Polar Effective Plastic Strain Research Articles

Use of uncoupled ductile damage models for fracture forming limit prediction during two-stage forming of aluminum sheet material

In this paper, failure limits of aluminum AA5052 sheet material were experimentally investigated, and subsequently, these were predicted using various uncoupled ductile fracture models. In this context, three different sets of experiments, namely two-stage stretch forming, two-stage deep drawing, and single point incremental forming experiments, were performed to estimate the failure limits under several different strain paths. Both the isotropic von Mises and anisotropic Barlat Yld2000 yield criteria were used to calibrate eight different fracture models, and found that incorporating an anisotropic model enhanced the accuracy of prediction for most of the fracture models. Moreover, it was identified that the incorporation of anisotropic yield theory in the Bao-Wierzbicki (BW) fracture model predicted the experimental fracture surface strains precisely for as-received sheet materials. This BW model-based fracture forming limit diagram (BW-FFLD) was transposed into a path-independent polar effective plastic strain (PEPS) locus to estimate the onset of fracture during two-stage forming experiments. Furthermore, the BW model was incorporated as a fracture initiation model in the finite element (FE) software, LS-Dyna, using the generalized incremental stress state dependent damage model (GISSMO) platform to predict the fracture location and dome height through the element erosion technique. It was observed that the dome height and cup height were predicted within 7 % and 5 % error margins in the FE simulation of two-stage stretch forming and deep drawing experiments, respectively. Furthermore, the damage evolution contour indicated that the accumulation of the damage value was rapid, which was responsible for the massive drop in the dome and cup heights during two-stage stretch forming and deep drawing experiments.

Forming Limit Analysis of Thin-Walled Extruded Aluminum Alloy Tubes under Nonlinear Loading Paths Using an Improved M-K Model

To meet the requirement of lighter weight and better performance in tube hydroforming, one of the most important tasks is to accurately predict the forming limit of thin-walled tubes under nonlinear loading paths. This work established the M-K+DF2012 model, a combination of the M-K model and the DF2012 ductile fracture criterion, for the forming limit prediction of thin-walled tubes under nonlinear loading paths. In this model, the failure of the groove is determined by the DF2012 criterion, and the corresponding strains in the uniform region are the limit strains. The limit strains of an AA6061 aluminum alloy tube under a set of linear loading paths and two typical nonlinear loading paths were tested. Parameter values of the M-K+DF2012 model for the tube were determined based on the experimental limit strains under linear loading paths, and the limit strains under the two nonlinear loading paths were predicted. Then the strain-based forming limit diagram (ε-FLD) and the polar effective plastic strain FLD (PEPS-FLD) of the tube under different pre-strains were predicted and discussed. The results show that the limit strains of the tube are obviously path-dependent, and the M-K+DF2012 model can reasonably capture the limit strains of the tube under both linear and nonlinear loading paths. The predicted ε-FLD shows a strong dependence on the pre-strain, while the predicted PEPS-FLD is weakly strain path-dependent and almost path-independent on the right-hand side for the AA6061 tube.

Polar effective plastic strain - forming limit diagram of DP 440 steel sheet with application to two-step forming test

In this work, experimental forming limit curve (FLC) and polar effective plastic strain -forming limit diagram (PEPS-FLD) are developed in order to predict the formability of dual phase (DP) steel grade 440. The Forming Limit Diagrams (FLD) of the examined steel are first obtained using the Nakajima stretch-forming test with a decreased hemispherical punch diameter of 50 mm in combination with Auto-Grid Vialux strain measurement system. To achieve a PEPS-FLD, an experimental FLC data must be completely projected onto the polar space using the results of FLC, Hill's 48 anisotropic yield criterion, and PEPS algorithm through plasticity calculation. Finally, a two-step forming test is conducted both experiments and simulation to demonstrate the practical applicability of the PEPS-FLD. It really would appear that the PEPS-FLD could predict the formability in non-linear strain path and can be utilized to enhance formability by creating non-linear strain path of DP440 more accurately than FLD.

