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Journal of Materials Processing Technology 178 (2006) 194–199

The effect of constitutive description of PIM feedstock viscosity innumerical analysis of the powder injection moulding process

V.V. Bilovol a,∗, L. Kowalski b, J. Duszczyk b,1, L. Katgerman b,2

a Netherlands Institute for Metals Research, Rotterdamseweg 137, 2628 AL Mekelweg 2, 2628 CD Delft, The Netherlandsb Delft University of Technology, Laboratory of Materials Science, Rotterdamseweg 137, 2628 AL Mekelweg 2, 2628 CD Delft, The Netherlands

Received 20 April 2003; received in revised form 13 March 2006; accepted 13 March 2006

bstract

Influence of the feedstock viscosity description has been studied on the potential errors during numerical simulation of the powder injectionoulding process. Pressure results obtained from the simulations with ProCAST analysis package using feedstocks that had differently described

iscosities have been compared with each other and the experimentally measured pressure. It has been shown that assumption of constant viscosityf the feedstocks leads to erroneous calculation of pressure. If described by the Carreau–Yasuda model, viscosity of the feedstock at the low shear

ates is usually extrapolated. Extrapolation should be performed very carefully. Underestimation of viscosity at the low shear rates range does notarm the predicted pressure results, while overestimation may cause numerical problems and unrealistic results. The best results can be obtainedf the simulations are performed with the feedstocks that have viscosity based on the experimental data measured in a wide range of shear rates.

2006 Elsevier B.V. All rights reserved.

titdwAed

eywords: Feedstock; Viscosity; Powder injection moulding; Simulation

. Introduction

Powder injection moulding (PIM) process is the technologyor manufacturing of complex-shaped components from metalnd ceramic powders. Potentially very promising, this technol-gy is restricted in use because of high sensitivity of the qualityf the product to the processing conditions and mould design.ptimisation of the PIM process for production of any new com-onent is long and expensive procedure. This decreases benefits

f this technology for the manufacturers. Essential help in facil-tating of the optimisation stage can be obtained from numericalimulations.

∗ Corresponding author. Present address: Delft University of Technology,epartment of Materials Science and Engineering, Rotterdamseweg 137, 2628L Mekelweg 2, 2628 CD Delft, The Netherlands. Tel.: +31 15 278 24 14;

ax: +31 15 278 67 30.E-mail addresses: V.Bilovol@tudelft.nl (V.V. Bilovol),

.Duszczyk@tudelft.nl (J. Duszczyk), Katgerman@tudelft.nl (L. Katgerman).1 Present address: Delft University of Technology, Department of Materialscience and Engineering, Rotterdamseweg 137, 2628 AL Mekelweg 2, 2628D Delft, The Netherlands. Tel.: +31 15 278 22 18; fax: +31 15 278 67 30.2 Present address: Department of Materials Science and Technology, TUelft, Rotterdamseweg 137, 2628 AL Mekelweg 2, 2628 CD Delft, The Nether-

ands. Tel.: +31 15 278 22 75; fax: +31 15 278 67 30.

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924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2006.03.163

Numerical simulation of the PIM process requires proper-ies of the feedstock as one of the input data. One of the mostmportant properties of the feedstock is its viscosity. Similarlyo pure polymers, PIM feedstocks, which are mixtures of pow-er materials and polymer binders, can be rhelogically testedith the capillary rheometers or extrusion plastometers [1–3].plastometer provides a single datum per test and is usually

mployed as a quality control tool. For simulation of the pow-er injection moulding process it is essential to have the viscosityata of the feedstock in the wide shear rates range. These data cane obtained only with the capillary rheometer. Because of higholume fraction of powder, which is typically about 65 vol%,iscosities of PIM feedstocks are higher than viscosities ofure polymers. Therefore testing of PIM feedstocks requiresery high pressures. Besides that, PIM feedstocks are abrasive,hich creates additional difficulty during viscosity measure-ents. Because of strong effect of parameters like properties

f the powder, volume fraction of powder in the feedstock, tech-ology of mixing, etc., until recently there was low applicabilityf viscosity data obtained from measurements performed with

ne batch of feedstock to viscosity of another batch of feedstock.tandard pre-formulated feedstocks that appeared on the marketelatively recently have increased reproducibility of properties.he results of characterisation of one feedstock now are appli-

Processing Technology 178 (2006) 194–199 195

cvc

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s(aftl

2

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η

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Fig. 1. Measured apparent viscosity of standard 316L feedstock [4].

