The engineering reasons for building a proto-type mould are several and include evaluationof the processability of candidate materials inthe mould and of the mechanical behaviourand moulded geometry of candidate parts,prior to committing to a costly productiontool. In order for the evaluation to be trulyvalid, moulding temperatures, pressures andcycle times should be as similar to thoseintended for production as possible. Forexample, polymers which have glass transitiontemperatures, Tg, above ambient usually showsome residual molecular orientation due toflow into the mould[1,2]. The amount oforientation depends on the cavity fill rate andon the rate of melt cooling. The part mechani-cal properties, strength for example, can beenhanced in the orientation direction andreduced transverse to the flow[3] and fractureenergy can be reduced as a consequence oforientation[4]. Consequently, engineers haveoften concluded that even prototype mouldsshould be made of the same materials as pro-duction moulds to ensure a proper evaluation.When faced with the time and productioncosts associated with this conclusion, mostengineers have decided not to build prototypetools, sometimes with very expensive conse-quences. The cost and time savings inherent inmodern rapid prototyping methods and mate-rials can help to solve this dilemma.
The University of Texas has developed arapid prototyping process for preparingmoulds that are suitable for injection mould-ing a limited quantity of polymeric materi-als[5-8]. In this process, selective laser sinter-ing (SLS) is used to form “green” mouldcavity inserts from metal powder which iscoated with fusible thermoplastic binder. Insubsequent steps, the binder is thermallyremoved and the metal powder is oxidized toform a porous metal/ceramic cavity thatshows little shrinkage and generally excellentretention of geometry, relative to the greenpart. The cavity is then strengthened andsealed by infiltration and cure of an epoxytooling resin. This mould-production processhas been called Rapid Mold (RM) by theinventors. Among the advantages of the RMsystem are ease and speed of manufacture,low-cost post treatment in a simple air oven,and good hardness, thermal conductivity andthermal expansivity, relative to filled epoxytooling.
A rapid mould-makingsystem: material properties and design considerations
Joel W. BarlowJoseph J. Beaman andBadrinarayan Balasubramanian
The authorsJoel W. Barlow is Professor of Chemical Engineering,Joseph J. Beaman is Professor of Mechanical Engineer-ing, and Badrinarayan Balasubramanian is a graduateResearch Assistant in the Department of Chemical Engineering, Centre for Materials Science and Engineering,The University of Texas at Austin, Austin, Texas, USA.
AbstractPresents the mechanical properties of a new mould-making material, proposed for producing rapidly proto-typed injection mould inserts for plastics by selective lasersintering. Explains that, although the strength of thismaterial is far below that of the tool steel usually used tofabricate moulds, design calculations indicate that it canstill be used for mould insert production. Points out thatthe thermal conductivity of this material is lower than thatfor steel but higher than that for plastic melts. Indicates,from the calculations, that proper choices of conductionlength and cycle time can minimize differences, relative tosteel moulds, in the operational behaviour of moulds madeof the new material. Discusses the longevity of examplemoulds.
The authors gratefully acknowledge financialsupport for portions of this work by DARPA/ONRGrant N00014-92-J-1394.
The RM system is named so as to distin-guish it from the Rapid Tool mould-makingsystem that was introduced recently by DTMCorporation, Austin, Texas. Both RM andRapid Tool can use the same polymer-coatedmetal powder feed stock, and the preparationof green shapes is identical. The processesdeviate from one another in the post-SLSprocessing steps. In the Rapid Tool process,the polymer is removed under reducing con-ditions to prevent metal oxidation, and theporosity is filled by infiltration of a lower-melting metal. The result is a mould that ismuch more durable and suitable for produc-tion tooling than that produced by the RMsystem. However this gain in tool durabilitycomes at greater cost owing to the need for ametallurgical-grade furnace to handle reduc-ing gases and for greater care during firingand infiltration. One interesting possibility isto use the RM process to prototype the plasticpart, then switch to the Rapid Tool process tobuild the production mould using the samepowder and cavity part file.