Effect of Strain Rate and Friction on Formability According to Major Deformation Modes in Sheet Metal Forming

The effects of strain rate and friction on the formability of the steel sheet are studied according to the three major deformation modes that are widely used in the industry. Experiments for circular cup stretch, plane strain stretch, and circular cup drawing are carried out at two speeds of 3 SPM and 30 SPM for SGACUD 0.7 t and DP 590 1.0 t steel sheets. The corresponding finite element simulations are carried out. A constitutive equation, which is a function of strain and strain rate, is used to account for the effect of strain rate on flow stress in the finite element analysis. The formability is evaluated using the polar effective plastic strain (PEPS) forming limit diagram. An experimental equation that takes the sliding velocity into account is utilized in this study. In conclusion, the effects of strain rate and friction are clearly understood; finite element analysis by using the constitutive equation to consider strain rate, and also the friction coefficient model according to the sliding velocity, can be effectively used to predict the formability as forming speed changes for the three deformation modes.

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.

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.

Formability and fracture in deep drawing sheet metals: Extended studies for pre-strained anisotropic thin sheets

In this study, experimental and numerical investigations were conducted to predict the formability and fracture behavior of as-received and pre-strained sheet materials during deep drawing process. In this context, various laboratory scale experimental setups were developed to impart different types and amounts of pre-strain such as 5% and 10% equi-biaxial pre-strains (5% EBP and 10% EBP), 10% plane strain pre-strain (10% PSP), and 10% uni-axial pre-strain (10% UP) on the extra deep drawing (EDD) steel and aluminum alloy (AA5052) sheets of 1.2 mm thickness. Further, all the pre-strained sheet samples were deformed using a cylindrical deep drawing setup. The forming limit diagrams (FLDs) of as-received sheets were predicted by the Marciniak–Kuczyński (MK) model incorporating different anisotropic yield functions such as Hill48 models identified based on r-values (Hill48-r), and yield stresses (Hill48-σ), and the non-quadratic plane stress Yld2000-2d model. Also, the Bao–Wierzbicki (BW) fracture curve was calibrated using different anisotropic yield functions. Subsequently, the formability in terms of limiting drawing ratio (LDR) was predicted using the MK-FLD. The BW fracture curve was incorporated into the generalized incremental stress state dependent damage model (GISSMO) platform in LS-Dyna software and the fracture behavior was predicted in terms of failure location and cup height at the onset of fracture. It was also found that the incorporation of Barlat Yld2000-2d yield function into the FE simulation efficiently predicted the necking and fracture behavior of as-received sheets. Furthermore, the concept of path independent polar effective plastic strain (PEPS) based failure model was used to predict LDR, thinning profile and fracture cup height of all the different pre-strained sheets. Finally, the strain paths and experimental fracture strains were plotted in 3D fracture locus to get insight into the deformation behavior during the deep drawing experiments.

Finite element modeling and durability evaluation for rubber pad forming process

Elastomer (or rubber pad) forming is a dieless forming process. The forming process has several advantages compared to general press forming process in terms of tool cost and scratch problem. However, when the elastomer is subjected to severe deformation during forming process, it can result in an expensive cost for the replacements of elastomer. Therefore, it is necessary to evaluate accurate tool life. In this study, the FE analysis was conducted for the rubber pad forming process and the fatigue life evaluation of the elastomer tool was investigated numerically using the reference experimental data. For the FE analysis, uniaxial and equibiaxial tension tests of natural rubber 50 were carried out in order to obtain the mechanical material properties of the elastomer. The hyperelastic behavior of the elastomer was characterized using Ogden model. The elastomer forming process was modeled using a commercial software LS-DYNA 3D. Two important factors of FE modeling were to calibrate the simulation conditions and to obtain the target product shape with a preformed elastomer. With the result of FE analysis, a durability of the elastomer was conducted focusing on fatigue life, because the elastomer is applied for repeated loadings during the forming process. Unlike general fatigue analysis, the fatigue life of the elastomer is predicted with respect to the strain measures due to Mullins effect. Furthermore, the Polar Effective Plastic Strain (PEPS) diagram [6] considering the strain path changes was used to check the failure of the blank during the forming process.

Failure strains of anisotropic thin sheet metals: Experimental evaluation and theoretical prediction

