Void Nucleation Effects in Biaxially Stretched Sheets

1980 ◽  
Vol 102 (3) ◽  
pp. 249-256 ◽  
Author(s):  
C. C. Chu ◽  
A. Needleman
Keyword(s):  
Plastic Strain ◽  
Volume Fraction ◽  
Void Nucleation ◽  
Hydrostatic Stress ◽  
Forming Limit ◽  
Stress Theory ◽  
Out Of Plane ◽  
Necking Criterion ◽  
Controlled Nucleation ◽  
Forming Limit Curves

The effects of void nucleation occurring during the deformation history on forming limit curves are considered for both in-plane and punch stretching employing a constitutive model of a porous plastic solid. Both plastic strain controlled and stress controlled nucleation processes are simulated by a two parameter void nucleation criterion. For in-plane stretching, plastic strain controlled nucleation can have, in certain circumstances, a significantly destabilizing effect on the forming limit curve. However, within the framework of plane stress theory which neglects the enhancement of the hydrostatic stress due to necking, a stress controlled nucleation process is not found to be significantly destabilizing. In punch stretching a ductile rupture criterion, which limits the maximum volume fraction of voids, as well as the appearance of a well defined thickness trough, is adopted as a localized necking criterion. Only plastic strain controlled void nucleation is considered here in out-of-plane stretching. The resulting forming limit curves have the same shape as those obtained previously with void nucleation neglected.

Forming Limits Under Stretch-Bending Through Distortionless and Distortional Anisotropic Hardening

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Ji He ◽  
Bin Gu ◽  
Yongfeng Li ◽  
Shuhui Li
Keyword(s):  
Detailed Comparison ◽  
Forming Limit ◽  
Anisotropic Hardening ◽  
Hardening Model ◽  
Stretch Bending ◽  
Bending Process ◽  
Hardening Models ◽  
Out Of Plane ◽  
Forming Limit Curves ◽  
Insight Into

The necking behavior of sheet metals under stretch-bending process is a challenge for the forming limit prediction. State-of-the-art forming limit curves (FLCs) allow the prediction under the in-plane stretching but fall short in the case under out-of-plane loading condition. To account for the bending and straightening deformation when sheet metal enters a die cavity or slide along a radius, anisotropic hardening model is essential to reflect the nonproportional loading effect on stress evolution. This paper aims to revisit the M-K analysis under the stretch-bending condition and extend it to accommodate both distortionless and distortional anisotropic hardening behavior. Furthermore, hardening models are calibrated based on the same material response. Then the detailed comparison is proposed for providing better insight into the numerical prediction and necking behavior. Finally, the evolution of the yield surface and stress transition states is examined. It is found that the forming limit prediction under stretch-bending condition through the M-K analysis strongly depends on the employed anisotropic hardening model.

Forming Limit Evaluation with Perturbation Approach Considering Through-Thickness Normal Stress

2019 ◽  
Vol 794 ◽  
pp. 48-54
Author(s):  
Qi Hu ◽  
Xi Feng Li ◽  
Jun Chen
Keyword(s):  
Plastic Strain ◽  
Normal Stress ◽  
Plane Stress ◽  
Fluid Pressure ◽  
Equivalent Plastic Strain ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Perturbation Approach ◽  
Thin Sheets ◽  
Forming Limit Curves

To predict material’s formability in the hydroforming processes, the plane stress assumption would be invalid. The instability perturbation approach proposed by Hu et al. [1] is extended with the through-thickness normal stress by combining Hill’48 and Hosford’s yield criteria. The influences of through-thickness normal stress on the predicted forming limit strains in the forms of traditional Forming Limit Diagram (FLD) and equivalent plastic strain (EPS) based FLD (epFLD) are investigated. The results show that forming limit curves (FLCs) in both forms of FLD enhance with increasing through-thickness normal stress under proportional and non-proportional loadings. This new model can be utilized to study the effects of fluid pressure on the formability of orthotropic thin sheets.

