Table Of ContentDetermination of the Structural Capabilities of
Thermoformed and Blow-molded Components
by
Scott Randall Hummel
Presented to the Graduate and Research Committee
of Lehigh University
in Candidacy for the Degree of
Doctor of Philosophy
in Mechanical Engineering
Department of Mechanical Engineering and Mechanics
Lehigh University
Bethlehem, PA 18015
May 1998
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Approved and recommended for acceptance as a dissertation in partial fulfillment
of the requirements for the degree of Doctor of Philosophy
Date
— A.
Professor Herman F. Nied
Dissertation Director
AcceptedjPate
Committee Members:
Professor John B. Ochs
Committee Chairperson
Professor Robert A. Lucas
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Professor Eric Varley
Professor Raymond A. Pearson
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Acknowledgements
This research was made possible by NSF grant number: DMI-9702443
I would like to thank my Ph.D. Committee members: Dr. John Ochs, Dr. Robert
Lucas, Dr. Eric Varley, and Dr. Raymond Pearson for their time and expert advise. I
especially would like to thank my advisor Dr. H.F. Nied for giving me the opportunity to
be involved with this research, always suggesting alternative solutions and helping me
along with viscoelasticity.
In addition to my committee, I would like to extend my sincere thanks to several
other people in the Lehigh community who have aided me in this endeavor. In particular,
Ann Marie Guttman for her reference contribution in regards to ABAQUS. My office
mate Chris Mordaunt for his conversation and encouragement, Daniel Sabatino and Tom
Praisner in the fluids lab for their help with the video system and data filtering.
I would like to thank my parents, Charles and Mary Ellen Hummel for their
support. I also thank Dick and Lois Carey for their encouragement. Lastly, I would like to
thank my wife Lisa for her confidence and encouragement in this endeavor. I cannot
possibly put into words how much I appreciate all that Lisa has done, but rest assured, I
will be thankful “Always and Forever”.
m
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Table of Contents
Abstract........................................................................................................................................1
Chapter 1 Introduction...........................................................................................................3
1.1. Motivation........ ------...........—.....____.............__.............—................ 3
1.2. Background.....................................................................................................................8
1.2.1. Rubber Elasticity.......................................................................................................................8
1.2.2. Viscoelasticity.........................................................................................................................17
Chapter 2 Experimental......................................................................................................24
2.1. Description of tensile testing machine.........................................................................24
2.2. Data acquisition and control.......................................................................................29
2.3. Optical strain measurement........................................................................................35
2.4. Pure shear test...............................................................................................................40
2.5. Uniaxial tension test......................................................................................................44
2.6. Stress relaxation test....................................................................................................46
Chapter 3 Correlation of experimental data.....................................................................50
3.1. Description of time-strain separable constitutive model..........................................50
3.2. Determination of the non-relaxed stress....................................................................53
3.3. Determination of the rubber-like material constants...............................................58
3.4. Stress relaxation data...................................................................................................61
3.5. Determination of the stress relaxation function constants.......................................64
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3.6. Post contact Young’s modulus— ......-----............---------....................................... 65
3.7. Time-temperature superposition ...------...----------------.....—.—.—... .... 71
Chapter 4 Results of experimental program....................................................................74
4.1. Stress relaxation test in the pure shear mode ____...---------- 74
4.2. Stress relaxation test in the uniaxial stress mode.......................................................80
4.3. Pure shear testing...........................................................................................................81
4.4. Uniaxial tensile testing..................................................................................................86
4.5. Large strain elastic material constants.......................................................................89
4.6. Coefficient of thermal expansion.................................................................................94
4.7. Mechanical anisotropy at room temperature of stretched samples.......................97
Chapter 5 Finite element model of the free inflation stage.........................................100
5.1. Testing the finite element simulation........................................................................105
5.2. Results of the finite element simulation of thef ree inflation stage.........................106
Chapter 6 Post contact finite element analysis.............................................................110
6.1. Description of the model.............................................................................................110
6.2. Material model............................................................................................................115
6.3. Results of the finite element analysis of a sample part...........................................117
6.3.1. Influence of process parameters on warpage and residual stress........................................120
6.3.2. Effect of inflation stress........................................................................................................120
6.3.3. Heat transfer from free surface............................................................................................122
6.3.4. Mold temperature.................................................................................................................125
6.3.5. Reduction of the heat transfer into the mold........................................................................126
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63.6. Effect of changing the sheet temperature..............................................................................129
63.7. No-slip/ slip boundary condition...........................................................................................130
Chapter 7 Conclusions.......................................................................................................133
7.1. Future research..........................................................................................................138
References...............................................................................................................................139
Appendix 1 Viscoelasticity..................................................................................................144
Appendix 2...............................................................................................................................151
Appendix 3..............................................................................................................................172
Vita............................................................................................................................................175
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List of Figures
Figure I Pressure forming and vacuum forming................................................................4