In the present study, experimental and theoretical analyses were performed to predict the failure strain of EDD and AA5052 sheet metals. In this context, uniaxial tensile tests and stack compression tests were conducted to assess the anisotropic constants of two different yield models viz. Hill48 and Yld2000-2d. Further, the calibrated models were used to estimate the directional properties and yield loci of the investigated sheet metals, and the results were successfully validated with the experimental data. Additionally, the forming limit diagram (FLD) and fracture forming limit diagram (FFLD) were analytically predicted using Marciniak–Kuczyński (MK) model and Bao–Wierzbicki (BW) ductile damage model implementing different yield theories. The estimated failure limits were compared with the experimental necking and fracture strain data obtained from the punch stretching (PS) tests, and found that the theoretical models incorporating Yld2000-2d yield theory best described the experimental limiting strains. Furthermore, the best predicted MK-FLD and BW-FFLD was used for failure strain analyses of three different sheet metal forming experiments such as two-stage forming, single point incremental forming (SPIF) and deep drawing. It was observed that the MK-FLD and BW-FFLD failed to predict the necking and fracture strain of different pre-strained sheets in the principal strain locus. Hence, all the strain data were transposed into polar effective plastic strain (PEPS) locus using Yld2000-2d yield model, and the PEPS based failure limit was developed. It was found that the MK-FLD and BW-FFLD predicted the respective limiting strains in PEPS locus efficiently. Moreover, all the experimental fracture strains were converted into 3D stress triaxiality locus and concluded that the calibrated BW fracture loci had a good predictive efficiency of all the fracture strains obtained from various forming tests.

Necking and fracture limit analyses of different pre-strained sheet materials in polar effective plastic strain locus using Yld2000-2d yield model

This paper aims to estimate and analyze both the necking and fracture based path-independent forming limit criteria during two-stage forming of anisotropic sheet materials. In this context, in-house experimental setups were fabricated to impart pre-strain along three distinct strain paths viz. equi-biaxial, plane strain and uniaxial in different automotive grade sheet materials namely EDD, AA5052 and DP600. Uniaxial tensile and stack compression tests were conducted, and the test results were used to evaluate the eight anisotropic coefficients of Yld2000-2d yield model. The predicted evolutions of the yield loci and both the strength and plastic strain ratio (r-value) directionalities of the pre-strained materials were calibrated with experimental data. In the second stage of deformation, all pre-strained sheet materials were stretch formed up to the onset of necking and further until the initiation of fracture. Correspondingly, the forming limit diagram (ε-FLD) and fracture forming limit diagram (ε-FFLD) were experimentally evaluated. The necking and fracture limit of as-received materials was theoretically predicted incorporating calibrated Yld2000-2d yield model in the geometrical imperfection based Marciniak-Kuczynski (MK) model and ductile fracture based Bao-Wierzbicki (BW) damage model, respectively. It is noteworthy that the dynamic shifting of pre-strained ε-FLDs and ε-FFLDs has been recorded in principal strain space (ε1, ε2) depending on the type and amount of pre-strain. Hence, the polar effective plastic strain (PEPS) based necking (PEPS-FLD) and fracture (PEPS-FFLD) limits were estimated using Yld2000-2d anisotropy plasticity theory, and it was observed that the shift of the limiting strains was restricted successfully. It was found that the maximum absolute error during necking and fracture dome height prediction of pre-strained materials was restricted up to 5% and 6%, respectively, when PEPS based failure limits were used as damage model in FE simulation.

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 failure model for non-proportional loading under plane stress condition based on GFLC in comparison to eMMFC and PEPS

A mathematical model is presented for a forming limit for non-proportional loading under plane stress condition. The model results in an approach to reduce the number of experiments needed for the Generalized Forming Limit Concept (GFLC) and presents a numerical approach to calculate the linearized FLC from real Nakajima measurements. The mathematical model has been analyzed in comparison to Polar Effective Plastic Strain (PEPS) diagram and enhanced Modified Maximum Force Criterion (eMMFC), discussing both consistency with plasticity modeling and industrial applicability. An experimental setup based on Nakajima specimens is presented and DIC measurements are used to capture loading paths. The measured loading paths are used to validate predictions made by PEPS, eMMFC and the presented mathematical approach. The latter model shows promising results for prediction of failure for non-proportional loading.

Material characterization and fracture prediction with advanced constitutive model and Polar EPS fracture diagram for AA 3104-H19

Material characterizations for plasticity and fracture have been conducted from uniaxial tensile tests, bi-axial bulge test, and disk compression test for a beverage can AA3104-H19 material. The results from the experimental tests are used to determine material coefficients for the Yld2004-18p model [1]. Finite element simulations are developed to evaluate the predicted earing profile. Excellent agreement with the experimental data for eight ears exhibited in AA3014-H19 is achieved using the Yld2004-18p constitutive model. Further mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on the samples with a central hole and notched specimens to achieve tensile and plane-strain conditions. A specially designed torsion test of a double bridge specimen is conducted to generate the points near pure shear conditions. The Nakajima test is also utilized to produce a bi-axial tension condition. The data from the experiments is used to generate the fracture locus in the principal strain space. Mapping from the principal strain space to Polar Effective Plastic Strain (PEPS) space is accomplished for a general yield function. Finite element modeling is used to validate the fracture diagram in the polar space. A hole expansion demonstrates the accuracy of the PEPS fracture theory for the direction for onset of failure.

