Analysis of Forming Limits Using the Hill 1993 Yield Criterion

1998 ◽  
Vol 120 (3) ◽  
pp. 236-241 ◽  
Author(s):  
Siguang Xu ◽  
Klaus J. Weinmann ◽  
Abhijit Chandra
Keyword(s):  
Bifurcation Analysis ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
Anomalous Behavior ◽  
Forming Limit ◽  
Forming Limits ◽  
Material Parameters ◽  
Localized Necking ◽  
Wide Range ◽  
The Hill

Forming limits of thin sheets are investigated using a yield criterion recently proposed by Hill (1993). This criterion utilizes five independent material parameters, which can be determined from uniaxial and balanced biaxial experiments, to describe a wide range of material properties of sheet metals, including the anomalous behavior of aluminum. In the present work, a bifurcation analysis is pursued to predict the onset of localized necking in strain rate insensitive sheet materials. A detailed parametric study is then conducted to evaluate the effect of various material parameters on the positive minor strain side of the forming limit diagram. It is observed that limit strains are strongly dependent on the shape of the yield locus. Forming limits predicted using Hill’s 1993 yield criterion are compared with those predicted using Hill’s 1948 and 1979 criteria. Results from the bifurcation analysis are also compared with experimental observations, as well as the limit strain predicitons based on the M-K analysis.

Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Shuhui Li ◽  
Ji He ◽  
Z. Cedric Xia ◽  
Danielle Zeng ◽  
Bo Hou
Keyword(s):  
Sheet Metal ◽  
Bifurcation Analysis ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
Experimental Result ◽  
Forming Limit ◽  
Forming Limits ◽  
R Value ◽  
Value Effect ◽  
The Hill

A bifurcation analysis of forming limits for an orthotropic sheet metal is presented in this paper. The approach extends Stören and Rice's (S–R) bifurcation analysis for isotropic materials, with materials following a vertex theory of plasticity at the onset of localized necking. The sheet orthotropy is represented by the Hill’48 yield criterion with three r-values in the rolling (r0), the transverse (r90) and the diagonal direction (r45). The emphasis of the study is on the examination of r-value effect on the sheet metal forming limit, expressed as a combination of the average r-value raverage and the planar anisotropy (Δr). Forming limits under both zero extension assumption and minimum extension assumption as well as necking band orientation evolution are investigated in detail. The comparison between the experimental result and predicted forming limit diagram (FLD) is presented to validate the extended bifurcation analysis. The r-value effect is observed under uniaxial and equal-biaxial loadings. However, no difference is found under plane strain condition in strain-based FLD which is consistent with Hill's theory. The force maximum criterion is also used to analyze FLD for verification.

An Investigation Into the Prediction of Forming Limit Diagrams for Normal Anisotropic Material Based on Bifurcation Analysis

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
A. Jaamialahmadi ◽  
M. Kadkhodayan
Keyword(s):  
Bifurcation Analysis ◽  
Work Hardening ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
Optimization Method ◽  
Forming Limit ◽  
Proportional Loading ◽  
Normal Anisotropy ◽  
Left Hand ◽  
Prediction Limit

In this paper, formula derivation for bifurcation analysis based on a constitutive model including Hill 48 yield criterion with normal anisotropy of a pointed vertex on subsequent yield loci to predict the entire forming limit diagram (FLD) is carried out. Proportional loading, total deformation theory of plasticity, and power law relation are assumed. Predicted limit strains for Hill’s zero and minimum extension of localized neck orientation is derived. The dominancy of zero extension and minimum extension on the left-hand side of FLDs for different work hardening components and r-values are investigated in detail. An implicit four order rational function equation for major strain, which preferred that the orientation of neck correspond to minimum value of limit strain, is found by a developed optimization method. Optimized predicted limit strains for typical work hardening components and different r-values are obtained and discussed. Limit strains vary directly on the left and reversely on the right-hand side of FLD when r-value increases. Comparison between the predicted and experimental results exhibits a better agreement compared with those from the isotropic material. In addition, on the left-hand side, the resulted prediction limit strains represent a full dependency to assumed yield criterion. A comparison between the current work and Chow et al. results are performed and discussed in detail.

