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

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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Viscoplastic Constitutive Modeling of Anisotropic Damage Under Nonproportional Loading

Journal of Engineering Materials and Technology ◽

10.1115/1.1395575 ◽

2000 ◽

Vol 123 (4) ◽

pp. 403-408 ◽

Cited By ~ 13

Author(s):

C. L. Chow ◽

X. J. Yang ◽

Edmund Chu

Keyword(s):

Constitutive Modeling ◽

Damage Evolution ◽

Damage Mechanics ◽

Evolution Equations ◽

Forming Limit ◽

Anisotropic Damage ◽

Limit Curve ◽

Forming Limit Curve ◽

Localized Necking ◽

Theory Of Damage

Based on the theory of damage mechanics, a viscoplastic constitutive modeling of anisotropic damage for the prediction of forming limit curve (FLC) is developed. The model takes into account the effect of rotation of principal damage coordinates on the deformation and damage behaviors. With the aid of the damage viscoplastic potential, the damage evolution equations are established. Based on a proposed damage criterion for localized necking, the model is employed to predict the FLC of aluminum 6111-T4 sheet alloy. The predicted results agree well with those determined experimentally.

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Damage-coupled FLD of Sheet Metals for Warm Forming and Nonproportional Loading

International Journal of Damage Mechanics ◽

10.1177/1056789510396331 ◽

2011 ◽

Vol 20 (8) ◽

pp. 1243-1262 ◽

Cited By ~ 9

Author(s):

M. Jie ◽

C. L. Chow ◽

X. Wu

Keyword(s):

Evolution Equation ◽

Damage Evolution ◽

Strain Softening ◽

Forming Limit ◽

Sheet Metals ◽

Nonproportional Loading ◽

Damage Evolution Equation ◽

Localized Necking ◽

Loading Paths ◽

Necking Criterion

A method of forming limit prediction for sheet metals at high temperatures and under nonproportional loading is presented. The method takes into account the strain-softening behaviors of the material at elevated temperatures. A localized necking criterion based on an isotropic damage-coupled acoustic tensor is developed and employed to determine the forming limits of strain-softening materials. The damage evolution equation is developed within the thermo-mechanical framework. A closed-form expression of the forming limit strains is derived by coupling the damage evolution equation into the localized necking criterion. A computer program, incorporating the incremental theory of plasticity, the damage evolution equation and the localized necking criterion, is developed to compute the forming limit strains under several nonproportional loading paths. A series of the uniaxial tensile tests is performed to measure the relevant mechanical properties of AA6061 at the elevated temperature of 450°C. The material damage variables are determined from the measured elastic modulii from a series of loading and unloading paths. The damage evolution equation of AA6061 at 450°C is formulated based on the test data. The computed limit strains are compared with the test results under various loading paths and a good agreement is observed. It is found that the critical damage value is independent on the stress states and loading paths. It may be concluded that the application of the material damage as a reliable criterion of localized necking including the nonproportional loading cases.

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A Generalized Mixed Kinematic-Isotropic Hardening Plastic Model Coupled With Anisotropic Damage for Sheet Metal Forming

Applied Mechanics and Biomedical Technology ◽

10.1115/imece2002-33019 ◽

2002 ◽

Author(s):

C. L. Chow ◽

X. J. Yang

Keyword(s):

Sheet Metal ◽

Sheet Metal Forming ◽

Metal Forming ◽

Kinematic Hardening ◽

Isotropic Hardening ◽

Strain History ◽

Anisotropic Damage ◽

Plastic Model ◽

Localized Necking ◽

Element Simulation

The paper presents a generalized mixed isotropic-kinematic hardening plastic model coupled with anisotropic damage for sheet metal forming. A nonlinear anisotropic kinematic hardening is developed. For the predication of limit strains at localized necking in stamping under complex strain history, the model and its associated damage criterion for localized necking are established and implemented into LS-DYNA3D by compiling it as a user subroutine. The finite element simulation of LS-DYNA3D based on the present model is carried out. The location of localized necking for sheet metal forming has been successfully identified.

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Constitutive Modelling of Anisotropy, Hardening and Failure of Sheet Metals

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.473.631 ◽

2011 ◽

Vol 473 ◽

pp. 631-636 ◽

Cited By ~ 3

Author(s):

Ivaylo N. Vladimirov ◽

Yalin Kiliclar ◽

Vivian Tini ◽

Stefanie Reese

Keyword(s):

Kinematic Hardening ◽

Plastic Anisotropy ◽

Forming Limit Diagram ◽

Material Model ◽

Constitutive Modelling ◽

Forming Limit ◽

Isotropic Hardening ◽

Continuum Damage ◽

Aluminium Sheets ◽

Good Agreement

The paper discusses the application of a newly developed coupled material model of finite anisotropic multiplicative plasticity and continuum damage to the numerical prediction of the forming limit diagram at fracture (FLDF). The model incorporates Hill-type plastic anisotropy, nonlinear Armstrong-Frederick kinematic hardening and nonlinear isotropic hardening. The numerical examples investigate the simulation of forming limit diagrams at fracture by means of the so-called Nakajima stretching test. Comparisons with test data for aluminium sheets display a good agreement between the finite element results and the experimental data.

