Necking Criterion Research Articles

Hostile neck anatomy contributes to higher rates of reintervention following endovascular aortic repair for ruptured infrarenal abdominal aortic aneurysm.

Ruptured abdominal aortic aneurysms (AAA) presenting with hostile neck anatomy can represent a challenge in surgical decision-making. We hypothesized that, patients who require reinterventions have higher rates of compromised neck anatomy at initial presentation and may indicate a need for altered surveillance paradigm. Patients presenting with ruptured AAA to a single tertiary care institution from 2014 to 2021 were retrospectively reviewed. Those treated with infrarenal EVAR, with no prior aortic surgeries, and with available pre-operative computed tomography (CT) scans were included. Demographics, timing and type of reintervention, follow-up, and survival were collected. CT scans were assessed for hostile neck anatomy via measurements of diameter, length, angle, taper, bulge, calcification, and thrombus. Demographics, comorbidities, and neck anatomy of those with and without reintervention were compared using Fischer's Exact and Student's T-test. Survival was analyzed via Kaplan-Meier and log-rank test. Eighty-nine patients were available for analysis, 37 of which met inclusion criteria. Intraoperative death occurred in 3 patients (8.1%) and 1 patient (2.7%) was intraoperatively converted to an open repair. Thirty-day and 1-year survival were 97% and 91%, respectively. The reintervention rate was 30% (n = 10), occurring at a median of 200days (18-2053days) after the index operation. All patients requiring reintervention met hostile neck criteria (p = .002) and had a statistically higher number of hostile neck criteria (1.80 vs 0.87, p = .03). Thirty percent (n = 3) of patients that received a reintervention had neck diameter greater than 3cm, compared to zero patients in the non-reintervention group (p = .022). Proximal reinterventions (n = 5) had statistically higher neck diameters and neck angle compared to the non-reintervention group. Infrarenal rEVAR is effective at preventing acute mortality despite specific anatomic considerations that may contribute to the higher reintervention rates, and therefore those parameters ought to be considered when following patients in the post-intervention period.

Experimental investigation and numerical simulation of the effect of type of bending die on the quality of tube forming in rotary draw bending process

This study introduces a new rotary draw bending method that utilizes a variable curvature bending die. Unlike traditional methods that bend tubes with a fixed radius, this method gradually deforms the tube from a large to a small radius. The curvature of the bending die is determined by using an involute curve as the equation for the geometric location of the variable curvature. Hydroforming technology, utilizing fluid under pressure, replaces the mandrel in the rotational tensile bending process. The research was conducted using a thin-walled AA6063 tube with a 13.88 diameter-to-thickness ratio. The bending process was examined at critical bending ratios of 1 and 1.6 times the diameter, with a 90° bending angle. The maximum pressure that can be applied in any bend radius ratio was predicted using the necking criterion. The simulation and experimental tests analyzed the effects of internal fluid pressure and bend die curvature on defects such as wall thinning in the outer curvature of the bend, thickening of the wall in the inner curvature of the bend, and cross-section non-roundness. The results indicate that, at constant pressure, the amount of thinning and thickening of the bent tube is significantly improved when using the variable radius bending die compared to the fixed radius die.

Proximal Instructions for Use Violations in Elective Endovascular Aneurysm Repair in the Vascular Quality Initiative: Retrospective Analysis.

