or 65.5 Ib I ft3. The convection heat transfer coefficient to forced air is hair =28.4 W/m2 0C or 5 Btu/ft2 h 0F. The air temperature is 75F or 24C. The heattransfer coefficient to the coolant is hcool = 284 W/m2 0C or 50 Btu/ft2 h 0F. Thecoolant temperature is 75F or 24C.

All the values for Equation 5.41 are known except the equilibrium moldtemperature, Tmold avg. The first term on the right is:

N rcp tavg(Tx - Tf) = 90 65.5 0.45 ~ (375 - 175) = 2650 J ^

This is the heat that must be removed from the sheet. The second term onthe right is the amount of heat convected from the sheet to the air. Here0cool/0T = 0.5. The average sheet temperature is Tavg = 375 175 = 275F.

ha i r(Tavg-Ta i r)-0.5 = 5 0 0 ^

The average heat loss from the uncovered mold is given as the third part ofthe right side of Equation 5.41:

hair(Tmold,avg - Tair)(l - 0.5) = 5 0.5 (TmokUvg - 75)And the average heat loss to the coolant is given as the term on the left inEquation 5.41:

hcool ' ( l m o l d , a v g ^ cool) = ^ ' V ^ mold,avg ' ^ )

The mold temperature is then obtained from:

(50 + 2.5) (TmokUvg - 75) = 2650 - 500 = 2150 J ^OrTm o l d , a v g=116For46.6C.

5.6 Transient Heat Transfer During Sheet Coolingon the Mold SurfaceComputer Models

As shown in Fig. 5.1, the convective and conductive elements discussed aboverepresent resistances to heat removal from the sheet. Time-dependent sheet tempera-ture is determined by simultaneously solving the transient heat conduction equationsfor both the formed plastic sheet and the mold1:

(5.42)

(5.43)

1 The general transient one-dimensional heat conduction equation was described in detail in

Chapter 3.

Previous Page

The first two equations represent convection conditions at the free surface and themold/coolant interface, respectively. The third set of three equations represents theheat conduction across the interfacial air trapped between the plastic sheet and themold surface. The last two equations represent the initial sheet and mold tempera-tures, respectively. The solution to these equations uses finite difference [14,15]. Theexplicit method uses a time step defined as:

At = Fo Ax2/oc (5.49)where Fo is the Fourier number. For mathematical stability, Fo

Figure 5.15 Schematic temperature profilesthrough coolant, mold and polymer with increas-ing mold thermal conductivity [top] and increas-ing coolant convection heat transfer [bottom]

cooling time is less important for prototype materials such as plaster than forproduction materials such as aluminum. The effect of mold thickness for productionmold materials such as aluminum is essentially nil.

In all conduction heat transfer models, such as that used to produce Fig. 5.12, theunaccomplished temperature change, Y, is shown to be proportional to the Fouriernumber of the polymer, Fo = oc9/L2, where a is the polymer thermal diffusivity, 6 istime and L is the thickness of the polymer sheet. If the average sheet temperature atremoval from the mold surface is fixed, the unaccomplished temperature change, Y,is fixed and so is the Fourier number. The time required to cool the sheet to thattemperature should then be proportional to the square of the sheet thickness:

ecooi = (Fofixed/a)-L2 (5.54)Doubling the sheet thickness should increase the cooling time by a factor of four.This concept is confounded in practice by the presence of the mold and the attendanttransient heat conduction to the coolant. Figure 5.16 shows that the effective coolingtime of a polymeric sheet in contact with a mold having finite thermal conductivityis not in proportion to the square of the sheet thickness, but rather to a powdersomewhat less than 21. The heat conduction square law, Equation 5.54, is thereforeconservative.

1 For the example shown, 0 is proportional to L17.

Tem

pera

ture

Tem

pera

ture

Coolant

Increasing MoldThermal Conductivity

Mold

Plastic

MoldCoolant

PlasticIncreasing Convection

Heat Transfer

Table 5.6 Parametric Study of Cooling of Polystyrene Sheet to an Average Temperature of 1500F Against a Mold of Various Materials

Surfacetemperature*(0F)

171.1187.6182.3183.5182.2162.8146.9149.2149.3152.6192.4187.6171.178.5

171.1171.3170.9167.8180.7171.3156.1135.2

Interfacetemperature*(0F)

77.777.186.285.688.1

117.6149.5144.1144.4145.076.877.177.778.177.777.176.176.176.577.175.272.6

Timeto cool(S)

19.426.428.328.828.545.5

236.4116.9116.9200.029.726.419.47.4

19.419.219.119.55.7

19.261.1

190.5

Moldthickness(in)

0.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5001.0002.0004.0001.0001.0001.0001.000

Plasticthickness(in)

0.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.0500.1000.2000.400

Surfacecooling

Forced airNatural airNatural airNatural airNatural airNatural airNatural airNatural airNatural airNoneNoneNatural airForced airWater spray

Forced airForced airForced airForced airForced airForced airForced airForced air

Coolanttype

WaterWaterOilOilOilOilOilOilNoneNoneWaterWaterWaterWaterWaterWaterWaterWater

WaterWaterWaterWater

Moldmaterial

AluminumAluminumSteelCu/bronzeZn alloyAl-epoxyMaplePlasterPlasterPlasterAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminum

* When average sheet temperature

Sheet Thickness, inFigure 5.16 Calculated sheet thickness-dependent cooling time and free surface temperaturepara-metric study

Interfacial Air

The actual thickness of the interstitial air layer between the polymer sheet and themold is unknown. Arithmetically, Equation 5.44 is used with two interfacial temper-atures, T11 being the polymer surface temperature at the polymer/air interface and T12being the mold surface temperature at the air/mold interface. With some manipula-tion, these interfacial temperatures are related to the interior plastic and moldtemperatures, Tp and Tm, respectively.

(5.55)(5.56)(5.57)

(5.58)

(5.59)

Free

Su

rface

Te

mpe

ratur

e, 0 F

or

Ti

me,

s

Free Surface Temperature,F

Time, s

The numerical solution to the coupled transient heat transfer equations proceeds asbefore, using standard finite difference equations. Table 5.7 shows the results of oneparametric study. As redone in Fig. 5.17 for this specific study, the overall cycle time

Cooli

ng Tim

e, s

Air lnnerlayer Thickness, in

Figure 5.17 The effect of trapped air gap thickness on cooling timeparametric study

Table 5.7 Parametric Study of Cooling of Polystyrene Sheet to anAverage Temperature of 1500F Against an Aluminum Mold UsingForced Air and Water as Coolants With an Air Interstitial Layer

(Plastic sheet thickness = 0.100 in)(Mold thickness = 1.00 in)

Interfacialair layerthickness(in)

00.00010.00100.00200.00300.00500.00800.0100

Surfacetemperature

(0F)171.2170.4165.8162.1158.8153.8149.4147.2

Plastic/airinterfacialtemperature(0F)

77.178.286.994.9

101.2110.7120.5124.9

Timeto cool

(S)

19.219.521.924.226.530.836.339.7

increases with interstitial layer thickness in a power-law fashion. Example 5.12 showsanother way in which this arithmetic can be used in thermoforming.

Example 5.12 Finding Air Bubbles

Can infrared scanning detect an air bubble in an opaque plastic sheet while it is incontact with the mold surface?

Consider the database used in the parametric study of Table 5.7. Assume thegap between the plastic and the mold in the air bubble is 0.005 in, Fig. 5.18.The bulk of the plastic, in intimate contact with the mold surface, reaches anaverage sheet temperature of 1500F in 19.2 s. At that time, the free sheetsurface temperature is 1710F. From the computer model at 19.2 s, theaverage temperature in the plastic over the air bubble is 185F, the temper-ature of the polymer/air bubble interface is 128F and the surface tempera-ture of the plastic over the air bubble is 1910F. The 2O0F temperaturedifference in plastic free surface temperature should be easily detected witha standard infrared scanning device.

