Designing Plastic Parts for Assembly · 0.2 in.per minute(5mm/min) toapproximate the material’s...

Designing Plastic Parts for Assembly

Paul A. Tres

ISBN 3-446-40321-3

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Contents

Introduction ....................................................................................................................................... xvii

1 Understanding Plastic Materials ............................................................................. 1

1.1 Basic Resins ................................................................................................................................. 11.1.1 Thermoplastics .................................................................................................................... 11.1.2 Thermosets .......................................................................................................................... 2

1.2 Basic Structures............................................................................................................................ 21.2.1 Crystalline ........................................................................................................................... 21.2.2 Amorphous.......................................................................................................................... 31.2.3 Liquid Crystal Polymer....................................................................................................... 31.2.4 New Polymer Technologies ................................................................................................ 41.2.4.1 Inherently Conductive Polymers (ICP) ............................................................................ 41.2.4.2 Electro-Optic Polymers (EOP)......................................................................................... 51.2.4.3 Biopolymers ..................................................................................................................... 6

1.3 Homopolymer vs. Copolymer ...................................................................................................... 61.4 Reinforcements............................................................................................................................. 71.5 Fillers ....................................................................................................................................... 7

1.5.1 Glass Sphere........................................................................................................................ 81.5.1.1 Microphere Properties ...................................................................................................... 81.5.1.2 Compounding ................................................................................................................... 91.5.1.3 Injection Molding............................................................................................................. 101.5.1.4 Mechanical Properties in Injection Molded Thermoplastic Applications........................ 10

1.6 Additives ...................................................................................................................................... 111.7 Physical Properties ....................................................................................................................... 12

1.7.1 Density and Specific Gravity .............................................................................................. 121.7.2 Elasticity ............................................................................................................................. 131.7.3 Plasticity.............................................................................................................................. 141.7.4 Ductility .............................................................................................................................. 141.7.5 Toughness ........................................................................................................................... 141.7.6 Brittleness ........................................................................................................................... 151.7.7 Notch Sensitivity................................................................................................................. 151.7.8 Isotropy ............................................................................................................................... 201.7.9 Anisotropy .......................................................................................................................... 201.7.10 Water Absorption ............................................................................................................. 201.7.11 Mold Shrinkage ................................................................................................................ 21

1.8 Mechanical Properties .................................................................................................................. 231.8.1 Normal Stress...................................................................................................................... 231.8.2 Normal Strain...................................................................................................................... 231.8.3 Stress-Strain Curve ............................................................................................................. 24

1.9 Creep ....................................................................................................................................... 261.9.1 Introduction......................................................................................................................... 261.9.2 Creep Experiments.............................................................................................................. 261.9.3 Creep Curves....................................................................................................................... 271.9.4 Stress-Relaxation ................................................................................................................ 29

1.10 Impact Properties.......................................................................................................................... 29

xii Contents

1.11 Thermal Properties ....................................................................................................................... 311.11.1 Melting Point.................................................................................................................... 311.11.2 Glass Transition Temperature .......................................................................................... 311.11.3 Heat Deflection Temperature ........................................................................................... 311.11.4 Coefficient of Thermal Expansion ................................................................................... 311.11.5 Thermal Conductivity ...................................................................................................... 331.11.6 Thermal Influence on Mechanical Properties .................................................................. 331.11.7 Case History: Planetary Gear Life Durability .................................................................. 34

2 Understanding Safety Factors................................................................................... 40

2.1 What Is a Safety Factor ................................................................................................................ 402.2 Using the Safety Factors .............................................................................................................. 40

2.2.1 Design Safety Factors ......................................................................................................... 402.2.1.1 Design Static Safety Factor .............................................................................................. 412.2.1.2 Design Dynamic Safety Factor ........................................................................................ 412.2.1.3 Design Time-related Safety Factor .................................................................................. 412.2.2 Material Properties Safety Factor ....................................................................................... 422.2.3 Processing Safety Factors ................................................................................................... 432.2.4 Operating Condition Safety Factor ..................................................................................... 43

3 Strength of Material for Plastics ............................................................................. 44

3.1 Tensile Strength............................................................................................................................ 443.1.1 Proportional Limit............................................................................................................... 453.1.2 Elastic Stress Limit ............................................................................................................. 453.1.3 Yield Stress ......................................................................................................................... 453.1.4 Ultimate Stress .................................................................................................................... 46

3.2 Compressive Stress ...................................................................................................................... 463.3 Shear Stress .................................................................................................................................. 473.4 Torsion Stress ............................................................................................................................... 483.5 Elongations................................................................................................................................... 49

3.5.1 Tensile Strain ...................................................................................................................... 493.5.2 Compressive Strain ............................................................................................................. 513.5.3 Shear Strain......................................................................................................................... 51

3.6 True Stress and Strain vs. Engineering Stress and Strain ............................................................ 513.7 Poisson’s Ratio............................................................................................................................. 523.8 Modulus of Elasticity ................................................................................................................... 54

