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.

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.

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.

Modified Swift Criteria for Residual Strength of Multiple Site Damage Structure

2009 ◽  
Vol 417-418 ◽  
pp. 881-884 ◽  
Author(s):  
Jian Yu Zhang ◽  
Rui Bao ◽  
Bin Jun Fei
Keyword(s):  
Residual Strength ◽  
Yield Criterion ◽  
Fatigue Cracks ◽  
Tensile Load ◽  
Maximum Load ◽  
Alloy Sheet ◽  
Multiple Cracks ◽  
Multiple Site ◽  
Multiple Site Damage ◽  
Aluminum Panels

As more aircrafts reach or exceed their design life, it is becoming very important to research multiple cracks damage, especially the multiple site damage (MSD) in order to re-evaluate their service life and damage tolerance/durability performance. The existing of MSD may remarkably reduce the residual strength of an aerospace structural component than those with a singe lead crack. This study investigated the residual strength of aluminum alloy sheet with MSD through three types of aluminum specimens test. Aluminum panels with bare collinear constant diameter holes were chosen as specimens. After some constant amplitude tension-tension load cycles, the MSD were found in these specimens since there were multiple fatigue cracks emanating from the saw cuts of holes. The residual strength was recorded as the maximum load when every specimen was subjected to monotonically increasing tensile load until failure occurred. In different failure prediction criteria that were often used in engineering in order to evaluate the accuracy of these criteria, Swift criterion (ligament yield) criterion got more accurate prediction results than other criteria. Although Swift criterion was more accurate than some other criteria, its error was still big for some specimens. Two modified approaches were proposed in order to get more accurate and appropriate failure criterion for MSD structure.

scholarly journals Determining the material model at elevated temperatures with different strain rates and simulating the warm forming process for Mg alloy AZ31B sheet

2015 ◽  
Vol 18 (2) ◽  
pp. 149-158
Author(s):  
Thien Tich Truong ◽  
Long Thanh Nguyen ◽  
Binh Nguyen Thanh Vu ◽  
Hien Thai Nguyen
Keyword(s):  
Magnesium Alloy ◽  
Constitutive Equations ◽  
Elevated Temperatures ◽  
Material Model ◽  
Alloy Sheet ◽  
Strain Rates ◽  
Functional Requirements ◽  
Temperature Dependent ◽  
Forming Process ◽  
Az31b Alloy

Magnesium alloy is one of lightweight alloys has been studied more extensively today. Because weight reduction while maintaining functional requirements is one of the major goals in industries in order to save materials, energy and costs, etc. Its density is about 2/3 of aluminum and 1/4 of steel.The material used in this study is commercial AZ31B magnesium alloy sheet which includes 3% Al and 1% Zn. However, due to HCP (Hexagonal Close Packed) crystal structure, magnesium alloy has limited ductility and poor formability at room temperature. But its ductility and formability will be improved clearly at elevated temperature. From the data of tensile testing, the constitutive equations of AZ31B was approximated using the Ramgberg-Osgood model with temperature dependent parameters to fit in the experiment results in tensile test. Yield locus are also drawn in plane stress σ1- σ2 with different yield criteria such as Hill48, Drucker Prager, Logan Hosford, Y. W. Yoon 2013 and particular Barlat 2000 criteria with temperature dependent parameters. Applying these constitutive equations were determined at various temperatures and different strain rates, the finite element simulation stamping process for AZ31B alloy sheet by software PAM- STAMP 2G 2012, to verify the model materials and the constitutive equations.