Influence of Different Pre-Stretching Modes on the Forming Limit Diagram of AA6014

2012 ◽  
Vol 504-506 ◽  
pp. 71-76 ◽  
Author(s):  
Alexandra Werber ◽  
Mathias Liewald ◽  
Winfried Nester ◽  
Martin Grünbaum ◽  
Klaus Wiegand ◽  
...  
Keyword(s):  
Plane Strain ◽  
Biaxial Loading ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Linear Strain ◽  
Forming Limits ◽  
Systematic Analysis ◽  
Measurement Systems ◽  
Non Linear ◽  
Strain Paths

In order to evaluate the formability of sheet materials forming limit diagrams (FLD) are recorded which represent the values of major and minor strain when necking occurs. FLDs are recorded based on the assumption that exclusively linear strain paths occur. In real forming parts, however, particularly in those with complex shapes, predominantly non-linear strain paths occur which reduce the accuracy of the failure prediction according to a conventional FLD. For this reason forming limits after loading with non-linear strain paths have to be investigated. In this contribution a systematic analysis of the forming limits of a conventional AA6014 alloy after loading with non-linear strain paths is presented. This material is pre-stretched in uniaxial, plane strain and biaxial direction up to several levels before performing Nakajima experiments in order to determine FLDs. During the pre-stretching process as well as during the Nakajima experiment the strain distribution can be measured online very precisely with the optical deformation measurement systems GOM Aramis or VIALUX. The gained curves are compared to the FLD of the as-received material. The results prove a significant influence of the pre-stretching condition on the forming limits of the used aluminum alloy. For a low pre-stretching in uniaxial as well as in biaxial direction the FLDs show a slightly reduced formability while after higher pre-stretching levels the forming limit can be improved such as for biaxial loading after uniaxial pre-stretching. The formability after pre-stretching in plane strain direction was changed. Also, a shift of the FLD depending on the direction of pre-stretching can be observed.

Forming limit analysis of Mg-2Zn-1.2Al-0.2Ca-0.2RE alloy sheet using ductile fracture models

2019 ◽  
Vol 29 (8) ◽  
pp. 1181-1198 ◽  
Author(s):  
Fei-Fan Li ◽  
Gang Fang ◽  
Ling-Yun Qian
Keyword(s):  
Magnesium Alloy ◽  
Ductile Fracture ◽  
Stress Triaxiality ◽  
Forming Limit Diagram ◽  
Alloy Sheet ◽  
Image Correlation ◽  
Forming Limit ◽  
Correlation Technique ◽  
Forming Limits ◽  
Fracture Models

This work was aimed to experimentally and theoretically investigate the formability of a new magnesium alloy sheet at room temperature. The fracture forming limit diagram was predicted by MMC3 and DF2014 models, where the non-linear strain path effect was taken into account by means of damage accumulation law. In order to obtain the instantaneous values of the stress triaxiality and the Lode parameter during the deformation process, strains tracked by digital image correlation technique were transformed into stresses based on the constitutive equations. The fracture forming limit diagram predicted by the fracture models was compared with the forming limits obtained by ball punch deformation tests. The prediction errors were evaluated by the accumulative damage values, which verified the advantages of ductile fracture models in predicting the forming limits of the magnesium alloy sheets.

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

2020 ◽  
Vol 856 ◽  
pp. 57-65
Author(s):  
Tanakorn Jantarasricha ◽  
Sansot Panich ◽  
Komkamol Chongbunwatana
Keyword(s):  
Aluminium Alloy ◽  
Yield Criterion ◽  
Forming Limit ◽  
Forming Limit Curve ◽  
Fracture Locus ◽  
Hardening Law ◽  
Stress Curve ◽  
Anisotropic Yield Criterion ◽  
Strain Space ◽  
The Hill

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.