3.8.1 Young’s Modulus................................................................................................................ 543.8.2 Tangent Modulus ................................................................................................................ 553.8.3 Secant Modulus................................................................................................................... 563.8.4 Creep (Apparent) Modulus ................................................................................................. 563.8.5 Shear Modulus .................................................................................................................... 573.8.6 Flexural Modulus ................................................................................................................ 573.8.7 The Use of Various Moduli ................................................................................................ 58

3.9 Stress Relations ............................................................................................................................ 583.9.1 Introduction......................................................................................................................... 583.9.2 Experiment .......................................................................................................................... 593.9.3 Equivalent Stress................................................................................................................. 593.9.4 Maximum Normal Stress .................................................................................................... 593.9.5 Maximum Normal Strain .................................................................................................... 603.9.6 Maximum Shear Stress ....................................................................................................... 603.9.7 Maximum Deformation Energy .......................................................................................... 61

3.10 Conclusions .................................................................................................................................. 62

Contents xiii

4 Nonlinear Considerations ............................................................................................ 63

4.1 Material Considerations ............................................................................................................... 634.1.1 Linear Material.................................................................................................................... 634.1.2 Nonlinear Material .............................................................................................................. 63

4.2 Geometry ...................................................................................................................................... 644.2.1 Linear Geometry ................................................................................................................. 644.2.2 Nonlinear Geometry............................................................................................................ 64

4.3 Finite Element Analysis (FEA) .................................................................................................... 654.3.1 FEA Method Application.................................................................................................... 654.3.2 Using FEA Method............................................................................................................. 654.3.3 Most Common FEA Codes ................................................................................................. 66

4.4 Conclusions .................................................................................................................................. 66

5 Assembly Techniques for Plastics ......................................................................... 67

5.1 Ultrasonic Welding ...................................................................................................................... 675.1.1 Ultrasonic Equipment ......................................................................................................... 675.1.2 Horn Design ........................................................................................................................ 705.1.3 Ultrasonic Welding Techniques.......................................................................................... 725.1.4 Control Methods ................................................................................................................. 755.1.5 Common Issues with Welding ............................................................................................ 785.1.6 Joint Design ........................................................................................................................ 815.1.6.1 Butt Joint Design.............................................................................................................. 825.1.6.2 Shear Joint Design............................................................................................................ 83

5.2 Ultrasonic (Heat) Staking............................................................................................................. 865.2.1 Standard Stake Design ........................................................................................................ 865.2.2 Flush Stake Design ............................................................................................................. 875.2.3 Spherical Stake Design ....................................................................................................... 885.2.4 Hollow (Boss) Stake Design............................................................................................... 895.2.5 Knurled Stake Design ......................................................................................................... 90

5.3 Ultrasonic Spot Welding .............................................................................................................. 915.4 Ultrasonic Swaging ...................................................................................................................... 925.5 Ultrasonic Stud Welding .............................................................................................................. 925.6 Spin Welding................................................................................................................................ 93

5.6.1 Process ................................................................................................................................ 935.6.2 Equipment ........................................................................................................................... 965.6.3 Welding Parameters ............................................................................................................ 965.6.4 Joint Design ........................................................................................................................ 97

5.7 Hot Plate Welding ........................................................................................................................ 1005.7.1 Process ................................................................................................................................ 1035.7.2 Joint Design ........................................................................................................................ 104

5.8 Vibration Welding........................................................................................................................ 1065.8.1 Process ................................................................................................................................ 1085.8.2 Equipment ........................................................................................................................... 1105.8.3 Joint Design ........................................................................................................................ 1115.8.4 Common Issues with Vibration Welding............................................................................ 113

5.9 Electromagnetic Welding............................................................................................................. 1145.9.1 Equipment ........................................................................................................................... 1155.9.2 Process ................................................................................................................................ 1155.9.3 Joint Design ........................................................................................................................ 116

5.10 Solvent and Adhesive Bonding .................................................................................................... 1185.10.1 Types of Adhesives .......................................................................................................... 1195.10.2 Advantages and Limitations of Adhesives....................................................................... 1205.10.3 Stress Cracking in Bonded Joints..................................................................................... 1205.10.4 Joint Design...................................................................................................................... 121

xiv Contents

5.11 Radio Frequency (RF) Welding ................................................................................................... 1235.11.1 Equipment ........................................................................................................................ 1235.11.2 Process.............................................................................................................................. 124

5.12 Laser Welding .............................................................................................................................. 1255.12.1 Equipment ........................................................................................................................ 1255.12.2 Process.............................................................................................................................. 1275.12.2.1 Surface Heating ............................................................................................................. 1285.12.2.2 Through Transmission................................................................................................... 1285.12.2.3 Staking ........................................................................................................................... 1295.12.3 Techniques for Laser Welding ......................................................................................... 1305.12.4 Polymers........................................................................................................................... 1325.12.5 Applications ..................................................................................................................... 134

