemming from a non-homogeneous cooling during rolling process, or local segregation of alloys and so on …. The result of these differences entails a significant scattering of material parameters as shown in (Milesi et al. J Mat Process Tech 245:134-148, 2017). This paper tackles the scattering of material parameters through an adapted Norton-Hoff behavior law. Then, four parameters have been identified with a standard Generalized Reduced Gradient method (GRG). Moreover, an exhaustive analysis of the entire rolled coil has been carried out to differentiate the variation coming from the material from the one due to the process. This study also encompasses the influence of strain rate on the forming limit diagram and therefore on the calculation of the forming limit stress diagram.

Formability limits of high-strength H240LA steel sheets under stress/strain gradients

Conventional sheet metal forming processes usually involve the simultaneous action of stretching and bending, inducing strain/stress gradients across the sheet thickness and complex strain paths, which decisively influence the onset and development of the failure mechanism by necking. Therefore, an accurate assessment of formability requires the use of strain path independent tools that take in to account the bending effects on the sheet failure. The use of the theory of critical distance (TCD), widely used in fatigue and fracture mechanics to account the effect of the stress/strain gradients in metal failure, has been satisfactorily analysed by the authors to predict failure by necking under stretch–bending conditions. The current work develops, using and experimental and numerical analysis, two failure models for strain/stress gradient situations which combine both the use of path-independent forming limit diagrams, particularly the forming limit stress diagram (FLSC) and the equivalent plastic strain based forming limit curve (epFLC), along with the concepts of critical distance to account for the effect of bending in the onset of necking. Both developed models are used to predict numerically the failure in a series of stretch–bending tests over H240LA steel sheets. Their predictive capabilities are discussed and compared in the light of the experimental results.

Formability prediction of advanced high-strength steel sheets by means of combined experimental and numerical approaches

Abstract In this work, a group of four capable prediction tools—Classical Forming Limit Curve (FLC), Forming Limit Stress Curve (FLSC), Damage Curve (DC) associating stress-triaxiality with plastic strain and Nonlinear Strain Path Forming Limit Curve (nonlinear strain path FLC) based on an innovative punch originally designed by the Institute for Metal Forming Technology (IFU), University of Stuttgart—are employed to evaluate formability of DP590 advanced high-strength steel (AHSS). The results are subsequently compared. A classical FLC is created with restriction to the Nakajima stretching-test guideline, in which a 100-Tonne universal tensile testing machine is operated to press 1-mm thick DP590 sheets. A nonlinear strain path FLC is generated with an application of an IFU-designed punch to realise nonlinear strain paths under a particular standardised Nakajima testing environment. A stress-based FLC is computationally obtained by transforming the classical FLC, realised in a major-minor strain space, into an FLSC in a principal-stress space using the Hill’48 yield criterion equipped with the Swift strain-hardening law. A DC is arithmetically determined through a combination of the plastic flow rule and Hill’48 yield criterion. To verify and compare those gained curves, both hole-expansion and Fukui stretch-drawing tests are conducted both experimentally and numerically. Regarding the simulation model for numerical investigation, material flow behaviour and deformation anisotropy are modelled by the Swift hardening law and Hill’48 yield criterion, respectively. This research has once again proved that FLSC, DC and nonlinear strain path FLC can obviously identify the forming limit of DP590 AHSS more realistically than the classical FLC can.

Effects of normal and through-thickness shear stresses on the forming limit curves of AA3104-H19 using advanced yield criteria

In the present study, the effects of normal and through-thickness shear (TTS) stresses are simultaneously considered to predict the generalized forming limit diagram (GFLD) of AA3104-H19 using Yld96 [1], Yld2004 [2] and Yld2011 [3] anisotropic yield criteria. For this purpose, considering the general stress state, including the normal and through-thickness shear stresses, the modified Marciniak–Kuczynski (M–K) model is employed. The Newton–Raphson numerical method is applied to solve the nonlinear equations set, and then the forming limit diagram (FLD) and forming limit stress diagrams (FLSD) are computed. First, the forming limit curves are presented by considering the through-thickness shear stress, and then the generalized forming limit curves are presented by applying the normal and through-thickness shear stresses simultaneously. The results show that the through-thickness shear stress has positive sensitivity on the limit strains. Also, the normal stress is more efficient than the through-thickness shear stress on the formability of the plate. Comparison between the results indicates that the predicted limit strains by the Yld2011 anisotropic yield function are lower than those predicted by Yld96.