Prediction of hot tearing during alloy solidification

Transcription

1 Prediction of hot tearing dring alloy solidification J Go and JZ Zh ESI US R&D, 6851 Oak Hall Lane, Site 119, Colmbia, MD 21045, USA Abstract In order to predict the mechanical properties of an in-serice part, it is ery important to nderstand the relationships between the alloy chemistry, the processing, and the final properties Sch prediction is possible to a certain degree from gien knowledge of the microstrctre, phase fractions, and defects present in a metallic part Hot tearing is one of the most serios defects for a casting It is belieed that this phenomenon occrs in the late stages of solidification In this paper, a hot tearing indicator, which is based on the accmlated plastic strain in the last stage of solidification, was introdced to ealate ssceptibility to hot tearing dring casting solidification processes The last stage of solidification is stdied This incldes the solidification ending temperatre, thermal and mechanical properties, and alloy chemistry and cooling history are considered The predictions are alidated by comparison with experimental measrements Keywords: Late stages of solidification, hot tearing, back diffsion, thermodynamic modelling, Mg-Al alloys 1 Introdction Simlation technologies are applied extensiely in casting indstries to nderstand aspects of heat transfer and flid transport phenomena and their relationships to the microstrctre, the formation of defects [1], and occasionally the final mechanical properties Hot tearing is a common defect encontered in castings Eskin et al [2] gae a ery detailed reiew of hot tearing It is belieed that this phenomenon occrs in the late stages of solidification when the fraction solid is close to one The alloy composition, casting geometry, cooling history, and mechanical properties of the casting are all related to the formation of hot tearing The correlation between ssceptibility to hot tearing and alloy composition is well established The relationship between hot tearing and mechanical properties is easy to nderstand In order to predict the formation of hot tearing which occrs in the last stage of solidification, it is critical to hae accrate thermophysical and mechanical properties, especially for the mshy zone, as inpt for complex solidification processes The solidification path and thermophysical properties can be calclated with the help of thermodynamic calclations of phase stability at gien temperatres and compositions A comprehensie mlti-component alloy solidification model, copled with a Gibbs free energy minimization engine and thermodynamic databases, has been deeloped A back-diffsion model is integrated so that the solidification conditions, sch as cooling rate, can be taken into accont Mch research has been done on the formation of hot tearing Proposed mechanisms of hot tearing can be fond in the literatre (see, eg, [2] and the references therein) Most of the existing theories of hot tearing are based on the deelopment of strain, strain rate, or stress in the semi-solid state of the casting For strain-based theory, it is belieed that hot tearing will occr when the accmlated strain exceeds its dctility [3 5] Strain rate-based theories sggest that hot tearing may form when the strain rate, or strain rate related pressre, reaches its critical limit dring solidification [6,7] Stress-based criteria, on the other hand, assme that hot tearing will start if the indced stress in the semi-solid exceeds some critical ale [8,9] These theories can be considered as somewhat related de to the fact that strain, strain rate and stress are themseles related Sch a relationship motiates s to deelop a hot tearing indicator, which ses the accmlated plastic strain as an indication of ssceptibility to hot tearing by considering the eoltion of strain, strain rate and stress in the last stage of solidification, for the nmerical simlation of solidification We beliee that the hot tearing indicator presented in or discssion can also be generalized to mch wider applications To compte an effectie hot tearing indicator, it is important to hae accrate inpts, so that the casting chemistry, casting geometry, and the cooling history can be properly considered In this paper, back diffsion thermodynamic calclation for some binary Mg-Al alloys are gien first so that the solidification path can be predicted accrately, followed by the thermophysical and mechanical properties calclation for those alloys A hot tearing indicator is introdced next Some experimental alidations are performed in the end 2 Thermodynamic calclation Solidification proceeds at arios rates The solidification path determines the solidification behaior for an alloy For 549

