A Hybrid Membrane/Shell Method for Rapid Estimation of Springback in Anisotropic Sheet Metals

1998 ◽  
Vol 65 (3) ◽  
pp. 671-684 ◽  
Author(s):  
F. Pourboghrat ◽  
K. Chung ◽  
O. Richmond
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Bending Moment ◽  
Isotropic Hardening ◽  
Normal Anisotropy ◽  
Bending Tests ◽  
Reverse Loading ◽  
Draw Bending ◽  
Springback Prediction ◽  
Good Agreement

A semi-analytical method to predict springback in sheet metal forming processes has been developed for the case of plane strain. In the proposed hybrid method, for each deformation increment, bending, and unbending stretches are analytically superposed on membrane stretches which are numerically obtained in advance from a membrane finite element code. Springback is then obtained by the unloading of a force and a bending moment at the boundary of each element treated as a shell. Hill’s 1948 yield criterion with normal anisotropy is used in this theory along with kinematic and isotropic hardening laws during reverse loading. The method has been applied for the springback prediction of a 2008-T4 aluminum alloy in plane-strain draw-bending tests. The results indicate the necessity of including anisotropic hardening (especially Bauschinger effects) and elastoplastic unloading in order to achieve good agreement with experimental results.

Advanced High Strength Steel Sheet Forming and Springback Simulation

2010 ◽  
Vol 97-101 ◽  
pp. 200-203 ◽  
Author(s):  
Ke Chen ◽  
Jian Ping Lin ◽  
Mao Kang Lv ◽  
Li Ying Wang
Keyword(s):  
High Strength Steel ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Sheet Material ◽  
High Strength ◽  
Material Model ◽  
Sheet Forming ◽  
Isotropic Hardening ◽  
Advanced High Strength Steel ◽  
Springback Prediction

With the increasing use of finite element analysis method in sheet forming simulations, springback predictions of advanced high strength steel (AHSS) sheet are still far from satisfactory precision. The main purpose of this paper was to provide a method for accurate springback prediction of AHSS sheet. Material model with Hill’48 anisotropic yield criterion and nonlinear isotropic/kinematic hardening rule were applied to take account the anisotropic yield behavior and the Bauschinger effect during forming processes. U-channel forming and springback simulation was performed using ABAQUS software. High strength DP600 sheet was investigated in this work. The simulation results obtained with the proposed material model agree well with the experimental results, which show a remarkable improvement of springback prediction compared with the commonly used isotropic hardening model.

Effective Elastic Constants for the Bending of Thin Perforated Plates With Triangular and Square Penetration Patterns

1973 ◽  
Vol 95 (1) ◽  
pp. 121-128 ◽  
Author(s):  
W. J. O’Donnell
Keyword(s):  
Plane Strain ◽  
Elastic Constants ◽  
Thin Plates ◽  
Perforated Plates ◽  
Bending Tests ◽  
Effective Elastic Constants ◽  
Asme Code ◽  
Aluminum Beam ◽  
Generalized Plane Strain ◽  
Good Agreement

Bending tests were run on a series of aluminum beam specimens perforated in triangular and square arrays. Progressively thinner specimens were tested down to 1/8 the thickness covered by the ASME Code. The results for the thick specimens show good agreement with the theoretical generalized plane strain values. The trend of the results with decreasing thickness agrees with the theoretical values for the bending of very thin plates. The applicability of the results is generalized using dimensionless parameters.

Prediction of spring-back in anisotropic sheet metals

2004 ◽  
Vol 218 (6) ◽  
pp. 651-661 ◽  
Author(s):  
V T Nguyen ◽  
Z Chen ◽  
P F Thomson
Keyword(s):  
Constitutive Equations ◽  
Bauschinger Effect ◽  
Yield Criterion ◽  
Yield Function ◽  
Alloy Sheet ◽  
Sheet Metals ◽  
Spring Back ◽  
Bending Tests ◽  
Numerical Predictions ◽  
Draw Bending

Constitutive equations for plane stress problems based on the modified form of a non-quadratic yield criterion suitable for aluminium alloy sheet were derived by Barlat et al. to account for the Bauschinger effect (BE). Numerical predictions of spring-back based on the original yield function and its modified form wer performed and compared with the results of draw-bending tests. The results show the necessity of including the BE in the constitutive equations to enhance the accuracy in predicting spring-back.

Plane-Strain Tension Tests on Aluminum Alloy Sheet

1995 ◽  
Vol 117 (2) ◽  
pp. 168-171 ◽  
Author(s):  
Fadi Taha ◽  
Alejandro Graf ◽  
William Hosford
Keyword(s):  
Aluminum Alloy ◽  
Plane Strain ◽  
Yield Criterion ◽  
Alloy Sheet ◽  
Isotropic Hardening ◽  
Aluminum Alloy Sheet ◽  
Strain Measurements ◽  
Plane Strain Tension ◽  
Tension Tests ◽  
High Exponent

A simple way of making plane-strain tension tests on sheet specimens has been developed. This method was used to test sheets of aluminum alloy 2008 T4 and the results were analyzed in terms of a high exponent yield criterion and isotropic hardening. Experimentally measured forces agreed with those calculated from strain measurements using uniaxial tension test curves.

