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Department of Mechanical Engineering

Solid Mechanics

ISRN LUTFD2/TFHF-06/5122-SE(1-80)

DROP TEST OF A SOFT

BEVERAGE PACKAGE

EXPERIMENTAL TESTS AND A

PARAMETER STUDY IN ABAQUS

Masters Dissertation by

Johanna Lonn

andJenny Navred

Supervisors

Eskil Andreasson, Tetra Pak R&D AB, SwedenHakan Hallberg, Div. of Solid Mechanics, Lund University, Sweden

Magnus Harrysson, Div. of Solid Mechanics, Lund University, Sweden

Copyright c 2006 by Div. of Solid Mechanics,Tetra Pak R&D AB, Johanna Lonn, Jenny Navred

Printed by Media-Tryck, Lund University, Lund, SwedenFor information, adress:

Division of Solid Mechanics, Lund University, Box 118, SE-221 00 Lund, SwedenHomepage: http://www.solid.lth.se

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MD

ZD

CD

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0 t = 0

X

j xiui

xi = xi(Xj , t)

dXj

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0

2 2

11

x

x , X

x , X

X

u

dxi

dxi = FijdXj

Fij

Fij = xiXj

det(Fij) > 0

Fij RikVkj

Fij = RikVkj

kj = ln(Vkj)

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vi = xit

dvi =vixj

dxj = Lijdxj

Lij =vixj

Lij

Lij = Dij + Wij

Dij

Dij =1

2

vixj

+vjxi

Wij

Wij =1

2

vixj

vjxi

ij

ti = ijnj

ti nj

Pij

t0i = Pijn0j

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0

F df

i

i j

df

n

0

j

j

-1jkdf

n

Reference configuration Deformed configuration

V S

bi

S

tidS+ V

bidV = V

uidV

uiqi

VqidV =

SqinidS

qi,i

qi,i =qixi

V

(ij,j + bi ui)dV = 0

ij,jV

ij,j + bi = ui

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wi

Vwi(ij,j + bi ui)dV = 0

V

[(ijwi),j ijwi,j]dV +

(wibi wiui)dV = 0

V

(ijwi),jdV =SijwinjdS=

SwitidS

VwiuidV +

Vwi,jijdV =

SwitidS+

VwibidV

xi = Xi + ui

uvi = xvi

wi uvi

wixj

=

xj

dxvidt

=

d

dt

xvixj

= Lvij

Lvijwi

VwiuidV +

VDvijijdV =

SwitidS+

VwibidV

Dvij = Lvij ij

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ij = eij +

pij

eij pij

DijDeij D

pij

Dij = Deij + D

pij

DijDt

= CijklDekl

Cijkl Dekl

GNij = CijklDekl RlkRlikj ikRklRjl

Rik Rlk

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F(s2s3)2+G(s2s1)

2+H(s3s1)2+2Ls223+2Ms

212+2Ns

2131 = 0

sij

sij = ij 1

3kkij

F = 12

1

(1y0)2

+ 1(3

y0)2 1

(2y0)2

G = 12

1

(1y0)2

+ 1(2

y0)2 1

(3y0)2

H= 12 1(3y0)2 + 1(2y0)2 1(1y0)2

L = 12(13y0)

2

M= 12(12y0)

2

N= 12(23y0)

2

y0

4

(1y0)2(3y0)

2>

1

(2y0)2

1

(3y0)2

+1

(1y0)2

2

F(ij) = 0

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von Mises yield surface

Hills yield surface

32

1

ij

f(ij,K) = 0

= 1, 2,...

f= F(ij) y0 = 0

y0

y0 = |0 + Q(1 ebp)

|0Q

b Q

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3

2

1

Initial yield surface

Current yield surface

f= F(ij ij) = 0

ij


3

2

1


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= C1

y0( )

p

0 p

f= F(ij ij) y0 = 0


3

2

1


= C1

y0( )

p

p

p

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u = Na

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u N

u = Na

Dv = Ba

b

w = Nc

cT

VNTNadV +

VB

TdV

SN

TtdS

VNTbdV

= 0

V

NTNdVa + V

BTdV

S

NTtdS

V

NTbdV = 0

M fint fext

M =VNTNdV

fint =VB

TdV

fext =SN

TtdS

VNTbdV

Ma = fext fint

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f(t)t

0 1 2 3 4 50

1

2

3

4

5

6

7

8

t

f(t)

f(t)t

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0 1 2 3 4 50

1

2

3

4

5

6

7

8

t

f(t)

Mu(i) = f

(i)ext f

(i)int

u

fext

fint

u(i) = M1 (f

(i)ext f

(i)int)

u(i+ 1

2) = u(i

1

2) +

t(i+1) + t(i)

2u(i)

u(i1

2)

u(i+1) = u(i) + t(i+1)u(i+

1

2)

u(0)

u(0)

u(+1

2)

u(1

2)

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u(+ 1

2) = u(0) + t(1)

2u(0)

u(1

2) = u(0)

t(1)

2u(0)

t 2

max(

1 + 2 )

max

cd

cd =

E

cd Lmin

t Lmincd

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cdt

EI + EV + EFD + EKE EW = ETotal =

EI EV EFDE

KEE

W

ETotal

%

EI = EE + EP + ECD EA

EE EP

ECDEA

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15

15

Sealing

5

150

(mm)

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%

%%

%

%

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Nominal strain (%)

Nominalstress(MPa)

