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Alloy Shrinkage Factors for the Investment Casting of 17-4PH Stainless Steel Parts

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Alloy Shrinkage Factors for the Investment Casting of 17-4PH Stainless Steel Parts
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   Alloy Shrinkage Factors for the Investment Casting Process ADRIAN S. SABAUThis study deals with the experimental measurements and numerical predictions of alloy shrinkagefactors (SFs) related to the investment casting process. The dimensions of the A356 aluminum alloycasting were determined from the numerical simulation results of solidification, heat transfer, fluiddynamics, and deformation phenomena. The investment casting process was carried out using waxpatterns of unfilled wax and shell molds that were made of fused silica with a zircon prime coat. Thedimensions of the die tooling, wax pattern, and casting were measured, in order to determine theactual tooling allowances. Several numerical simulations were carried out, to assess the level of accu-racy for the casting shrinkage. The solid fraction threshold, at which the transition from the fluiddynamics to the solid dynamics occurs, was found to be important in predicting shrinkage factors(SFs). It was found that accurate predictions were obtained for all measured dimensions when theshell mold was considered a deformable material. I.INTRODUCTION D ETERMINATION of the pattern-tooling dimensionsis the first and most important step in the investment castingprocess; it is critical for obtaining cast parts with accuratedimensions. The dies for investment are prepared in threesteps. First, wax patterns are prepared by injecting waxinto previously prepared dies. Second, ceramic shells aremade by the successive application of ceramic coatings overthe wax patterns. Finally, the alloys are cast into the dewaxedshell molds. The dimensional changes associated with eitherthe wax, the shell mold, or the alloy are referred to as wax,shell mold, or alloy shrinkage factors (SFs) (or toolingallowances), respectively. It is the typical practice to calcu-late the dimensions of the die tools by adjusting the nomi-nal casting dimensions by the SFs. At the end of the castingprocess, the nominal casting dimensions can be achieved if the die tools were dimensioned with the appropriate degreeof accuracy.Rosenthal [1] indicated that metal shrinkage during castingis one of the largest components of the overall dimensionalchanges between the pattern tooling and the part. For partsthat have only unrestricted dimensions ( i.e ., parts in whichneither die pieces nor cores restrict the shrinkage of the part),predictions of the final part of the dimensions based solelyon their thermal expansion property are appropriate. How-ever, most of the parts fabricated in the investment castingprocess are very complex and have constrained dimensions.For constrained dimensions, investment casting engineersadjust the unconstrained shrinkage allowances based on theirexperience and on trial and error.The critical properties of the alloy materials that have tobe considered for calculating casting dimensions werereviewed by Sabau and Viswanathan. [2] They concluded thatthe solidification, heat transfer, stress state, and ensuingdeformation behavior of the metal in the semisolid and solidstate must be considered, in order to predict the final dimen-sions in the investment casting process. For permanent moldcastings, Bellet et al . [3] found that the combined effect of thermoelastic, plastic, and creep-induced strain-stress fieldsmust be considered, in order to predict the final shape. Thestresses generated during casting solidification has been atopic of many studies, including those by Drezet and Rappaz; [4] Schwerdtfeger et al .; [5] and Dahle et al . [6] Miller [8] used themodel introduced by Kim et al . [9] to study the deformationof aluminum alloy parts during the diecasting process, whileSabau and Viswanathan [2] reviewed constitutive equationsfor alloy deformation.The effects of shell properties on alloy deformation werediscussed in more detail by Snow. [10] Piwonka [11] indicatedthat the deformation of the mold must be considered in orderto predict the final dimensions of the investment casting parts.However, there are no results that illustrate the effect of shellmold deformation on the final dimensions of diecast parts.The main goal of this study is to predict the alloy toolingallowances, based on a combined analysis of heat-transfer anddeformation phenomena, for the A356 aluminum alloy. Thewax patterns were invested at Minco, Inc. (Midway,TN), andcasting