Prediction of fracture limits of IN625 alloy by coupling ductile damage models and anisotropic yielding functions with the classical Marciniak and Kuczyński model

2021 ◽  
pp. 095440542110518
Author(s):  
Ayush Morchhale ◽  
Nitin Kotkunde ◽  
Swadesh Kumar Singh ◽  
Navneet Khanna
Keyword(s):  
Manufacturing Industry ◽  
Forming Limit Diagram ◽  
Ductile Damage ◽  
Inconel 625 ◽  
Forming Limit ◽  
Uniaxial Tensile ◽  
Forming Limits ◽  
Damage Models ◽  
Uniaxial Tensile Testing ◽  
Anisotropic Yielding

The fracture forming limit diagram (FFLD) is gaining special attention in high strength materials where the necking tendency rarely occurs during sheet metal forming processes. In the present work, the classical Marciniak and Kuczyński (MK) model has been modified by coupling it with different ductile damage models (Cockcroft and Latham, Brozzo, Oyane, Ko, Oh, Rice and Tracey, McClintock and Clift) and anisotropic yielding functions (Hill 1948 and Barlat 1989) to predict the fracture limits of Inconel 625 (IN625) alloy at different temperatures. Firstly, uniaxial tensile testing has been conducted for the determination of important mechanical properties. Consequently, stretch forming experiments have been performed to analyze the forming limits of a material. It has been found that the safe and fracture forming limits of the material increased by approximately 17.26% and 22.22%, respectively, on increasing the temperature from 300 to 673 K. From the comparative analysis of different combinations of ductile damage models and yielding functions, the Cockcroft and Latham (C-L) damage model in combination with the Barlat 1989 yielding function helped in best predicting the theoretical FFLD as it displayed the least average root mean square error (RMSE) of 0.033. The other ductile damage models used for predicting the theoretical fracture limits displayed large error; hence, they should not be considered while designing a critical component in the manufacturing industry using IN625 alloy.

Application of Barlat Yld-96 Yield Criterion for Predicting Formability of Pre-Strained Dual Phase Steel Sheets

2016 ◽  
Author(s):  
Shamik Basak ◽  
Sushanta Kumar Panda
Keyword(s):  
Dual Phase Steel ◽  
Yield Criterion ◽  
Thin Sheet ◽  
Damage Model ◽  
Forming Limit Diagram ◽  
Plasticity Theory ◽  
Forming Limit ◽  
Dual Phase ◽  
Strain Paths ◽  
Anisotropy Coefficients

The selection of advanced material model considering the anisotropy mechanical properties of the thin sheet is vital in order to estimate stress based forming limit diagram (σ-FLD). In present study associative plasticity theory was applied indulging Barlat Yld-96 anisotropy yield function and the Swift hardening law was implemented for estimating the limiting stresses from the conventional strain FLD (ε-FLD) of an automotive grade dual phase steel DP600. Three different approaches were made to evaluate Yld-96 anisotropy coefficients using experimental results of stack compression and tensile tests. To impose complex strain path, two stage stretch forming processes were simulated in finite element solver LS-DYNA. After biaxial pre-straining, the sample geometries were varied to achieve different strain paths during the second stage of deformation. The results indicated that there was negligible difference in limiting stress estimated by Yld-96 plasticity theory when the anisotropy coefficients were calculated based on plastic strain at ultimate tensile strength compare to that by minimum plastic work method. It was concluded that the dynamic shift of ε-FLD could be restricted by σ-FLD estimated using Yld 96 plasticity theory, and hence it was proposed to be a suitable damage model to evaluate formability of pre-strained DP600 steels.