5.13 Conclusion.................................................................................................................................... 137

6 Press Fitting ......................................................................................................................... 138

6.1 Introduction .................................................................................................................................. 1386.2 Definitions and Notations............................................................................................................. 1386.3 Geometric Definitions .................................................................................................................. 1396.4 Safety Factors ............................................................................................................................... 1396.5 Creep ....................................................................................................................................... 1406.6 Loads ....................................................................................................................................... 1406.7 Press Fit Theory ........................................................................................................................... 1416.8 Design Algorithm......................................................................................................................... 1436.9 Case History: Plastic Shaft – Plastic Hub .................................................................................... 144

6.9.1 Shaft and Hub Made of Different Polymers ....................................................................... 1446.9.2 Safety Factor Selection ....................................................................................................... 1446.9.3 Material Properties.............................................................................................................. 1456.9.3.1 Shaft – Material Properties at 23 °C ................................................................................ 1456.9.3.2 Shaft – Material Properties at 93 °C ................................................................................ 1496.9.3.3 Creep Curves at 23 °C ...................................................................................................... 1506.9.3.4 Creep at 93 °C .................................................................................................................. 1516.9.3.5 Pulley at 23 °C ................................................................................................................. 1526.9.3.6 Pulley at 93 °C ................................................................................................................. 1556.9.3.7 Creep, Pulley at 23 °C ...................................................................................................... 1566.9.3.8 Creep, Pulley at 93 °C ...................................................................................................... 157

6.10 Solutions: Plastic Shaft – Plastic Hub .......................................................................................... 1586.10.1 Case A .............................................................................................................................. 1586.10.2 Case B .............................................................................................................................. 1596.10.3 Case C .............................................................................................................................. 1606.10.4 Case D .............................................................................................................................. 161

6.11 Case History: Metal Ball Bearing – Plastic Hub.......................................................................... 1636.11.1 Fusible Core Injection Molding ....................................................................................... 1636.11.2 Upper Intake Manifold Background ................................................................................ 1646.11.3 Design Algorithm............................................................................................................. 1676.11.4 Material Properties ........................................................................................................... 1686.11.4.1 CAMPUS....................................................................................................................... 1696.11.5 Solution ............................................................................................................................ 1706.11.5.1 Necessary IF at Ambient ............................................................................................... 1746.11.5.2 IF Available at 118 °C ................................................................................................... 1756.11.5.3 IF Verification at –40 °C ............................................................................................... 1756.11.5.4 Stress Check at –40 °C, Time = 0.................................................................................. 1766.11.5.5 Stress Level at –40 °C, Time = 5,000 h......................................................................... 1766.11.5.6 Stress Level at 23 °C, Time = 5,000 h........................................................................... 1766.11.5.7 Stress Level at 118 °C, Time = 5,000 h......................................................................... 1776.11.6 Conclusion........................................................................................................................ 177

Contents xv

7 Living Hinges ..................................................................................................................... 178

7.1 Introduction .................................................................................................................................. 1787.2 Basic Design for PP, PE ............................................................................................................... 1787.3 Common Living Hinge Design .................................................................................................... 1807.4 Basic Design for Engineering Plastics ......................................................................................... 1807.5 Living Hinge Design Analysis ..................................................................................................... 181

7.5.1 Elastic Strain Due to Bending............................................................................................. 1817.5.1.1 Assumptions ..................................................................................................................... 1817.5.1.2 Geometric Conditions ...................................................................................................... 1827.5.1.3 Strain Due to Bending ...................................................................................................... 1827.5.1.4 Stress Due to Bending ...................................................................................................... 1837.5.1.5 Closing Angle of the Hinge.............................................................................................. 1847.5.1.6 Bending Radius of the Hinge ........................................................................................... 1847.5.2 Plastic Strain Due to Pure Bending..................................................................................... 1847.5.2.1 Assumptions ..................................................................................................................... 1847.5.2.2 Strain Due to Bending ...................................................................................................... 1847.5.3 Plastic Strain Due to a Mixture of Bending and Tension ................................................... 1867.5.3.1 Tension Strain .................................................................................................................. 1867.5.3.2 Bending Strain.................................................................................................................. 1897.5.3.3 Neutral Axis Position ....................................................................................................... 1907.5.3.4 Hinge Length.................................................................................................................... 1907.5.3.5 Elastic Portion of the Hinge Thickness ............................................................................ 193

7.6 Computer Flow Chart................................................................................................................... 1947.6.1 Computer Notations ............................................................................................................ 194

7.7 Computer Flow Chart Equations.................................................................................................. 1967.8 Example: Case History................................................................................................................. 198