Table 1The summary on the viscosities of feedstocks used in the present research

Viscosity model Viscosity

Feedstock 1 Constant 100 Pa sFeedstock 2 Constant 300 Pa sFeedstock 3 Constant 500 Pa sFeedstock 4 Constant 1000 Pa sFeedstock 5 Shear-thinning Carreau–Yasuda. Initial data for 26–105 s−1

Feedstock 6 Shear-thinning Carreau–Yasuda. Initial data for 26–105 s−1.Fixed viscosity between zero and 26 s−1

FF

FfiamdsfFa

m(dbstaconstant and amounts 2000 Pa s.

Fixing the viscosity value of Feedstock 6 in the low shear rates range was jus-tified by the following considerations. From the rheology of polymers it is known[6] that typical viscosity versus shear rate curves in logarithmic coordinates have

Table 2Coefficients for the Carreau–Yasuda fitting functions

Feedstock 5 Feedstock 6 Feedstock 7 Feedstock 8

ηinf −16 −28 −15 0

V.V. Bilovol et al. / Journal of Materials

able to another one of the same type. However, until now onlyery few data on rheological properties of the PIM feedstocksan be found in the literature.

Software packages used for numerical simulation of the PIMrocess offer different possibilities with regard to description ofaterial’s viscosity. Because of limited experimental data, it is

ommon practice that in the analysis packages viscosity of PIMeedstock is described in a simplified way. It can be described,or example, as a constant, or by an approximating function, builtn the basis of experimentally measured viscosity data. Simpleiscosity models facilitate calculations and decrease calcula-ion time. Complex models are potentially more accurate, butequire more tests in wide ranges of shear rates and tempera-ures. Because of difficulties with measurements the viscosityata for PIM feedstocks are often available only for relativelyarrow shear ranges. There is no guarantee that extrapolation ofhe fitting functions beyond the range of shear rates used dur-ng the experimental tests will correctly describe the feedstock’siscosity there. Possible deviations of the calculated viscosityrom the real one may be a source of errors during the simula-ions. This work was aimed at estimation of the potential errorsaused by different description of viscosity during numericalimulation of the powder injection moulding process.

In most cases, the published results on viscosity of PIM feed-tocks are restricted to the relatively narrow range of shear rates102–103 s−1). In this work, the measured results of viscosity ofpre-formulated standard 316L BASF feedstock are presented

or a wide range of shear rates (26–105 s−1). With this respect,he obtained viscosity results seem to be unique in the publishediterature.

. Experimental

To estimate the influence of different forms of viscosity description on theumerical results, several simulations of the PIM process have been performedith different hypothetical feedstocks. Experimentally measured viscosity dataf the commercial 316L stainless steel feedstock, produced by BASF werepproximated by eight different methods. In such a way eight hypotheticalaterials entitled Feedstock 1 through Feedstock 8 have been created. First four

eedstocks had constant viscosities of different values. Viscosities of Feedstocks–8 have been described by the Carreau–Yasuda formula:

= η∞ + (η0 − η∞)[1 + (λγ̇)a](n−1)/a, (1)

here η∞ is the viscosity at infinite shear rate, η0 is the viscosity at zero shearate, λ is the phase shift coefficient, γ̇ is the shear rate, a is the Yasuda parameternd n is the power coefficient. Formula (1) allows taking into account dependencef viscosity of PIM feedstock with regard to temperature and shear rate. Theerformed earlier experiments have proven that the viscosity of the standard pre-ormulated 316L feedstock had low dependence on temperature in the range ofemperatures 185–210 ◦C (Fig. 1) [4].

Therefore data for only one temperature of the feedstock (185 ◦C) have beensed during the numerical simulations. Experimental results shown in Fig. 1 haveeen obtained in the range of shear rates from 26 to 105 s−1. Viscosity valuest shear rates lower than 26 s−1 were not obtained due to excessive pressuresequired during the capillary rheometry tests. To the experimental data shownn Fig. 1 Rabinowitsch correction was applied [5]. Subsequently these data have

een used to create approximating viscosity functions for Feedstocks 5–8 on theasis of Carreau–Yasuda formula. Approximation functions have been chosensing least squares fitting method. Viscosity of Feedstock 5 was based on thexperimental results obtained for the maximum range of shear rates from 26 to05 s−1. Viscosity of Feedstock 6 was based on the same initial data as data for