MD

CD

yo E

= C

C

112233121323

=

1E11

12E13

13E33 0 0 0

12E11

1E22

23E33

0 0 013E11

23E22

1E33

0 0 0

0 0 0 1G12

0 0

0 0 0 0 1G13

0

0 0 0 0 0 1G23

112233121323

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E3 =E1

200

G12 = 0.39E1E2

G13 =E155

G23 =E235

e

p

tij = eij +

pij

true = ln(1 + nom)

true = nom(1 + nom)

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nom

nom

total

ep

e p total

p = nom e = nom true

E

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Strain [%]

Stress[MPa]

Test Data Packaging materialABAQUS Isotropic Hardening

MD

CD

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Strain [%]

Stress[MPa]

Test Data Packaging materialABAQUS Kinematic Hardening

MD

CD

Strain [%]

Stress[MPa]

Test Data Packaging materialABAQUS Combined Hardening

MD

CD

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c0 s 0c0

c0 =

K

K

K = 2.2 = 1000 3

c0 = 1483 s 0

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3

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1.5 107

S4R S3R S4RS3R

S4R S3R C3D8R

C3D8RC3D4

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R3D4

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mgh1 +mv21

2= mgh2 +

mv222

v2 =

2g(h1 h2)

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%

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I=t0F(t)dt = m(v0 v)

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(Ave. Crit.: 75%)

SNEG, (fraction = -1.0)

S, Mises

-3.5e+07-2.5e+07-1.5e+07-5.0e+06+5.0e+06+1.5e+07+2.5e+07+3.5e+07+5.0e+07

(Ave. Crit.: 75%)


S, S11

-4.9e+07-3.5e+07-2.3e+07-1.2e+07+1.0e+00+1.2e+07+2.3e+07+3.5e+07+5.0e+07

(Ave. Crit.: 75%)


S, S11

-4.9e+07-3.5e+07-2.3e+07-1.2e+07+1.0e+00+1.2e+07+2.3e+07+3.5e+07+5.0e+07

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(Ave. Crit.: 75%)


S, S12

-1.1e+07-7.0e+06-4.7e+06-2.3e+06-2.5e-01+2.3e+06+4.7e+06+7.0e+06+1.1e+07

(Ave. Crit.: 75%)


S, S12

-1.1e+07-7.0e+06-4.7e+06-2.3e+06-2.5e-01+2.3e+06+4.7e+06+7.0e+06+1.1e+07

(Ave. Crit.: 75%)


S, S12

-1.1e+07-7.0e+06-4.7e+06-2.3e+06-2.5e-01+2.3e+06+4.7e+06+7.0e+06+1.1e+07

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0 2 4 6 8 100

200

400

600

800

1000

1200

1400

Time [ms]

Reactionforce[N]

Drop height 1.30 m

Drop height 0.8 m

Drop height 0.3

0 2 4 6 8 100

100

200

300

400

500

600

700

Time [ms]

Reactionforce[N]

First impact

150 155 160 165 1700

100

200

300

400

500

600

700

Time [ms]

Reaction

force[N]

Second impact

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0 5 10 15 20 25 300

100

200

300

400

500

600

700

Time [ms]

Reactionforce[N]

Horizontal drop 0.8 m

Vertical drop 0.8 m

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%

%

%

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0 5 10 15 200

0.5

1

1.5

2

2.5

3

Time [ms]

Energy[J]

total energykinetic energy

internal energy

0 5 10 15 200

0.5

1

1.5

2

2.5

3

Time [ms]

Energy[J]

total energykinetic energy

internal energy

0 5 10 15 20

0

0.5

1

1.5

2

2.5

3

Time [ms]

Energy

[J]

plastic dissipationartificiall strain energystrain energy

0 5 10 15 20

0

0.5

1

1.5

2

2.5

3

Time [ms]

Energy

[J]

plastic dissipationartificiall strain energystrain energy

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&

&

&

&

&

// #

&

&

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FE-mo

4. Step

Output variables

Field output

Select from list

reaction forces

displacement

stressstrain

velocity

energy

Space intervalnumber=200

History Output

Select from listenergy

Space intervalnumber=200

Dynamic explicit

Time period0.2 secNlgeom-on (default)

Bulk viscocitylinear - 0.06 (default)

quadratic - 1.2 (default)

5. Interaction

Frictionm = 0

Contact*all with self

6. Load

Rigid floor

Gravity9.81 [m/s2]

Initial velocityvz = -3.96 [m/s]

7. Mesh

Hourglass controlenhanced control

Elements

SolidC3D4

C3D8R

ShellS3R

S4R

2D-rigid-floorR3D4

Seededge by number

Mesh controls

Tetrahedralfree

Quadraticstructured

Nodesshared on surface

8. Job

double precision

CPU=2

9. Visualization

Reaction forces

Deformation

shear stress

stress

displacement

Energy

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del

1. Part

Floor 3D - discrete, rigid [m]

Fluid 3D - deformable, solid [m]

Package 3D - deformable, shell [m]

2. Property

Skin

Materials

Water

EOS

c0=1482 [m/s]

s=0

0=0

Density 1000 [kg/m3]

TFA2

Density 895 [kg/m3]

Elasticity Engineering constants Orthotropic

PlasticityIsotropic hardening potential (Hll)

Sections(shell homogenous)

Package t - thickness

LS 2*t

TS

2*t

3*t (with LS)

width 5mm

Material orientation TFA2

MD

CD

ZD

3. Assembly

Package with fluid inside

Floor

Translated 0.001 mm

Horizontal fall

Vertical fall

Impact point

Sketch

(SI-units)

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