5.7 Shrinkage

As with all materials, plastics increase in specific volume or decrease in density withincreasing temperature1. The specific volume of any polymer changes in slope withtemperature at the glass transition temperature (Fig. 5.19). The specific volume of acrystalline polymer shows a distinct discontinuity in slope during melting. The

1 Volumetric change at thermodynamic equilibrium, Ve, the result of increased molecular motion,

such as rotation and reptation, is related to the coefficient of thermal expansion, COE, in thefollowing way. Volumetric change is a function of temperature and pressure, according to:

(5.60)

(5.61)

(5.62)

where k is the volume expansivity or coefficient of thermal expansion, k = COE, with units oftemperature"1, and P is the isothermal or bulk compressibility, with units of pressure"1. Thermalexpansion is usually restricted to dimensional changes of the polymer over a temperature rangein which the polymer has no thermodynamic transitions. Typical values for coefficients of thermalexpansion of many polymers and some mold materials are given in Table 5.8.

Rearranging:

Figure 5.18 Schematic of air bubble or lake in molded part

volumetric change in the polymer during cooling from the forming temperature toroom temperature is called "shrinkage". All polymers shrink when cooled, regardlessof the process. Shrinkage occurs in thermoforming when the hot polymer sheet iscooled against a rigid mold. There are two general types of shrinkage:

Unconstrained shrinkage, sometimes called isotropic shrinkage. The formed partdecreases uniformly in dimension to the densities shown in Fig. 5.19. The finalpart is said to be in thermodynamic equilibrium.

Constrained shrinkage. The formed part is constrained from shrinking in at leastone direction. The final part density may not achieve the thermodynamicallyequilibrated value until some time after the part has been removed from the moldand trimmed from its web.

Unconstrained Shrinkage

Crystalline polymers heated above their melt temperatures typically have greaterunconstrained shrinkage values than amorphous polymer, as seen in Fig. 5.19 andTable 5.9 [16]. This figure shows the difference in volumetric change between anamorphous and a crystalline polypropylene. The volumetric change is convertedto isotropic linear dimensional change as follows. Volumetric shrinkage, Sv is definedas [17]:

(5.63)

Air Bubble or ,,Lake"

Sheet

Mold

Air Gap

Table 5.8 Coefficients of Thermal Expansion For Plastics[ASTM D 696]

Material

ABSABS/PVCABS/PC20% GR ABSPOM acetal copolymerCast PMMAExtruded PMMAEthyl celluloseCellulose acetateCellulose butyrateCellulose propionatePCTFEPVDFPTFEPolyamide 6 (PA 6)Polyamide 66 (PA 66)PolybutylenePolycarbonatePolybutylene terephthalatePolyethylene terephthalatePETGPolyetherimideLDPEHDPEPolyimidePolymethyl pentenemPPOPPSPP homopolymerPP copolymerPSunmodifiedFR PSrubberizedSANSMAThermoplastic polyurethanePolysulfonePolyether sulfoneThermoplastic elastomerPVC-rigidPVC-flexible

Thermal expansion (solid)

CF)"1

60-13050-90702060-8550-9050-90

100-20080-180

110-17080-12035-7070-14070-1208080

125-1507060-956550-7050-55

100-22060-11045-556540-7025-5080-10070-9550-804565-7080

100-200555585-1907070-250

(0C)-1

35-7030-50401035-4530-5030-9055-11045-10060-9545-6520-4040-8040-65454570-854035-553530-403055-12035-6025-303520-4015-3045-5540-5530-452535-404555-110303050-1054040-140

Temperature, 0C

Figure 5.19 Temperature-dependent specific volume of amorphous and crystalline polypropylene,PP homopolymer [16]. Figure used with permission of copyright owner

where Vm and Vf are the specific volumes of the polymer at room temperature andthe forming temperature, respectively. Linear shrinkage, S1, is given as:

(5.64)

When the cube root is expanded in series form, the linear shrinkage is approximatedas:

S1 -^ + higher order terms (5.65)Shrinkage values are usually given as ranges. The actual values depend on thetemperature difference between forming temperature and room temperature. Table 5.9gives representative shrinkage ranges for thermoformed polymers. The recommendedshrinkage values are used when actual experience with shrinkage of a specific polymeris unknown. The following processing aspects influence the extent of shrinkage [18]: Part Design. Draft on both female and male surfaces influence the extent of

constraint on the sheet as it cools. This is discussed below and again in the

Spec

ific Vo

lume,

cm

3 /g

Amorphous PP

Crystalline PP

Table 5.9 Shrinkage Values for Thermoformable Polymers

Polymer Shrinkage range (%) Recommended shrinkage (%)

ABS-Medium impact 0.6-0.9 0.7ABS-Heat resistant 0.5-0.8 0.7ABS-Flame retarded 0.5-0.8 0.7Cellulose acetate 0.4-0.9 0.5Cellulose butyrate 0.3-0.9 0.4Cellulose propionate 0.3-0.9 0.5Ethylene vinyl acetate (20%) 0.3-0.8 0.6FEP fluoropolymer 1.5-4.5 3.0PTFE fluoropolymer 5.0-10.0 7.0Polycarbonate 0.5-0.7 0.6Polyetherimide 0.6-0.8 0.7PEEK 0.8-1.0 0.8Polyethersulfone 0.6-0.8 0.7LDPE 1.5-4.5 3.0HDPE 2.0-4.5 2.5PMMA 0.2-0.8 0.6mPPO 0.5-0.7 0.7PP 1.0-2.5 2.0HIPS 0.5-0.8 0.6PS 0.5-0.7 0.6Polysulfone 0.7-0.9 0.8Thermoplastic urethane 0.5-1.0 0.8Flexible PVC 10.0-15.0 12.0Flexible PVC (filled) 2.0-3.5 3.0Rigid PVC 0.1-0.5 0.3PVDC 0.5-2.5 1.5Rubberized styrene (Kraton) 0.1-0.5 0.3SMA 0.5-0.9 0.7SAN 0.3-0.5 0.5K-Resin 0.4-0.8 0.7PBT 0.2-0.4 0.4Amorphous PET 0.3-0.6 0.5Crystallized PET 10.0-18.0 12.0XT Polymer 0.4-0.8 0.7

chapter on mold design. Male elements such as posts, bosses, partitions andgussets in female molds also influence shrinkage.

Part Wall Thickness Uniformity. Thin sections cool more rapidly than heavysections and as a result differential shrinkage will result when part wall thick-nesses are not very uniform.

Mold Temperature. A 100C or 18F difference in mold surface temperature maychange shrinkage values by as much as 0.1%.

Depth of Draw. Deeply drawn parts are usually characterized by nonuniform wallthickness, part regions that are formed at lower temperatures than others, and

Temperature

Figure 5.20 The schematic effect of cooling rate on specific volume of an amorphous polymer

regions that have contacted lower temperature plugs. All these aspects influencelocal shrinkage.

Initial Sheet Forming Temperature. Lower forming temperatures result in lowershrinkage.

Constrained Shrinkage

Applied stresses inhibit shrinkage. When the plastic sheet is constrained against themold surface by part design, mold temperature or applied force, complete isotropicshrinkage may be inhibited. Even if mold design and processing conditions are ideal,differential shrinkage may result due to differences in part wall thickness. When thestresses holding the sheet against the mold surface are removed, shrinkage continues.As noted, volumetric change is temperature dependent. Rapid cooling of the plasticsheet forces the polymer into a thermodynamically non-equilibrium state since thereis insufficient time for molecular relaxation before the molecular mobility is inhibited.Consider the temperature-dependent volumetric change schematic of Fig. 5.20. Thespecific volume of the polymer is written as:

(5.66)

Spec

ific Vo

lume

Rapid Cooling Rate

Slow Cooling Rate

Mobile State

Solid State

Time

Figure 5.21 Characteristic time-dependent change in specific volume of an amorphous polymer to astep change in environmental temperature [19]. Figure used with permission of copyright owner. V1is the initial volume. Ve is the final volume of the polymer

where T is temperature and 9 is time. The differential form for the volume is:

(5.67)

(5.68)where r = dT/d6, the rate of cooling. Consider a time-dependent change in specificvolume in response to a step change in environmental temperature for an amorphouspolymer such as polystyrene (Fig. 5.21) [19]. The initial change in specific volume isgiven as V1 and the time-dependent change is:

(5.69)where Ve is the equilibrium value of the specific volume and x is the isothermal rateconstant. If the constant pressure temperature-dependent equilibrium volume iswritten as:

Ve = aT + b (5.70)the rate of change of actual volume with temperature is given as:

(5.71)Equation 5.71 shows that the maximum amount of shrinkage owing to a step changein sheet temperature for an amorphous polymer is a function of the isothermal rateconstant, x, and the degree of quench, r. The isothermal rate constant, x, is relatedto material relaxation once applied stresses are removed. Stress relaxation time, X9