experiments were conducted at Precision Metalsmiths,Inc. (PMI, Cleveland, OH), using the shell molds that weremade of fused silica with a zircon prime coat. The propertiesof the shell molds made of fused silica with a zircon primecoatwere provided in Sabau and Viswanathan. [2] Sabau [12] showedthat accurate temperature predictions were obtained whenheat-transfer coefficients (HTCs) at mold surfaces were basedon natural convection correlations. Two visco-elastoplasticconstitutive equations that were proposed by Bellet et al . [3] and Kim etal . [9] for aluminum alloys were used in this study. II.THERMOPHYSICAL PROPERTY DATA The first step in predicting alloy SFs was the determina-tion of the thermophysical properties of the A356 aluminumalloy. Density measurements in a temperature range of 20°Cto 800 °C were carried out, using a push-rod dilatometer. Thesolid fraction distribution depends on the temperature and thecooling rate. The cooling rate was estimated from the cool-ing curves that were obtained for a similar mold and casting. [12] The estimated cooling rate for the alloy was approximately METALLURGICAL AND MATERIALS TRANSACTIONS BU.S. GOVERNMENT WORKVOLUME 37B, FEBRUARY 2006—131NOT PROTECTED BY U.S. COPYRIGHT ADRIAN S. SABAU, Staff Member, is with the Metals and CeramicsDivision, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6083.Contact e-mail: sabaua@ornl.govManuscript submitted April 11, 2005.  132—VOLUME 37B, FEBRUARY 2006METALLURGICAL AND MATERIALS TRANSACTIONS B Table III.Critical Solid-Mass Fractions for A356Aluminum Alloy [17] Solidification Solid FractionCharacteristicsTemperature (°C)(pct)Liquidus610 to 6170Dendrite coherency598 to 60419 to 29Eutectic565 to 57051 to 56Rigidity point565 to 56763 to 74Solidus540 to 5331 Table II.Fluid-Flow and Deformation MechanismsDepending on the Solidifying Microstructure [7] SolidificationFluid DomainMicrostructureFlowDeformation  f  s   f  ch floating mass not applicable equiaxedfeeding( i.e ., no yieldcrystalsstrength)  f  ch   f  s   f   pk  dendritic mass low-yield network feedingpointgets reduces; increasesestablished; interdendriticslowly (0 topacking feeding 0.01 MPa)increasesincreases  f   pk    f  s dendritic interdendriticyield point networkfeedingincreases faster (0.01 to 0.9 MPa) 0.5 °C/s, or 30 °C/min. The alloy solidification was studiedusing a differential scanning calorimetry (DSC) instrument.The DSC measurements were conducted at cooling rates of 20 °C/min. The distribution of the solid fraction was deter-mined by post-processing the srcinal DSC data, [13,14] usinga desmearing procedure similar to those by Dong and Hunt [15] and Boettinger and Kattner. [16] Thus, instead of simply inte-grating the DSC signal, a more accurate distribution of thesolid fraction was obtained. The thermophysical properties of A356 aluminum alloy are shown in Table I.The thermal conductivity of the liquid phase and the spe-cific heat of the A356 aluminum alloy were measured as90W/m/K and 1.17 J/g/K, respectively. The latent heat wasdetermined by DSC to be 456 J/g. The density variation withtemperature was used to estimate the thermal expansionproperty that was needed for the thermomechanical model. III.THERMOMECHANICAL ALLOYDEFORMATION Several advanced models for the numerical simulationofstress, strain, and the ensuing displacement fields duringcasting have been developed in academia over the lastdecade. [3,4] These models were recently implemented in thecommercialsimulation software ProCAST.* The stress module *ProCAST is a trademark of ESI Group, France. was coupled with the fluid-flow module in ProCAST, suchthat appropriate constitutive equations were available for theliquid, semisolid, and solid states that coexist during cast-ing solidification. Depending on the amount of solid frac-tion, the deformation or fluid-flow phenomena takes placeas shown in Table II, where  f  s is the mass solid fraction,  f  ch is the mass solid fraction at the coherency point, and  f   pk  isthe mass solid fraction at the maximum packing point. Themaximum packing point represents the instant at which thesolid particles interlock with each other, providing rigidity. [7] The solid fractions critical to the thermomechanical behav-ior of the A356 aluminum alloy during alloy solidificationwere determined from experimental data obtained by Arnberg et al . [17] (Table III).According to the small-strain theory, the total strain canbe decomposed into strain components that correspond tothe elastic, viscoplastic, thermal, and liquid-solid phase-trans-formation effects. The elastic strain was related to the inter-nal stresses, by Hook’s law. Bellet et al . [3] developed amethodology for modeling the casting solidification byincluding constitutive equations for the mushy zone and liq-uid regions in a solid model that is based on Perzyna’swork. [18] A Norton–Hoff power law to describe the vis-coplastic behavior of an Al-7Si-0.3Mg alloy [3] is as follows:[1]where  the plastic strain rate; the operator  .  