η

�

aN

eedstock 7 Shear-thinning Carreau–Yasuda. Initial data for 26–104 s−1

eedstock 8 Shear-thinning Carreau–Yasuda. Initial data for 26–103 s−1

eedstock 5, but during the fitting procedure zero shear rate viscosity η0 wasxed at the level of 2000 Pa s, which approximately corresponded to the viscosityt the lowest shear rate achieved in the tests. Coefficients of the Carreau–Yasudaodel of Feedstocks 7 and 8 have been defined on the basis of the experimental

ata limited to shear rates values not exceeding 104 and 103 s−1, respectively. Theummary on the viscosities of Feedstocks 1–8 is given in Table 1. Coefficientsor the Carreau–Yasuda functions for the Feedstocks 5–8 are shown in Table 2.ig. 2 shows the experimentally measured apparent viscosity of 316L feedstockt 185 ◦C and Carreau–Yasuda functions for Feedstocks 5–8.

Good match between the experimentally measured data and those approxi-ated by the Carreau–Yasuda viscosity model is observed for all the feedstocks

except for Feedstock 8) in the range of shear rates between 26 and 105 s−1. Theifference between the curves for different feedstocks can be seen at shear rateselow 26 s−1, where viscosity plots have been extrapolated. Viscosities of Feed-tocks 5, 7 and 8 have been obtained by extrapolation of the measured results tohe low shear rates range without any correction of the graph curvature. It canlso be seen that viscosity of the Feedstock 6 at the shear rates below 26 s−1 is

0 16000 2000 6434 31321.039 0.038 0.372 0.110.373 5.524 0.561 1.030.465 0.528 0.493 0.5

196 V.V. Bilovol et al. / Journal of Materials Processing Technology 178 (2006) 194–199

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ig. 2. Experimentally measured viscosity of 316L feedstock at 185 ◦C andarreau–Yasuda viscosity functions for Feedstocks 5–8.

lmost horizontal part at low shear rates. Until some critical shear rate the vis-osity remains practically constant. The shear-thinning begins to manifest itself,hen the critical shear rate is exceeded. Since the experimental measurements

howed that the viscosity of the feedstock monotonously decreased with thencrease of shear rate in the whole range of applied shear rates, it was suggestedhat viscosity plot should have shelf between zero and the lowest measured shearate. Viscosity of Feedstock 8 calculated by the Carreau–Yasuda formula showedood agreement with the results of experimental measurements in the range from6 to 104 s−1. Outside of this shear rates range the calculated viscosity deviatedrom the experimental results. Deviation of the viscosity of Feedstock 8 at highhear rates is explained by fewer experimental data used to determine the coef-cients of the Carreau–Yasuda viscosity model. The Carreau–Yasuda model foreedstock 7 turned to be a good match in the whole range of shear rates. How-ver, good agreement between the calculated and measured viscosities at thehear rates above 104 s−1 could not be predicted in advance and is, most likely,coincidence rather then a rule.

The process of powder injection moulding was studied using the componenthown in Fig. 3. The PIM process has been simulated with ProCAST analysisackage. This FEM code has been chosen because it employs Carreau–Yasudaiscosity model to describe the behaviour of shear-thinning fluids. Applicationf ProCAST for simulation of the PIM process has already been validated [7].mong the advantages of ProCAST in comparison with other commercially

vailable packages for numerical simulation are its capability of simulating fluidow in the fully three-dimensional space and possibility to include model of theould in the analysis.

The parameters used in all the simulations were chosen to be as close asossible to those during the real powder injection moulding process. The injec-ion rate was velocity-controlled. Ram velocity was constant and correspondedo injection rate of 0.5 m/s. The initial temperature of the feedstock was set at85 ◦C. The temperature of the mould was set at 120 ◦C. The thermal conduc-

ig. 3. 3D model of a complex-shaped component used in the simulations.

wrnt

Fw

ig. 4. Maximum calculated pressure at the injection point from the simulationsith Feedstocks 1–4.

ivity and heat capacity of the 316L feedstock were described as reported in thearlier works [8,9]. During the real powder injection moulding process pressuret the gating position was registered by a piezoelectric pressure transducer builtn the research mould.