Table I shows a comparison of the materialproperties achieved with the RM with that ofa tool steel which typically is used to makeinjection moulds. The properties in Table Iresult from a feed stock that contains 40 volper cent copolymer (20mol per cent butylmethacrylate and 80mol per cent methylmethacrylate (7)) mixed with 60 vol per cent -325 mesh iron powder (Hoeganaes ANCORATW 230). The SLS produced test bars werethen oxidized in an air oven, according to aproprietary temperature schedule, and subse-quently infiltrated with epoxy resin (DowDER 331). DTM Corporation, Austin,Texas, has recently announced a polymer-coated metal powder, Rapid Steel, that uses asmaller amount of a similar copolymer binderand a larger metal particle size than were usedin this study. The properties obtained whenusing Rapid Steel powder in the RM processshould be similar to those in Table I.
Thermal analysis
The thermal conductivity of the RM materialis seen in Table I to be substantially lowerthan that of steel, however it is still aboutseven times higher than the typical 0.2W/m-°C seen for unfilled polymeric materials[9].Consequently, the limiting resistance to heattransfer in many circumstances will remainthat associated with the polymer melt. Asdiscussed below, careful design and the flexi-bility of manufacture provided by the additive
SLS system can lead to comparable and evenimproved thermal performance relative toconventional materials and processes. Forexample, one could design build coolingchannels in the mould that could not easily beconstructed by conventional subtractivemachining techniques.
Some estimates of the relative thermalperformances of moulds made of steel and ofthe RM material system can be made bysolving the simultaneous partial differentialequations that describe the transient heattransfer from polymer melt, through themould material, to the cooling water. Forsimplicity, we have idealized the conductionpath to be one dimensional. The governingequations are given by:
Polymer melt:∂∂
α ∂∂
∂∂
∂∂
α ∂∂
Tt
T
xTx
at x t
T T at t x H
T
xT f x
T T at t x L
T T at t x H
K
PP
P
P
p PO
MM
M
M
P M
P
=
= = ≥
= = ≤
=
== ≥ =
= > =
2
2
2
2
0
0 0 0 1
0
0
0
B.C
I.C.
Mould:
Tt
I.C.
B.C.
Cavity surface:
M
. , ( )
,
( )
,
,
∂∂∂
∂∂
Tx
KTx
at t x H
PM
M=
> =
, .0
5
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Table I Material properties
Rapid Conventional mould tool
Material property system steel
Tensile modulus, 106 psi 0.40 30Tensile strength, 103 psi 10 150Compress strength, 103 psi 24 –Shear strengtha, 103 psi 12 75 (estimated)Estimated Poisson’s Ratio 0.45 0.35Glass transition temperature, °C 130-150 –CTE, ppm/C 26 12Thermal diffusivitya, in2/min 0.121 1.181Specific heat, cal/g 0.16 0.11Density, g/cm3 1.72 7.86Thermal conductivity, K, W/m °C 1.47 50Note: a Compression failure is actually in failure in shear for RMmaterial
In equation (1), the subscript, P, correspondsto the polymer melt while subscript, M, corre-sponds to the mould described in Table I. Arepresentative[9] polymer thermal diffusivity,αP = 0.0067in2/min, and polymer thermalconductivity, KP = 0.2W/m°C, were used.Equation (1) is solved for TM and TP by theGalerkin finite element method that is incor-porated in the PDEase2 software package(SPDE, Inc., Bass Lake, CA, marketedthrough MacSyma, Inc., Arlington, MA).The software is run under the DOS systemwith a personal computer that contains a80486 micro-processor operating at 66MHz.
Several cases were calculated to comparemoulds made from the RM system with thosemade from steel, using the properties in TableI. In all cases, the initial polymer melt temper-ature, TPO, was set to 275°C, a reasonablethough somewhat high melt temperature forthe moulding of many commodity thermo-plastics[9]. In all cases, the water/mouldboundary temperature, T0 at X = L, was keptat 25°C, indicating an infinite heat transfercoefficient at this boundary. The effect ofcavity or part thickness was studied over therange 0.0625 - 0.250 inches, and the mouldconduction length, L - H, was studied over therange from 0.9375 to 0.4375in. Two generalconditions were considered:(1) injection of polymer melt, one time, into a
cold mould at f(x) = 25°C; and(2) repetitive injection of polymer melt into
the mould with a fixed cooling time until“steady state” is achieved.
For the latter case, f(x) is determined by themould temperature profile from the previousinjection cycle at the prescribed cooling time.
