rare metals volume 27 issue 1 2008 [doi 10.1016%2fs1001-0521%2808%2960032-7] zhu, h -- damage and...

8/9/2019 Rare Metals Volume 27 Issue 1 2008 [Doi 10.1016%2FS1001-0521%2808%2960032-7] ZHU, H -- Damage and Frac

1/6

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-. A?

ELSFMER

?-cienceDirect

RARE

METALS,

Vol.

27, No.

I

Feb 2008,

p .

64

Damage and fracture mechanism of

6063

aluminum alloy under three kinds of

stress states

ZHU Hao, ZHU Liang,

and

CHEN

Jianhong

Key Laboratory of the Ministry of Educution of China or Nonferrous Metal Alloys, Lanzhou University of Technology, Lunzhou

7300S0

hina

Received 20 September

2006;

received in revised

form 5

Decem ber 2006; accepted

10

December 2006

Abstract

To study the damage and fracture mechanism of 6063 luminum alloy under different stress states, three kinds of re presentative triaxial stress

states have been adopted, namely smooth tensile, notch tensile, and pure shear. The results of the study indicate the following. During the

notch tensile test, a relatively higher stress triaxiality appears in the root of the no tch. With the applied load ing increasing, the volume frac-

tion of microv oids in the

root

of the notch increase s continuously. When it reach es the critical volume fraction

of

microvoids, the specimen

fractures. During the pure shea r test, the stress triaxiality almost equals to zero, and there is almo st no microvoids but a shear band a t the cen-

ter of the butterfly specimen.

The

shear band results from nonuniform deformation constantly under the shear stress. With stress concentra-

tion, cracks are produced w ithin the she ar band and

are

later coalesced. When the e quivalent plastic strain reaches the critical value (equiva-

lent plastic fracture strain), the butterfly specimen fractures. During the sm ooth tensile test, the stress triaxiality in the gau ge of the sp ecime n

remains constant at

0.33. Thus,

the volume of microvoids of the smooth tensile test is less than that

of the

notch tensile test and the smooth

specimen fractures due to shearing between m icrovoids. The G-T-N damage model and Johnson-Cook model are

used

to simulate the notch

tensile and shear test, resp ectively. The simulated engineering stress-strain curves fit the measu red engineering stress-strain curves very we ll.

In add ition, the emp irical dama ge evolution equation for the notch spec imen is obtained from the experimental data and F EM simulations.

Keywords: 6063 aluminum alloy; damage mechanism; fracture mechanism; G-T-N model; Johnson-Cook model

1. Introduction

Aluminum alloys are increasingly applied to produce

automobiles, since they are capable of reducing the mass of

vehicles, fuel consum ption, and environmen tal pollution. An

important quality for vehicles is crashworthiness [I] . During

the impacting process of

an

automobile, the stress state at

each part in its components is different. Moreover, the stress

state at each part changes with passing time. Different stress

states result in different damage and fracture forms. There

are

several reports

on

ductile damage and ductile fracture.

Ductile fracture (based on initiation, growth, and coales-

cence of voids) and shear fracture (based on shear band lo-

cahzation) are primary two kinds of fracture forms for duc-

tile materials [2-41. El-Magd

et

al

[ 5 ]

studied the d eforma-

tion and dam age behaviors of AA7075 alum inum alloy un-

der two loadings and found that deformation localization

and shear band caused the damage in AA7075 aluminum

alloy under compression loading and under tensile loadmg,

AA7075 aluminum alloy failed due to nucleation, growth,

Corresponding

author: ZHU

Hao

E-mail:

[email protected]

and coalescence of m icrovoids. Smerd et al. [6] found that

the damage forms of AA5754 and

AA5

182 aluminum alloys

were microvoids and fracture due to shea r amongst the mi-

crovoids through high strain rate tensile testing of automo -

tive aluminum alloy sheets. The damage forms of 606 3 alu-

minum alloy under crushmg loading change with the

changing of stress state. Thus, any o ne damage m odel can-

not adequately describe the dam age and deformation forms

of 6063 aluminum alloy and there are also few reports on

the damage and fracture of 6 063 aluminum alloy. This arti

cle studies the damage and fracture mechanism of 6063

aluminum alloy under three kinds of

stress

states. At the

same time, the G-T-N model and Johnson-cook model are

used to simulate the damage behaviors of notch tensile and

pure shear, respectively.

2. Experimental

The experimental material was 6063 T5) extruded alu-

minum alloy and its microstructure is shown in Fig. 1,


2/6

Zhu H. et

aL,

Damage and fracture mechanism

of

6063 aluminum alloy under three kinds

of

stress states

65

which shows that the size of grains varied greatly, with the

maximum reaching 100 Fm, while the minimum was only

several microns. Its chemical composition was given in

wt.% as follows: Mg, 0.45-0.9; Si, 0.2-0.6; Zn, Cr, Ti and

Mn

< 0.1;

and Fe

< 0.35.