7.8.1 World Class Connector ....................................................................................................... 1987.8.1.1 Calculations for the ‘Right Way’ Assembly .................................................................... 1997.8.1.2 Calculations for the ‘Wrong Way’ Assembly .................................................................. 2017.8.2 Comparison Material .......................................................................................................... 2037.8.2.1 ‘Right Way’ Assembly..................................................................................................... 2037.8.2.2 ‘Wrong Way’ Assembly................................................................................................... 2047.8.3 Ignition Cable Bracket ........................................................................................................ 2057.8.3.1 Initial Design .................................................................................................................... 2067.8.3.2 Improved Design .............................................................................................................. 206

7.9 Processing Errors for Living Hinges ............................................................................................ 2087.10 Coined Hinges .............................................................................................................................. 2097.11 Conclusion.................................................................................................................................... 2127.12 Exercise ....................................................................................................................................... 212

8 Snap Fitting .......................................................................................................................... 218

8.1 Introduction .................................................................................................................................. 2188.2 Material Considerations ............................................................................................................... 2198.3 Design Considerations.................................................................................................................. 221

8.3.1 Safety Factors...................................................................................................................... 2238.4 Snap Fit Theory ............................................................................................................................ 224

8.4.1 Notations ............................................................................................................................. 2248.4.2 Geometric Conditions ......................................................................................................... 2258.4.3 Stress Strain Curve and Formulae....................................................................................... 2268.4.4 Instantaneous Moment of Inertia ........................................................................................ 2298.4.5 Angle of Deflection............................................................................................................. 2298.4.6 Integral Solution.................................................................................................................. 2298.4.7 Equation of Deflection........................................................................................................ 231

xvi Contents

8.4.8 Integral Solution.................................................................................................................. 2328.4.9 Maximum Deflection .......................................................................................................... 2328.4.10 Self-locking Angle ........................................................................................................... 235

8.5 Case History: One-way Continuous Beam with Rectangular Cross Section ............................... 2358.5.1 Geometrical Model ............................................................................................................. 237

8.6 Annular Snap Fits......................................................................................................................... 2408.6.1 Case History: Annular Snap Fit – Rigid Beam with Soft Mating Part ............................... 2418.6.2 Notations ............................................................................................................................. 2418.6.3 Geometric Definitions......................................................................................................... 2428.6.4 Material Selections and Properties...................................................................................... 2428.6.5 Basic Formulas.................................................................................................................... 2438.6.6 Angle of Assembly ............................................................................................................. 244

8.7 Torsional Snap Fits....................................................................................................................... 2458.7.1 Notations ............................................................................................................................. 2458.7.2 Basic Formulae ................................................................................................................... 2478.7.3 Material Properties.............................................................................................................. 2488.7.4 Solution ............................................................................................................................... 248

8.8 Case History: Injection Blow Molded Bottle Assembly .............................................................. 2508.9 Tooling ....................................................................................................................................... 2518.10 Assembly Procedures ................................................................................................................... 2528.11 Issues with Snap Fitting ............................................................................................................... 2548.12 Serviceability................................................................................................................................ 2558.13 Conclusions .................................................................................................................................. 255

Appendix A: Enforced Displacement .................................................................................................... 257Appendix B: Point Force ....................................................................................................................... 266References ............................................................................................................................................. 276World Wide Web References Related to Plastic Part Design ............................................................... 283Index ...................................................................................................................................................... 287


Paul A. Tres

ISBN 3-446-40321-3

Leseprobe



05.05.2006http://www.hanser.de/deckblatt/deckblatt1.asp?isbn=3-446-40321-3&style=Leseprobe

3 Strength of Material for Plastics

3.1 Tensile Strength

Tensile strength is a material’s ability to withstand an axial load.In an ASTM test of tensile strength, a specimen bar (Figure 3-1) is placed in a tensile

testing machine. Both ends of the specimen are clamped into the machine’s jaws, whichpull both ends of the bar. Stress is automatically plotted against the strain. The axial loadis applied to the specimen when the machine pulls the ends of the specimen bar inopposite directions at a slow and constant rate of speed. Two different speeds are used:0.2 in. per minute (5 mm/min) to approximate the material’s behavior in a hand assembly operation; and 2.0 in. per minute (50 mm/min) to simulate semiautomatic or automaticassembly procedures. The bar is marked with gauge marks on either side of the mid point of the narrow, middle portion of the bar.

As the pulling progresses, the specimen bar elongates at a uniform rate that is propor-tionate to the rate at which the load or pulling force increases. The load, divided by thecross-sectional area of the specimen within the gage marks, represents the unit stress resistance of the plastic material to the pulling or tensile force.

Figure 3-1 Test specimen bar

3.2 Compressive Stress 45

The stress (σ-sigma) is expressed in pounds per square inch (psi) or in Mega Pascals(MPa). 1 MPa equals 1 Newton per square millimeter (N/mm2). To convert psi into MPa,multiply by 0.0069169. To convert MPa into psi, multiply by 144.573.