Spec

ific Vo

lume,

cm

3 /gv-ve

Ve

V1

The temperature-dependent volumetric change is given as:

at the glass transition temperature, Tg, for most polymers is about 1000 s [20]. Thestress relaxation time, X, usually increases exponentially with increasing temperature:

X = A exp(AE/RT) (5.72)where A is a pre-exponential constant and AE is the energy of activation. Values forAE are predicted for amorphous and some crystalline polymers for temperaturesabove Tg [21]. Extrapolation to most crystalline polymers and to temperatures belowTg is unwarranted. The isothermal rate constant, T, mirrors the stress relaxation timeconstant, X:

T = K e-c/T (5.73)where K has the units of time"1 and C has the units of temperature. The solution toEquation 5.71 with Equation 5.73 substituted for x is not available in closed form.For intense quenching, r-> oo. Thus:

g - > x (5.74)That is, the final specific volume change simply equals the initial instantaneousvolume change. When r->0, V = Ve. Figure 5.22 shows the effect of quenching onthe final specific volume of polystyrene. Example 5.13 illustrates the time-dependencyof specific volume as determined through stress relaxation. As a practical example,the effect of mold temperature on HDPE shrinkage is seen in Table 5.10 [22].

Example 5.13 Temperature-Dependent Stress RelaxationConsider a polymer with AE 40 kcal/g mol K. Its glass transition temperatureTg= WO0C= 2100F. Determine the stress relaxation time at T= 800C= 176Frelative to that at the glass transition temperature.

Taking the logarithm of Equation 5.72 yields:AF

In(X) = InA + -

For the two temperatures:

in (X100) - in (X80) ~ ( ^3 " 3^3) ~ (2-681 - 2.833) = -3.058X80 = 21.3 times that of X100

As noted for most polymers, XT 1000 s. As a result, the approximaterelaxation time for PS at 800C is5.9 h.

About 70% to 80% of the dimensional change due to shrinkage occurs as thesheet cools from the forming temperature to the set temperature or the heatdistortion temperature at 455 kPa or 66 lbf/in2 [23]. Stabilization to final dimensionmay take several hours, however. Strain recovery is one of the major causes of the

Temperature, 0KFigure 5.22 Temperature-dependent specific volume of amorphous polystyrene, PS. r is the rate ofquenching. Figure used with permission of copyright owner

Table 5.10 Effect of Mold Tempera-ture on HDPE Shrinkage Drawninto a H:D = 1 Symmetric Mold [22]

Mold temperature Shrinkage(0C) (%)40 1.865 1.975 1.990 2.4

long times needed to achieve stable part dimensions. Uneven strain recovery causedby nonuniform orientation in the trim area, as an example, is the major cause oflong-term part distortion and warping [18]. In difficult cases, 24 h annealing attemperatures approaching mold temperature or maximum part use temperature priorto trimming can reduce warping.

Spec

ific Vo

lume,

cm

3 /g

Shrinkage can cause serious part removal problems when forming onto malemolds. Draft angles are estimated from:

0draft = tan"1 (2 x shrinkage fraction) (5.75)Example 5.14 shows the difference in recommended draft angles for amorphous andcrystalline polymers [24]. For amorphous plastics, draft angles can be as small as \degree to 1 degree. For crystalline polymers, it should be greater than 2 degree to 3degrees. Female portions of molds require no draft if smooth and \ degree iftextured. Draft angles are also discussed in Chapter 6 on mold design.

Example 5.14 Draft Angles for Amorphous and Crystalline PolymersA mold designed for PS has recently been used to run PC. Are the draft anglescorrect? Can this mold be used to run POM, acetal? POM has a recommended

- shrinkage value of 3.0%.

From Table 5.9, the recommended shrinkage values for both PS and PC are0.6%. Therefore if the draft angles for PS were initially correct, they arecorrect for PC.

To estimate draft angles for POM, consider Equation 5.75:9draft = tan"1 (2 x shrinkage fraction)

For PS and PC, the recommended draft angle is:0draft = tan-1 (2 x 0.006) = 0.7 degrees

For POM:6draft = tan-1 (2 x 0.03) = 3.4 degrees

The original draft angles are too small for POM.

5.8 Trimming

There are many acceptable ways of efficiently separating formed parts from thesurrounding plastic. Thin-gage parts are usually trimmed automatically. Very heavy-gage parts are trimmed manually. Medium-gage and heavy-gage parts are usuallyfixtured and trimmed manually or with computer-aided robots. Routers, water-jetsand lasers are used for automatic trimming. As discussed below, the cutting surfacemust be fed at a fixed rate in a plane - perpendicular to the cutting direction.Prototype parts are usually trimmed manually with routers and bandsaws. Very thinparts can be trimmed with a paper cutter or hand scissors.

Typical trimming devices are shown in schematic in Fig. 5.23. The trimmingdevices include: Manual knives, including

Bread knives for low-density foams,

Linoleum knives or knives with recurving blades,Knives with replaceable blades,

Routers, such asHand-held, high-speed routers at 20,000 RPM with carbide router tips,Table-mounted fixed-position routers,Multi-axis routers,

Band saws, Circular saws, including

Stationary saws,Hand-held, small diameter saws,Saws with toothless blades for foams,

Abrasive wheels,

Toothed Saw or Router

Bandsaw

Hot Wire

Die Cut, Prototype

Nibble Cut

Shear Cut

Hot Gas Jet

Water Jet

Laser

Abrasive Wheel

In-MoId Die Cut

Figure 5.23 Schematic examples of various trimming methods

Sharp-edged compression blades, includingSteel-rule dies,Ground forged dies,Machined dies,

Guillotines, includingOne-sided linear shear,Two-sided linear shear,

Flames, Lasers, Water jets, and So on.

Trimming Heavy-Gage Parts

Heavy-gage parts are usually removed from the molds with the web attached, thenplaced on trimming fixtures and trimmed with manual or computer-aided trimmingdevices. For prototype parts and a few hundred parts, hand operated routers, sawsand bandsaws are commonly used. For parts having a planar trim path, simplecompression or dinking presses are used (Fig. 5.24). The press consists of a steel ruledie mounted in a wooden frame and mounted to the movable top platen and aductile cutting surface mounted to the stationary bottom platen. The part and webis registered against stops on the bottom platen cutting surface and the press is closedpneumatically, mechanically or hydromechanically.

For production runs, steel rule dies are mounted in rigid steel or aluminumframes (Fig. 5.25). The trim is removed by compression. Specifications for the steelrule die are given below. For very heavy-gage plastic where the trim surface is

Figure 5.24 Schematic of steel rule die prototype trim or dink station

Upper Platen

Hold-Down ScrewShim

Steel Rule DieFormed Part

UHMWPE Pad

Lower Platen

Figure 5.25 Characteristic steel rule die mounting assembly

piecewise linear, a standard sheet guillotine is used. Forged and machined dies arealso growing in popularity. For longer production runs, computer-driven multi-axisrouters and saws are used. Figure 5.26 shows a typical five-axis table used to drivea multiple router head. When using a multi-axis trimmer, the part to be trimmed isfastened tightly against a fixture using clips or vacuum. The cut is initially pro-grammed by leading the router head manually around the fixture. The computer

Figure 5.26 Multiple-axis computer-driven router trimmer. Figure used with permission of Therm-wood Corporation

Trim Die Platen

Bracket

Adjusting Screw

Steel Rule Die

learns the correct path in this manner. Minor changes in the cutting path are usuallyincorporated in this first-pass program in order to fine tune the trim path.

For heavy-gage parts, trimming can also involve other post-molding operationssuch as:

Drilling, Slotting, Grooving, Ultrasonic welding, Solvent welding or other forms of gluing, Ultrasonic insertion of fasteners, Grinding or milling local wall thickness to tolerance, and So on.