Figures 1 and 2 show calculated tempera-ture profiles at the centreline of a 1/8 inchthick polymer part and at the cavity wall,respectively, for the case where the mouldtemperature is initially 25°C and the mouldconduction length is 0.9375 inches. Very littledifference is seen in the performance of thetwo moulds, tool steel and RM, in terms ofthe time required for the centreline to reachsome required value. For example, if thepolymer centre needs to reach 100°C,
before the part can be ejected, the requiredcooling time in the steel mould is only 9 sec-onds shorter, 24 versus 33 seconds, than that
in the RM produced mould. While this differ-ence could be important for production tool-ing, it is probably not a great issue whenprototyping. As one might expect from analyt-ical solutions to unsteady state conductionproblems[10] where the reduced time isαt/H2, halving the part thickness, H, to0.0625 inches (not shown) causes the calcu-lated cooling time difference to be reduced to2.4 seconds. While larger than 9/4 = 2.25, thisdifference still suggests that conductionthrough the polymer melt largely limits thecooling rate when polymer is injected into acold mould. Figure 2 follows the cavity sur-face temperature versus time after injectioninto the 25°C mould. The surface tempera-ture of the steel rises to only 41°C eventhough the initial melt temperature in contact
T T
T
– 0
0
3=
6
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Figure 1 Calculated plastic part centreline temperature vs.time after injection into 1/8 in cavity at T0 = 25°C. (A) RMmould; (B) steel mould
12
10
8
6
4
2
00 0.2 0.4 0.6 0.8 1Time (minutes)
( ) /T T T− 0 0
KeyRM mouldSteel mould
Figure 2 Calculated cavity surface temperature vs. timeafter injection into 1/8 in cavity at T0 = 25°C. (A) RMmould; (B) steel mould
2
1.5
1
0.5
0–0.2
Time (minutes)
( ) /T T T− 0 0
0 0.2 0.4 0.6 0.8 1
KeyRM mouldSteel mould
with it is at 275°C, again because of the muchhigher thermal diffusivity of the steel, relativeto the polymer. Because it has a lower thermaldiffusivity than steel, the cavity made from theRM material shows a higher initial surfacetemperature, however it is no higher than75°C, as a consequence of its greater thermaldiffusivity than the injected polymer.
Figure 3 shows the calculated mould tem-perature profile after 30 seconds cooling timefor the same conditions used to generateFigures 1 and 2. Clearly, the RM material hasconducted less heat than the steel and shows ahigher mould temperature. In contrast to thenearly linear temperature profile in the steel,the non-linearity of the temperature profile inthe composite also suggests that heat transferin the composite is far from steady state after30 sec and that temperature could build withrepeated use of the mould on a 30 secondcycle.
To study this possibility, the computerprogram was modified to permit the insertionof the mould temperature profile calculated ata specified cooling time as the initial conditionfor the next cycle. Figure 4 shows the maxi-mum temperatures in the steel mould on a 40second cycle as a function of the number of1/8 inch thick parts moulded in sequence.After the second part cycle, the steel mouldseems to come to steady state, and all steadystate maxima are well below 100°C.
In contrast (Figure 5), steady state is onlyapproached after nine or so sequential partsare prepared in the RM mould, and the maxi-mum temperatures after nine parts are allsubstantially elevated with respect to those in
the steel mould and to those obtained after thefirst cycle. These temperatures are all in excessof 100°C, leading one to conclude that mostpolymers could not successfully be moulded at1/8 inch thickness in this mould on a 40
7
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Figure 3 Calculated mould temperature at 30 secondsafter injection into 1/8 in cavity at 25°C. (A) RM mould; (B)steel mould
1.6
1.2
0.8
0.4
00 0.2 0.4 0.6 0.8 1Distance (inches)
( ) /T T T− 0 0
KeyRM mouldSteel mould
T0 = 25˚CT
Figure 4 Calculated maximum temperatures for 275°Cpolymer melt injected into 1/8 in steel mould cavity on a 40second cycle. Mould has 1.0 in conduction length toboundary at 25°C.
60
55
50
45
40
35
30
250 1 2 3 4 5Part number
KeyCentreline temperature of polymer partafter 40 seconds coolingCavity surface immediately afterinjection of polymer meltCavity surface after 40 seconds cooling
Temperature (˚C)
Figure 5 Calculated maximum temperatures for 275°Cpolymer melt injected into 1/8 in RM mould cavity on a 40second cycle. Mould has 1.0 in conduction length toboundary at 25°C.