Endovascular aneurysm repair (EVAR) is often attempted in patients with marginal anatomy. These patients' midterm outcomes are available in the Vascular Quality Initiative for analysis. Retrospective analysis of prospectively collected data in the Vascular Quality Initiative from patients who underwent elective infrarenal EVAR between 2011 and 2018. Each EVAR was identified as either on- or off-instructions for use (IFU) based on aortic neck criteria. Multivariable logistic regression models were used to assess associations between aneurysm sac enlargement, reintervention, and type Ia endoleak with IFU status. Kaplan-Meier time-to-event models estimated reintervention, aneurysm sac enlargement, and overall survival. We identified 5,488 patients with at least 1 follow-up recorded. Those treated off-IFU included 1,236 patients ([23%] mean follow-up 401 days) compared with 4,252 (77%) treated on-IFU (mean follow-up 406 days). There was no evidence of significant differences in crude 30-day survival (96% vs 97%; p = 0.28) or estimated 2-year survival (97% vs 97%; log-rank p = 0.28). Crude type Ia endoleak frequency was greater in patients treated off IFU (2% vs 1%; p = 0.03). Off-IFU EVAR was associated with type Ia endoleak on multivariable regression model (odds ratio 1.84 [95% CI 1.23 to 2.76]; p = 0.003). Patients treated off IFU vs on IFU experienced had increased risk of reintervention within 2 years (7% vs 5%; log-rank p = 0.02), a finding consistent with results from the Cox modeling (hazard ratio 1.38 [95% CI 1.06 to 1.81]; p = 0.02). Patients treated off IFU were at greater risk for type Ia endoleak and reintervention, although they had similar 2-year survival compared with those treated on IFU. Patients with anatomy outside IFU should be considered for open surgery or complex endovascular repair to reduce the probability for revision.

Simultaneously enhancing strength and ductility of HCP titanium via multi-modal grain induced extra dislocation hardening

According to Considère necking criterion, enhancing strength of a material will decrease its elongation to failure, i.e. ductility, even if the strain hardening rate remains unchanged. Unfortunately, four traditional strengthening mechanisms including grain refinement, deformation, solid solution and 2nd-phase particle strengthening increase the yield strength by increasing the critical shear stress for slip initiation and unexceptionally reduce the strain hardening ability and ductility. Recent experiments revealed that implementation of heterostructures can produce extra hetero-deformation induced (HDI) hardening and thus reduce ductility loss while enhancing strength. However, the improved ductility was still less than that of coarse-grained counterparts. Here we fabricated a bulk heterostructured Ti with a uniform multi-modal grain size distribution in which the single individual micro-grain is surrounded and constrained by three-dimensional ultrafine grains. Tensile tests revealed the multi-modal Ti has a high yield strength of 800 MPa, ductility of 28.5%, and outstanding HDI hardening effect compared with its coarse-grained counterparts (a yield strength of 550 MPa and ductility of 26.5%). These mechanical properties of our multi-modal Ti are also superior to other literature reported data of heterostructured Ti. Microstructural characterization further reveals the uniform distribution between hard and soft domains produces maximum interface density and HDI hardening effect. Moreover, the HDI causes extra 〈c + a〉 geometrically necessary dislocations piling ups in the constrained micro-grains, which produce enough and extra strain hardening to maintain and even enhance slightly the ductility. Our work provides a strategy to simultaneously enhance strength and ductility of metals via enough and extra strain hardening capability increase.

EndoSuture aneurysm repair versus fenestrated aneurysm repair in patients with short neck abdominal aortic aneurysm.