Trimming Thin-Gage Parts

Typically, many parts are simultaneously formed on roll-fed presses. Thin-gage,roll-fed parts are typically trimmed either: After forming but while the sheet and web are still on the mold, usually referred

to as "trim in place", or After the sheet and web are stripped from the mold, in a separate in-line

mechanical or hydromechanical press.These trimming systems are quite different and represent a major early decision whenchoosing a thermoforming line. Trim-in-place punch-and-die systems are usuallyconsidered as part of the mold design (Fig. 5.27). If the parts are completely punchedfrom the web, methods must be used to remove the parts from the mold region asquickly and thoroughly as possible. Common methods are vacuum suction, mechan-ical part removal and mold rotation [25]. For vacuum suction, a vacuum tube is usedfor each cavity. The parts adhering to the tubes are shuttled from the press to a dropbox. The drop box feeds an orienting and stacking device. In mold rotation, themold containing the parts drops free of the web plane, then rotates to dump the partsinto the drop box (Fig. 5.28). Frequently, air assist blows the parts free of the cavity.Frequently, the trim die is tabbed so that a small portion of the part remainsattached to the web. As a result, the parts are not quite separated from the web inthe mold. However, once the tabbed part-web structure is free of the mold, air ormechanical assists punch the parts from the web. The primary concerns withon-mold trimming are:

Incomplete separation of all parts from the web. The parts that are still attachedto the web as it exits the mold area may foul downstream machinery or webwind-up equipment. In addition, these good parts are not saleable,

Parts that remain in some mold cavities after the removal process, due toundercuts, poor mechanical or vacuum picking, or static charge between the partand the mold cavity,

Figure 5.27 Trim-in-place or in-situ trim die. As shown, trimming is by compression

Parts that accidentally drop back into the cavity plane after picking, and Dust and microflbers that remain on the mold surface. This detritus is usually

transferred to as-molded parts.Punch-and-die design and tabbing are discussed in detail below.

In most thin-gage forming operations, the web and formed part sheet isremoved from the mold to an in-line trimming press. Usually the sheet is held ina vertical plane while being trimmed. As a result, the sheet is brought fromthe horizontal position to the vertical position by means of a hump-back orcamel-back arch (Fig. 5.29). The hump-back trimming press allows the punchedout parts to be collected on horizontal tables, thus simplifying the counting andbagging process. The die used in in-line trimming can be steel rule die, but isusually machined or forged. Again, punch and die design is discussed in detailbelow. Technically, punch and die trimming uses the shear mechanism of cutting, asdescribed below.

5.9 Mechanics of Cutting

There are five general mechanisms of cutting (Fig. 5.30) [26]. They are: In-plane uniaxial compression or die-cutting, Mode III antiplane pure shear or nibbling and shear cutting,

Sheet

Sheet

Die As Isolator

Die As Trim

Steel Rule DiePlug

Mold

Steel Rule DiePlug

Mold

Figure 5.29 Camel-back or hump-back in-line roll-fed former trimming press with cam-operatedpunch-and-die trimmer. Figure redrawn from [27]

Abrasion or abrasive cutting, grinding, riling, buffing and water jet cutting, Brittle tensile fracture or routering, drilling and sawing, and Thermal or hot knife, hot wire and laser cutting.

A: Forming Step B: Trimming Step

Hot SheetTrim Die

Mold

Web

Formed Parts

Rotating Mold

Collection Bin

D: Part RemovalC: Mold and Web Separation

Figure 5.28 In-mold trimming with part removal by mold rotation

Formed Parts

Web

Registry CamFormed Parts

Trim DieCam

TrimPunch

Figure 5.30 Five characteristic cutting mechanisms. Figure redrawn from [26]

Mechanical compression and shear cutting dominate the trimming industry. Thecharacteristics of some of these mechanisms are detailed below.

The Trim Region

Typically, the trim region is relatively well-defined as the linear edge where the partends. In certain cases, the region is demarked in the forming process as a trimchannel (Fig. 5.31). The accuracy of trimming to tolerance depends on severalelements: Local polymer shrinkage at the trim line, Whether the polymer is crystalline or amorphous, Whether the polymer continues to shrink for some time after forming but before

trimming, Whether the polymer is tough or brittle at the trim temperature, The tightness of the fixture to the formed part, The allowable variation in part temperature at the trim station, The presence of registry or locating cones, The trim die temperature and its variation with time, The thickness and thickness variation of the part at the trim line, The allowable variation in local part wall thickness,

Compression

Abrasion

Shear Thermal

Chip or Fracture Cutting

Figure 5.31 Compression (left) and shear or pinch trimming (right) configurations

The increase in trim die temperature from the temperature at which the die gapswere set,

The strength of the die clamping frames, and The amount of flexure in the die during cutting.

Registering the Trim Site

Trim registers or locators are usually designed into the mold. These are cones ortruncated pyramidal structures, as shown in schematic in Fig. 5.32. For heavy-gagesheet, risers or indentations are used by the operator to positively position the sheetagainst the trim fixture prior to trimming. For thin-gage sheet, the locators catchindexing lugs ahead of the in-line trim die. For thin-gage sheet, peripheral locatorsare located on the four corners of the multicavity mold and interstitial locators are

Trim Die Trim Die

0.003 to 0.005 in

Trim Channel

Figure 5.32 Various shapes for sheet registry on punch station

Pyramidal Conical Cubical

3 to 10 Times Local Sheet Thickness

located on at least a few of the web regions between cavities. The indexing lugs onthe trim press are usually adjusted to ensure full engagement of all locators on thesheet surface prior to start-up and then once or twice a shift as the various elementsof the forming and trimming presses warm to equilibrium. During long productionruns, periodic examination of locators after contact with trimming lugs may indicateif long-term forming problems are developing.

The actual number of trim locators is not as important as the shape. Typically,the locator riser should have substantial draft of at least 15 degrees. Truncated conesare frequently used. Truncated boxes, wedges and pyramids are used, albeit with verygenerous vertical side radii, where trimming tolerance is critical and where thepolymer may move locally between the forming and trimming stations.

The Nature of the Cut

The toughness of the polymer at the time of trimming dictates the nature of thefracture, as discussed below. The polymer toughness is best demonstrated by thepolymer resistance to applied compression stress, as delivered by a toothless trim die(Fig. 5.33). As seen, for tough, ductile or hot polymers such as HDPE, PC andFPVC, the cutting blade forces the polymer to essentially flow away from the bladetip. The tip of the cut is therefore just ahead of the blade tip. For brittle polymerssuch as PS, APET and PMMA, the crack propagates very quickly from the initialpoint of blade tip insertion. For rubber-modified polymers such as HIPS and ABS,the crack propagation is arrested by the rubber particles. Microscopic examination of

Figure 5.33 Characteristic polymer response to trim die penetration

Soft, Hot Polymer

Hard, Cold, Brittle Polymer

Hard, Cold, Tough Polymer

Distance

PlasticForce

Distance

ForceTrim Die

Trim Die

Plastic

PlasticForce

Trim Die

Distance

Figure 5.34 Characteristic problems in trimming of brittle polymers

the trim surface of rubber-modified polymers shows fragments of rubber and holeswhere the rubber particles have been torn from the crack surface. Since the crackpropagates very rapidly during compression cutting of brittle polymers, the crack pathcan meander (Fig. 5.34). Multiple cracks can occur as the cutting blade passes throughthe cutting zone. These cracks generate discrete particles, which are typically calledtrim dust. Microscopic examination of these particles reveals chunky, sharp-edgedparticles of 1 to 50 (xm in dimension. The high surface area of these high-surface energyparticles implies high static attraction to surrounding ungrounded surfaces, such asthe plastic parts and web structure. Although PS has the most tenacious trim dust,adhering trim dust is a problem with PMMA, APET, CPET, PC and other brittle andtough-brittle polymers. In addition to the production of micron-sized particles, edgemicrocracks are also formed perpendicular to the cutting plane during trimming ofbrittle plastics. These microcracks produce near-serrated edges under 30-power optical

Figure 5.35 Optical microphotograph of compression cut of polystyrene, PS

Meandering Crack Multiple Cracks

micrography (Fig. 5.35). In addition to yielding an undesirable rough lip, thesemicrocracks are sources for crack propagation or splitting into the part.