2 Fraction of Solid % Al 4% Al Figre 1: Solidification path for different binary Mg-Al alloys based on 100 K/s cooling rate and a back diffsion thermodynamic calclation Fraction of Solid % Al 4% Al Figre 2: Last stage of solidification for different binary Mg-Al alloys based on 100 K/s cooling rate and a back diffsion thermodynamic calclation Thermal Expansion Coefficient (10-5 /K) Figre 3: Thermal expansion coefficient ariation with temperatre for different alloys Yong's Modls (MPa) Figre 4: Yong s modls ariation with temperatre for different alloys complex mlti-component alloys, the solidification path is ery complicated Hence the eqilibrim of each phase at different temperatre needs to be calclated The thermodynamics as well as the kinetics calclation is the basis for the prediction of solidification The diffsie transport in the solid phase needs to be soled for each element This reqires knowledge of the diffsion coefficient, the length scale, and the cooling conditions Recently, thermodynamic modeling has become increasingly sed to predict the eqilibrim and phase relationships in mlti-component alloys [1,10,11] Back diffsion is inclded for all elements in the solidification calclation Cooling rate is taken into accont in this model Frther detailed information abot the back diffsion thermodynamic calclation can be fond in [12] Here solidification of seeral binary Mg-Al alloys is inestigated dring die casting process For a die casting, the cooling rate is arond 100 K/s Figre 1 shows the solidification paths of Mg-Al alloys with 025, 06, 10, 20, 40, and 80 wt% alminm, at 100 K/s cooling rate The last stage of solidification of these alloys is shown in Figre 2 It can be seen that the start and end solidification temperatres are qite different for different alloy compositions Based on the Scheil model, the ending solidification temperatre will be the etectic temperatre for these binary Mg-Al alloys Becase of back diffsion, not all of the ending solidification temperatres for these alloys, sch as Mg-025%Al and Mg-06%Al, are at the etectic temperatre The temperatre differences between fraction solid at 09 and end of solidification are qite different between these alloys too Since hot tearing occrs in the last stage of solidification, obiosly this difference can affect the hot tearing calclation greatly 3 Thermophysical and mechanical properties calclation To obtain the thermophysical properties experimentally at low temperatre can be time consming and expensie It becomes een more difficlt at high temperatre especially when close to or aboe the solids temperatre With the help of thermodynamic calclation, the thermophysical properties can be predicted [1] An extensie database for the calclation of thermophysical properties has been deeloped which tilizes the phase fraction information predicted with the minimization rotines deeloped by Lkas et al [10] and extended by Kattner et al [11] These properties inclde density, specific heat, enthalpy, latent heat, electrical condctiity and resistiity, thermal condctiity, liqid iscosity, Yong s modls, and Poisson s ratio The thermodynamic calclation is based on the thermodynamic 550

3 database from CompTherm LLC (Madison, WI USA) A simple pair-wise mixtre model which is similar to that sed to model thermodynamic excess fnctions in mlticomponent alloys is sed to calclate the properties [1] = xi Pi + xi x j i j> i P Ω ( x x ) i j (1) where P is the phase property, P i is the property of the pre element in the phase, Ω is a binary interaction parameter, and x i and x j are the mole fractions of elements i and j in that phase Becase of the different amonts of Al and the different solidification paths, the density cres are ery different for these alloys Based on the density calclation, the thermal expansion coefficients are calclated and shown in Figre 3 Figre 4 shows the calclated Yong s modls ales The calclated data is sed for the thermal, flid flow, and stress analyses 4 Hot tearing indicator The constittie model sed to describe the material behaior in the semi-solid state is the Grson model [13 15], which was originally deeloped for stdying the progressie micro-rptre throgh ncleation and growth of micro-oids in a dctile and poros solid When the material is considered as elastic-plastic, the yield condition in the Grson model is of the form p p p φ( σ, x, T, ε, G ) = F( σ ) G ( σ, ε, f ) κ ( ε, T ) = 0 (2) where F(σ) = (3(s x) : (s x)/2) 1/2 is the Mises stress in terms of the deiatoric stress s = σ (trσ)i/3, κ represents the plastic flow stress de to isotropic hardening, and x denotes back stress de to kinematic hardening The accmlated effectie plastic strain is written as with p t p p ε = 0 ( 2/ 3) ε : ε dτ (3) p φ ε = γ (4) σ and γ being the plastic flow parameter The Grson coefficient G is defined as tr( σ ) 2 G = 2 f * q cosh( ) + {1 + ( q f *) } 1 2κ 1 in which, q 1 is a material constant and f * = f f f * = f c + f F fc ( f fc ) fc for f fc for f > fc (5) (6) Here, f = 1/q 1, f c is the critical oid olme fraction and f F is the failre oid olme fraction Following Tergaard and Needleman [14], their ales are chosen as q 1 = 15, f c = 015, and f F = 025 The Grson coefficient characterizes the rapid loss of material strength de to the growth of oid olme fraction f When f = f F then f* = f = 1/q 1, we hae G = 0, for zero stress, ie, the stress carrying capacity of the material anishes The eoltion of the oid olme fraction is described by the ncleation of new oids and the growth of existing oids, ie f fncleation + f growth with the rate of oid growth defined as = (7) * * p * 3 f q ( ) ( 1 ) ( ) γ (1 )( 1 tr σ f growth = f tr ε = f )sinh( ) (8) κ 2κ In or stdy, oid ncleation is assmed to be strain controlled and is written as f = e (9) where ncleation t p p eht = t 2/ 3) : dτ c ht ( ε ε (10) t t t c s is defined as or hot tearing indicator (HTI) t c represents time at coherency temperatre and t s denotes time at solids temperatre It is obsered that the hot tearing indicator is in fact the accmlated plastic strain in the semi-solid region and it corresponds to the oid ncleation Therefore, it shold proide a good indication of the ssceptibility to hot tearing dring solidification The ale of the hot tearing indicator is determined by finite element analysis [16] For materials described by iscoplastic or creep model, the yield condition does not exist The fnction φ defined in Eqation 2 can be sed as a potential for the inelastic flow, so that the inelastic part of the strain rate is still gien in the form of Eqation 4 5 Experimental alidation Cao et al [17] performed an experiment to stdy the hot tearing formation dring solidification of binary Mg-Al alloys in a steel mold The steel mold is shown in Figre 5 It casts for 95 mm diameter rods of lengths 51, 89, 127, and 165 mm There is a 19 mm diameter ball at the end of each rod to restrain the rod from free contraction dring solidification A hot cracking ssceptibility (HCS) was introdced which is a fnction of maximm crack width, crack length factor, and the crack location It was fond that it is easier to hae cracks at the spre end than at the ball end It is less likely to crack in the middle of the rod Also, the longer the rod the easier it is to hae a crack Figre 6 shows the simlated reslts of the hot tearing indicator for a Mg-2%Al alloy casting The compted hot tearing indicator agrees ery well with the experiments Figre 7 shows the experimental reslts of hot tearing at the spre end of the rods for three different alloys The calclated hot tearing indicators are shown in Figre 8 accordingly It can be seen that hot tearing is less seere as the Al content increases from 2% to 4% and then to 8% at the same location for the same casting with the same casting conditions Again, the simlated hot tearing indicators agree well with the obserations Figre 9 shows the hot cracking ssceptibility (HCS) defined by Cao et al [17] from their experiments This ssceptibility rises sharply from pre Mg, reaches its maximm at Mg-1%Al and decreases gradally with frther increase in the Al content The hot tearing indicator is calclated at the end of spre for the longest rod for different alloy compositions For comparison, the hot tearing indicators as well as a crack ssceptibility coefficient (CSC), which is defined as the temperatre difference between fraction solid at