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Viscoplastic Constitutive Modeling of Anisotropic Damage Under Nonproportional Loading

10.1115/imece2000-1873 ◽

2000 ◽

Author(s):

C. L. Chow ◽

X. J. Yang ◽

Edmund Chu

Keyword(s):

Constitutive Modeling ◽

Damage Evolution ◽

Damage Mechanics ◽

Evolution Equations ◽

Forming Limit ◽

Anisotropic Damage ◽

Limit Curve ◽

Forming Limit Curve ◽

Localized Necking ◽

Theory Of Damage

Abstract Based on the theory of damage mechanics, a viscoplastic constitutive modeling of anisotropic damage for the prediction of forming limit curve (FLC) is developed. The model takes into account the effect of rotation of principal damage coordinates on the deformation and damage behaviors. With the aid of the damage viscoplastic potential, the damage evolution equations are established. Based on a proposed damage criterion for localized necking, the model is employed to predict the FLC of aluminum 6111-T4 sheet alloy. The predicted results agree well with those determined experimentally.

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Prediction of the forming limit diagram on the basis of the damage criterion under non-proportional loading

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406011520832 ◽

2001 ◽

Vol 215 (4) ◽

pp. 405-414 ◽

Cited By ~ 1

Author(s):

C L Chow ◽

X-J Yang

Keyword(s):

Damage Mechanics ◽

Evolution Equations ◽

Damage Model ◽

Forming Limit Diagram ◽

Forming Limit ◽

Proportional Loading ◽

Damage Criterion ◽

Arbitrary Loading ◽

Anisotropic Plastic ◽

Theory Of Damage

Based on the theory of damage mechanics, a recently developed anisotropic plastic damage model for the prediction of forming limit diagrams (FLDs) is extended to take into account the effect of rotation of the principal damage coordinates on the deformation and damage behaviour. With the aid of the damage plastic potential, the damage evolution equations are established. A damage criterion for localized necking under arbitrary loading 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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The forming limit diagram of sheet metals and effects of strain path changes on formability: a dislocation treatment

Materials Science and Engineering ◽

10.1016/0025-5416(82)90181-1 ◽

1982 ◽

Vol 56 (1) ◽

pp. 47-61 ◽

Cited By ~ 13

Author(s):

Y. Bergström ◽

S. Ölund

Keyword(s):

Strain Path ◽

Forming Limit Diagram ◽

Forming Limit ◽

Sheet Metals ◽

Strain Path Changes

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Prediction of forming limit diagram with mixed anisotropic kinematic–isotropic hardening plastic constitutive model based on stress criteria

Journal of Materials Processing Technology ◽

10.1016/s0924-0136(02)01006-3 ◽

2003 ◽

Vol 133 (3) ◽

pp. 304-310 ◽

Cited By ~ 7

Author(s):

C.L. Chow ◽

X.J. Yang

Keyword(s):

Constitutive Model ◽

Forming Limit Diagram ◽

Forming Limit ◽

Isotropic Hardening ◽

Model Based ◽

Stress Criteria

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Integrated Hydraulic Bulge and Forming Limit Testing Method and Apparatus for Sheet Metals

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.626.171 ◽

2014 ◽

Vol 626 ◽

pp. 171-177 ◽

Cited By ~ 2

Author(s):

Yan Yo Chen ◽

Yu Chung Tsai ◽

Ching Hua Huang

Keyword(s):

Forming Limit Diagram ◽

Close Correlation ◽

Biaxial Stress ◽

Forming Limit ◽

Hydraulic Pressure ◽

Sheet Metals ◽

Stress Strain ◽

Testing Method ◽

Hydraulic Bulge ◽

Strain Relationship

This paper proposes an integrated hydraulic bulge and forming limit testing method and apparatus for sheet metals. By placing a PU (Polyurethane) plate between molds and uniformly applying hydraulic pressure to sheet metals, a biaxial stress-strain relationship and forming limit diagram (FLD) displaying both left and right sides were acquired using the same apparatus. An uniaxial tension test and traditional drawing test were conducted to compare the results obtained from the proposed hydraulic bulge and forming limit testing methods, respectively. A close correlation between the results of the stress-strain relationship and FLD in both comparisons verified the feasibility and capability of this integrated hydraulic testing method and apparatus for use with sheet metals.

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A Suitable Criterion for Precise Determination of Incipient Necking in Sheet Materials

Materials Science Forum ◽

10.4028/www.scientific.net/msf.519-521.111 ◽

2006 ◽

Vol 519-521 ◽

pp. 111-116 ◽

Cited By ~ 17

Author(s):

Q. Situ ◽

Mukesh K. Jain ◽

M. Bruhis

Keyword(s):

Strain Rate ◽

Sheet Material ◽

Forming Limit Diagram ◽

Precise Determination ◽

Forming Limit ◽

Strain History ◽

Flow Localization ◽

Major Strain ◽

Strain Paths

Forming limit diagram (FLD) is a measure of the formability of a sheet material. The major-minor strain pairs that are closest to the neck on multiple specimens of various strain paths are utilized to construct a boundary between safe and unsafe zones. The challenge to obtain the FLD is the determination of incipient necking. Three approaches to determine the limit strains have been investigated and compared in this research in order to establish the optimal one for implementation: (1) commonly used Bragard criterion ( 1)e Br with periodic grids; (2) tracking the region of large local strains from strain history to locate the instance when critical major strain ( 1)e cr happens; (3) post-processing of strain history to locate the inflection in the major strain rate curve 1 max (e&&) at the onset of localization. The last criterion of inflection in strain rate 1 max (e&&) carries both a numerical and a physical meaning towards developing an understanding of flow localization, formability and fracture.

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