For the notch tensile test, dou-

ble-side notch specimens were used. Tensile direction was

parallel to the direction

of

extrusion. The shapes and dimen-

sions of smooth tensile specimens and the notch tensile

specimen are shown in Fig. 2. For the pure shear test, the

butterfly specimens and modified Arcan fixture were used

and their shapes and dimensions are shown in Fig.

3.

The

schematic diagram of the pure test using modified Arcan

fixture is shown in Fig. 4.

Fig.

1.

Microstructure of 6063 extru sion aluminum alloy.

L

Fig.

2.

Shapes and dimensions of a smooth tensile specimen a)

and a notch tensile specim en h).

The tests were performed on the smooth, notch, and but-

terfly specimens by the universal test machine with a cross

head speed of

0.5

mm/min at room temperature. The yield

stress, work hardening coefficient, and work hardening ex-

ponent were measured by the engineer stress-strain curve of

the smooth tensile test. The power-law hardening relation-

ship was used for

ABAQUS

calculations as material

Fig. 3. Butterfly specime n a) and modified Arcan fiitu re

b)

for the shear test.

Pure shear test

I

Fig. 4. Schem atic diagram

of

the pure test.

property.

3. Results and discussion

3.1.

Analysis of experimental curves

The engineer stress-stain curves of three kinds of experi-

ments are shown in Fig. 5. The yield stress ny=195.4 MPa

was drawn from the engineer stress-strain curve of the s-

mooth tensile test. The work hardening coefficient and work

hardening exponent were 281.8 and 0.07, respectively,

which were drawn from the true stress-strain curve

of


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66

200

RARE METALS, Vol.27 No.

1

Feb 2008

-

f

- 200

smooth tensile test.

Fig. 5 shows that the fracture strain of the smooth tensile

test is larger than that of the notch tensile test, and the yield

stress and peak stress of the smooth tensile test are less than

those of the notch tensile test. Those can be explained by Fig.

6,

which shows the stress triaxiality distribution curves of

three kinds of tests. The stress triaxiality of smooth tensile

keeps always 0.33, but the maximal stress aiaxiality of

notch tensile can be up to 0.515. The relatively larger stress

triaxiality makes the specimen s deformation difficult and

more stress is needed to reach the same strain. Therefore, the

larger stress triaxiality has a higher fracture driving force,

which results in the fracture of the specimen at a lower strain.

Thus, the fracture strain of notch tensile test is less than that

of

smooth tensile specimen [2,

71.

Fig. 6 also shows that the

stress triaxiality of the pure test is close to 0.1 (because it is

difficult to get the pure shear state in experiment). The frac-

ture strain of the pure shear test is far bigger than that of the

smooth tensile test.

3.2.

Metallographic

results

and discussion

To

study the damage mechanism, the specimens of the

smooth tensile, notch tensile, and shear tests were loaded

and then unloaded when the strain designated was reached.

The unloaded specimens were cut at the center along the

vertical planes parallel to the direction of applied load and

mounted and then polished on 180-grit paper. All the pol-

ishing was done by wet polishing papers to prevent particles

from extraction from the soft aluminum matrix. The metal-

lographic pictures are shown in Fig. 7,

n

t 1 5 0

a

.

m

Notch tensile

0

Smooth tensile

,,i it -A-

Pure shear ~

1-7

7 0

.0 0.2 0.4

0.6 0.8

1 0

E J Y ,

Fig. 5. Stress-strain curves of the tests.

otch tensile

- - - - .

mooth tensile

0.2

Pure shear

0.1

0.0 0.5

1.0

1.5 2.0 2.5 3.0

Path along central section

of

specimen / nm

Fig. 6. Curves of stress triaxiality distribution.

Fig. 7. Metallographic pictures

of

unloaded specimens: a) particle and void damage in a smooth tensile specimen with an unload-

ing strain of 0.1; b) particle and void damage in a notch tensile specimen with

an

unloading strain of0.09, c) shear band crack in a

pure shear specimen with an unloading strain of 1.05.

Fig. 7(a) shows the unloaded metallographic pictures of a

smooth tensile specimen, from which it can be seen that

there are a few microvoids in the smooth tensile specimen

and the volume of microvoids is relatively small. This is

because the stress triaxiality amongst the smooth tensile

specimen

is

relatively small and the driving force of voids

growing is normal stress. The higher the normal stress is, the

higher the stress triaxiality is, the more rapidly the voids

grow and the bigger the volume of voids. Fig. 7(b) shows

the unloaded metallographic picture of a notch tensile


4/6

Zhu

H . etal.