The aim of this study was to compare midterm results of EndoAnchors in EndoSuture aneurysm repair (ESAR) versus fenestrated endovascular aneurysm repair (FEVAR) in short neck abdominal aortic aneurysm (AAA). All patients who underwent an ESAR procedure for a short neck AAA at our center between September 2017 and May 2020 were considered for analysis. To form the control group, preoperative computed tomography angiography of patients who underwent FEVAR for juxtarenal AAA between April 2012 and May 2020 were reviewed and patients who met short neck criteria selected. A propensity-matched score on neck length and neck diameter was calculated, resulting in 18 matched pairs. AAA shrinkage, type Ia endoleaks (EL), AAA-related reinterventions, and AAA-related deaths were compared. The median AAA diameter was 54mm (interquartile range [IQR], 52-61mm) versus 58mm (IQR, 53-63mm) with a median neck length of 8mm (IQR, 6-12mm) vs 10mm (IQR, 6-13mm) in ESAR and FEVAR patients, respectively. Technical success was 100% in both groups. Procedural success was 94% in the ESAR group versus 100% in the FEVAR group. The median procedure duration was 138mm (IQR, 113-182mm) vs 240mm (IQR, 199-293mm) ( P< .001) and the median length of stay was 2days (IQR, 2-3days) vs 7days (IQR, 6-7days) (P< .001) in ESAR and FEVAR patients, respectively. No major hospital complications were observed in ESAR patients compared with two in FEVAR patients (11%) with one transient acute kidney injury and one transient paraplegia. The median follow-up was 23months (IQR, 19-33months) vs 36months (IQR, 22-57months) with 67% versus 61% AAA shrinkage in the ESAR and FEVAR groups, respectively (P= .73). No type Ia EL, proximal neck-related reinterventions, or AAA-related deaths were observed in either group. No AAA-related reintervention was observed in the ESAR group versus three reinterventions in the FEVAR group (P= .23). ESAR seems to be a safe technique with no major postoperative complications or reinterventions observed during follow-up. It seems to offer similar midterm results as FEVAR in terms of type Ia EL, aneurysm shrinkage, and aneurysm-related mortality. ESAR seems to be a good off-the-shelf alternative to FEVAR in case of technical constraints.

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.

Plastic instability criterion based on new necking parameters for Cu–Al, Cu–A5052, and Cu–A5083 roll-bonded laminated metal composites fabricated without post-annealing

Although laminated metal composites fabricated by accumulative roll bonding (ARB) undergo kink-band formation, there are no guidelines for optimizing their fabrication to avoid necking and shear localization without post-annealing. The necking of the composite layers during rolling generates non-uniformities that may degrade the mechanical performance of the composite. This paper proposes a model for laminated metal composites that aims to quantitatively assess and predict necking based on the work-hardening of each layer. Cu–Al-, Cu–A5052-, and Cu–A5083-laminated metal composites were fabricated using ARB at room temperature (~300 K) without post-annealing, and they were subjected to mechanical and microstructural analyses. A normalized neck amplitude was introduced as a new parameter that accurately predicted the degree of necking observed experimentally. Another new parameter, an instability index, was introduced to frame the necking criterion of the hard layers. A plastic instability criterion framed based on the new parameters accurately predicted the degree of necking in the hard layers of the as-prepared laminated metal composites. These findings may be applied to guide the fabrication of metal composites of any composition using the ARB process.

Influence of criteria on the determination of forming limits in thickness reduced cruciform specimens

Biaxial tensile test methods using cruciform specimens have been drawing attention as an effective approach to characterize sheet metal formability. The cruciform specimens usually adopt a thickness reduction at the central area to achieve a relatively large strain gradient for localized necking and fracture investigation. For conventional tests, many criteria have been proposed to determine the forming limits at necking, however, none has been widely accepted and applied to the cruciform specimens with non-uniformed thickness reduction. Therefore, in this work, different existing necking criteria are applied and discussed for numerical procedure in order to define an appropriate necking criterion for the thickness reduced cruciform specimens. AA6061-T4 sheet with a thickness of 2mm is used as a target material. The predicted forming limit curves are compared for different criteria, and the feasibility of each criterion is discussed in detail. Thanks to two dedicated specimens proposed by the authors, forming limits are determined for a wide range of strain states.

Numerical analysis of necking in stretch-bending based on modified maximum force criteria

The necking criteria based on the maximum force principle, such as the Swift and Hill necking models, have been extensively used in the past to study sheet formability. Many extensions or modifications of these criteria have been proposed to improve necking predictions under only stretching conditions. Recently, the authors proposed two approaches to predict necking under stretch-bending conditions: a generalisation of classical maximum force criteria to stretch-bending; and a necking criterion based on critical distance concepts, suggesting that necking is controlled by the damage of a critical material volume located at the inner side of the sheet. Both approaches were evaluated with analytical models and the failure was successfully predicted in different materials, such as steel, brass and aluminium. This work presents a numerical study of the proposed necking criteria in stretch-bending processes with different punch radii. The simulations are validated with experimental tests over H240LA steel sheets.