For certain ductile polymers such as PP, HDPE and CPET under certain cuttingconditions, microfibers are formed. These microfibers are usually called angel hair orfuzz, are typically 50 to 150 um in cross-sectional dimension and can be 50 mm long.Although there is no consensus as to the primary cause of microfibers [27,28], theyusually occur when trimming fiber-forming or crystalline polymers. Some of theconditions that are thought to minimize microfibers include:

Reducing the polymer temperature prior to trimming, Resharpening the cutting blade, Using a single-sided honed blade with a hardened tip, Increasing the rate of travel of the blade into the sheet, Ensuring that the cutter blade fully contacts the cutting anvil for steel rule dies, Ensuring that the steel rule die does not move out of plane during its travel

through the sheet, Reducing the gap between the punch and die for in-line trimming, Ensuring that the blade engages the sheet at all places on the trim line simulta-

neously, and Ensuring that the only mode of cutting is compression cutting.The dulled cutting tip is probably the most common cause of microfiber generation.Like cutter dust, microfibers are tenacious, particularly on PP and CPET. Since foodcontainers are the primary products of these polymers, microfibers are unacceptableboth from an appearance viewpoint, as they resemble human hair, and a healthviewpoint, since these polymers are not approved as "food additives" [29].

Fracture Mechanics

Trimming is semi-controlled fracture mechanics. The purpose of the trimmingprocess is to separate one piece of plastic into at least two pieces. Mechanicalchipping such as drilling, abrasive sanding, multi-tooth cutting and routering, resultsin many granular pieces of plastic, in addition to the desired part and the web.Ideally, compression and shear cutting with toothless blades should result only in thedesired part and the web. Unfortunately, such is not the case. The toughness of thepolymer at the time of trimming dictates the nature of the fracture, as discussedabove. The mechanics of multi-tooth and toothless cutting are relatively well known.Kobayashi [30] considers all mechanical cutting as controlled tensile fracture of theplastic. This section develops the mechanics of fracture as it pertains to trimming.

Mechanical Chipping

As a first step to understanding trimming parameters, examine the interaction of asingle cutting-edge tool with the polymer (Fig. 5.36). A single cutting-edge tool is

Figure 5.36 Orthogonal single-edge cutting geometry [30]. Figure used with permission of copyrightowner

used in machining, turning and shaping but not in trimming of thermoformed parts.But the cutting actions of tools having multiple edges, such as saws, drills, routersand mills represent the sum of cutting actions of many single-edged tools. Thephysical factors affecting cutting actions on plastics are summarized in Table 5.11.Tool geometry factors are more complex for multiple-edged tools. The nature of the

Table 5.11 Factors Affecting Cutting Characteristics of Plastics1

X = Major effectx = Minor effect

Cutting Tool

Polymer

Factor

Tool design:Tool geometry*:Rake angleRelief anglePoint radius

Tool materialMachining conditions:Depth of cut**Cutting speedFeeding speedAmbient work

Temperature:Cooling system

Effect

Chipformation

X

XXXX

Cut surfaceroughness

X

X

Toolwear

X

XXX

Heatgenerated

x

X

X

X

X

Gumming,burning

X

X

X

X1 Adapted from [26], with permission of the author

* For single-edged cutting tools. Tool geometry effects are more complicated for multiple-edgedcutting tools

** Tooth depth of cut

chip formed in cutting is used as a guide cutting tool selection, and as an indicationof how cutting is proceeding (Table 5.12). For example, PS chips in multiple-edgesaw cutting should be discrete and separate easily, with no evidence of softening,gumming, or threadlines.

Multiple-Edged Tool or Toothed Saw Performance

Kobayashi [26] presents extensive experimental results for plastics performance whencut with single-edge tools. A cutting force balance is shown in Fig. 5.36. When theperpendicular cutting-force component F t is zero, the cutting tool obtains themaximum cut surface accuracy. The cutting tool rake angle at this condition isknown as the critical rake angle. All tools should have cutting angles equal to orgreater than this value. The optimum cutting conditions for nearly all polymersshould produce continuous chips of uniform thickness. If the cutting depth or toothdepth is too large, discontinuous chips are produced and the cutting surface hasmany microcracks. If the cutting depth is too small, the plastic will heat from frictionand may burn or gum the cutting tool.

Multiple-edged tool performance is determined by comparing the tooth depth ofcut and the cutting speeds with single-edged tool performance. For a circular saw(Fig. 5.37), the tooth depth of cut, g, is:

g = V - ^ (5.76)

where U is the peripheral speed of the blade [m/min], U = TTDN, D is its outsidediameter [m], D = 2R, N is the blade speed [RPM], v is the cut-off speed or the workfeed rate [m/min], and p is the tooth spacing [mm]. The angle is given as:

= co,-'^> (5.77)

where h is the cut-off height or the distance between the saw centerline and thebottom of the plastic sheet [m], and b is the sheet thickness [m]. Example 5.15illustrates these relationships.

Figure 5.37 Toothed saw trimming geometry [30]. Figureused with permission of copyright owner

Table 5.12 Classification of Plastic Machining Chips1

Commentson cause

High elasticdeformation

Slippage con-tinuously byshear stress

Plastic fractureby simple shearshear

Plastic fractureby shear withcompressive and/ortensile stress

Elastic fracture,brittle fracture

Plastic fractureby shear withcompressive and/ortensile stress

Typicalplastics

PE, PTFE,FEP, PP

PS, ABS

PMMA

PMMA, PS

PMMA, PS

High modulus,Low-elongation

Cuttingspeed

Slow

Medium-high

Medium

High,

sticky

High

High

Materialtype

High elongation,rubber-like

Brittle

Brittle

Brittle

Brittle

Brittle

Nature ofdeformation

Elastic

Plastic

Plastic

Elastic

Brittle,elasticfracture

Brittlefracture

Surfaceroughness

Small

Irregular,shear marks

Irregular

Very irreg-ular, wavy

Hacklemarks

Gouges

Cuttingforcefluctuation

Small

Small

Moderate

Large

Verylarge

Verylarge

Thickness-to-cut depth

> 1

>1

Irregular

Irregular

>1

IrregularChips

Nature ofchip

Continuous

Continuous

Discontinuous

Discontinuous

Discontinuous

Discontinuous

Classification

Continuous-flow

Continuous-shear

Discontinuoussimple shear

Discontinuous-complex

Discontinuous-crack

Discontinuous-complex

(shear withcracks)1 Adapted from [26], with permission of author

Example 5.15 Cutting with a SawConsider a D = 15.2 cm or 6 in diameter saw having four teeth per in. The bladerevolves at 1000 RPM. The sheet is 0.100 in or 0.254 cm thick. The cut-off heightis 2 in or 5.1 cm. A minimum tooth depth, g, is selected to be 0.004 in or 0.1 mmto minimize gumming or burning. Determine the maximum feed rate.

From Equation 5.76:v _ u - g

p sin (j)p is the tooth spacing or 1/4 (teeth/in) = 0.25 in or 0.637 cm. The peripheralspeed of the blade, U = TCDN. For this example:

U = Ti 15.2 cm = 47,750 cm/minmm

The angle is given from Equation 5.77 as:. l (h-b/2) 1 (5.1-0.254/2)

* = C0S

- D / ^ = C0S 15.2/2(j) = 49 degrees

Therefore:47,750 0.01 cm2/min , .

v = = 990 cm/mm =16.5 cm/s = 6.5 m/s0.637 cm 0.756This is the maximum feed rate of this stock into the saw.

Note that the feed rate is proportional to blade speed and diameter and inverselyproportional to tooth spacing. Thermal damage to the plastic is minimized by: Wide tooth spacing, Coarse toothed blades, Small blades, Low speed blades, and High feed rates.However wide tooth spacing causes relatively rough cut edges with many brittlepolymers such as PS, ABS, SAN, PMMA, and RPVC. Hollow-ground blades withno tooth set and wide-kerf carbide blades yield smooth cut edges. Spring-set andswag-set teeth also produce quality cut edges (Fig. 5.38).

Abrasive Cut-Off Wheel

Abrasive wheels with 30- to 200-grit surfaces produce relatively smooth cut surfacesat high cut-off rates with about one-half to one-third the heat generated by toothed

Feed Rate, v, mm/min

Figure 5.39 Comparison of abrasive disk and toothed saw trimming forces as function of polymerfeed rate [30]. Figure used with permission of copyright owner

saws [26]. Typical abrasives include aluminum oxide or alumina, silicon carbide,tungsten carbide and diamond. Diamond abrasive wheels are the most expensive butlast longest. Abrasives are held together with thermosetting binders such as pheno-lics, ureas and epoxies. Cutting forces are usually higher for abrasive wheels than fortoothed wheels at the same feed rate (Fig. 5.39). Abrasive wheel cut surfaceroughness is usually smaller (Table 5.13). Finer grit wheels produce smoothersurfaces but at reduced cut-off rates (Table 5.14).