4 Figre 6: Hot tearing indicator for a Mg-2%Al alloy casting Figre 5: Steel mold for constrained rod casting [17] Figre 7: Close-p iews of hot tears (cracks) in the bottom of rods near the spre: (a) Mg-2%Al; (b) Mg-4%Al; (c) Mg-8%Al Figre 8: Hot tearing indicator in the bottom of rods near the spre: (a) ; (b) 4% Al; (c) 552

5 HTI CSC Hot Tearing Indicator CSC (Ts09-Ts (K)) Alminm Content, wt% Figre 9: Hot cracking ssceptibility s Al content for Mg-Al alloys [17] Figre 10: Comparison between the hot tearing indicator and crack ssceptibility coefficient, both s Al content for Mg-Al alloys and at the end solidification, are shown in Figre 10 Jst as in the experiment, the ssceptibility to hot tearing rises sharply from pre Mg, reaches its maximm at Mg-1%Al and decreases gradally with frther increase in the Al content It tells s that the crrent hot tearing indicator can predict the trend of hot tearing formation ery well The alloy chemistry, casting geometry, and cooling conditions all contribte to the formation of hot tearing and they are inclded in this model directly or indirectly 12 J Go and MT Samonds, J Phase Eqilibria and Diffsion, in press, AL Grson, J Engng Mater Tech, 1977, 99;2 14 V Tergaard and A Needleman, Acta Metall, 1984, 32; A Needleman and V Tergaard, J Mech Phys Solids, 1987, 35; OC Zienkiewicz and RL Taylor, The Finite Element Method: For Solid and Strctral Mechanics, 2005, Elseier 17 G Cao, S Ko, and YA Chang, in: Magnesim Technology 2006, Edited by AA Lo et al, TMS, 2006, pp Conclsion A comprehensie mlti-component alloy solidification model, which is copled with thermal-flid-stress macromodels, has been deeloped and implemented in a commercial software code, ProCAST The model can accrately predict formation of hot tearing dring casting solidification The alloy chemistry, casting geometry, and cooling conditions are all inclded in this model directly or indirectly The predicted reslts agree well with the experiments This model can be applied to mlti-component casting alloys other than binary Mg-Al alloys as well References 1 J Go, and MT Samonds, in: Modeling of Casting, Welding and Adanced Solidification Processes-X, Edited by DM Stefanesc, et al, 2003, pp DG Eskin, Syitno, and L Katgerman, Progr Mater Sci, 49 (2004) B Magnin, L Maenner, L Katgermann, and S Engler, Mater Sci Form, 1996, 1209; L Zhao, B Wang, V Sahajwalla, and RD Pehlke, Internat J Cast Metals Res, 2000, 13(3);167 5 WS Pellini, Fondry, 1952, 80;124 6 M Rappaz, JM Drezet, and M Gremad, Metall Mater Trans A, 1999, 30A;449 7 NN Prokhoro, Rssian Castings Prodction, 1962, 2;172 8 CH Dickhas, L Ohm, and S Engler, AFS Trans, 1994, 101;677 9 J Langlais and JE Grzleski, Mater Sci Form, 2000, 167; HL Lkas, J Weiss, and ETh Henig, CALPHAD, 6, No 3, pp (1982) 11 UR Kattner, JOM, Dec 1997, pp