Comparative Investigation of the Experimental Determination of AA5086 FLCs under Different Necking Criteria.

The construction of a forming limit diagram (FLD) is a conventional approach to obtain limit strains and to evaluate the formability of sheet metal. Appropriate necking criteria should be applied to determine the forming limit curve (FLC) accurately. In recent years, deep research on the determination of the FLC has been carried out; meanwhile, several necking criteria have been proposed. However, the application of inappropriate necking criteria would cause deviations when determining FLCs. In this study, both Marciniak and Nakajima tests were carried out on the AA5086 aluminum sheet to make a comparative investigation of different necking criteria in the determination of FLCs. In the Marciniak test, four existing necking criteria were chosen to construct FLCs, and analyzed in detail. The well-performed time dependent and position dependent methods were selected for the Nakajima test. Meanwhile, the modified Wang method based on the height change of the adjacent points was proposed. The comparative results showed that the time and position dependent methods were relatively conservative in both experiments, while the modified Wang method could identify the onset of localized necking more accurately.

Determination and predication of formability on 22MnB5 steel under hot stamping conditions using Gleeble

ABSTRACT Hot stamping process is a thermo-mechanical process in which blank is heated to austenitization temperature and then subsequent forming and quenching are done simultaneously. Due to complex process cycle in hot stamping conditions, like high temperature and cooling etc., determination of formability is difficult. Therefore, in this work a series of experiment was performed on thermomechanical simulator (Gleeble-3800) at different temperatures (750oC, 800 oC, 850 oC) and strain rates (0.01/s, 0.1/s, 1/s) to obtain flow behavior and formability of 22MnB5 Steel. Due to limitation of the uniaxial deformation in Gleeble-3800, modified tensile specimen was used to obtain plain strain conditions. Thickness gradient-based necking criterion was validated for high temperature forming at different strain rates. This criterion was further used to determine the formability of 22MnB5 steel. Thickness distribution and thickness gradient for modified specimen and simple tensile specimen is observed under various conditions. It was found that with increase in temperature and strain rate formability of 22MnB5 steel increased as well as uniform deformation occurs. Thickness gradient necking criteria indicates that at point of necking thickness gradient ratio falls below the critical value of 0.92. .

Experimental and Numerical Analysis on Dual Phase Steel (DP780) Sheet Forming Limit and Effect of Microstructure Evolution on Formability

The application of dual phase steel in the automotive sector is increasing due to its high strength-to-weight ratio and good shock absorption capacity. The formability of dual phase steel is complex due to its multiphase microstructure which results in inaccurate formability prediction using numerical methods. The present study is aimed at analyzing the forming behavior and microstructure evolution of a dual phase steel, DP780, at different strain paths. The forming behavior of this steel was analyzed in terms of forming limit diagram (FLD) using Nakazima tests and finite element method. Various necking criteria were used to construct the FLD. Samples deformed at different dome height for three principal strain paths and strain levels were subjected to detailed microstructure and texture investigations. The microstructure and texture study was mainly focused on analyzing the development of deformation texture, misorientation development and orientation hardness. These studies showed that the formability of DP780 steel is largely affected by the development of γ fiber texture. Also, the evolution of other microstructure and texture quantifiers such as texture intensity, misorientation and relative orientation hardness at different strain paths was correlated with the formability of the material.

Numerical modelling and formability of with and without heat-treated AA 6023-T6 alloy sheet with various necking/failure criteria