. Results and discussion

Figs. 4 and 5 show the maximum pressures at the injectionoint calculated with the assumption of different values of vis-osity and viscosity models. Fig. 4 shows results obtained withhe assumption that the feedstock had Newtonian type of vis-osity. Results shown in Fig. 4 demonstrate that viscosity hastrong influence on the calculated filling pressure. It can be seen,hat with the exception of Feedstock 1, the calculated maxi-

um pressures are unrealistically high. The maximum pressurealculated for Feedstock 1 is comparable with the maximumressures calculated for shear-thinning Feedstocks 5–8, shownn Fig. 5. Feedstock 1 was assigned to have a constant viscos-ty of 100 Pa s. This viscosity seems to be too low as compared

ith the experimentally measured one, at least until the shear

ates remain below 9000–10,000 s−1. Shear rates of such mag-itude and higher surely are developed in the feedstock duringhe filling of the mould, but in the relatively small areas like gate.

ig. 5. Maximum calculated pressure at the injection point from the simulationsith Feedstocks 5–8.

V.V. Bilovol et al. / Journal of Materials Processing Technology 178 (2006) 194–199 197

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poa

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Another evidence that numerical problems have occurredduring the simulation process with Feedstock 5 can be seen fromthe pictures of the simulated melt front advancement shown inFig. 8. The filling pattern with Feedstock 5 is characterised by the

ig. 6. Calculated distribution of shear rates during the filling stage of the powIM component.

his can be seen in Fig. 6, showing distribution of shear ratesbtained from the simulation of the PIM process.

The shown values of shear rates have been calculated for aertain combination of the processing parameters and particularould design. Optimisation of the PIM process requires sim-

lations with different moulding conditions (injection speed,emperature of the feedstock and the mould, etc.) and some-imes, different size and lay-out of the runners and gate in the

ould. The values of shear rates obtained from different sim-lations may, therefore, significantly differ. Higher values thanhose shown in Fig. 6 cannot then be excluded. Fig. 6 clearlyemonstrates that shear rates in the feedstock are distributed veryon-homogeneously. Correspondingly, viscosity of the feed-tock will also vary in a wide range. In the shown example theighest observed shear rate has value about 32,000 s−1 (Fig. 6a)ccording to Fig. 1 viscosity of the feedstock at such con-itions will be around 20 Pa s. But in the major part of theeedstock shear rates remain below 1500 s−1 (Fig. 6b). The cor-esponding to this range of shear rates viscosity has values above00–200 Pa s (Fig. 1). At the walls and in the corners shear ratesay be lower than 10 s−1. Because of so large variations of the

iscosity and non-homogeneous viscosity distribution duringhe filling process using constant viscosity value in the simu-ation setup can never be a good option. Reasonable match ofhe maximum pressure obtained from the simulation with Feed-tock 1, having constant viscosity, with the pressures calculatedith shear-thinning Feedstocks 5–8 may be misleading. Should

ombination of the processing parameters change, the constantiscosity of 100 Pa s would result in wrong predictions of pres-ure. Taking into account very complex pattern of distributionf shear rates in the feedstock, selection of a constant viscosityhat would be appropriate for any new simulation seems to be

ore difficult task that the use of shear-thinning viscosity modeln the simulations.

Strong influence of constant viscosity value on the calculatedressure is the expected result. Less obvious is the dependencef the shape of the viscosity curve in the range between zerond the lowest shear rate used in the tests on the calculated

Fs

jection moulding process; (a) at the gating position and (b) in the bulk of the

lling pressure. Viscosity values in this range are not avail-ble from the experiments. Therefore they are usually obtainedy extrapolation of the approximation function. Comparisonf the calculated pressure for Feedstocks 5 and 6 presented inig. 5 evidences that the difference only in the low shear ratesange may cause substantially different pressure results. Vis-osity curves for Feedstocks 5 and 6 practically coincided in thehear rate range above 26 s−1, but differed below that value. Vis-osity of Feedstock 6 was fixed at the level of 2000 Pa s, whileiscosity of Feedstock 5 was extrapolated to 16,000 Pa s at zerohear rate (Table 2). Fig. 5 shows that assumption of constantiscosity value of 2000 Pa s leads to the increase of the max-mum injection pressure by approximately 30% (144 MPa foreedstock 5 and 195 MPa for Feedstock 6). This paradox can bexplained by the calculated pressure versus time curves shownn Fig. 7. The curve, representing pressure development duringhe injection with Feedstock 5, has several sharp erratic peakshat indicate simulation problems, most likely associated with

eeting of the convergence criteria.

ig. 7. Calculated (at the injection point) injection pressure during the fillingtage.