The machinability of a plastic, r\, is written as [26]:

^V^s{ (5-78)where V1n is the volume of polymer cut per unit time [mm3/min], Vw is the amountof tool wear per unit time [mm3/min], HP is power consumption [kg m/min], and Sfis the cut surface roughness [urn]. For properly selected cutting wheels, the amountof tool wear is essentially negligible, and machinability is redefined as:

Tang

entia

l Cut

ting

Forc

e, F t

, kg

f

Figure 5.38 Typical saw tooth designs

CarbideTip

HollowGround Spring-Set Swaged

36 Grit SiliconCarbide Abrasive

Hollow-GroundTooth Saw, No Set

36 Grit AluminumOxide Abrasive

Hollow-GroundTooth Saw, Spring-Set

1 After [26], with permission of author

Key:A: 36 Grit silicon carbide, resinoidmedium gradeB: 36 Grit aluminum oxide, resinoidmedium gradeC: Saw, hollow-ground, zero-set teeth, 300 mm, diameter, 2 mm

thick, 2.3 teeth/cm or 5.8 teeth/in, 0 rake-angle, 60 relief angleD: Saw same as C except 0.2 mm set to teeth

Table 5.14 Finishing Operations Sanding Belt Surface Roughness1

Silicon carbride sanding belt2000 m/min, 0.5 kg/cm2 applied force, 20 min

1 Adapted from [26], with permission of author

For cutting wheels:

where b is the sheet thickness, B is the wheel thickness and Ft is the tangentialcomponent of the cutting force. The ratio of efficiencies of abrasive and toothedwheels operating at the same feed rates and peripheral speeds is written as:

(5.81)

(5.79)

(5.80)

Polymer

PMMARPVCPC

Surface roughness (um)60 Grit

363941

240 Grit

222

Amount removed (g)60 Grit

295360235

240 Grit

2889

Removal rate (mg/s)60 Grit

246300196

240 Grit

23.36.77.5

Table 5.13 Cutting-Off Operation1

Peripheral speed 2500 m/min

Polymer

SANABSPA-610 (a nylon)PC

Surface roughess (urn)

Abrasive wheel

A

3228348

B

2316166

Circular saw

C

81065

D

2002003625

Abrasive wheels are typically 2 to 5 times thicker than toothed wheels. Both produceabout the same surface roughness on the cut edge at the same cut-off speeds (Table5.13). The cut-off forces for abrasive wheels are about 2 to 5 times those for toothedwheels. Therefore:

Although the cut-off efficiencies of abrasive and toothed wheels are about the same,the cost of operating abrasive wheels is about 5 to 10% that of toothed wheels. Whenloaded, abrasive wheels are redressed with a gum block or a wire brush. Toothedwheels require resharpening and tooth resetting.

Toothless or Shear and Compression Cutting

Saw cutting depends on brittle tensile fracture of the plastic under the force of thetooth. In solids, Young's modulus, E, is the proportionality between pure elastictensile stress and strain:

G = E - e (5.83)When a solid is sheared, the proportionality between pure shear stress and strain isthe modulus of rigidity or shear modulus, G:

O5 = G es (5.84)The bulk modulus, B, is the ratio of hydrostatic pressure to solid volume change perunit volume. Solid compressibility is the reciprocal of the bulk modulus. Thesemoduli are related through Poisson's ratio, v, the ratio of unit width change to unitlength change [31]:

E = 2G (1 + v) = 3B (1 - 2 v) (5.85)Poisson's ratio, v = 0.5 for a material with constant volume under stress. For mostplastics, 0.3

Table 5.15 Poisson's Ratio forSeveral Thermoformable Poly-mers [50]

Polymer Poisson's ratio

LDPE 0.49HDPE 0.47PP 0.43PIB 0.47PS 0.38Rigid PVC 0.42PCTFE 0.44PTFE 0.46PMMA 0.40mPPO 0.41PPS 0.42PET 0.43PBT 0.44PA 66 0.46PA 6 0.44PC 0.42Polysulfone 0.42Polyimide 0.42

by the stress in the direction parallel to the crack [32]. Shear cutting is considered asMode III, antiplane shear. This fracture mode is also found in torsion of notchedrods. Mode I fracture, cleavage or tensile-opening, dominates classical fractureanalysis since it is the most common form of material failure and since it is theeasiest to study in the laboratory.

If the plastic is not held tightly, Mode III crack propagation control is difficult tomaintain. The advancing crack tends to meander uncontrollably, and secondly,tangent cracks can form. The amount of force required to propagate a crack in anymode and the rate at which a stable crack is propagated can only be estimated fromthe extensive studies of Mode I failures. The amount of energy needed to initiate acrack in any polymer is substantially less than its theoretical cohesive strength.Cracks begin at flaws or defects in the polymer. They propagate when the decreasein elastic strain energy equals or exceeds the energy needed to create a new cracksurface. When a tensile specimen with a small horizontal crack, a in length, isstressed, it is in plane stress. The stress needed to propagate that crack is:

(5.86)

(5.87)where E is Young's modulus and G* is the fracture energy:

Figure 5.40 Characteristic fracture modes [32]. Redrawn Figure used with permission of Prentice-Hall Publications, Inc.

where P is the plastic work done during yielding and y is the surface energy of thepolymer. In Equation 5.86, Kc is the fracture toughness. The stress needed to initiatea crack is frequently far greater than that needed to sustain crack propagation [33].For PMMA for example, the ratio of stress levels is about 1000. For vulcanizednatural rubber, it is about 325. The plastic deformation stretching energy is usuallymuch greater than the surface energy. For ductile plastics such as PTFE, PP, PETand TPO, P y. Even for very brittle plastics such as PS and PMMA, P > 2 y.Example 5.16 illustrates these relative values. One measure of the fracture toughnessof a polymer is the area under its tensile stress-strain curve. If the area is large, thepolymer is tough. Polymers that show great plastic flow after yielding, such asHDPE, PP and PET, have high fracture toughness. If the area under the tensilestress-strain curve is small, as with PS and PMMA, the polymer is brittle. The stresslevel that produces fracture is analogous to the crack tip stress intensity level thatproduces sustained fracture. As noted in the second part of Equation 5.86, fracturetoughness or stress intensity factor, Kc is written as:

(5.88)

(5.89)Characteristically, the stress intensity factor is written as:

Mode III, Anti-Plane Shearor Tearing Fracture

Mode II, In-Plane Shear orSliding Fracture

Mode I, Tensile Fracture

Example 5.16 Fracture Energies for Ductile and Brittle PolymersConsider vulcanized rubber and PMMA as typical of ductile and brittle polymers,respectively. Determine the relative ratio of yielding work to surface energy of eachof these polymers.

The plastic work during yielding of PMMA is P = 0.185 ft-lbf/in2 = 0.211kJ/m2. The surface energy for PMMA is about y = 0.039 kJ/m2 = 0.0342ft-lbf/in2. The fracture energy is given as:

G* = 2(P + Y) = 2(0.211 + 0.039) = 0.5 kJ/m2 = 0.44 ft-lbf/in2

The ratio of plastic work to surface energy, P/y = 0.211/0.039 = 5.4. This isa strong indication of a very brittle polymer.

The plastic work for vulcanized rubber, P, is unknown. However, thefracture energy, G* = 13 kJ/m2= 11.4 ft-lbf/in2 and the surface energy forvulcanized rubber is about y = 0.012 kJ/m2 = 0.010 ft-lbf/in2. The calculatedvalue of plastic work is:

P = ^ - - Y = y - 0.012 = 6.49 kJ/m2 = 5.67 ft-lbf/in2

Thus the ratio of plastic work to surface energy, P/y 6.49/0.012 = 567.This is a strong indication of a very ductile polymer.

The coefficient C depends on the geometry of the crack and the surface beingfractured. One example of C is given in Fig. 5.41 [32], for an edge crack of length ain a sheet of width W under uniaxial tension. For unreinforced polymers, values forKc range from about 0.5 to 10. Typical values for Kc for a few polymers are givenin Table 5.16. The fracture stress given in Equation 5.88 is written symbolically as:

Material Parameter ^_a = : (5.90)Geometric Parameter

Stre

ss In

tens

ity Fa

ctor

Reduced Crack Width, a/W

Figure 5.41 Geometric parameters for stress concen-tration factor for mode I, tensile fracture [32]. Re-drawn Figure used with permission of Prentice-HallPublications, Inc.