F TENSILE LOAD= =

A AREAσ (3.1)

Proportional limitElastic limit

Yield point Ultimate stress

Strain

Stress

psi(MPa)

%

3.1.1 Proportional Limit

The proportional relationship of force to elongation, or of stress to strain, continues untilthe elongation no longer complies with the Hooke’s law of proportionality. The greateststress that a plastic material can sustain without any deviation from the law ofproportionality is called proportional stress limit (Figure 3-2).

3.1.2 Elastic Stress Limit

Beyond the proportional stress limit the plastic material exhibits an increase in elongationat a faster rate. Elastic stress limit is the greatest stress a material can withstand withoutsustaining any permanent strain after the load is released (Figure 3-2).

3.1.3 Yield Stress

Beyond the elastic stress limit, further movement of the test machine jaws in oppositedirections causes a permanent elongation or deformation of the specimen. There is a point beyond which the plastic material stretches briefly without a noticeable increase in load.This point is known as the yield point. Most unreinforced materials have a distinct yieldpoint. Reinforced plastic materials exhibit a yield region.

Figure 3-2 Typical stress/strain diagramfor plastic materials


It is important to note that the results of this test will vary between individualspecimens of the same material. If ten specimens made out of a reinforced plasticmaterial were given this test, it is unlikely that two specimens would have the same yieldpoint. This variance is induced by the bond between the reinforcement and the matrix material.

3.1.4 Ultimate Stress

Ultimate stress is the maximum stress a material takes before failure.Beyond the plastic material’s elastic limit, continued pulling causes the specimen to neck

down across its width. This is accompanied by a further acceleration of the axial elongation(deformation), which is now largely confined within the short necked-down section.

The pulling force eventually reaches a maximum value and then falls rapidly, with littleadditional elongation of the specimen before failure occurs. In failing, the specimen testbar breaks in two within the necking-down portion. The maximum pulling load,expressed as stress in psi or in N/mm2 of the original cross-sectional area, is the plasticmaterial’s ultimate tensile strength (σULTIMATE).

The two halves of the specimen are then placed back together, and the distancebetween the two marks is measured. The increase in length gives the elongation,expressed in percentage. The cross-section at the point of failure is measured to obtainthe reduction in area, which is also expressed as percentage. Both the elongationpercentage and the reduction in area percentage suggest the material ductility.

In structural plastic part design it is essential to ensure that the stresses that wouldresult from loading will be within the elastic range. If the elastic limit is exceeded,permanent deformation takes place due to plastic flow or slippage along molecular slipplanes. This will result in permanent plastic deformations.

3.2 Compressive Stress

Compressive stress is the compressive force divided by cross-sectional area, measured inpsi or MPa.

It is general practice in plastic part design to assume that the compressive strength of aplastic material is equal to its tensile strength. This can also apply to some structuraldesign calculations, where Young’s modulus (modulus of elasticity) in tension is used,even though the loading is compressive.

The ultimate compressive strength of thermoplastic materials is often greater than theultimate tensile strength. In other words, most plastics can withstand more compressivesurface pressure than tensile load.

The compressive test is similar to that of tensile properties. A test specimen is compressed to rupture between two parallel platens. The test specimen has a cylindricalshape, measuring 1 in. (25.4 mm) in length and 0.5 in. (12.7 mm) in diameter. The load is applied to the specimen from two directions in axial opposition. The ultimatecompressive strength is measured when the specimen fails by crushing.

3.2 Compressive Stress 47

A stress/strain diagram is developed during the test, and values are obtained for thefour distinct regions: the proportional region, the elastic region, the yield region, and theultimate (or breakage) region.

The structural analysis of thermoplastic parts is more complex when the material is incompression. Failure develops under the influence of a bending moment that increases as the deflection increases. A plastic part’s geometric shape is a significant factor in its capacity to withstand compressive loads.

P COMPRESSIVE FORCE= =

A AREAσ (3.2)

Figure 3-3 Compressive test specimen

The stress/strain curve in compression is similar to the tensile stress/strain diagram,except the values of stresses in the compression test are greater for the correspondingelongation levels. This is because it takes much more compressive stress than tensilestress to deform a plastic.

3.3 Shear Stress

Shear stress is the shear load divided by the area resisting shear. Tangential to the area,shear stress is measured in psi or MPa.

There is no recognized standard method of testing for shear strength (τ-tau) of a thermo-plastic or thermoset material. Pure shear loads are seldom encountered in structural partdesign. Usually, shear stresses develop as a by-product of principal stresses, or wheretransverse forces are present.


The ultimate shear strength is commonly observed by actually shearing a plastic plaquein a punch-and-die setup. A ram applies varying pressures to the specimen. Theram’s speed is kept constant so only the pressures vary. The minimum axial loadthat produces a punch-through is recorded. This is used to calculate the ultimate shear stress.

Exact ultimate shear stress is difficult to assess, but it can be successfully approximatedas 0.75 of the ultimate tensile stress of the material.