140
120
100
80
60
40
200 2 4 6 8 10Part number
KeyCentreline temperature of polymer partafter 40 seconds coolingCavity surface immediately afterinjection of polymer meltCavity surface after 40 seconds cooling
Temperature (˚C)
seconds cycle. Just as worrisome, the initialcavity surface temperature is approaching thesoftening temperature, Tg, of the epoxy infil-trant. While it is cross-linked and will notmelt, the mechanical integrity of the compositemould can be compromised as thermal stress-es that are associated with material expansivitynear Tg begin to become important.
A design solution to the mould-overheatingproblem, above, is simply to reduce the con-duction length, L. Figure 6 shows the calculat-ed maximum temperatures on a 40 secondcycle when the conduction length is 0.4375in.Steady state for this case is reached after aboutthree part cycles, the plastic part centrelinetemperature stays below 100°C, and the maxi-mum surface cavity temperature is below110°C. This mould is probably acceptable andparts moulded from it will probably be quitesimilar to those obtained from conventionalsteel moulds. Typical cycle times for 1/8 inchthick parts moulded in steel are usually closeto 40 seconds, with 5 seconds of the cycleassociated with melt injection and part ejec-tion and 30-35 seconds associated with cool-ing the part[11].
One of the potential advantages of the RMsystem is the ability of the shaping step byselective laser sintering to form cooling chan-nels with complex geometry at desired loca-tions without the usual fabrication concerns.
Structural considerations related to channeldesigns in the RM system are discussed below.
Mould temperature and material properties
The room temperature mechanical propertiesof the RM system in Table I are quite similarto those of the epoxy infiltrant used to con-struct the test parts[7]. Figure 7 furtherdemonstrates that the modulus (and probablythe strength) of the system will decrease astemperature is increased beyond the glasstransition temperature, Tg, near 130-150°C, ofthe epoxy. Below Tg, the coefficient of thermalexpansion, CTE, of the RM system is substan-tially lower than the 60ppm/°C of the unfilledepoxy, although it is still higher than that ofsteel by about a factor of two. Generally, injec-tion moulds are temperature controlled totemperatures below 100°C, and these differ-ences between CTE values are not expected topose insurmountable problems for the designer.
Stress analysis
The tensile strength of the RM material issubstantially lower than that of steel. For thisreason, the RM material is not recommendedfor construction of the entire mould. Asdiscussed below, a composite mould design inwhich the cavity geometry is provided by theRM system and mould strength is provided bysurrounding the cavity with steel has beendemonstrated successfully and is recommended.
8
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Figure 6 Calculated maximum temperatures for 275°Cpolymer melt injected into 1/8 in steel mould cavity on a 40sec cycle. Mould has 0.50 in conduction length to bound-ary at 25°C.
120
100
80
60
40
20
Part number
KeyCentreline temperature of polymer partafter 40 seconds coolingCavity surface immediately afterinjection of polymer meltCavity surface after 40 seconds cooling
Temperature (˚C)
30 1 2 4 5 6
Figure 7 Dynamic modulus and tan δ vs. temperature traces for RM material
10
9.5
9
8.5
8
00
Temperature (˚C)50 100 150 200 250 300
0.5
0.4
0.3
0.2
0.1
0
Log E′ (Pa)E Tan δIron/epoxy-2
Moulds for the injection moulding of poly-meric materials typically are made from avariety of steel materials including mediumcarbon steel, AISI 4130 (heat treated to300Bhn), AISI-SAE H13, and T-420 stainlesssteel[12,13]. These materials are chosen fortheir exceptional hardness and strengths whenheat treated. For example, the tensile strengthof 4140, a close cousin to 4130, is reported tobe 95,000psi when annealed and 185,000psiwhen tempered at 500°C for one hour[14].Melt injection pressures can be momentarilyquite high, 10,000-30,000psi, during the“cavity packing” portion of the injectioncycle[2, Ch. 14], yet the use of high strengthsteels permits stress concentration factors,
where σult is the ultimate strength, P is thecavity pressure and N a factor of safety, in therange 3-9 to be employed, and the strength ofthe mould material is often of little concern.As the strength of the mould material isreduced, however, the allowed pressure can betoo low to be practical for injection mouldingof typical polymer melts. One solution to thisproblem is to prepare composite moulds inwhich the high strength steel is to reinforceand constrain a lower strength material used toform the cavity. Some of the design detailsassociated with this approach are discussedbelow.