Plastic anisotropy and failure in thin metal: Material characterization and fracture prediction with an advanced constitutive model and polar EPS (effective plastic strain) fracture diagram for AA 3014-H19

Material characterizations for plasticity and fracture have been conducted from uniaxial tensile tests, bi-axial bulge test, and disk compression test for a beverage can AA3104-H19 material. The results from the experimental tests are used to determine material coefficients for the Yld2004-18p model (Barlat et al., 2005). Finite element simulations are developed to evaluate the predicted earing profile. It is shown that the Yld2004-18p model is capable of accurately predicting the complex earing profile. Excellent agreement with the experimental data for eight ears exhibited in AA3014-H19 is achieved using the Yld2004-18p constitutive model. Further mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on the samples with a central hole and notched specimens to achieve tensile and plane-strain conditions. A specially designed torsion test of a double bridge specimen is conducted to generate the points near pure shear conditions. The Nakajima test is also utilized to produce a bi-axial tension condition. The data from the experiments is used to generate the fracture locus in the principal strain space. Mapping from the principal strain space to stress triaxiality space, principal stress space, and Polar Effective Plastic Strain (PEPS) space is accomplished for a general yield function. Finite element modeling is used to validate the fracture diagram in the polar space. A model of a hole expansion during cup drawing demonstrates the robustness of the PEPS fracture theory for a condition with a highly anisotropic material and accurately predicts the direction for onset of failure.

Implementation of Yld96 anisotropy plasticity theory for estimation of polar effective plastic strain based failure limit of pre-strained thin steels

In present work, tensile and stack compression tests were performed along different orientations to evaluate the yield behaviour and strength directionalities of several equi-biaxial, plane strain and uniaxial pre-strained extra deep drawing (EDD) thin steel sheets. Strain based forming limit diagrams (ε-FLD) were evaluated by deforming along six different paths with strain ratio ranging from 0.91 to −0.34, and the dynamic shift of failure strains was established with the cusp moved equal to the amount and direction of minor strain component of the pre-strained materials. Hence, polar effective plastic strain based FLD (PEPS-FLD) was estimated using the Yld96 anisotropy plasticity theory to restrict the dynamic shift of failure strains irrespective of the amount and type of pre-strain. Unlike ε-FLD, the consideration of PEPS-FLD along with Yld96 anisotropy coefficients of as-received EDD steels in FE model was encouraging to predict the limiting dome height (LDH) close to experimental data within 6% error. Also, insights into the role of effective plastic strain consumed and strain path on decrease in LDH of pre-strained steels were analysed.

Computational assessment of residual formability in sheet metal forming processes for sustainable recycling

This paper introduces a new computational scheme addressing a problem of cold recyclability of sheet-metal products based on the assessment of their post-manufacture residual formability. Formability of sheet metals has been studied for several decades, and various techniques were suggested since a Forming Limit Diagram was first introduced in the 1960s. At the same time, cold recycling, or re-manufacturing, of sheet metals is an emerging area studied mostly empirically; in its current form, it lacks theoretical foundation. In order to address the challenge of residual formability for sheet-metal products, a reformability index is introduced in this study. The proposed method takes advantage of the latest developments in the area of evaluating multiple-path formability and introduces a quantitative reformability index for the manufactured material. This index represents possible levels of strains for deformation along different paths, based on Polar Effective Plastic Strain (PEPS). PEPS provides robustness against non-linear strain-path effects, thus making a reliable basis for such analysis. Based on residual formability, a predictive model was sought to assess a degrading effect of the flattening process. Taking advantage of extensive numerical simulation, a wide range of geometrical parameters in an unbending process, as a predominant mechanism in flattening, was studied.The reformability index alongside prediction of degradation in flattening allows evaluation of prospective re-manufacturing. The significance of this research is its advancement towards recycling of sheet-metal products without melting them by facilitating design for sustainability. The proposed scheme also provides a subroutine friendly framework for numerical simulations.