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.

Special Issue on Engineering Plasticity: Prediction of spring-back in anisotropic sheet metals

2004 ◽  
Vol 218 (9) ◽  
pp. 1087-1087
Author(s):  
V T Nguyen ◽  
Z Chen ◽  
P F Thomson
Keyword(s):  
Constitutive Equations ◽  
Bauschinger Effect ◽  
Yield Criterion ◽  
Yield Function ◽  
Alloy Sheet ◽  
Spring Back ◽  
Bending Tests ◽  
Numerical Predictions ◽  
Draw Bending ◽  
Engineering Plasticity

Constitutive equations for plane stress problems based on the modified form of a non-quadratic yield criterion suitable for aluminium alloy sheet were derived to account for the Bauschinger effect (BE). Numerical predictions of spring-back based on the original yield function and its modified form were performed and compared with the results of draw-bending tests. The results show the necessity of including the BE in the constitutive equations to enhance the accuracy in predicting spring-back.

Elastic-Plastic Plane-Strain Solutions With Separable Stress Fields

1969 ◽  
Vol 36 (3) ◽  
pp. 528-532
Author(s):  
D. B. Bogy
Keyword(s):  
Stress Field ◽  
Plane Strain ◽  
Yield Criterion ◽  
A Priori ◽  
Equivalent Plastic Strain ◽  
Uniaxial Stress ◽  
Stress Fields ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Elastic Plastic

A stress field σij(χ, t) depending on position χ and time t will be called separable if the time-dependence enters only through a scalar multiplier; i. e., if σij(χ,t)=s(χ,t)σˆij(χ). It is shown here that elastic-plastic plane-strain solutions in the infinitesimal (flow) theory of plasticity satisfying Tresca’s yield criterion and associated flow rule with linear isotropic hardening, based on either equivalent plastic strain or total plastic work, can occur with separable stress fields only in the following instances: (a) solutions with uniaxial stress fields, as in bending, (b) solutions with stress fields such that the entire domain changes from elastic to plastic at the same time, and (c) solutions with stress fields for which the elastic-plastic boundary coincides with a principal shear stress trajectory. Whether or not a plasticity solution has a separable stress field can be determined a priori by examining the corresponding elasticity solution.

scholarly journals Springback Analysis of AA5754 under Warm Stamping Conditions

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Jun Liu
Keyword(s):  
Empirical Model ◽  
Elevated Temperatures ◽  
Stress Gradient ◽  
Bending Moment ◽  
Analytical Models ◽  
Cold Forming ◽  
Bending Tests ◽  
Model Predictions ◽  
Gradient Models ◽  
Good Agreement

Prediction of springback has been thoroughly investigated for cold forming processes; however with the rising prominence of lightweight materials and new forming technologies, predicting springback at elevated temperatures has become essential. In this paper, three analytical models and one empirical model were proposed to predict springback of an aluminium alloy AA5754 at warm forming conditions. The analytical models developed were based on the effect of the linear bending moment, uniform bending moment and through-thickness stress gradient respectively on springback, while the empirical model was developed using the results of L-shape bending tests. The model predictions were compared with the experiment results for various forming conditions. At room temperature, all four models had very good agreement. At elevated temperatures, the linear bending moment model was preferred for a die radius of 8mm, whereas empirical and stress gradient models were more suitable for a die radius of 4mm; in both cases, very close agreement was achieved where errors were within 5%.

Assessment of the load carrying performance of composite cross joints

2019 ◽  
Vol 54 (11) ◽  
pp. 1431-1439
Author(s):  
Liyang Liu ◽  
Mengfei Cai ◽  
Xiaoliang Geng ◽  
Peiyan Wang ◽  
Zhufeng Yue
Keyword(s):  
Damage Model ◽  
Bending Moment ◽  
Comparative Assessment ◽  
Progressive Damage ◽  
Bending Tests ◽  
Air Inlet ◽  
Four Point Bending ◽  
Load Carrying ◽  
Progressive Damage Model ◽  
Good Agreement

Composite cross joints are common structures in an airframe. When this type of joint is used on an air inlet stiffened structure, it will undertake large bending moment, especially under overpressure of the engine. In this paper, two types of cross joints are tested experimentally and simulated to investigate the load bearing characteristics and make comparative remarks. Four-point bending tests are conducted and the load deflection curves are obtained; besides, the damage pattern of the joints is reported. Based on composite progressive damage model, the numerical simulations have a good agreement with experimental results, revealing the joint failure mechanism and fastener force feature of various joints. The comparative assessment of two types of joints is summarized.

scholarly journals Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1166
Author(s):  
Stanislav Strashnov ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Plane Strain ◽  
Kinematic Hardening ◽  
Tensile Force ◽  
Plastic Region ◽  
Equivalent Plastic Strain ◽  
Isotropic Hardening ◽  
Finite Plane ◽  
Present Solution ◽  
Bending Under Tension ◽  
Elastic Unloading

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

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