Stress analysis of an injection mould isconcerned primarily with determining theinfluences of injection pressures and mouldgeometry on mould material stresses. In theanalysis that follows, we have approximatedthese stresses in two dimensions using theequations for plane strain. We argue, in sodoing, that the effect of pressure in the direc-tion of the third dimension is compensated bythe mould closing or clamping force that isprovided by the moulding machine. Suchcompensation is not provided in the other twodirections where the mould material itselfmust resist the effect of injection pressure.The equations for stress and strain in twodimensions arise from the balance of forces inthe material[15,16], expressed as
where SX and SY are the normal stresses, TXY= TYX is the shear stress, and FX and FY arethe body forces in the X and Y directions. The
deformation strains of the material are
described in terms of the displacements U and
V by,
Equations (3) and (4) are related through the
elastic constitutive equations of the material.
Under isothermal conditions, for an isotropic
material, the relationships between stresses
and strains are given by:
where E is the tensile modulus and ν is Pois-
son’s ratio. The displacement form of the
stress equations at uniform temperature with
no body forces is then,
Equation (6) is solved for U and V by the
same Galerkin finite element method that was
used to determine temperature profiles,
above. The shear stress in the mould plane is
then determined by the expression,
The X-directed tensile stress is determined
from the expression,
Three general cases are considered here:
(1) a square cavity in a non-reinforced, circu-
lar mould made of the RM material;
SE U
XVYX =
++
( )( – )
( – ) . ( )1 1 2
1 8ν ν
ν ∂∂
ν ∂∂
TE U
XVYXY =
++
2 1
7( )
. ( )ν
∂∂
∂∂
∂∂
ν ∂∂
ν ∂∂
ν ∂∂
∂∂
∂∂
ν ∂∂
∂∂
∂∂
∂∂
ν ∂∂
ν ∂∂
XUX
VY
YUY
VX
XUY
VX
YUX
VY
( – )
( )
( )
( – )
( – ) .
1
1 22
0
6
1 22
1 0
+
+
− +
=
+
+
+
=
S
S
T
EX
Y
XY
X
Y
XY
=+
×
( )( – )
–
–
. –
( )
1 1 2
1 0
1 0
0 0 0 5
5
ν ν
ν νν ν
ν
εε
γ
ε ∂∂
ε ∂∂
γ ∂∂
∂∂
X
Y
XY
U
XV
YU
Y
V
X
=
=
= + . ( )4
∂∂
∂∂
∂∂
∂∂
SX
TY
F
SY
TX
F
X XYX
Y XYY
+ + =
+ + =
0
0 3( )
K PN= σ ult /( ) ( )2
9
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
(2) a square cavity in a circular mould madeof RM material, surrounded by a steelring; and
(3) slit cavity in a steel ring reinforced circu-lar mould made of RM material.
In all three cases, a unit normal load (normalstress if the mould is one unit thick) is placedon the cavity boundaries to represent thecavity pressure. The cavity dimensions andthe ring thickness were varied to determinethe effects of geometry on the maximumtensile and shear stresses.
Figures 8 and 9 show calculated contoursfor case (1) with an outer diameter of 10inches and a centrally located, square cavitywith side length L = W = 3inches. The shearstress, Figure 8, is highest near the corners ofthe cavity and falls towards zero at the freeboundary. The maximum shear stress for thisparticular configuration is approximately thevalue of the cavity pressure (actually 1.07times the pressure). The shear strength of theRM material, Table I, is approximately12,000psi, as estimated from failure in com-pression[17]. Using a factor of safety, N = 2,one would need to limit the cavity pressure inthis design to about 6,000psi, if shear strengthwere limiting. Figure 9 shows that the maxi-mum tensile stress also occurs in the cornersof the cavity and is about 1.6 times the cavity
pressure for this particular design. For atensile working stress, σw = σult/N, of5,000psi, the allowed cavity pressure is just5,000/1.6 or 3,100psi. Clearly, it is possible toinjection mould plastic materials into a non-reinforced cavity at an injection pressure of3,100psi, however the non-reinforced mouldis just as clearly not robust, and great carewould need to be used to prevent mouldfailure due to packing and accidental over-pressures.