Q SHEAR LOAD=

A AREAτ = (3.3)

Q

Q

3.4 Torsion Stress

Torsional loading is the application of a force that tends to cause the member to twist about its axis (Figure 3-5).

Torsion is referred to in terms of torsional moment or torque, which is the product ofthe externally applied load and the moment arm. The moment arm represents the distancefrom the centerline of rotation to the line of force and perpendicular to it.

The principal deflection caused by torsion is measured by the angle of twist or by thevertical movement of one side.

Figure 3-4 Shear stress sample specimenexample: (a) before; (b) after

Figure 3-5 Torsion stress

3.4 Torsion Stress 49

When a shaft is subjected to a torsional moment or torque, the resulting shear stress is:

t tM M r= =

J Iτ (3.4)

Mt is the torsional moment and it is:

tM F R= (3.5)

The following notation has been used:J polar moment of inertiaI moment of inertiaR moment armr radius of gyration (distance from the center of section to the outer fiber)F load applied

3.5 Elongations

Elongation is the deformation of a thermoplastic or thermoset material when a load is applied at the ends of the specimen test bar in opposite axial direction.

The recorded deformation, depending upon the nature of the applied load (axial, shear or torsional), can be measured in variation of length or in variation of angle.

Strain is a ratio of the increase in elongation by initial dimension of a material. Again,strain is dimensionless.

Depending on the nature of the applied load, strains can be tensile, compressive, or shear.

L= (%)

Lε

Δ(3.6)

3.5.1 Tensile Strain

A test specimen bar similar to that described in Section 3.1 is used to determine thetensile strain. The ultimate tensile strain is determined when the test specimen, beingpulled apart by its ends, elongates. Just before the specimen breaks, the ultimate tensilestrain is recorded.

The elongation of the specimen represents the strain (ε-epsilon) induced in the material,and is expressed in inches per inch of length (in/in) or in millimeters per millimeter (mm/mm). This is an adimensional measure. Percent notations such as ε = 3% can also beused. Figure 3-2 shows stress and strain plotted in a simplified graph.


Figure 3-7 Compressive specimen showing dimensional change in length. L is the original length; P is the compressive force. ΔL is the dimensional change in length

Figure 3-6 Tensile specimen loaded showingdimensional change in length. The differencebetween the original length (L) and theelongated length is ΔL

3.5 Elongations 51

3.5.2 Compressive Strain

The compressive strain test employs a set-up similar to the one described in Section 3.2.The ultimate compressive strain is measured at the instant just before the test specimenfails by crushing.

3.5.3 Shear Strain

Shear strain is a measure of the angle of deformation γ – gamma. As is the case withshear stress, there is also no recognized standard test for shear strain.

Q

Q

Q

Q

γ

Figure 3-8 Shear strain: (a) before; (b) after

3.6 True Stress and Strain vs. Engineering Stress and Strain

Engineering strain is the ratio of the total deformation over initial length.Engineering stress is the ratio of the force applied at the end of the test specimen by

initial constant area.True stress is the ratio of the instantaneous force over instantaneous area.Formula 3.7 shows that the true stress is a function of engineering stress multiplied by

a factor based on engineering strain.

( )TRUE = +1σ σ ε (3.7)

True strain is the ratio of instantaneous deformation over instantaneous length.Formula 3.8 shows that the true strain is a logarithmic function of engineering strain.

( )TRUE = +ln 1ε ε (3.8)


By using the ultimate strain and stress values, we can easily determine the true ultimatestress as:

( )1TRUEULTIMATE ULTIMATE ULTMATE= +σ σ ε (3.9)

Similarly, by replacing engineering strain for a given point in Equation 3.8with engineering ultimate strain, we can easily find the value of the true ultimate strainas:

( )ln 1TRUEULTIMATE ULTIMATE= +ε ε (3.10)

Both true stress and true strain are required input as material data in a variety of finiteelement analyses, where non-linear material analysis is needed.

Initialarea

Reducedarea

3.7 Poisson’s Ratio

Provided the material deformation is within the elastic range, the ratio of lateral tolongitudinal strains is constant and the coefficient is called Poisson’s ratio.

LATERAL STRAIN=

LONGITUDINAL STRAINν (3.11)

In other words, stretching produces an elastic contraction in the two lateral directions.If an elastic strain produces no change in volume, the two lateral strains will be equal tohalf the tensile strain times –1.

Figure 3-9 True stress necking-down effect

3.7 Poisson’s Ratio 53

bb

b'b'

L

L

Δ

Under a tensile load, a test specimen increases (decreases for a compressive test) inlength by the amount ΔL and decreases in width (increases for a compressive test) by theamount Δb. The related strains are:

LONGITDINAL

LATERAL

=

=

L

Lb

b

Δε

Δε

(3.12)

Poisson’s ratio varies between 0, where no lateral contraction is present, to 0.5 for which the contraction in width equals the elongation. In practice there are no materials with Poisson’s ratio 0 or 0.5.

