In this study it was investigated how a thinner strip in the edge to edge model influences the mechanical behavior of the sealing. Since a thickness of each strip of 100µm for the two strips is rather large, it was decreased to 50µm. The behavior of the two simulations were similar, but failure occurred earlier when the thickness was decreased, as shown in Figure 6.8. All the loading has to be transferred by the strips into the laminate, thus a thinner strip results in a slightly weaker behavior.
0 0.5 1 1.5 2 2.5 3 3.5
0 50 100 150 200 250
Displacement [mm]
Force [N]
Simulation edge to edge, 0.1 mm PET Simulation edge to edge, 0.05 mm PET
Figure 6.8: Variation of thickness of the PET-strip
Discussion
The tension tests performed of the LS shows an initial elastic part followed by plastic behavior and kinematic hardening. The mechanical behavior of the LS is determined by the properties of the laminate, whereas the ultimate strength of the sealing is determined by the geometry and the of the sealing and the material properties of the paper.
The longitudinal overlap width has significant influence on the the mechanical be-havior of the sealing up to a width of approximately 12 mm, due to the decreasing rotation of the cross section. From the experimental tests it was concluded that an increase of the overlap width from 8.0 to 10.5 mm (31.3 %) increases the ultimate strength from 170.2 N to 196.2 N (15.2 %). The mechanical work required increases at the same time from 189.1 Nmm to 282.1 Nmm (49 %), which is quite remarkable.
The FE-simulations with the 3DM employed shows very good agreement with the experimental tests for the case when the CD is oriented in the horizontal length dimension. The ultimate strength is difficult to capture, especially for the sealing type no strip, but the overall mechanical behavior is very well predicted.
The edge to edge sealing remarkably reduces the stresses in the ZD, since there is no rotation of the cross section as in the overlap sealings. Therefore it manages to be subjected to higher loads. The strip and folded strip sealing have very similar be-havior. The most interesting difference is that the strip sealing may to be subjected to some loading after the fracture has propagated through the paperboard, which the folded strip cannot do. Therefore is the mechanical work required to break the strip sealing somewhat higher compared to the folded strip sealing.
The paper thickness seem to have great influence of the mechanical behavior of the sealing. A decrease of the paper thickness does not influence the ultimate strength, but it gives a more ductile fracture with a higher mechanical work required, see Fig-ure 6.7. Unfortunately is the paper thickness also a parameter with great influence on the grip stiffness of a package, see Andreasson and Bengtsson [3].
61
7.1 Proposals for future work
From the results in this work it has been shown that the 3DM shows quite good agreement with reality for tension load cases in CD. The future work could therefore focus on the following subjects:
• Why there is worse agreement for the MD case
• Try to capture the ultimate strength in the simulations in a better way.
• The relationship between the height of fall for a package and the mechanical influence of the longitudinal sealing or
• A model of an entire package simulating a fall
• A more thorough investigation of the sealing type edge to edge, for example an experimental study.
• Determine whether it is a high ultimate strength or a high mechanical work required to break the sealing that is most important to receive a sealing with good performance.
[1] ABAQUS Inc., (2005) ABAQUS/Standard manuals, version 6.5, Pawtucket, RI, USA.
[2] Andersson H., (1998) IH sealing: Induction Heating as sealing method at Tetra Pak,Tetra Pak Research & Developement AB, Sealing Technology, Lund [3] Andreasson E. and Bengtsson T., (2002) Grip stiffness in beverage packages
- An experimental and finite element study,Division of Structural Mechanics, Lund University, Sweden.
[4] Elison O. and Hansson L., (2005) Evaluating the 3DM model - an experimental and finite element study, Division of Solid Mechanics, Lund University, Sweden.
[5] Nyg˚ards M.,(2005), The 3DM model 3.22, STFI-Packforsk
[6] Ottosen N.S. and Petersson H.,(1992), Introduction to the Finite Element Method, Prentice Hall Europe, Great Britain.
[7] Ottosen N.S. and Ristinmaa M.,(1999), The Mechanics of Constitutive Mod-elling, Volume 1, Classical topics, Division of Solid Mechanics, Lund University, Sweden.