Figure 2 Blowmolding process.............................................................................................5
Figure 3 Loading condition of simple extension...............................................................10
Figure 4 Pure shear loading conditions...............................................................................11
Figure 5 Schematic diagram of the heated tensile testing machine................................25
Figure 6 Photograph of heated tensile testing machine...................................................26
Figure 7 Isometric view of underside of chamber cover.................................................27
Figure 8 Schematic diagram of digital data acquisition and control system.................30
Figure 9 Front Panel of Lab VIEW VI for the tensile testing machine...........................32
Figure 10 Lab VIEW Diagram to measure temperature.....................................................33
Figure 11 Proportional integral control system..................................................................35
Figure 12 Experimental arrangement of optical strain measuring equipment.................36
Figure 13 Typical video image......................... 37
Figure 14 Deformation of the specimen versus crosshead displacement........................39
Figure 15 Pure shear loading...............................................................................................41
Figure 16 Actual deformation in pure shear test................................................................42
Figure 17 Pure shear specimen............................................................................................44
Figure 18 Uniaxial tensile sample........................................................................................45
Figure 19 Typical stress relaxation plot...............................................................................47
Figure 20 Normalized stress relaxation curve....................................................................51
Figure 21 Stress response of ABS during a rapid and a slow deformation tests............53
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Figure 22 Stress response to n step loading.........................................................................54
Figure 23 Partitioning of a finite deformation test..............................................................57
Figure 24 Non-relaxed stress-stretch behavior of ABS at 143C.......................................58
Figure 25 Stress relaxation data filtered with a low pass filter.........................................64
Figure 26 True stress (non-relaxed) vs. true strain in ABS at 143.3° C..........................69
Figure 27 Time-temperature superposition from To to T...................................................72
Figure 28 Stress relaxation at various temperatures..........................................................75
Figure 29 Master stress relaxation curve for ABS at 110° C............................................76
Figure 30 Stress relaxation of ABS at various temperatures............................................78
Figure 31 Stress relaxation of ABS after being pre-stretched..........................................79
Figure 32 Comparison of uniaxial and biaxial mode stress relaxation experiments 81
Figure 33 Non-relaxed stress in ABS during pure shear loading.....................................82
Figure 34 True stress versus true strain in ABS................................................................83
Figure 35 Non-relaxed stress in ABS in uniaxial tension.................................................87
Figure 36 True stress-strain curves of ABS in uniaxial tension.......................................88
Figure 37 Strain energy models of ABS at 143.3 C in pure shear mode..........................92
Figure 38 Experimental arrangement for measuring the CTE..........................................94
Figure 39 Coefficient of thermal expansion of ABS as a function of temperature 96
Figure 40 Stress versus strain in pre-stretched samples....................................................98
Figure 41 Example of a plane strain mold........................................................................100
Figure 42 Schematic diagram of the forming process simulation..................................102
Figure 43 Free inflation stage boundary conditions........................................................102
Figure 44 Symmetry boundary conditions of free inflation stage..................................103
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Figure 45 Single finite element used to model the free inflation stage..........................104
Figure 46 Stretch ratio history used in finite element simulation...................................107
Figure 47 True strain history used in finite element simulation.....................................108
Figure 1 Elements of post contact finite element model..................................................Ill
Figure 2 Post contact boundary conditions.......................................................................112
Figure 3 Result of multi-point constraint used after de-molding....................................114
Figure 4 Young’s modulus at a stretch of 3.0 as a function of temperature...................116
Figure 5 Stress versus normalized component thickness after de-molding...................118
Figure 6 Radius of curvature of an initially flat plate......................................................119
Figure 7 Residual stress at various inflation pressures....................................................122
Figure 8 Influence of the coefficient of heat transfer on the warpage............................123
Figure 9 Residual stresses resulting from convection at free surface.............................124
Figure 10 Warpage reduction as a function of mold temperature..................................126
Figure 11 Warpage of a function of heat transfer coefficient at the mold......................128
Figure 12 Residual stress through thickness for different heat transfer rates................128
Figure 13 Residual stresses of components with various initial temperatures..............130
Figure 14 Residual stresses from slip boundary condition at mold.................................131
Figure 62 Stress as a function of time for a given load program....................................146
Figure 63 Assembly of heated tensile testing machine...................................................155
Figure 64 Mounting plate...................................................................................................156
Figure 65 Encoder bracket.................................................................................................157
Figure 66 Cover top, cover assembly................................................................................158
Figure 67 Internal base plate, chamber assy......................................................................159
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Figure 68 Cylinder side end plate, chamber assy..............................................................160
Figure 69 Cover bottom, cover assembly..........................................................................161
Figure 70 External end plate, chamber assy.......................................................................162
Figure 71 Internal end plate, chamber assembly..............................................................163
Figure 72 Load cell bracket................................................................................................164
Figure 73 Internal side plate, chamber assembly..............................................................165
Figure 74 Side plate, chamber assembly............................................................................166
Figure 75 Spacer, chamber assembly.................................................................................167
Figure 76 Clamp plate, slide assembly..............................................................................168
Figure 77 Connecting link..................................................................................................169
Figure 78 End plate, load cell, chamber assembly............................................................170
Figure 79 Slide plate, slide assembly.................................................................................171
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