198 V.V. Bilovol et al. / Journal of Materials Processing Technology 178 (2006) 194–199

lling p

mofd5

otrtFtotscimbbomgcdi

lbaFta

6asspFtvhavlspIwvc((

aosIlnmm

Fig. 8. Calculated fi

elt front hesitation, presence of melt drops and excessive lossf volume, which usually indicate numerical problems. There-ore the numerical results obtained with Feedstock 5 seem to beubious. Most likely low pressure results obtained for Feedstockare attributed to the erroneous calculations.Since viscosities of Feedstock 5 and Feedstock 6 differed

nly in the shear rates range below 26 s−1, it can be concludedhat difference in this particular shear rates range was the directeason of the numerical errors. This conclusion is supported byhe results obtained for Feedstock 7. The viscosity curve foreedstock 7 obtained during the fitting procedure in the men-

ioned earlier low shear rates range (0–26 s−1) lies between thosebtained for Feedstock 5 and Feedstock 6, though very closeo the curve for Feedstock 5 (see Table 2 and Fig. 2). At thehear rates above 26 s−1 viscosity of Feedstock 7 almost coin-ided with the viscosities of Feedstocks 5 and 6. From Fig. 8t can be seen that some difficulties with advancement of the

elt front were also noticeable for Feedstock 7. Melt fronts ofoth Feedstocks 5 and 7 had similar spear-like shape. However,esides some melt front hesitations, there were no other signsf numerical problems in case of Feedstock 7. Similar values ofaximum injection pressures for Feedstocks 6 and 7 (Fig. 5) and

ood match between the respective pressure curves (Fig. 7) indi-ate that possible numerical difficulties that might have occurreduring the simulation with Feedstock 7 had minimal, if any,nfluence on the simulated results.

Extrapolation of the calculated viscosity of Feedstock 8 atow shear rates range (0–26 s−1) provided values that fittedetween the viscosities of Feedstock 6 and Feedstock 7 (Table 2

nd Fig. 2). The calculated melt front advancement pattern ofeedstock 8 appeared to be smooth and without any signs of

he melt front hesitation (Fig. 8). From this point of view it wasnalogous to the melt front advancement pattern of Feedstock

laRt

attern during PIM.

. Smoothness and steady advancement of the melt front andbsence of erratic oscillations on the pressure versus time curveuggest that there where no numerical difficulties during theimulation of filling with Feedstock 8. The maximum injectionressure calculated for this feedstock was higher than that foreedstock 7% by 11.6% (Fig. 5). This result can be explained by

he deviation of viscosity of Feedstock 8 in the direction of higheralues at the shear rates above 104 s−1. Higher viscosity requiredigher filling pressure. Comparison of viscosities from Fig. 2nd filling patterns from Fig. 8 allows concluding that very largealues of viscosity at low shear range may cause numerical prob-ems. The exact value of viscosity at low shear rates (<26 s−1)eems to have little effect on the calculated pressure results. Thishenomenon can be explained by the results presented in Fig. 6b.t is to be noticed that there are very few domains of feedstockhere shear rates below 26 s−1 are present. On the contrary,iscosity at high shear rates considerably affects the results ofalculation of pressure. Increase of viscosity of Feedstock 8see Fig. 2) resulted in the increase of the injection pressureFigs. 2 and 5).

Taking into account that the best match between measurednd described by the approximating function viscosities wasbserved for Feedstocks 6 and 7, the “best” pressure resultshould be expected from simulations with these two feedstocks.n order to support that supposition, a comparison of the calcu-ated pressures at the gating position has been performed. Theumerical results are also compared with the experimentallyeasured value of pressure. Fig. 9 shows the calculated andeasured maximum pressures at the gating position. The calcu-

ated pressures at the gate are related to each other in similar ways the maximum pressures at the injection point shown in Fig. 5.esults obtained with Feedstock 5 have the lowest values and

he worst match with the experiment. The predicted maximum

V.V. Bilovol et al. / Journal of Materials Proc

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ig. 9. Calculated and measured maximum pressures at the gating position.

ressures at the gate for Feedstocks 6 and 7 turned to be 43.1nd 40.8 MPa, respectively. These results can be recognised as aood match with the experimentally measured viscosity, whichas 44.7 MPa. It is to be noticed that the numerical results foreedstocks 5–7 underestimated the real pressure. Simulationith Feedstock 8 resulted in maximum pressure at the gate of9.0 MPa. This numerical result overestimates the experimen-ally measured pressure by 9.6% The results from Fig. 9 confirmhe suggestion that the best results are obtained with the feed-tocks that are described by the approximation functions, whichrovide accurate match of the calculated viscosity data at highhear rates and, at the same time, do not predict extra high vis-osity at the low shear rates range. For the considered examplehe maximum acceptable zero shear rate viscosity η0 can bestimated to amount 6000–6500 Pa s.