Damage and fracture mechanism of 6063 aluminum alloy under three kinds of stress states

67

specimen, which shows that there are a lot of microvoids

amongst the unloaded notch specimen and the volume of

microvoids is bigger than that of the smooth tensile speci-

men. This is because the stress triaxiality amongst the notch

tensile specimen is higher than that amongst the smooth ten-

sile specimen. At the same time, the microvoids have started

to coalesce and then microcracks are produced due to coa-

lescence of microvoids. With coalescence of microcracks,

the notch specimen fractures. Fig. 7(c) shows that there is a

shear deformation band in the unloaded shear specimen and

the shear deformation band is a result from plastic deforma-

tion localization. Since the stress triaxiality amongst the pure

specimen is close to 0.1 and the less the stress triaxiality, the

larger the shear stress. The driving force of materials defor-

mation is the shear stress and the higher the shear stress, the

more easily the materials deform. At the same time, there is

a crack in the shear deformation band and the crack was

produced due to deformation incompatibility. With the

cracks extending and coalescence, the butterfly specimen

fractures.

Fig. 8 shows the typical fracture surfaces of smooth ten-

sile, notch tensile, and pure shear specimens, from which it

can be seen that the features of fracture surfaces of the s-

mooth tensile specimen, notch tensile specimen, and shear

specimen are obviously different. Figs. 8(a) and 8(b) show

the fracture surfaces of the smooth tensile specimen and Fig.

8(a) is the macroscopical fracture surface, which shows that

the macroscopical fracture surface

is

relatively smooth and

there is no obvious change in the direction of width and

thickness. It is revealed that the smooth specimen did not

neck before fracture. Therefore, the stress triaxiality of the

smooth tensile specimen can always remain constant. Fig.

8(b) shows the magnified fracture surface, where there are a

lot of dimples and also the volume of dimples

is

relatively

small. At the same time, the direction of the dimples is not

perpendicular to the direction of tensile loading. Therefore,

it can be concluded that the fracture mode of the smooth

tensile specimen is the voids shearing mechanism, which is

the combination of dimpled fracture and shear fracture. Figs.

8(c) and 8(d) show the fracture surfaces of the notch tensile

specimen and Fig. 8(c) shows its macroscopical fracture

surface, which shows that there is obvious change in the di-

rection of width and thickness for the notch tensile specimen

due to necking before fracture. Therefore, the maximum

Fig. 8. Fracture surfaces of three kinds of tests: a,

b)

fracture surfaces of the smooth tensile test; c, d) fracture surfaces o f the

notch tensile test; e, f) fracture surfaces of the shear test.


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8

RARE METALS, Vol. 27, No. 1 Feb 2008

stress triaxiality amongst the notch specimen can be up to

0.515. At the same time, it also can be seen that the macro-

scopical fracture surface takes on a cup-cone shape. It is

because the stress triaxiality along the path of m inimum

transverse area is different, as shown in Fig. 6 and the stress

triaxiality can reach the maximum value of 0.515 at the cen-

ter of the specimen. Therefore, the fracture mechanism is

voids-coalescence fracture at the center of the specimen,

while the fracture mechanism is shearing fracture on the

surface of the specimen and the parts close to it. Fig.

8 d)

shows the magnified fracture surface, which show s several

dimples on the fracture surfaces of the notch tensile spec i-

men and the dimples are the produce of microvoids. The d i-

rection of dimples is perpendicu lar to the direction of tensile

loading and the volume of dimples is bigger than that of the

smooth tensile specimen. In a word, for ductile materials,

the material instability starts with the forming of a necking.

It is followed by the initiation of fracture at the cente r of the

necking with linkage of adjacent voids due to hydrostatic

stress. The coalescence of voids usually forms a zig-zag

configuration and this is perpendicular to the loading direc-

tion. Figs. 8(e) and

8 f)

show the fracture surfaces of the

shear specimen and Fig. 8(e) is its macroscopical fracture

surface, which shows that the m acroscopical fracture surface

is very flat and smooth. Fig.

8 f)

shows the magnified frac-

ture surface, where there are typical snaky slipping and

ripple waves on the shear fracture surfaces and the direc-

tion of shear fracture surfaces is parallel to that of the

maximum shear stress. Under the shear stress, the micro-

voids are elongated and form the parabola or half-ellipse

dimples on the fracture surfaces [2-31. Therefore, it

is

re-

vealed that the fracture mechanism is shear fracture.

4. Finite element simulations

The G-T-N model [7-81 was used to give a numerical

description of the notch tensile test. The yield flow function

is

where Q is the macroscopical Mises equivalent stress,

P

is the macroscopical hydrostatic stress,

R 3 )

s the yield

stress of the undamaged matrix material,

41, qa

and

q3

are

modulation parameters considering the interaction of voids,

and

f *

is the volume fraction of voids revised.