An Analytical Solution to Metal Plane Problem in Terms of Orthotropic Anisotropy and Strain Hardening

2010 ◽  
Vol 97-101 ◽  
pp. 348-356
Author(s):  
Yao He Liu ◽  
Guo Feng Yi ◽  
Jian Ming Xiong
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Plane Stress ◽  
Yield Criterion ◽  
Research Result ◽  
Yield Condition ◽  
Plane Stress State ◽  
Yield Function ◽  
Anisotropic Parameter ◽  
Symmetric Plane

In this paper, the yield condition of Hill’s orthotropic yield criterion under axial symmetric plane stress state was discussed. The yield function of orthotropic material was proposed and the analytical solution to meet the condition of equations of equilibrium and compatibility under axial symmetric plane stress state is obtained, in which the conditions of power hardening materials was considered. The research result indicates that hardening coefficient and anisotropic parameter have substantial influence over stress and strain. However, in the presence of the coefficient R90=H/F，the influence appears to be quite weak.

scholarly journals An Extended Drucker Yield Criterion to Consider Tension–Compression Asymmetry and Anisotropy on Metallic Materials: Modeling and Verification

Metals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 20
Author(s):  
Bingtao Tang ◽  
Zhongmei Wang ◽  
Ning Guo ◽  
Qiaoling Wang ◽  
Peixing Liu
Keyword(s):  
Aluminum Alloys ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Function ◽  
Close Packing ◽  
Bending Test ◽  
Rolled Plate ◽  
Face Centered Cubic ◽  
Metallic Materials ◽  
Stress Invariant

Pressure sensitive asymmetric Drucker yield criterion is developed to deal with pressure dependent sheet metals for instance steels and aluminum alloys. The sensitivity to pressure is conserved by introducing three-dimensional anisotropic parameters in the first stress invariant; while the third deviatoric stress invariant is remained in odd function form to consider the strength differential effect (SDE). To describe the flow stress directionalities of metallic materials, the Drucker yield function is extended using two transformation matrix consisting of anisotropic parameters. The proposed Drucker yield criterion is utilized to predict the anisotropic yield and plastic deformation of aluminum alloys with weak SDE: AA 2090-T3 with face-centered cubic (FCC) crystal systems and AA 2008-T4 with body-centered cubic (BCC) crystal systems as well as metals with strong SDE: Zirconium clock-rolled plate with hexagonal close packing (HCP) crystal systems. The comparison between the predicted anisotropic behavior and experimental results reveals that the extended anisotropic Drucker yield criterion can precisely model the anisotropy for FCC, BCC and HCP metals. The proposed function is implemented into ABAQUS VUMAT subroutines to describe the four-point bending test which is used to consider the effect of various yield functions and material orientations on deformation behavior. The obtained contours of the cross-section, strain components distribution and also the shift of neutral layer indicate that the extended Drucker yield function can well predict the final geometric configuration of the deformed Zirconium beam.

Plasticity Model and Numerical Simulation of Extruded Oilseeds in Closed Cell

2011 ◽  
Vol 304 ◽  
pp. 235-240
Author(s):  
Xiao Zheng ◽  
Ya Xin Zhang ◽  
Guo Xiang Lin ◽  
Zhi Xian Sun
Keyword(s):  
Numerical Simulation ◽  
Constitutive Equations ◽  
Theoretical Basis ◽  
Inverse Method ◽  
Yield Criterion ◽  
Model Parameters ◽  
Plasticity Model ◽  
Power Curve ◽  
Experimental Stress ◽  
Closed Cell

By using of Kuhn`s yield criterion, plasticity constitutive equations of extruded oilseeds in a closed cylinderical cell were developed. The model parameters were identified from experimental stress—strain using an inverse method. The maximum relative deviations between the measured and the simulated value of soybean and cottonseed are 8.5% and 5.1% respectively, and the average relative deviations are 4.9% and 3.8% respectively. The results of numerical simulation for confined pressing of granular soybeans and cottonseeds in the closed cylinderical cell indicated the following facts that granular soybeans and cottonseeds conform to the model of three power curve, the plasticity constitutive equations can describe the plastic deformation for extruded soybean and cottonseed, and Kuhn`s yield criterion can be used as theoretical basis for plasticity model of granular soybeans and cottonseeds.