1 Adapted from [33], with permission of copyright holder

* J-Contour Integral. See [33: p. 82]

In the tensile Mode I, an infinite stress is needed to initiate a crack of zero length.Once the crack is propagating, the stress diminishes rapidly.

The rate of crack propagation is also important. For fatigue failure where theload is applied in cyclic fashion, the following relationship is used:

^ = Af-AK (5.91)

where N is the number of cycles, AK is the stress intensity factor range, AK =Kmax Kmm, and m and Af are polymer material properties [33]. Some values for Afand m are given in Table 5.17. AK is proportional to Kc, the fracture toughness. Formany polymers [33,34], 0.5 < [AK/KJ < 0.67. Cyclic crack propagation rate is usedonly as a guide to determine crack speed in Mode I tensile fracture. Cyclic fatigue crackgrowth occurs at substantially lower stress levels than those needed to sustain crackgrowth in continuous loading. In turn, this guideline can be used only as an estimateof the shear stress needed to control crack propagation in Mode III antiplane shearfracture. As noted, Mode III fracture is the apparent mode occurring during shearcutting of plastics such as guillotining, diagonal brake cutting, nibbling and papercutting. An appropriate relationship for the rate of crack propagation, a = da/d9 is:

daa = = P am ocm/2 (5.92)d(3

where a is the shear stress and (3 includes geometric factors and material constants.If the crack length ahead of the shear is to remain stable, or a is to be constant, the

Materials

Vulcanizedrubber

PolyethylenePSHIPSPMMAEpoxyRubber-mod-ified epoxy

FRPGlassWoodAluminum

Young's modulus, E

(GPa)

0.001

0.153.02.12.52.82.4

7702.1

69

(1000 lbf/in2)

0.145

21.8435305363406348

1,01510,150

30510,000

Fracture energy, G*

(kJ/m2)

13

20*0.4

15.8*0.50.12

70.0070.12

20

(ft-lb/in2)

11.4

17.50.35

13.80.480.0871.75

6.120.00610.105

17.5

Stress intensity factor, K

(MN/m3/2)

( 0.114)

( 1.73)1.1)

( 5.76)1.10.52.2

70.70.5

37

(1000 lb/in3/2)

( 2.05)

( 31.2)19.8

(104)19.89.0

39.8

12612.69.0

666

Table 5.16 Stress Intensity Factors for Some Plastics and Other Materials1

Values in parentheses obtained from Kc ^JE G*

Table 5.17 Crack Propagation Parametersda/dN = Af AKm

da/dN units are mm/cycleAK units are MN/m3/2

Af units are [MN/m1 / 2]-m

Note: For crystalline polymers, the general relationship is:da/dN = A* (AK/E)7 where 0.5 < A* < 3

(AK/E) units are m1/2

Polymer Af x 1000 m Range of AK

PS 2.65 3.73 0.5 to 1.2PMMA 99 10.0 0.4 to 1.0PES 1.5 9.5 0.6 to 1.2HDPE 0.35 5.22 1.0 to 2.5PC 0.118 4.81 1.0 to 3.0mPPO 0.0365 6.2 1.0 to 3.0RPVC 0.164 2.2 0.5 to 1.0PA 66 0.00728 3.63 1.5 to 8.0PVF 0.0087 3.2 1.5 to 8.0

rate of shear is approximately proportional to the applied force to the mth power. ForRPVC in Table 5.17, m = 2.2 and the shear rate should increase about four timeswhen the applied load is doubled. On the other hand, for PMMA, m = 10 and theshear rate should increase about four times with only a 15% increase in applied load.

Compression cutting occurs when the steel rule die is pressed perpendicularly intoplastic sheet that is resting on an unyielding surface. Load compression follows thetrue material stress-strain curve. A modification of compression molding that em-ploys uniaxial plane-strain compression is used to determine stress-strain curves forpolymers that neck or fracture easily [35]. Compression cutting is particularly usefulwhen the polymer yields in compression but fractures brittlely in tension or shear.RPVC, PC and PMMA are typical polymers that lend themselves well to compres-sion cutting. Compression yield stresses are usually higher than tensile or shear yieldstresses (Table 5.18). Thus more force per unit cutting area is required to die cut aplastic than to shear cut it. Comparison of typical stress-deformation curves, Fig.5.42 [35], shows that the area under the compression curve continues to increase withincreasing strain. As a result, crack propagation in compression is more stable forpolymers that are brittle or neck badly. Compression cutting is the preferred methodfor cutting LDPE and should be considered for trimming PET, PA or nylon, POMor acetal, low-density foams and thin-gage OPS and PMMA.

For a very brittle polymer being trimmed with a very sharp, wide die, aperpendicular crack is created ahead of the blade. The crack can propagate as aMode I fracture, as shown in schematic in Fig. 5.43. The crack can be uncontrollablewith an irregular reverse side cut surface, microcracking and crazing. The stressrequired to cut through the material is given in terms of the stress intensity factor,

Table 5.18 Yield Stresses and Cutting Shear Stresses

Sharp knife cutting stressFlexure stress (yield)Compressive stress (yield)Tensile yield stress

(10001bf/in2)

13-1815.8

8.66.4-7.1

(MPa)

91-126110

6045-50

(10001bf/in2)

6.51413.5111155

1217654

1314

(MPa)

4598947777353584

1194235289198

(10001bf/in2)

3

61212.51012

61115

12

16

(MPa)

20

4183866983

4176

103

2183

110

(10001bf/in2)

41.55

96

357

8

10

(MPa)

281034

6241

213448

55

69

Polymer

HDPELDPEPPPETPCRPVCPSHIPSABSmPPOPA 66*CACABCAPPMMA

POM**

* Dry nylon** Polyoxymethylene, acetal homopolymer

Figure 5.43 Characteristic mode I fracture with wedge effect of trim die into brittle polymer sheet

Equation 5.89, and is frequently much less than the compression yield strength. Oneway of partially controlling crack propagation in very brittle polymers such as PSand PMMA is to place a very slightly resilient mat between the plastic sheet and thetable. Very hard rubber or heavy-gage UHMWPE works well. If the plastic orrubber is too soft, the plastic may bind the cutting blade and chipping, splitting anduncontrolled fracture may be aggravated.

Typically the force required to cut through a polymer sheet is proportional to thecut length and the sheet thickness to some power a,

Force a (cut length) x (sheet thickness)a (5.93)Since the crack proceeds the cutting blade tip, the force required to cut through abrittle polymer may be only weakly dependent on sheet thickness.

For a ductile polymer and a blunt die, the deformation stress is obtained directlyfrom the stress-strain curve. Since most polymers strain harden to some extent in

Stre

ss

Deformation

Figure 5.42 Stress-strain curves for various typesof fracture in a notch-sensitive ductile polymer[35]. Figure used with permission of John Wiley &Sons, Inc.

Uniaxial Compression

Uniaxial Tension

Tension on a Notched Specimen

Trim Die

Polymer

Figure 5.44 Characteristic combined shear and compression punch- and die-cutting of tough orductile polymer

compression, the force required to cut through a tough polymer increases with thedepth of cut [36] and a 1:

Force oc (cut length) x (sheet thickness)1 (5.94)For ductile polymers, a combination shear and compression die cut is used (Fig.5.44). With this type of cut, the lower force of a shear cut is combined with the stablecrack propagation at increasing stress-strain of a compression cut. Heavy-gageplasticized PVC or FPVC, HDPE and PP are cut in this way. Combination shearcutting forces for several cutter blade designs are shown in Figs. 5.45 and 5.46 [37]for RPVC and PS, respectively. It is apparent that cutter force is proportional tosheet thickness, or a = 1 in Equation 5.93. Cutting forces for dull knives at 200C or680F are measurably higher for polymers that yield, such as PVC, as seen in Table5.19. These values compare well with blanking force guidelines for thin-gage sheet(Table 5.20) [38]. Values for effective shear stress or cutting force per unit thicknessand cutter length are about the same as compressive yield stress values in Table 5.18.Cutting forces at 600C or 1400F are about 10% lower than those at 200C or 68F.