[8] Persson K., (1991), Material model for paper: Experimental and Theoretical Aspects, Divison of Structural Mechanics, Lund University, Sweden.
[9] Xia Q.S., (2002), Mechanics of inelastic deformation and delamination in pa-perboard, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
[10] www.tetrapak.com. 20050908
63
Results from experimental tests
65
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 1, 6.2 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 1, 8.0 mm
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 1, 10.5 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 1, 16.5 mm
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 1, 23.0 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 2, 6.8 mm
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 2, 8.8 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 2, 10.5 mm
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 3, Machine package 8.2 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 3, Rig package 7.8 mm
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 3, Juice package 1, 6.5 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 3, Juice package 2, 8.2 mm
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 5, 18.0 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 4, 10.2 mm
0 0.5 1 1.5 2 2.5 3 3.5 4 0
50 100 150 200 250
Displacement [mm]
Force [N]
Test series 5, 18.0 mm
0 0.5 1 1.5 2 2.5 3 3.5 4
0 50 100 150 200 250
Displacement [mm]
Force [N]
Test series 6
Results from simulation
75
(Ave. Crit.: 75%) S, S11
+0.000e+00 +0.000e+00 +0.000e+00 +0.000e+00
Figure B.1: S11, time frame 0
(Ave. Crit.: 75%) S, S22
-7.456e+00 -1.326e+00 +4.803e+00 +1.093e+01 Step: Displace Frame: 0
Figure B.2: S22, time frame 0
(Ave. Crit.: 75%) S, S12
+0.000e+00 +0.000e+00 +0.000e+00 +0.000e+00 Step: Displace Frame: 0
Figure B.3: S12, time frame 0
(Ave. Crit.: 75%) S, S11
-7.700e+00 +2.565e+01 +5.899e+01 +9.234e+01 -1.064e+01
Step: Displace Frame: 20
Figure B.4: S11, time frame 20
(Ave. Crit.: 75%) S, S22
-1.142e+01 -4.370e+00 +2.677e+00 +9.723e+00 Step: Displace Frame: 20
Figure B.5: S22, time frame 20
(Ave. Crit.: 75%) S, S12
-3.331e+00 -1.029e+00 +1.273e+00 +3.575e+00 -3.689e+01 +3.487e+01 Step: Displace Frame: 20
Figure B.6: S12, time frame 20
(Ave. Crit.: 75%) S, S11
-7.700e+00 +2.565e+01 +5.899e+01 +9.234e+01 -1.126e+01 +9.462e+01 Step: Displace Frame: 40
Figure B.7: S11, time frame 40
(Ave. Crit.: 75%) S, S22
-1.235e+01 -4.963e+00 +2.424e+00 +9.810e+00 +1.248e+01 Step: Displace Frame: 40
Figure B.8: S22, time frame 40
(Ave. Crit.: 75%) S, S12
-4.614e+01 -1.470e+01 +1.675e+01 +4.819e+01 Step: Displace Frame: 40
Figure B.9: S12, time frame 40
(Ave. Crit.: 75%) S, S11
-7.700e+00 +2.565e+01 +5.899e+01 +9.234e+01 -1.135e+01 +9.334e+01 Step: Displace Frame: 80
Figure B.10: S11, time frame 80
(Ave. Crit.: 75%) S, S22
-7.334e+00 -9.901e-01 +5.354e+00 +1.170e+01 Step: Displace Frame: 80
Figure B.11: S22, time frame 80
(Ave. Crit.: 75%) S, S12
-4.614e+01 -1.470e+01 +1.675e+01 +4.819e+01 Step: Displace Frame: 80
Figure B.12: S12, time frame 80
(Ave. Crit.: 75%) S, S11
-7.700e+00 +2.565e+01 +5.899e+01 +9.234e+01 Step: Displace Frame: 165
Figure B.13: S11, time frame 165
(Ave. Crit.: 75%) S, S22
-7.456e+00 -1.326e+00 +4.803e+00 +1.093e+01
Figure B.14: S22, time frame 165
(Ave. Crit.: 75%) S, S12
-3.902e+01 -1.165e+01 +1.572e+01 +4.308e+01 Step: Displace Frame: 165
Figure B.15: S12, time frame 165
ABAQUS Input File
An example of an input file for ABAQUS. The sealing type was no strip and the longitudinal overlap width was set to 10 mm.