In the notch tensile test, the parameters of the G-T-N

model flow function are set as the following.

ql

= 1.25, q 2 =

1

O

q3 = 1.625;

fo

nitial volume fraction of v oids, = 0.0025;

fc

volume fraction of voids at coalescence, = 0.035; &,

volume fraction of voids at fracture, = 0.0475;

n

volume

fraction of voids forming particles, = 0.02;

EN,

medium

strain for voids formation,

=

0.3;

SN,

standard deviation,

=

0.1.

The Johnson-Cook model [9- 1 ] was used to simulate the

pure shear test. T he Johnson-Cook constitutive relation and

fracture strain relation are as follows.

The constitutive relation:

r = A+

B E )

1

+

C l n E ) [ 1- T ) ]

EO

The fracture strain relation:

Ef = [

D l + D 2 e x p

D3-

) ] ( l + i ) D 4 ( l + D 5 T * )

3)

Here, T

=

T - ,

)

T m

-

T ) is the strain rate, gois

the reference strain rate,

T ,

is the reference temperature,

T , is the melt temperature, s the hydrostatic stress,

6 , s the e quivalent stress.

A ,

B ,

C , n m

l ,

D2

3, D4.

and

D5

re materials constants.

In the Johnson-Cook model: A = 176.45 MPa,

B

= 63.99

MPa, n = 0.07, = 0.0036, m = 0, D l 0.07413, 02 =

0.0892,

D3

-2.441, 0 4

=

-4.76, and

Ds 0.

Simulated re-

sults by ABAQUS are shown in Fig. 9.

Fig. 9(a) shows that the engineering stress-strain curves

of simulation with the G-T-N model is close to the m easured

engineering stress-strain curve of the notch tensile. It proves

that the G-T-N model can be used to simulate the damage

behavior of the notch tensile test. The engineering

stress-strain curve of simulation without adopting the G-T-N

damage mod el overestimates the stress of the notch tensile

test. Fig. 9(b) shows that the Johnson-Cook model can be

used to sim ulate the shear test. Fig. 9(c) shows the curve of

voids growth versus time by simulating the notch tensile test.

As can be seen in Fig. 9(c), voids grow stably before A, and

the curve produces fluctuation from A to B, indicating that

certain voids start to coalesce. During the process of growth,

several voids start to coalesce after

B,

so it results in fracture

of the specimen. The following em pirical dama ge evolution

equation in the root of the notch specimen is obtained from

the experimental data on void volume fraction and the cor-

responding local equivalent plastic strain and stress triaxial-

ity computed from FEM simulations:

(4)

where a b, and c are empirical constant whose values de-

pend on the alloys composition, heat treatment, and micro-

structure. Eq. (4) is only applied

to

6063 (T5) Al-alloy. In

this

experiments,

a =

-0.35, b

=

0.25, and

c =

1.32.

f =

a

+

bln(Z,,)

+c

Bm

6,

5.

Conclusions

(1) The damage mechanism and fracture mechanism are


6/6

Zhu H. eta/. Damage and fracture mechanism of 6063 aluminum alloy under three kinds of stress states

69

J;=0.035

T

m Experiment

00

.

b

0 Without damage model

-V-

Curson model

0.00 0.02 0.04 0.06 0.08

Ec

F

>

I60

120

f:

80

eU

2

0 Experiment

0 Johnson-Cook model

0.030

1'

0.020

0.0 10

0.000

0.000 0.002 0.004 0.006

/oalescence

0.020 -

.....................................................uleation Gowh

0.0 10

-

0.000

0.000 0.002 0.004 0.006

Time / s

Fig. 9. Simulation

r sults

of FEM: a) notch tensile simula-

tion;

b)

shear simulation; c) VVFG void volume fraction due

to growth) versus time of notch tensile.

obviously different for smooth tensile, notch tensile, and

pure shear. In the smooth tensile test, the specimen fractures

due to shearing between microvoids. In the notch tensile test ,

the specimen fractures due to microvoid-coalescence. In the

pure test, the shear deformation band is produced at the cen-

ter of the butterfly specimen and the cracks are produced

and later coalesced in the shear band and result in fracture

of

the specimen.

(2) The

G-T-N

damage model and Johnson-Cook model

can be used to simulate the notch tensile test and pure shear

test, respectively.

3)The empirical damage evolution equation

in

the notch

specimen of 6063 (T5) Al-alloy is obtained:

f

=-0.35+0.251nFp+1.32 8,/o,).

This equation is only applied to 6063 T5)aluminum alloy.

Acknowledgement

'I

esearch is financially supported by the Ministry of

Science and Technology

of

China (No. 2004CCA04900).

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rare metals volume 27 issue 1 2008 [doi 10.1016%2fs1001-0521%2808%2960032-7] zhu, h -- damage and...

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