is definedas   f    f  when  f   0 and zero otherwise;    the fluid-ity of the material; m  the strain rate sensitivity coefficient; K   the viscoplastic consistency;   0  the yield stress; and   eq  the von Mises equivalent stress.Both   and m were temperature-dependent coefficients.For example, at low temperatures, when the alloy tends tobehave elastoplastically, m has very small values, while   has very large values. In ProCAST, [19] the power exponent n and a viscous parameter   are used instead of the vari-ables m and   , respectively. The following relationships pro-vide a connection between the variables used by Bellet etal . [3] and those in ProCAST (Table IV):[2] n  1/  m  and h  1 > 1  1.5  #  pl #   pl  g    h s  eq s  0  1 i 1/  m , g   1 1  3  a s  0 1  3 K  b  1 m Table I.Volumetric Solid Fraction,  g  s , Volumetric Fractionof Eutectic Solid Phase,  g  E , Liquid Phase Density,   l  , SolidPhase Density,    s , and Average Phase Density,   0 , for A356Aluminum Alloy T (°C) g s g  E     l ( g/cm 3 )    s ( g/cm 3 )    0 ( g/cm 3 )20.37————2.670545.01.000.5302.582.452.562554.00.9700.5002.582.452.560559.00.9500.4802.582.452.558561.00.9300.4602.582.452.555568.00.8900.4202.582.452.550572.00.8500.3802.582.452.545575.00.7800.3102.582.452.536577.00.7300.2602.582.452.529579.00.4700.002.542.452.495594.70.3600.002.542.442.476606.70.2500.002.542.432.456618.70.06300.002.542.422.424620.00.000.002.542.412.415800.0————2.368  METALLURGICAL AND MATERIALS TRANSACTIONS BVOLUME 37B, FEBRUARY 2006—133 Table V.Mechanical Properties Used in ProCAST, Basedon Kim et al  . [9] Temperature (°C)  E  (MPa)    0 (MPa)  H  (MPa)2071,705186717020069,636172696330063,776116637740057,22654572250036,5423136545506894—68955614349143616143114 Table IV.Mechanical Properties Used in ProCAST Basedon Bellet et al  . [3] Temperature (°C)  E  (MPa)    0 (MPa) vn    (s)2560,0002000.33500100———21.38.320  10  17 200———12.45.000  10  10 300———8.753.040  10  7 400———6.761.000  10  5 54534,00010.3351.656  10  4 57234,00010.335—5730.010.010.490.2—579———0.2—600———1—6150.010.010.4911.656  10  4 Fig. 1—Wax pattern dimensions (cm) and step index. ProCAST allows modeling of the liquid regions by theNavier–Stokes equations, eliminating the need to artificiallyextend the stress model to liquid regions. Kim et al . [9] pro-posed an elastoplastic model based on the linear hardeningmodel (Table V), which is now a part of the stress databasein ProCAST. According to this model, the linear hardeninglaw is defined as[3]where   0   the yield stress;   pl  the plastic strain;  H    the plastic modulus; and   Y    the modified yield stressdue to linear hardening. The viscoplastic behavior isdescribed by the following equation:[4]where   is the applied stress. A linear temperature variationbetween consecutive data points was assumed to calculatethe variables shown in Tables IV and V. IV.EXPERIMENTAL RESULTS The parts with six steps were examined in this study(Figure 1). The 2.54-cm-thick step is considered to be step1. Two types of stepped parts were made: parts without holesand parts with holes, on steps 3 and 5. In the remainderofthis study, the alloy castings and wax patterns are simplyreferred to as parts and patterns. The patterns without holesand patterns with two holes are referred to as no-hole, orunre-  #  pl  1 h     s    s  Y   n   s   s   s  Y   s  0   H    pl strained, patterns and two-hole, or restrained, patterns, respec-tively. The two-hole patterns were made by placing coresinthe die. The two cores provided geometrical restraint onthelength dimension of the part. For this work, wax patternswere made at M. Argueso & Co. (Muskegon, MI), by injec-tion ofliquid unfilled wax, CERITA* 29-51 at a pressure of  *CERITAis a trademark of M. Argueso & Co. 1.7 MPa (250 psi), at 65 °C, with a dwell time of 120 seconds.The casting configuration used in this study consisted of a downsprue, a runner, and one casting (Figure 2). The spruewas dimensioned such that there was enough metallostatichead to fill the entire part. The heights of the downsprueand pouring cup were 17 and 6.35 cm, respectively. Thehorizontal cross-section dimensions were 6.35  6.35,2.54   2.54, and 2.54  1.9 cm at the top and the end of the pouring cup and at the end of the sprue, respectively.The shell mold contained the following