Appearance of numerical problems during the simulation ofhe PIM process may depend on the particular solver used inhe package for numerical analysis. Depending on convergenceriteria, type and size of used 3D mesh, assumptions related tohe properties of the feedstocks, etc., the numerical problems

ay become more or less evident.The best way to avoid numerical problems is to use as input

arameters the measured viscosity data in wide range of shearates. However, this is not always possible. PIM feedstocks havesually properties of a Bingham body and possess yield stress.his factor together with high viscosity of PIM feedstocks ineneral, creates an obstacle for direct measurements of viscosityt low shear rates.

Approximating functions built on the basis of data that cane obtained from the usual tests with a capillary rheometer mayave good fit to the experimental data, but, at the same time, doot guarantee adequate representation of viscosity outside theange of shear rates used in the tests. The exact behaviour ofhe viscosity versus shear rate curve depends on the range ofhe experimental data and the fitting procedure. Approximatingunction does not always fit properly the viscosity outside thehear rate range used in experiments. The chance that viscosity

n the low shear rates range will be overestimated is higher thanhe chance that it will be underestimated because of the fact thatiscoplastic polymers usually have a “shelf” on the viscosityersus shear rates graphs in the range of low shear rates. Extrap-

[

essing Technology 178 (2006) 194–199 199

lation of measured viscosity to the low shear rates range mayherefore result in very high viscosity values.

. Conclusions

It has been shown that during the powder injection mouldingrocess wide range of shear rates is developed. In the consid-red example the maximum shear rate was about 32,000 s−1.n case of different mould design and lay-out of the sprue, run-ers and gate, even higher values of shear rates can be expected.n such conditions variations of viscosity of the feedstock arelso high. Therefore assumption of constant viscosity of theeedstocks during numerical simulation is ungrounded. Real-stic numerical results can be expected only when real viscosityt high shear rates is precisely known. The minimum upper lim-ts of shear rates for viscosity measurements can be estimateds 5 × 104–105 s−1.

This study shows that special attention should be paid to vis-osity at low shear rates when using Carreau–Yasuda viscosityodel in ProCAST simulation code. Numerical problems may

ccur during simulations with feedstocks possessing very highiscosity in low shear rates range. They can be identified by thehape of the melt front advancement pattern and shape of theressure versus time curve.

Attempts should be made to measure also viscosity in the lowhear rate range. If measurements are not performed, extrapola-ion of viscosity data to the low shear range must be executedarefully. Underestimation of viscosity at the low shear ratesange does not harm the pressure results of simulation performedith ProCAST, while overestimation may cause numerical prob-

ems and lead to unrealistic results.

eferences

1] K.M. Kulkarni, G. Eberl, Extrusion plastometer testing of MIM feedstockAdvances in Powder Metallurgy and Particulate Materials, vol. 5, MPIF,1993, pp. 23–29.

2] M.Y. Cao, B.O. Rhee, C.I. Chung, Usefulness of the viscosity mea-surement of feedstock in powder injection molding Advances in PowderMetallurgy and Particulate Materials, vol. 2, MPIF, 1991, pp. 59–73.

3] M. Wright, L.J. Hughes, S.H. Gressel, Rheological characterisation offeedstocks for metal injection molding, J. Mater. Eng. Perf. 3 (1994)300–306.

4] V.V. Bilovol, L. Kowalski, J. Duszczyk, Characterisation of PIM feed-stocks for computer simulation, in: Proceedings of the Second EuropeanSymposium on Powder Injection Moulding, Munich, Germany, EPMA,2000, pp. 105–112.

5] J.A. Brydson, Flow Properties of Polymer Melts, 2nd ed., Godwin, Lon-don, 1981, pp. 22–24.

6] H.-G. Elias, An Introduction to Polymer Science, 1st ed., VCH, Wein-heim, 1997, p. 470.

7] V.V. Bilovol, L. Kowalski, J. Duszczyk, L. Katgerman, Comparison ofnumerical codes for simulation of powder injection moulding, PowderMetallurgy 46 (2003) 55–60.

8] L. Kowalski, J. Duszczyk, L. Katgerman, Specific heat of metal-polymer

feedstock for powder injection moulding, J. Mater. Sci. Lett. 18 (1999)1417–1420.

9] L. Kowalski, J. Duszczyk, L. Katgerman, Thermal conductivity of metalpowder-polymer feedstock for powder injection moulding, J. Mater. Sci34 (1999) 1–5.