A Yield Criterion for Porous Ductile Media at High Strain Rate

1997 ◽  
Vol 64 (3) ◽  
pp. 503-509 ◽  
Author(s):  
Ze-Ping Wang ◽  
Qing Jiang
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Yield Surface ◽  
High Strain ◽  
Yield Criterion ◽  
Matrix Material ◽  
Yield Function ◽  
Inertial Effects ◽  
The Matrix ◽  
Dynamic Yield

An approximate yield criterion for porous ductile media at high strain rate is developed adopting energy principles. A new concept that the macroscopic stresses are composed of two parts, representing dynamic and quasi-static components, is proposed. It is found that the dynamic part of the macroscopic stresses controls the movement of the dynamic yield surface in stress space, while the quasi-static part determines the shape of the dynamic yield surface. The matrix material is idealized as rigid-perfectly plastic and obeying the von Mises yield. An approximate velocity field for the matrix is employed to derive the dynamic yield function. Numerical results show that the dynamic yield function is dependent not only on the rate of deformation but also on the distribution of initial micro-damage, which are different from that of the quasi-static condition. It is indicated that inertial effects play a very important role in the dynamic behavior of the yield function. However, it is also shown that when the rate of deformation is low (≤103/sec), inertial effects become vanishingly small, and the dynamic yield function in this case reduces to the Gurson model.

Stress Concentration and Stress Intensity for Pressurized Eroded Autofrettaged Thick Cylinders With Bauschinger Effect

2010 ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Stress Intensity ◽  
Stress Concentration ◽  
Bauschinger Effect ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Short Cracks ◽  
Finite Element Package ◽  
Von Mises ◽  
Walled Cylinder

Our previous studies have shown that stress intensity factors (SIFs) are influenced considerably from the presence of the Bauschinger Effect (BE) in thick-walled pressurized cracked cylinders. For some types of pressure vessels, such as gun barrels, working in corrosive environment, in addition to acute temperature gradients and repetitive high-pressure impulses, erosions can be practically induced. Those erosions cause stress concentration at the bore, where cracks can readily initiate and propagate. In this study, The BE on the SIFs will be investigated for a crack emanating from an erosion’s deepest point in a multiply eroded autofrettaged, pressurized thick-walled cylinder. A commercial finite element package, ANSYS, was employed to perform this type of analysis. A two-dimensional model, analogous to the authors’ previous studies, has been adopted for this new investigation. Autofrettage with and without BE, based on von Mises yield criterion, is simulated by thermal loading and the SIFs are determined by the nodal displacement method. The SIFs are evaluated for a variety of relative crack lengths, a0/t = 0.01–0.45 emanating from the tip of the erosion of different geometries including (a) semi-circular erosions of relative depths of 1–10 percent of the cylinder’s wall thickness, t; (b) arc erosions for several dimensionless radii of curvature, r′/t = 0.05–0.4; and (c) semi-elliptical erosions with ellipticities of d/h = 0.5–1.5, and erosion span angle, α, from 6 deg to 360 deg. The effective SIFs for relatively short cracks are found to be increased by the presence of the erosion and further increased due to the BE, which may result in a significant decrease in the vessel’s fatigue life. Deep cracks are found to be almost unaffected by the erosion, but are considerably affected by BE.

Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

2003 ◽  
Vol 125 (3) ◽  
pp. 260-265 ◽  
Author(s):  
C. L. Chow ◽  
M. Jie ◽  
S. J. Hu
Keyword(s):  
Strain Hardening ◽  
Deformation Theory ◽  
Yield Criterion ◽  
Strain Ratio ◽  
Yield Function ◽  
Forming Limit ◽  
Sheet Metals ◽  
Theory Of Plasticity ◽  
Von Mises Yield Criterion ◽  
Von Mises

This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory, which was developed by Sto¨ren and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford’s high-order yield criterion (1979), Hill’s quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J2-theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill’s zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997).

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