Sheet metal forming is a process widely used in the manufacturing industry. There are numerous sheet metal forming processes to evaluate and understand the formability. Among all formability tests, the basic formability can be formulated through tensile tests and followed with specialized tests. In the present paper, the formability of AA 6023-T6 sheet of 2mm thickness by modelling for stretching test namely limit dome height (LDH) test was performed using PAM STAMP 2G a commercial finite element software. For the simulation, input mechanical properties like yield strength (c), material strength coefficient (K), strain hardening exponent (n), plastic strain ratio (R) etc., were considered from the existing literature. For the simulation, two different conditioned sheet such as at room temperature and annealed sheet at 400°C. For all the simulations, four strain paths 100 × 200mm, 125 × 200mm, 150 × 200mm, 175 × 200mm and 200 × 200 mm were taken. Results are drawn based on the three localized necking criteria namely the effective strain rate-based criterion (ESRC – R1), major strain rate-based criterion (MSRC –R2), thickness strain rate-based criterion (TSRC – R3). Form the obtained results, forming limit diagrams are developed for the both condition of sheet metal. It is observed that, formability of AA 6023-T6 sheet in-plane condition (i.e. 100x100 mm) annealed sheet at 400°C is shown better forming whereas in bi-axial condition (i.e. 200x200 mm) got reduced compared to room temperature sheet. The same phenomenon is noted in all the necking criteria too.

Rate-dependent combined necking and fracture model for predicting ductile fracture with shell elements at high strain rates

This paper introduces a rate-dependent extension of the Hosford-Coulomb ductile fracture initiation model combined with a non-local localized necking criterion (rate-dependent DSSE-HC model) for predicting ductile fracture initiation in metals with shell finite elements at high strain rates. A Johnson-Cook-type hardening model, which consists of strain hardening, rate-sensitivity, and thermal softening terms, was adopted together with an associated flow rule. The temperature was treated as an internal state variable that was calculated from the plastic strain energy using a strain-rate-dependent weighting function between the isothermal and adiabatic conditions. The parameter associated with the localized necking locus for a specific strain rate was obtained using the instantaneous strain hardening rate. The proposed extension of the DSSE-HC model was implemented in a user-defined material subroutine and validated for virtual DP590 notched tension and punch-loaded circular disc specimens by comparing with fine mesh solid element solutions.

Plastic instability of mechanical bulging process for Zircaloy-4 cladding tube based on localized necking criterion

Plastic instability of mechanical bulging process, different from the traditional tube hydroforming, is developed for Zircaloy tube based on localized necking criterion. Based on the observation of published experiments of bulging, an elementary analyzed model of plastic deformation is proposed and applied for examining the variation of bulging process and its limitation. The developed model comprises two deformation regions, one is bulged part with friction effect and the other is flattened part but without friction effect. All mentioned process parameters, such as contact friction, material properties (strain hardening exponent and normal anisotropy), and process geometries conditions (tube radius and thickness), are taken into account for in such mechanical bulging model. Plastic instability in bulging is examined using localized necking criterion based on the proposed model. A published experiment was initially used to verify the present model. Then, the effects of process parameters on the variation of bulging limit are investigated. The developed model allowed us to better understand the failure mechanism through the localized necking criterion, and also can be defined as a sign of fracture for a bulged tube. Moreover, a proposal will be made to examine the limitation of bulging for practical needs.

The Influence of Physiotherapy on Neck Disability and Headache among Dental Professionals

This study aim was to identify the impacts of physiotherapy program on reducing neck disability and headache among dental professionals. According to the Neck Disability Index and criteria, set by the International Headache Society, 24 dentists, with neck pain, were selected. To evaluate pain intensity we used visual analog pain scale (VAS). 24 individuals (age 23–39 yr.) were split into 2 groups of 12 people. The first group (age – 27.83 ± 5.0 yr.) had a six – week combined physiotherapy program. The second group was the control group (age 26.17 ± 2.4 yr.) for who physiotherapy was not applied. Physiotherapy program took 45–60 min, twice a week, and consisted of: • soft tissues mobilization techniques; • cervical and thoracic spine mobilization; • active / passive stretching of neck muscles; • exercises which increase neck range of motion; • exercises which increase endurance and strength of upper back muscles. The subjects were assessed before yhe research, 6 and 12 weeks later. The study results showed, that after a six-week physiotherapy program the neck disability index significantly (p &lt; 0.05) decreased. No neck disability index changes were reported in the control group. Daily activity performance significantly improved (p &lt; 0.05), reading and sleeping quality increased and the subjects could lift weights significantly easier. We found a tendency (p &lt; 0.1) that after six weeks of physiotherapy headaches decreased. The neck disability index of the controls did not significantly improve. Six weeks of physiotherapy program significantly reduces neck pain, headache and improves neck disability index in all domains.Keywords: physiotherapy, neck pain, headache, the neck disability index.