81
*Heading ** Job name: 3dm_10 Model name: NoStrip_3dm_10 *Preprint, echo=NO, model=NO, history=NO, contact=NO **
9900, 10901, 3982, 12, 3983
**
*Solid Section, elset=Set-MTRL_LDPE_Bot, material=LDPE 15.,
**
*Solid Section, elset=Set-MTRL_ALU, material=Alu 15.,
**
*Solid Section, elset=Set-MTRL_LK, material=LK 15.,
9900, 10901, 3982, 12, 3983
**
**
*Solid Section, elset=Set-MTRL_LDPE_Bot, material=LDPE 15.,
**
*Solid Section, elset=Set-MTRL_ALU, material=Alu 15.,
**
*Solid Section, elset=Set-MTRL_LK, material=LK 15.,
**
*End Part
**
3, 486, 1986, 1987, 485 .
. .
1980, 2973, 1235, 5, 1236
**
*Solid Section, elset=Set-MTRL_LDPE_Top, material=LDPE 15.,
3960, 4955, 1239, 5, 1240
**
*Solid Section, elset=Set-MTRL_PAPER_IN, material=Paper_Mech 15.,
3, 486, 1986, 1987, 485 .
.
.
1980, 2973, 1235, 5, 1236
**
*Solid Section, elset=Set-MTRL_PAPER_OUT, material=Paper_Chem 15.,
*Coupling, constraint name=Reference, ref node=RF, surface=Disp
*Kinematic
*Plastic
*User Material, constants=44, unsymm
3400., 25., 8900., 0., 0.14, 0., 38., 2400.
58., 0., 5.4, 1.5, 1.5, 4., 16.5, 22.
8., 6.3, 6.3, 7.4, 44., 18., 12.5, 12.
160., 260., 375., 310., 160., 160., 800., 200.
225., 300., 0.9912, -0.1322, -0.4472, 0.8944, 0.7071, -0.9912 0.1322, 0.4472, -0.8944, -0.7071
**
**
*Material, name=Paper_Mech
*Depvar 45,
*User Material, constants=44, unsymm
960., 16., 3400., 0., 0.10, 0., 15., 800.
20., 0., 5.4, 1.5, 1.5, 4., 6.5, 10.7
6., 6.3, 6.3, 7.4, 19., 7.5, 9., 6.
160., 260., 375., 310., 160., 160., 800., 200.
225., 300., 0.9912, -0.1322, -0.4472, 0.8944, 0.7071, -0.9912 0.1322, 0.4472, -0.8944, -0.7071
**
*Surface Interaction, name=IntProp_Mid-Mid, USER, DEPVAR=20, PROPERTIES=15, UNSYMM 15
640.0, 320.0, 1.18, 0.35, 640.0, 1.18, 0.28, 0.8, 0.085, 0.97, 0.87, 0.87, 0.97, 0.87, 0.87
**
**
*Surface Interaction, name=IntProp_Mid-Out, USER, DEPVAR=20, PROPERTIES=15, UNSYMM 15
800.0, 400.0, 1.45, 0.45, 800.0, 1.45, 0.28, 0.8, 0.085, 0.97, 0.87, 0.87, 0.97, 0.87, 0.87
**
**
*Surface Interaction, name=IntProp_Out-Out, USER, DEPVAR=20, PROPERTIES=15, UNSYMM 15
800.0, 400.0, 1.45, 0.45, 800.0, 1.45, 0.28, 0.8, 0.085, 0.97, 0.87, 0.87, 0.97, 0.87, 0.87
**
**
*Contact Pair, interaction=IntProp_Out-Out
*Step, name=Displacement, nlgeom=YES, inc=50000 apply dislacment
** Name: Disp Type: Displacement/Rotation
**
*Boundary RF, 1, 1, 5.
RF, 6, 6
**
** Name: Fixed Type: Displacement/Rotation
*Boundary
** FIELD OUTPUT: F-Output-1
**
*Output, field, variable=PRESELECT
**
** HISTORY OUTPUT: H-Output-1
**
*Output, history, variable=PRESELECT
*End Step