‘…Probably the best solution is toconstrain the RM material with a closefitting, steel ring or pocket cavity…’
Probably the best solution is to constrain theRM material with a close fitting, steel ring orpocket cavity. Figures 10 and 11 show thecalculated shear stress, TXY, and X-directedtensile stress, SX, distributions, respectively,in both the RM material and in a 1 inch thicksteel constraining ring. Note that the maxi-mum stresses, TXY = 1.8P and SX = 2.7P,where P is the cavity pressure, now occur inthe steel ring, not in the RM material. Againusing the factor of safety N = 2, and the steelmechanical properties in Table I, the maxi-mum cavity pressure for shear failure in the
10
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Figure 8 Calculated shear stresses in non-reinforced RM material for unit pressure on walls of a square cavity
ring is 21,000psi and that for tensile failure inthe ring is 27,800psi. The deformation of theRM material is greatly constrained by thepresence of the steel ring and, as a result, TXYin the corners of the cavity is reduced to 0.2P.Using the working shear stress for the RMmaterial, 6,000psi above, the working cavitypressure with the steel ring in place would beabout 30,000psi, as opposed to 6,000psiwithout the reinforcing ring. With the ring inplace, SX is limited to –P in the RM material,indicating its fluid-like compression. Thecompressive strength of the RM material isabout 24,000 psi and seems to follow thebehaviour seen in many materials, includingconcrete and filled epoxy systems, which showcompression strengths that are ten[17, p. 508]to two to five[17, pp. 582-3] times as great astheir tensile or bending strengths, respectively.
‘…Of course, the use of different cavityand ring geometry from the exampleabove will influence the permittedcavity pressure…’
Again, using a factor of safety of two, thelimiting cavity pressure for failure by com-pression of the composite is approximately12,000psi, well within the usual workingrange for injection moulding. Failure of this
particular design therefore results from com-pression failure in the RM material. In actual-ity, cavity pressure can probably be raisedabove this conservative estimate; however, itshould not exceed approximately 24,000psifor the RM material.
Of course, the use of different cavity andring geometry from the example above willinfluence the permitted cavity pressure. As adesign aid, equations (3)-(8) were solved for avariety of cases. The relationships betweenmaximum tensile and shear stresses in thesteel ring, cavity pressure and cavity geometryare presented in Figure 12. No safety factorsare provided for these calculations. The tensile stress in the ring increases as the ratioof cavity edge, L, to ring thickness, t, isincreased. Using N = 2, a square cavity, L/W= 1, five inches on a side, constrained with aten-inch OD, one inch thick, steel ring wouldbe limited to a cavity pressure of (75,000/3.7)= 20,300psi. For this design, shear failure inthe steel limits the cavity pressure to37,500/2.6 = 14,400psi, while considerationof the composite shear strength and tensilestrengths again limit the cavity pressure toabout 24,000psi. Tensile stress in the ring alsoincreases as the cavity becomes less square,owing to additional moments on the ring. Forexample, a 5 inch by 0.5 inch cavity (L/W =10) constrained by the same steel ring
12
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Figure 11 Calculated X-directed tensile stresses in steel-reinforced RM material for unit pressure on walls of a square cavity
(L/t = 5) is limited to a cavity pressure of(75,000/5.7) = 13,100psi by the design tensilestress in the ring and to (37,500/1.85) =20,300psi by the design shear strength of thering. As in the previous cases, the allowedcavity pressure of 24,000psi based on thecompressive strength of the RM materialwould be the limiting pressure in this case aswell. Of course, reducing the steel thicknessor further increasing the cavity L/W ratiowould cause the cavity pressure to be limitedby the properties of the steel ring, and wouldresult in lower design cavity pressure. Littledifference is seen between L/W = 10 andgreater cavity L/W ratios.