A New Approach to the Evaluation of Forming Limits in Sheet Metal Forming

2015 ◽  
Vol 639 ◽  
pp. 333-338 ◽  
Author(s):  
Marion Merklein ◽  
Andreas Maier ◽  
Daniel Kinnstätter ◽  
Christian Jaremenko ◽  
Emanuela Affronti
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Strain History ◽  
Failure Behavior ◽  
Forming Limits ◽  
Optical Strain Measurement ◽  
Optical Strain

The forming limit diagram (FLD) is at the moment the most important method for the prediction of failure within sheet metal forming operations. Key idea is the detection of the onset of necking in dependency of different sample geometry. Whereas the standardized evaluation methods provides very robust and reliable results for conventional materials like deep drawing steels, the determined forming limits for modern light materials are often too conservative due to the different failure behavior. Therefore, within this contribution a new and innovative approach for the identification of the onset of necking will be presented. By using a pattern recognition-based approach in combination with an optical strain measurement system the complete strain history during the test can be evaluated. The principal procedure as well as the first promising results are presented and discussed.

A Unified Damage Approach for Predicting Forming Limit Diagrams

1997 ◽  
Vol 119 (4) ◽  
pp. 346-353 ◽  
Author(s):  
C. L. Chow ◽  
L. G. Yu ◽  
M. Y. Demeri
Keyword(s):  
Plastic Deformation ◽  
Sheet Metal ◽  
Damage Model ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Unified Approach ◽  
Nonuniform Deformation ◽  
Localized Necking ◽  
Micro Cracks ◽  
Three Phases

Plastic deformation in sheet metal consists of four distinct phases, namely, uniform deformation, diffuse necking, localized necking, and final rupture. The last three phases are commonly known as nonuniform deformation. A proper forming limit diagram (FLD) should include all three phases of the nonuniform deformation. This paper presents the development of a unified approach to the prediction of FLD to include all three phases of nonuniform deformation. The conventional method for predicting FLD is based on localized necking and adopts two fundamentally different approaches. Under biaxial loading, the Hill’s plasticity method is often chosen when α(=ε2/ε1) <0. On the other hand, the M-K method is typically used for the prediction of localized necking when α > 0 or when the biaxial stretching of sheet metal is significant. The M-K method, however, suffers from the arbitrary selection of the imperfection size, thus resulting in inconsistent predictions. The unified approach takes into account the effects of micro-cracks/voids on the FLD. All real-life materials contain varying sizes and degrees of micro-cracks/voids which can be characterized by the theory of damage mechanics. The theory is extended to include orthotropic damage, which is often observed in extensive plastic deformation during sheet metal forming. The orthotropic FLD model is based on an anisotropic damage model proposed recently by Chow and Wang (1993). Coupling the incremental theory of plasticity with damage, the new model can be used to predict not only the forming limit diagram but also the fracture limit diagram under proportional or nonproportional loading. In view of the two distinct physical phenomena governing the cases when α(=ε2/ε1) < or α > 0, a set of instability criteria is proposed to characterize all three phases of nonuniform deformation. The orthotropic damage model has been employed to predict the FLD of VDIF steel (Chow et al, 1996) and excellent agreement between the predicted and measured results has been achieved as shown in Fig. 1. The damage model is extended in this paper to examine its applicability and validity for another important engineering material, namely aluminum alloy 6111-T4.

Prediction of Forming Limit Diagram Based on Damage Coupled Kinematic-Isotropic Hardening Model Under Nonproportional Loading

2002 ◽  
Vol 124 (2) ◽  
pp. 259-265 ◽  
Author(s):  
C. L. Chow ◽  
X. J. Yang ◽  
E. Chu
Keyword(s):  
Damage Mechanics ◽  
Kinematic Hardening ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Isotropic Hardening ◽  
Strain History ◽  
Sheet Metals ◽  
Nonproportional Loading ◽  
Localized Necking ◽  
Theory Of Damage

Based on the theory of damage mechanics, an anisotropic damage coupled mixed isotropic-kinematic hardening plastic model for the prediction of forming limit diagram (FLD) is developed. The model includes the formulation of nonlinear anisotropic kinematic hardening. For the prediction of limit strains under nonproportional loading, a damage criterion for localized necking of sheet metals subjected to complex strain history is proposed. The model is employed to predict the FLDs of AL6111-T4 alloy. The predicted results agree well with those determined experimentally.

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