Forming Limit Curves for Complex Strain Paths

2013 ◽  
Vol 58 (2) ◽  
pp. 587-593 ◽  
Author(s):  
J. Rojek ◽  
D. Lumelskyy ◽  
R. Pęcherski ◽  
F. Grosman ◽  
M. Tkocz ◽  
...  
Keyword(s):  
Plastic Strain ◽  
Strain Path ◽  
Experimental Studies ◽  
Polar Coordinates ◽  
Forming Limit ◽  
Effective Plastic Strain ◽  
Steel Blank ◽  
Strain Paths ◽  
Complex Strain ◽  
Forming Limit Curves

This paper presents results of experimental studies of forming limit curves (FLC) for sheet forming under complex strain paths. The Nakazima-type formability tests have been performed for the as-received steel blank and for the blank pre-strained by13%. Prestraining leads to abrupt change of strain path in the blank deformation influencing the forming limit curve. The experimental FLC of the pre-strained blank has been compared with the FLC constructed by transformation of the as-received FLC. Quite a good agreement has been found out. The concept of strain-path independent FLCs in polar coordinates has been verified. Two types of the polar diagrams have been considered, the first one with the strain-path angle and effective plastic strain as the polar coordinates, and the second one originally proposed in this work in which the thickness strain has been used instead of the effective plastic strain as one of the polar coordinates. The second transformation based on our own concept has given a better agreement between the transformed FLCs, which allows us to propose this type of polar diagrams as a new strain-path in dependent criterion to predict sheet failure in forming processes.

A Finite Element Analysis of Void Evolution in 2-D Machining

2002 ◽  
Author(s):  
Q. Cao ◽  
K. C. Ee ◽  
O. W. Dillon ◽  
I. S. Jawahir
Keyword(s):  
Damage Mechanics ◽  
Volume Fraction ◽  
Void Nucleation ◽  
Hydrostatic Stress ◽  
Effective Strain ◽  
Machining Process ◽  
Void Coalescence ◽  
Machining Parameters ◽  
Machined Surface ◽  
Void Evolution

The objective of this paper is to study void evolution and its effects on material failure during the machining process. The influence of cutting conditions on void nucleation, growth and coalescence is studied. The ultimate goal of this approach, as applied to machining, is to predict chip breakage and surface conditions via damage mechanics. A damage mechanics model proposed by Komori [1] is chosen to study the evolution of the void volume fraction in the chip and workpiece being machined with a grooved tool. A Thomason [2] type criterion as modified by Dhar et al. [3], that uses the variables calculated by FEM analysis, is used to predict void coalescence (failure). The distribution of the variables, such as effective strain-rate, nondimensional hydrostatic stress, and effective strain are obtained using the FEM methodology described by Zhang [4]. It is found that void coalescence always occurs in the newly machined surface below the flank face of the tool and in the chip flowing around the chip-groove region near the upper end of the face land. On the other hand, whether void coalescence occurs inside the chip or not, depends on the complex interactions between the machining parameters and chip geometry.

scholarly journals The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

2021 ◽  
Vol 11 (8) ◽  
pp. 3378
Author(s):  
Jie Chen ◽  
Darby J. Luscher ◽  
Saryu J. Fensin
Keyword(s):  
Growth Model ◽  
Damage Evolution ◽  
Volume Fraction ◽  
Void Nucleation ◽  
Nucleation And Growth ◽  
Void Coalescence ◽  
Hydrodynamic Simulations ◽  
Void Evolution ◽  
Void Nucleation And Growth ◽  
Nucleation Growth

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

scholarly journals Forming Limit Stress Diagram Prediction of Pure Titanium Sheet Based on GTN Model

Materials ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 1783 ◽  
Author(s):  
Tao Huang ◽  
Mei Zhan ◽  
Kun Wang ◽  
Fuxiao Chen ◽  
Junqing Guo ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Pure Titanium ◽  
Void Volume Fraction ◽  
Void Volume ◽  
Forming Limit ◽  
Stress And Strain ◽  
Gtn Model ◽  
Stress Diagram ◽  
Limit Stress ◽  
Hemispherical Punch

In this paper, the initial values of damage parameters in the Gurson–Tvergaard–Needleman (GTN) model are determined by a microscopic test combined with empirical formulas, and the final accurate values are determined by finite element reverse calibration. The original void volume fraction (f0), the volume fraction of potential nucleated voids (fN), the critical void volume fraction (fc), the void volume fraction at the final failure (fF) of material are assigned as 0.006, 0.001, 0.03, 0.06 according to the simulation results, respectively. The hemispherical punch stretching test of commercially pure titanium (TA1) sheet is simulated by a plastic constitutive formula derived from the GTN model. The stress and strain are obtained at the last loading step before crack. The forming limit diagram (FLD) and the forming limit stress diagram (FLSD) of the TA1 sheet under plastic forming conditions are plotted, which are in good agreement with the FLD obtained by the hemispherical punch stretching test and the FLSD obtained by the conversion between stress and strain during the sheet forming process. The results show that the GTN model determined by the finite element reverse calibration method can be used to predict the forming limit of the TA1 sheet metal.

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