One of the primary advantages of additiveprocesses, such as SLS, is their ability to makestructures with complex geometry that cannot be made by conventional methods. Onepotential advantage that SLS brings to themould-making art is the ability to build spa-tially-curved cooling channels that can beplaced to follow closely the cavity outlinewhile avoiding spatial interferences fromknock-out pins and other mould hardware.Another potential advantage is the ability ofthe SLS process to build cooling channelswith elliptical or other non-circular cross-section that could reduce local stress concen-tration while increasing the area available forheat transfer from the channel. For example,an elliptical cross-section formed with amajor/minor axis ratio, a/b = 3, has 28 per
cent more heat transfer area per unit lengththan a circular cross-section with the samecross-sectional area. According to Inglis[18],the stress concentration factor for an ellipticalhole in a uniaxially stressed plate is approxi-mated by,
where a is the length of the elliptical axis thatis perpendicular to the applied stress. If themajor axis of this elliptical hole is parallel withthe direction of applied stress and the a/b ratiois selected to be 1/3, the stress concentrationfactor, k, near the hole edge is only 1.67,whereas a circular cross-section hole, where a= b, shows a stress concentration of k = 3. Theempiricism, equation (9), has been checkedby the Galerkin method, outlined above, forthe case where a normal load per unit lengthwas applied to one long edge of a 16 inches ×8 inches, two-dimensional slab, while theother three edges were constrained to have nodeformation. The hole was centred in theslab. Substantially the same results as given byequation (9), k =1.35 for the elliptical channelcross-section, a/b = 1/3, and k = 2.63 for thecircular cross-section, were obtained. Theseresults suggest that channels with properlyoriented elliptical cross-sections couldimprove both the heat transfer and the struc-tural rigidity of the mould channel, relative tochannels with circular cross-sections. Toachieve this benefit in the design of realmoulds, however, one must obviously takegreat care to ensure that the long axis of theelliptical hole is parallel to the direction ofapplied stress.
Anecdotes
Because even rapid prototype moulds areexpensive to build, only three have beenconstructed and tested. Consequently, thereis very little information with which to checkthe veracity of the predictions above. The firstmould was built to test the material, not themould-making process[6]. As pictured inFigure 13, a simple slab mould insert wasconstructed by machining a slab that hadbeen cast from the mixed iron and binderpowders in an air oven, then oxidized andinfiltrated with epoxy in the usual way. Themachined insert was fastened to a standardMUD mould base and knock-out pin assem-bly with two bolts and was further constrainedon two opposing boundaries by close fitting
kab
= +
1 2 9 ( )
13
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Figure 12 Effect of cavity geometry on maximum shearand X-directed tensile stresses in ten-inch OD steel ringwith thickness, t. L and W are rectangular cavity walllengths (L is perpendicular to X direction)
7
6
5
4
3
2
1
01 2 3 4 5 6L/t
Stress/pressure
L w t/ , .= =1 0 5
L w t/ , .= =1 0 5
KeyTensileShear
L w t/ , .= =1 0 5
metal plates. The cavity was only 0.125-0.187inches deep. This mould was used to preparea total of 176 parts with no mould cooling anda one minute cycle from four different plasticswhose moulding conditions ranged from 200-300°C melt temperature and from 8,000-35,000psi injection pressure. Two smallfailures, a hairline after shot number 125 anda small chip breakout around an ejector pin atshot number 123, were observed; however, nocatastrophic failure resulted. The mould waschecked for wear, however none was found.Two lessons emerge from this study:(1) the RM material is machinable. It can be
drilled, tapped and surface ground andbehaves much like cast iron during theseoperations; and
(2) one should probably install sleeves for theejector pins if one needs more than 50-100 parts.
A small mould was built for injection mould-ing polymer-ceramic slurries[5]. This mouldwas unconstrained and failed, prompting thepresent study.
Recently, L. Apelskog-Killander of theSwedish Institute of Production Research(SIPR), Stockholm, Sweden, prepared arather complex mould insert with the DTMRapid Steel powder and the University ofTexas RM process. A photograph of the greeninsert half is shown in Figure 14. The insertwas constrained in a pocket cavity and pro-duced about 50 parts before failing as a conse-quence of a pre-existing and knowndefect[19]. More details about insert prepara-tion, geometric accuracy and failure are pre-sented in [20]. A photograph of one of themoulded parts in polypropylene is shown inFigure 15. This particular part appears to have been incom-pletely filled, probably because the injectionpressure and temperature were too low. Nev-ertheless, the complexity of the part suggeststhe potential of the RM process for rapidlypreparing moulds of commercial interest.