Table 3-1 Typical Poisson’s ratio values for different materials

Material Type Poisson’s Ratio at 0.2 in./min (5 mm/min) Strain Rate

ABS 0.4155Aluminum 0.34Brass 0.37Cast iron 0.25Copper 0.35High density polyethylene 0.35

Figure 3-10 Dimensional change in only two ofthree directions


Table 3-1 (Continued)

Material Type Poisson’s Ratio at 0.2 in./min (5 mm/min) Strain Rate

Lead 0.45Polyamide 0.38Polycarbonate 0.3813% glass reinforced polyamide 0.347Polypropylene 0.431Polysulfone 0.37Steel 0.29

The lateral variation in dimensions during the pull-down test is:

b = b b′Δ − (3.13)

Therefore, the ratio of lateral dimensional change by the longitudinal dimensionalchange is:

bb=L

L

Δ

νΔ

(3.14)

Or, by rewriting, the Poisson’s ratio is:

LATERAL

LONGITUDINAL

=ε

ν

ε

(3.15)

3.8 Modulus of Elasticity

3.8.1 Young’s Modulus

The Young’s modulus or elastic modulus is typically defined as the slope of thestress/strain curve at the origin.

The ratio between stress and strain is constant, obeying Hooke’s Law, within theelasticity range of any material. This ratio is called Young’s modulus and is measured inMPa or psi.

STRESSE = = = CONSTANT

STRAIN

σ

ε

(3.16)

Hooke’s Law is generally applicable for most metals, thermoplastics and thermosets,within the limit of proportionality.


Paul A. Tres

ISBN 3-446-40321-3

Vorwort



05.05.2006http://www.hanser.de/deckblatt/deckblatt1.asp?isbn=3-446-40321-3&style=Vorwort

Preface to the Sixth Edition

As a design engineer in the automotive industry, I have experienced firsthand how powerful a resource Paul Tres’ Designing Plastic Parts for Assembly can be. Not only does the text cover the general properties of most plastics; it also utilizes contemporary,real-world examples to illustrate how these properties impact product design. The book is an excellent reference for experienced engineers and, at the same time, it does a superbjob of educating the novice designer. A noteworthy addition in the sixth edition is a new cutting-edge materials section.

The book’s early chapters start out by defining the differences between thermosets andthermoplastics, and go on to discuss crystalline versus amorphous plastic properties. This sounds simple enough, but I see the effects of poor material selection in my position alltoo frequently, and the end result is always wasted money. With the basics defined, Tres goes on to discuss the typical mechanical and thermal properties of common plastics.This, combined with the “Strength of Materials for Plastics” overview, leads the reader into the design chapters of the book equipped with the tools needed to maximize themessages of Tres’ real-world examples. It quickly becomes obvious that spending theappropriate amount of time in the design phase of any component, especially wheretooling costs are high, is critical to the functional and economic success of the part.

Tres also does a good job describing the joining techniques available to present-day plastic part designers. His inclusion of the surface preparation requirements associatedwith the various welding techniques is of particular importance to novice designers, as it details the sometimes hidden costs associated with each selection. From here, Tres guides the reader through the proper design of press fits, living hinges and snap fits. Again, eachdesign section is reinforced with modern examples and common pitfalls.

I think it’s worth mentioning that I have personally coordinated two three-day seminarswith Paul at the Mercedes-Benz Training Institute, to investigate injection molding part-design and tooling issues introduced in the book in greater detail. I have alsorecommended his services to other organizations inside and outside the auto industry.Since reading the book years ago and using Paul Tres as a consultant, Designing PlasticParts for Assembly has become must-have literature for anyone joining the interiorsdesign department at Mercedes-Benz U.S. International. I have no reservations aboutenthusiastically recommending this book to anyone involved in the field of plastic partsdesign.

Don’t let the patchy beard Paul is sporting on the jacket of this book fool you – he is truly a gifted professional in the plastics field.

Tuscaloosa, Alabama Jeff Lubbers, P.E.Mercedes-Benz U.S. International

Foreword to First Edition

Knowing well the work and many special talents of Paul A. Tres, I take delight in theopportunity to introduce his new book, Designing Plastic Parts for Assembly, andrecommend it to a broad range of readers. Material engineers, design and manufacturingengineers, graduate and under-graduate students, and all others with an interest in designfor assembly or plastic components development now have a clearly written, method-oriented resource.

This practical book is an outgrowth of the like-named University of Wisconsin –Madison course which is being offered nationally and internationally. Just as his lectures in the course provide a detailed yet simplified discussion of material selection,manufacturing techniques, and assembly procedures, this book will make his uniqueexpertise and effective teaching method available to a much larger audience.

Mr. Tres’s highly successful instructional approach is evident throughout the book.Combining fundamental facts with practical techniques and a down-to-earth philosophy,he discusses in detail joint design and joint purpose, the geometry and nature of thecomponent parts, the type of loads involved, and other vital information crucial tosuccess in this dynamic field. Treatment of this material is at all times practice-orientedand focuses on everyday problems and situations.