Nibbling

Nibbling is a cyclic trimming process. An estimate of nibbling force is made fromMode I tensile fracture crack propagation. Example 5.17 illustrates this. As notedearlier, the force required to initiate a crack is as much as 1000 times greater thanthat needed to sustain it. Nibbling is a process requiring crack initiation at eachstroke. Further additional force is required to overcome friction between the nibbler

Trim Die

Polymer

Shear AnvilPinch Gap

Forc

e, 10

0 kg

f

Dulled Cutter

CutterDesign 4CutterDesign 3

SandwichCutter

RPVC

Thickness, mm

Figure 5.45 Experimental sheet thickness-dependent shearcutting force for rigid polyvinyl chloride, RPVC, for severaltrim dies [37]

Table 5.19 Shear Cutting Forces Data from Figs. 5.45 and 5.46 [37]Blade length = 10 in or 250 mm

Sheet thickness = 0.039 in or 1 mm

Polymer

PVC

PS

Bladedesign

# 3#4SandwichDull*#3#4SandwichDull**

Total force

(kgf)26002710310039002680268026802900

(Ib)

57205960682085805900590059006380

Cutting stress

(MPa)

104108124156107107107116

(10001bf/in2)

15.115.818.022.615.515.515.516.8

* Exhibits a "zero thickness" resistance of 1360 kgf or 2990 lbf, or an equivalent shear stressof 54 MPa or 7900 lbf/in2

** Exhibits a "zero thickness" resistance of 460 kgf or 1000 lbf, or an equivalent shear stressof 18 MPa or 2700 lbf/in2. In addition, the force-thickness curve is nonlinear

blade and the plastic and to push the cut-off plastic piece from the kerf. As withcompression cutters, a good first approximation of the value of the cutting-off shearstress is the yield strength value of the plastic (Table 5.18).

Example 5.17 Nibbling Force for PMMA

Thin-gage PMMA sheet, 0.025 in or 0.1 cm thick, is to be cut in one cycle.Determine the force needed to sustain a crack. For PMMA, Af= 0.1 (MN/m1/2)~mand m = 10.

Forc

e, 10

0 kg

f

Thickness, mmFigure 5.46 Experimental sheet thickness-dependent shear cut-ting force for polystyrene, PS, for several trim dies [37]

Table 5.20 Blanking Force Guidelines for 0.25 mm or 0.010 in Sheet [38]

Nature ofpolymer

Soft

MediumHard,Tough

Type ofpolymer

Polyolefins,cellulosicsFlexible PVCOPS, PET, PSPMMA, RPVC

Force

(kgf/cm)

27

4691

(lbf/in)

150

250500

Total forcein 10 in or 25 cm

(kgf)680

11402280

(lbf)

1500

25005000

PS

Dulled Cutter

Sandwich CutterCutter Design 4

Cutter Design 3

From Equation 5.91, the stress intensity factor range is obtained:AK = (da/dN)1/m-Af-1/m

Now da/dN>0.1 cm. Assume da/dN=l. Then AK =1.26 MN/m1/2. IfAK = 0.5 Kc, the critical stress intensity factor for crack propagation andC = 2, the tensile stress needed to sustain the crack is given as:

a = ^ V ^ = 1-26 V*-0.001 = Q m M N / m 2 = 1Q 3 ^ 2

This is the tensile stress needed to propagate the crack. The tensile yieldstress of PMMA is about 45 MN/m2 or 8500 lbf/in2. Since nibble-cuttingshould require about the same expenditure of force as compression-shearcutting, the apparent force needed to sustain a crack in PMMA is onlyabout 0.1% of the total force needed to cut the plastic.

Brittleness, Orientation and Trimming Temperature

Many brittle plastics exhibit uncontrolled fracture, secondary crack propagation,reverse-side chipping, crazing and splitting when compression or shear cut. Brittlefracture occurs when the brittle strength of the polymer is less than its yield strength.The brittle strength of a polymer below its glass transition temperature, Tg, is weaklydependent on temperature over a wide range of temperature, 1000C or more. On theother hand, polymer yield stress is essentially a linearly decreasing function oftemperature (Table 5.21) [35]. As the polymer temperature increases, the probabilityof fracture at stresses below the yield stress decreases. The problems associated withbrittle fracture trimming diminish as well. At elevated temperatures approaching Tg,the polymer is ductile and high-speed cutting-ofT techniques that depend on brittlefracture crack propagation such as routering and sawing, become inefficient.

Table 5.21 Temperature Effect on Yield Stress For Various Polymers1

Polymer

PMMAPTFEPE*RPVCPP

PA 66APETPC

Linear region

(0C)50 to 100

-250 to -140- 6 0 to 20- 8 0 to 60- 4 0 to 20

-100 to 60- 2 0 to 60- 4 0 to 120

(0F)

122 to 212-420 to -220- 7 6 to 68

-112 to 140- 4 0 to 68

-150 to 140- 4 to 140

- 4 0 to 250

Temperature coefficientof yield stress

(MPa/C)

0.970.850.820.800.740.740.490.32

(lbf/in2 - 0F)

78.268.566.164.559.659.639.525.8

3 Adapted from [35], with permission of copyright owner

* Chlorinated polyethylene

Thermoformed shapes frequently have high degrees of orientation in the trimareas. Part shape can enhance nonuniform orientation. Cutting relieves local stresses.Although this aids crack propagation to some degree, particularly in shear cutting, itcan also cause: Nonuniform part dimensions, Binding of the cutting tools, Part warping, and Part distortion.Secondary fracture effects such as crazing can result. Uncontrolled crack propagationcan proceed in the orientation direction rather than in the desired cut path, or thecrack can meander. This results in splitting and splintering, dust and angel hair.Highly nonuniformly oriented parts of brittle polymers are frequently formed on hotmolds and then the parts with the trim attached are partially annealed prior totrimming. The trim is then cut away while the parts are still warm. Heavy-gageamorphous polymers such as RPVC and ABS and easily oriented crystalline polymerssuch as PA 66 and PP benefit by this trimming approach.

As a general rule for all polymers, dust and angel hair problems and part warpageand distortion may be minimized by increasing the part temperature at the time oftrimming. Increasing trim die temperature is usually ineffective. Part of the difficultyin trimming with hot dies is in conduction heat transfer from the heating source tothe cutting tip. The die is envisioned as a metal fin. The effectiveness of conductionheat transfer to fins decreases rapidly with the length-to-thickness ratio of the fin [39].This is due primarily to convection heat transfer to the cool ambient air:

where mL is given as:

mL = / ^ L (5.96)where h is the convection heat transfer coefficient between the heated trim die and theambient air (Table 5.4), k is the thermal conductivity of the trim die steel, L is thedistance between the heater and the cutting tip and t is the thickness of the trim die.As is apparent in Fig. 5.47 [40], the energy efficiency of heated dies decreases rapidlywith L/t ratio, for both rectangular and tapered dies. In words, since heated dies arevery inefficient heat transfer devices, it is usually difficult to maintain cutting tips atthe proper temperature.

5.10 Steel Rule Die

As noted, the steel rule die is the most common method of cutting prototype sheethaving thickness less than about 0.100 in or 2.5 mm. Steel rule dies are most effective

Next Page

Front MatterTable of Contents5. Cooling and Trimming the Part5.1 Introduction5.2 Overall Cooling Heat Balance5.3 Cooling the Formed Shape5.4 Steady State Heat BalanceInterfacial ResistanceShape FactorConvection Heat Transfer Coefficient

5.5 Cyclic Heat BalanceCooling the Free Surface of the SheetCooling Thin Sheet in Ambient AirTransient Heat Removal from the SheetQuiescent Ambient AirMoving Ambient AirCooling on Nonmetallic Molds

5.6 Transient Heat Transfer during Sheet Cooling on the Mold Surface - Computer ModelsInterfacial Air

5.7 ShrinkageUnconstrained ShrinkageConstrained Shrinkage

5.8 TrimmingTrimming Heavy-Gage PartsTrimming Thin-Gage Parts

5.9 Mechanics of CuttingThe Trim RegionRegistering the Trim SiteThe Nature of the CutFracture MechanicsMechanical ChippingMultiple-Edged Tool or Toothed Saw PerformanceAbrasive Cut-Off WheelToothless or Shear and Compression CuttingFracture Mechanics in TrimmingNibblingBrittleness, Orientation and Trim Temperature

5.10 Steel Rule DieResharpeningTabbing and Notching

5.11 Punch and Die TrimmingForged and Machined Dies

5.12 Drilling5.13 Other Cutting TechniquesThermal CuttingWater Jet Cutting

5.14 Trimming - a Summary5.15 References

Index