Conclusions and recommendations
The RM system shows good potential forrapidly making prototype mould inserts withsufficient accuracy and strength to provide thelimited numbers of plastic parts needed forengineering evaluation and development.Two successful mould inserts have been builtfrom the RM material, a result that seems toverify the results of stress calculations whichsuggest that steel boundary constraints arenecessary to prevent mechanical failure. Toprovide some guidance to the designer, stresscalculations are presented for a steel ring-
14
A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
Rapid Prototyping Journal
Volume 2 · Number 3 · 1996 · 4–15
Figure 14 SIPR mould inset, prior to firing and infiltration steps (courtesy of L. Apelskog-Killander)
Figure 15 SIPR moulded part in polypropylene (courtesy of L. Apelskog-Killander)
Figure 13 Mould assembly with RM insert
reinforced RM insert with variable cavity
geometry; however, given the low cost, high
quality and ease of use associated with multi-
dimensional PDE equation solvers such as
PDEase2, the direct use of such numerical
packages for helping to design each particular
insert is highly recommended. The RM mate-
rial is less conductive than steel, and when
designing and using a RM mould, care should
be taken to adjust conduction lengths and
cycle times, respectively, if one requires that
parts from the prototype mould closely simu-
late those from production tooling. These
simulations are also relatively easy to accom-
plish with modern numerical methods and are
recommended as part of the design process.
Finally, the ability of the SLS process to
prepare production moulds or prototype
mould inserts with complex cooling channel
geometry needs to be exploited more fully,
especially for situations where careful control
of mould temperature is required.
References
1 Progelhof, R.C. and Throne, J.L., Polymer EngineeringPrinciples. Properties, Processes, Tests for Design,Hanser/Gardner Publications, Cincinnati, OH, 1993,Ch.5.
2 Tadmor, Z. and Gogos, C.G., Principles of PolymerProcessing, John Wiley & Sons, New York, NY, 1979, Ch. 14.
3 Progelhof, R.C. and Throne, J.L., Polymer EngineeringPrinciples, Hanser, New York, NY, pp. 445-50.
4 Hsiao, C.C., “Molecular orientation-dependent fracturestrength”, in Rosen, B. (Ed.), Fracture Processes inPolymeric Solids, Interscience, New York, NY, 1964.
5 Badrinarayan, B. and Barlow, J.W., “Manufacture ofinjection moulds using SLS”, in Marcus, H.L. et al.(Eds), Solid Freeform Fabrication Proceedings, Sep-tember 1994, The University of Texas at Austin:Austin, TX, 1994, pp. 371-8.
6 Tobin, J.R., Badrinarayan, B., Barlow, J.W., Beaman, J.J.and Bourell, D.L., “Indirect metal composite partmanufacture using the SLS process”, in Marcus, H.L.et al. (Eds), Solid Freeform Fabrication Proceedings,September 1993, The University of Texas at Austin,Austin, TX, 1993, pp. 303-7.
7 Badrinarayan, B., Study of the Selective Laser Sinteringof Metal-Polymer Powders, The University of Texas atAustin, Austin, TX, 1995.
8 Barlow, J.W. et al., “Mould useful for injection mould-ing of plastics and methods of production and usesthereof”, US Patent Appl. No. 08/339/988, 14 Novem-ber 1994.
9 Jurand, R. (Ed.), Modern Plastics Encyclopedia,McGraw-Hill, New York, NY, 1989, pp. 576-619.
10 Carslaw, H.S. and Jaeger, J.C., Conduction of Heat inSolids, Clarendon Press, New York, NY, 1959.
11 Bernhardt, E.C., Processing of Thermoplastic Materi-als, Van Nostrand Reinhold, New York, NY, 1959, pp. 359-78.
12 DME Mould Base Catalog, DME Division of VSI Corp.,Madison Heights, MI, 1973.
13 Round Mate Catalog, Pleasant Precision, Inc.Huntsville, OH, 1994.
14 Van Vlack, L.H., Elements of Materials Science andEngineering, Addison-Wesley, New York, NY, 1989, p. 321.
15 Burnett, D.S., Finite Element Analysis: From Conceptsto Applications, Addison-Wesley, New York, NY, 1988.
16 Bickford, W.B., A First Course in the Finite ElementMethod, R.D. Irwin, Inc., Homewood, IL, 1990.
17 Marin, J. and Sauer, J.A., Strength of Materials,Macmillan Company, New York, NY, 1954, pp. 76-85.
18 Inglis, C.E., Engineering (London), Vol. 95, 1913, p. 415.
19 Apelskog-Killander, L., private communication.
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A rapid mould-making system: material properties
Joel W. Barlow, Joseph J. Beaman and Badrinarayan Balasubramanian