In addition to plastics, Mr. Tres has expert knowledge in computer software, havingdirected the development of DuPont’s design software. The course at the University ofWisconsin – Madison is indirectly an outgrowth of the software he designed for livinghinges and snap fits at DuPont.

Mr. Tres holds numerous patents in the plastics field. He is known worldwide for his expertise in computer programming, manufacturing processes, material selection andproject management on both a national and international scale.

Most recently, Mr. Tres’s accomplishments have earned him the DuPont AutomotiveMarketing Excellence Award as well as recognition in the 1994–1995 edition of Who’s Who Worldwide.

Whether you are just entering the field, or are a seasoned plastic parts designer,Designing Plastic Parts for Assembly is an excellent tool that will facilitate cost-effectivedesign decisions, and help to ensure that the plastic parts and products you design standup under use.

Madison, WI Dr. Donald E. BaxaUniversity of Wisconsin-Madison

Preface to First Edition

It gives me great pleasure to write this preface for such an important contribution toengineering design. It is rather sad fact that while the creative use of plastics has changedthe very structure of consumer products over the past decade, many engineering studentsgraduate with very little knowledge of polymer engineering or plastic design principles.This book written by a recognized expert and practitioner in the field of plasticcomponent design is both a valuable text for engineering courses and a resource for practicing design engineers.

The full potential for the use of plastics in consumer products became recognized in themid 1980s through the pioneering development of the IBM ProPrinter. The ProPrinter destroyed the myth, prevalent amongst product engineers at that time, that such designelements as plastic springs, plastic bearings, plastic securing elements, etc., lacked thestructural integrity of their more common metal counterparts. In the ProPrinter, not only were these plastic design features shown to have the required reliability in regular use andabuse, they were combined into single parts to produce a new level of design elegance.For example, the injection molded side-frames of the ProPrinter, which support therollers and lead screw, incorporated bearings for all of these rotating members, springs tomaintain the required paper pressure, and cantilever securing elements to allow theframes to be snap fitted into the base. The result of such innovative design detailsproduced a desktop printer which could be assembled in only 32 final assembly steps compared to the 185 steps required to assemble its main competitor in the marketplace.

Since the emergence of the ProPrinter, smart plastic design has become an essential tool inthe competitive battle to produce products which have simpler structures with smaller numbers of discrete parts. Part count reduction, in particular, has been shown, throughnumerous case studies published over the past five years, to have a ripple effect on product manufacture which improves the efficiency of the entire organization. Fewer parts means fewer manufacturing and assembly steps, and fewer joints and interfaces, all of which have apositive effect on quality and reliability. Moreover, a reduction in the number of the parts results in a direct attack on the hidden or overhead cost of an organization. Thus, fewer parts also mean fewer vendors for purchasing to deal with, less documentation, smaller inventory levels, less inspection, simpler production scheduling and so on.

Designing Plastic Parts for Assembly tackles all of the important issues to be faced indesigning multi-feature complex plastic parts. The book is thus much more than its titlesuggests. It deals with essential fundamentals for the development of competitiveconsumer products.

Providence, Rhode Island Dr. Peter DewhurstDepartment of Industrial and Manufacturing Engineering

University of Rhode Island

Acknowledgments

A special thank you to Mr. Tom Matano, Director of Industrial Design at the Academy of Art University, San Francisco, CA, who made it possible to use the futuristic car designs on the cover, which were created by his students John Liu and John Lazorack.

The author gracefully thanks Horia Blendea with Schukra North America, a division ofLeggett & Platt, and Dr. Andrew D’Souza with 3M for their contributions to the 6thedition of this book.

A special thank you to Dr. Jessica Schroeder, Staff Research Scientist, Ms. LisaStanick, Leader – Brand Management, and Mr. Mike Meyerand, Communications, allthree with General Motors Corporation which made it possible to use 2003 Chevrolet Corvette C5 see-through image on the cover of the 5th edition.

The author gracefully thanks David Grewell with the Iowa State University in Ames,IA, for his contribution entitled Laser Welding of Section 5.12.

The author gratefully acknowledges the assistance and encouragement of Professor Dr.Donald E. Baxa, Dino S. Tres, Dragos Catanescu, and Dr. Ranganath Shastri for their helpful suggestions.

I also thank BASF Corporation, Borg-Warner Automotive, Branson UltrasonicCorporation, CAMPUS Consortium, DaimlerChrysler Corporation, Dukane Corporation,ETS Inc., Forward Technology Industries, Inc., Hewlett-Packard Company – Corvallis Division, Leister Corporation, Miniature Precision Components, Inc., MoldingTechnology, Inc., Ohio State University, Sonics and Materials, Inc., Solvay Automotive,and TWI who supplied illustrations for this book.

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