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PLASTIC YIELDING OF AN ANISOTROPIC ALUMINUM ALLOYUNDER PLANE STRESS CONDITIONS

Dung-An Wang

Institute of Precision Engineering, National Chung Hsing University250 Kuo Kuang Rd., Taichung 402, Taiwan

[email protected]

ABSTRACT- The influence of plastic anisotropy on the plastic behavior of an aluminumalloy AA 6016-T4 is investigated by a two-dimensional finite element analysis. BarlatsYld2000-2d anisotropic yield function is used to describe the material anisotropy including

planar anisotropy and normal anisotropy. The sheet material is assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the edge of thesheet element for various loading conditions. Yield contours of the sheet material based onYld2000-2d yield function and the finite element computations under different loadingconditions are investigated.

INTRODUCTION: Accurate description of the plastic behavior and ductile failure processes of sheet metals under biaxial loading conditions is necessary for accurate prediction of the failure in sheet metal forming processes. Sheet metals for stampingapplications usually display certain extent of plastic anisotropy due to cold or hot rolling

processes. In general, an average value of the anisotropy parameter R is used tocharacterize the sheet anisotropic plastic behavior. Here, R is defined as the ratio of thetransverse plastic strain rate to the through-thickness plastic strain rate under in-planeuniaxial loading conditions. Numerous anisotropic yield criteria have been proposed over years. In this paper, a two-dimensional finite element analysis of a sheet element is carriedout to test the applicability of Barlats Yld2000-2d (Barlat et al. [2003]) anisotropic yieldcriterion. Barlats Yld2000-2d yield criterion is used to describe the material anisotropyincluding planar anisotropy and normal anisotropy. A user subroutine for BarlatsYld2000-2d yield function is developed for its implementation in the finite element codeABAQUS. Since sheet metals under forming operations are usually under plane stressconditions, the sheet element is assumed to be subjected to plane stress conditions. Theanalysis is performed for AA6016-T4 when the material is assumed to be perfectly plastic.The results of finite element computations are compared with those based on BarlatsYld2000-2d yield criterion.

PROCEDURES, RESTULTS AND DISCUSSION: In this investigation, we adopt theYld2000-2d (Barlat et al. [2003]] anisotropic yield criterion to characterize plasticanisotropy of an aluminum alloy AA6016-T4 under plane stress loading conditions.Fig. 1(a) shows a schematic plot of a sheet element under applied normal uniformdisplacements (shown as the bold arrows). The Cartesian coordinates coincide with theorthotropy symmetry axes of the sheet metal. Here, 1 X represents the rolling direction,


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2 X represents the transverse direction, and 3 X represents the thickness direction.Barlats Yld2000-2d anisotropic yield criterion (Barlat et al. [2003]) can be writtenas

a 2=+= (1)

a X X 21 = (2)

aa X X X X 2112 22 +++= (3)

where i X and i X , 2,1=i , are the principal values of two linear transformations on thestress deviator, represents a reference yield stress. The linear transformation on thestress deviator are

=

12

22

11

66

2221

1211

12

22

11

00

0

0

s

s

s

C

C C

C C

X

X

X

(4)

=

12

22

11

66

2221

1211

12

22

11

00

0

0

s

s

s

C

C C

C C

X

X

X

(5)

where ij are the stresses, ijC and ijC are material constants. We can calculate thematerial constants

11C ,

22C , 66C ,

11C ,

12C ,

21C ,

22C and 66C from the yield stresses

0 , 45 , 90 , and b and the anisotropy parameters 0 R , 45 R and 90 R which representthe values of the yield stress and R when the tensile axis is at 0 , 45 , and 90 fromthe rolling ( 1 X ) direction and b R represents the in-plane strain ratio, 12 , in the equal

biaxial tension test, respectively.

We consider an aluminum alloy AA6016-T4 used as benchmark materials in the Numisheet99 conference. The material properties of the AA6016-T4 are listed in Table 1.Finite element computations for a unit cell of AA 6016-T4 for different loading conditions arecarried out. Fig. 1(b) is a finite element mesh of the sheet element. The material isassumed to be elastic perfectly plastic. The material constants of Barlats anisotropic yieldfunction Yld2000-2d for AA6016-T4 are listed in Table 2. The commercial finite element

program ABAQUS is used to perform the computations. A user subroutine is written for the application of Barlats Yld2000-2d anisotropic yield criterion in ABAQUS. Under different loading conditions, the macroscopic stresses are calculated by averaging thesurface tractions acting on the edges of the sheet element. The macroscopic yield point isdefined as the limited stress state where massive plastic deformation occurs. Fig. 2 shows


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finite element computational results and the yield contour for AA 6016-T4 with the sheetmaterial described by Yld2000-2d anisotropic yield function. The computationalmacroscopic effective stresses 11 and 22 are normalized by the yield stress 0 . Acomparison of the computational results with the yield contour based on Barlats Yld2000-2d anisotropic yield criterion reveals that Barlats Yld2000-2d yield criterion can describethe plastic anisotropic behavior of the aluminum alloy considered here well.

Table 1: Material properties of AA 6016-T4Youngs modulus (GPa) Poissons ratio

0 (MPa) 45 (MPa) 90 (MPa) b (MPa)

69 0.3 194.1 191.0 183.2 194.1

0 R 45 R 90 R b R0.94

0.39 0.64

1.60

Table 2: Material constants of Barlats anisotropic yield function Yld2000-2d

11C 12C 21C 22C 66C 11C 12C 21C 22C 66C 0.958 0 0 1.04

50.920 1.009 078.0 030.0 096.1 148.1

Fig. 1. (a) A schematic plot of a sheetelement under the applied normal

uniform displacements (shown as the bold arrows). (b) A finite element meshof the sheet element. .

Fig. 2. Finite element computationalresults and the yield contour for AA6016-T4 with the sheet material

described by Yld2000-2d anisotropicyield function.

REFERENCES:


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Barlat F., Brem J. C., Yoon J. W., Chung K., Dick R. E., Lege D. J., Pourboghrat F.,Choi S.-H. and Chu, E., 2003, Plane stress yield function for aluminum alloy sheets

part 1: theory, Int. J. Plasticity, 19, 1297.

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