types of sub-strates: face coats, intermediate coats, backup coats, andseal coats. Each coat was generally made of two layers: aslurry layer and a stucco layer. In this study, zircon and fused-silica shell materials were used (Table VI). The shell moldhad eight coats: a zircon prime coat, one intermediate coat,five backup coats, and one dip coat. The shell mold thick-ness was approximately 8.5 mm. The molds were preheatedin two furnaces. The first furnace was used for sinteringthe molds at temperatures of 1000 °C. After sintering, theshell molds were placed in the second furnace and held at400 °C, in order to insure a uniform temperature distribu-tion in the molds.The dimensions of the die tool, the wax patterns, and thecasting were measured at the same locations, using a coor-dinate measurement machine (CMM). The CMMs are widelyused throughout manufacturing industries to meet high-qual-ity standards and achieve dimensional accuracy. The probesize of the CMM was 3 mm in diameter. The probe tipswere round to within 0.0005 mm, and the diameters werewithin 0.003 mm of the nominal diameter. The actual diam-eter of the probe tip was calibrated against a reference spherewith a roundness uncertainty of plus or minus 0.0001 mmand a diameter uncertainty of 0.0002 mm. The measurementprecision was plus or minus 0.02 mm.The dimensions of the wax pattern were measured, to pro-vide a base line for the casting dimensions. The wax pat-terns were examined under magnification, to insure that nodeformation was present in the surfaces after probing. The  134—VOLUME 37B, FEBRUARY 2006METALLURGICAL AND MATERIALS TRANSACTIONS B position of the CMM measurement points are shown inFigure 3. The width shrinkage was calculated from the widthcoordinates for each pair of points, which were located atthe same length and height, but were situated at oppositesides of the pattern. A representative length dimension waschosen to be L2-5, between the ends of steps 2 and 5. Fourno-hole patterns and four two-hole patterns were injected.Since the wax pattern showed good reproducibility, onlytwo castings were made for each case. The parts were labeledas shown in Table VII.The dimensional variations were calculated using the fol-lowing relationships:wax shrinkage ( w s )  pattern dimensions  die dimensions wax patternalloy shrinkage ( a s )  casting dimensions  pattern dimensionscasting shrinkage ( c s )  pattern dimensions  casting dimensionsThe shrinkage of L2-5 was calculated by subtracting thelength coordinate of the points on step 5 from that of thecorresponding points on step 2. The percentage of theshrinkage was calculated for all examined dimensional vari-ations and the results are shown in Figures 4 and 5: thewidth shrinkage was nonlinear along the pattern length,in all cases. There was a high degree of reproducibility for Fig. 3—The position of coordinate measurement points for ( a ) the widthdimensions and ( b ) length L2-5, between ends of steps 2 and 5. ( a )( b )( a )( b ) Fig. 2—Shell molds were invested at Minco, Inc., and casting experiments were conducted at PMI, Inc.: ( a ) wax pattern, ( b ) shell mold, and ( c ) aluminumcasting. ( c ) Table VI.Shell Materials Selected for This Study(TheSlurry Was Colloidal Silica, for All Coats) Shell Stucco StuccoFlour CoatMaterialSizeMaterialFlour SizeFacezirconGFN 110zircon50 pct 200 mesh and 50 pct325 meshIntermediatefused  50  100 fusedsilicameshsilica120 meshBackupfused   30  50 fused silicameshsilica120 meshSeal——fusedsilica120 mesh  METALLURGICAL AND MATERIALS TRANSACTIONS BVOLUME 37B, FEBRUARY 2006—135 Table VII.Index of Wax Patterns and Castings Part IndexNumber of Holes in PartPart Number0a1—10a2—22a1212a222 hole was made for the restrained pattern. The lowest waxshrinkage was observed at step 5, where the smaller holewas made. This effect is likely to be due to the small thick-ness of the steps, which results in faster cooling in thisregion.For the L2-5 dimension, the shrinkage of the wax pat-tern had approximately the same values for both therestrained and unrestrained patterns, although the unre-strained pattern showed larger scatter in shrinkage. Thepoints with a zero-width coordinate were located on thesymmetry plane of the patterns, or centerline. The shrinkagethe wax patterns. The only difference in wax shrinkagebetween the dimensions of the unrestrained pattern and therestrained pattern was observed at step 3, where the longer( b )( c )( a ) Fig. 4—Width-dimension SFs: ( a ) w s , ( b ) c s , and ( c ) a s . ( c )( a )( b ) Fig. 5—The SFs for the length dimension, L2-5: ( a ) w s , ( b ) c s , and ( c ) a s .
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