Prediction of necking in HCP sheet metals using a two-surface plasticity model

In the present contribution, a two-surface plasticity model is coupled with several diffuse and localized necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse necking is predicted by the general bifurcation criterion. As to localized necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and localized necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.

Investigation of various necking criteria for sheet metal formability analysis using digital image strain data

The precise determination of the forming limit strains of a sheet metal is necessary in order to accurately predict the onset of failure in sheet metal forming processes. The method used to detect the onset of necking (i.e. the necking criterion) is a most important factor in formability analysis as it significantly affects the forming limit strains. Many different necking criteria have been developed, which take advantage of the flexibility and high resolution of digital image correlation (DIC) strain measurements. Several time-dependent and time/geometry-dependent necking criteria were carefully investigated in order to evaluate their ability to reliably and consistently detect the onset of necking of TRIP780 sheet specimens that were stretch-formed over a hemispherical punch. It was found that the geometry-dependent, surface slope criterion was the most robust and consistent criterion of those evaluated.

Acromioaxillosuprasternal Notch Index and Old Head and Anatomic Neck Criteria in Predicting Difficult Laryngoscopy in Tracheal Intubation in Children under General Anesthesia

Introduction: Currently, various methods are being used for determining difficult laryngoscopy. The present study aimed to compare the acromioaxillosuprasternal notch index function with the old head and neck anatomic criteria in predicting difficult laryngoscopy with respect to trachea intubation under general anesthesia in children. Materials and Methods: In this cross-sectional study, 379 children under intubation with general anesthesia entered the study. Patients were divided into two groups: easy laryngoscopy (grades 1 and 2) and difficult laryngoscopy (grades 3 and 4) based on Cormack-Lehane score. The thyromental distance systems, height to thyromental distance, Upper-Lip-Bite test, neck circumference, and acromioaxillosuprasternal notch index were studied and compared. Results: Laryngoscopy was difficult in 48 subjects (38 were grade 3 and 10 were grade 4). Interestingly, no significant difference was detected between easy and difficult laryngoscopies based on the thyromental distance, neck circumference, height to thyromental distance, and acromioaxillosuprasternal notch index (P&gt;0.05). height to thyromental distance , acromioaxillosuprasternal notch index , and neck circumference have a sensitivity of 32.2%, 47.9%, 51.1%, respectively, and the specificity was 52.7%, 45.6%, and 48.9%, respectively. Conclusion: Neck circumference and acromioaxillosuprasternal notch index outperform the height to thyromental distance. On the other hand, Modified Mallampati test is better than Upper-Lip-Bite test in determining difficult laryngoscopy in children.

A Graphical Method to Estimate Forming Limit Curve of Sheet Metals

Since its foundation, the concept of forming limit diagram has been widely accepted in sheet metal forming community as a powerful tool for studying formability. There are pyramid models that were developed to estimate the forming limit curve theoretically, for example, Swift's diffuse necking criterion, Hill's localized necking criterion, Marciniak and Kuczynski model, Modified Maximum Force Criterion, etc.. Implement of these models, however, is a laborious task. To simply the task, this study presents a graphical method to estimate forming limit curve of sheet metal. Some new insights into the Modified Maximum Force Criterion, the Hora method, are discussed. The insights pertain to the use of a graphic tool to estimate limit strains at three critical forming modes in sheet metal forming that are the uniaxial tension, plane strain, and equi-biaxial tension. Connecting three points by linear lines yields to a simple graph of forming limit curve. Method validation is supported by comparing the estimated forming limit curve with experimentally measured data for several automotive sheet metals.