Advances in Constitutive and Failure Models for Sheet Forming Simulation

Non-Associated Flow Rule (Non-AFR) can be used as a convenient way to account for anisotropic material response in metal deformation processes, making it possible for example, to eliminate the problem of the anomalous yielding in equibiaxial tension that is mistakenly attributed to limitations of the quadratic yield function, but may instead be attributed to the Associated Flow Rule (AFR). Seeing as in Non-AFR based models two separate functions can be adopted for yield and plastic potential, there is no constraint to which models are used to describe each of them. In this work, the flexible combination of two different yield criteria as yield function and plastic potential under Non-AFR is proposed and evaluated. FE simulations were carried so as to verify the accuracy of the material directionalities predicted using these constitutive material models. The stability conditions for non-associated flow connected with the prediction of yield point elongation are also reviewed. Anisotropic distortion hardening is further incorporated under non-associated flow. It has been found that anisotropic hardening makes the noticeable improvements for both earing and spring-back predictions. This presentation is followed by a discussion of the topic of the forming limit & necking, the evidence in favor of stress analysis, and the motivation for the development of a new type of forming limit diagram based on the polar effective plastic strain (PEPS) diagram. In order to connect necking to fracture in metals, the stress-based necking limit is combined with a stress- based fracture criterion in the principal stress, which provides an efficient method for the analysis of necking and fracture limits. The concept for the PEPS diagram is further developed to cover the path-independent PEPS fracture which is compatible with the stress-based fracture approach. Thus this fracture criterion can be utilized to describe the post-necking behavior and to cover nonlinear strain-path. Fracture modeling in the stress space including mean stress contribution is also conducted and compared with M-C criterion. Strain-path effect on fracture criteria and the role of a damage parameter have been also discussed.

Numerical assessment of residual formability in sheet metal products: towards design for sustainability

A new computational scheme is presented to addresses cold recyclability of sheet- metal products. Cold recycling or re-manufacturing is an emerging area studied mostly empirically; in its current form, it lacks theoretical foundation especially in the area of sheet metals. In this study, a re-formability index was introduced based on post-manufacture residual formability in sheet metal products. This index accounts for possible levels of deformation along different strain paths based on Polar Effective Plastic Strain (PEPS) technique. PEPS is strain-path independent, hence provides a foundation for residual formability analysis. A user- friendly code was developed to implement this assessment in conjunction with advanced finite- element (FE) analysis. The significance of this approach is the advancement towards recycling of sheet metal products without melting them.

Fracture prediction using modified mohr coulomb theory for non-linear strain paths using AA3104-H19

Experiment results from uniaxial tensile tests, bi-axial bulge tests, and disk compression tests for a beverage can AA3104-H19 material are presented. The results from the experimental tests are used to determine material coefficients for both Yld2000 and Yld2004 models. Finite element simulations are developed to study the influence of materials model on the predicted earing profile. It is shown that only the YLD2004 model is capable of accurately predicting the earing profile as the YLD2000 model only predicts 4 ears. Excellent agreement with the experimental data for earing is achieved using the AA3104-H19 material data and the Yld2004 constitutive model. Mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on specimens with a central hole and notched specimens. Torsion of a double bridge specimen is conducted to generate points near pure shear conditions. The Nakajima test is utilized to produce points in bi-axial tension. The data from the experiments is used to develop the fracture locus in the principal strain space. Mapping from principal strain space to stress triaxiality space, principal stress space, and polar effective plastic strain space is accomplished using a generalized mapping technique. Finite element modeling is used to validate the Modified Mohr-Coulomb (MMC) fracture model in the polar space. Models of a hole expansion during cup drawing and a cup draw/reverse redraw/expand forming sequence demonstrate the robustness of the modified PEPS fracture theory for the condition with nonlinear forming paths and accurately predicts the onset of failure. The proposed methods can be widely used for predicting failure for the examples which undergo nonlinear strain path including rigid-packaging and automotive forming.

Path-independent forming limit models for multi-stage forming processes

Many practitioners of the metal forming community remain faithful to the idea that strain metrics are useful for formability assessment. However, it is only valid when deformation occurs along linear strain paths. Current simulations of multi-stage sheet forming processes for rigid-packaging and automotive components result in higher rejection rates due to the inaccuracy of forming and fracture limit models. In this work, we establish a new approach considering path-independency in forming limits based on the stress-based forming limit and polar EPS (Effective Plastic Strain) diagram which appear to be an effective solution for nonlinear effects. The related theory has been implemented into a user material model in commercial software.