PREDICTION OF CET-ZONE POSITION USING
THE CELLULAR AUTOMATONFINITE ELEMENT METHOD FOR Al-Si ALLOYS CASTINGS
Zenon Ignaszak, Jakub Hajkowski
PoznanUniversity of Technology, Poznan, Poland
Abstract.In the paper it was presented the process validation of CAFE-Calcosoft (ESI-Group) models tests. It was shown the short description of Cellular Automaton Finite Element (CAFE-3D) method which was applied in system to solidification process identification and to predict the structure of chosen Al-Si alloy. It was determined the sensitivity of thermal model and model to forecast the microstructure on the variability of particular parameters applied in the models taking into consideration the columnar-to-equiaxed transition (CET) zone. The cylindrical casts which solidified in homogenous silica (quartz-Q) sand mould (A) and also in high insulation (HI) mould with chill (B) which coerces high axial temperature gradient, was investigated. The experiment gave the basis to the validation test of CAFE model considering the CET zone which was preceeded bytwocorresponding cases of solidification in respect to thermal conditions of cast-mould system. The virtual structures of studied casts were compared with real structures. It was shown the satisfactory conformity of both structures.
INTRODUCTION
The investigations related to the improvement of foundry processes virtualization are the most important directions of study under prediction of local properties of casts. These investigations go to validation of identification of properties gradient in castings and show the areas which could carry the higherweight than average stresses determined only by specimen static test (mean, formally acceptable). For specific material of casting, the acceptable stress is defined on the results of strength test of sample base which was made as cast (in use it is the static tensile test rarely on the fatigue strength test). It is well known that the sample structure doesn’t represent the properties map of whole casting (7). The zones in casting which crystallize in oriented (direct) solidification conditions are characterized by local texture and can have significant better properties than these obtained by classic sample cast. The one way to obtain the reliable information about localityof structure and resulting of this fact the properties of casting leads through the crystallization process modeling. Experimental model validation as the relation: local structure – local properties is than the necessary condition of advantage resulting from virtual prediction.
Modeling of crystallization phenomena concerns the formation of alloy structure during the changing the aggregation state from liquid to solid (solidification in the sense that it viewed in macro scale) related to physical conditions of process. First of all it was developed on the basis of deterministic models describing nucleation and growth of equiaxed (globular) crystals only (8,9). Developing of these models which contain somedifferent types simplificationsallow their virtualization. The models contain considerable simplifications and limitations, what was clearly described in (1). For these reasons the models based on stochastic (probabilistic) methods were introduced and developed. The example of that kind of models and its utilitarian value was describe in this publication.
SHORT DESCRIPTION OF CAFE MODEL
Calcosoft-CAFE model was elaborated in the Calcom Centre in Lausanne and it is the tool to simulate the virtual castings structure in which columnar and equiaxed crystals are formed (2). This coupled model is based on combination of heat transfer modelsolved by means of finite elements method (FE) with the model of crystal nucleation and growth by means ofcellular automaton (CA).
In the Calcosoft-CAFE model it was assumed that nucleation process takes place on the surface of the mould and in the bulk of liquid volume according to different curves of nucleation intensity in the function of undercooling. This undercooling is calculated in the base on macro model and is moved to the nucleation and growth model. In (3)Gandin et all proposed Gaussian distribution (1)to describe the nucleation intensity dn/d(ΔT) (fig.1b). At given undercooling ΔT (fig.1b) the density of nucleation is described by integral (cumulative distribution function) from distribution of nucleation sites from zero to ΔT (fig.1c):
(1)
where: T – the calculated local undercooling,
Tm-(i) – mean undercooling related to the maximum of nucleation intensity,
where i=s (surface nucleation) or i=v (volume nucleation),
Tσ standard deviation,
nmaxtheoretical maximal nucleation density which can be reached when whole nucleation sites will be activated during cooling (nmax is determined experimentally for the given alloy).
The crystal growth in CAFE–3D model is based on the assumption of octahedron formation (fig.2a) bounded by faces <111>. The main diagonals of the octahedron correspond to the crystallographic orientations [100] along which dendrite arms develop.The increment along arms diagonals of the octahedron is given by the equation (2):
(2)
where:
calculated velocity of dendrite tip growth for given undercooling ΔTvin cellν, according to equation:(a2, a3- kinetics coefficients) (4).
In CAFE model used to hypoeutectic alloys there was made certain simplification witch is based on taking into account only the crystallization of pre-eutectic phase (in this paper: the α-phase in hypoeutectic Al-Si alloy). Eutectic phase doesn’t appear in virtual structure and because of that reason the comparison of virtual structure with real one should be handled as conventional interpretation.
a)b)
Fig.1.Nucleation model (6) (a) and grow model (b)(5)
METHODOLOGY OF INVESTIGATIONS
The investigations have been carried out on cylindrical castings because of axial symmetry and consequent facilitiesin thermal model and description of crystalline structure parameters. Experimental tests have been carried out on uninoculated AlSi7Mg alloy casting the 70mm diameter and 220mm height. The castings were made in the mould shown in fig.2a. Two combinations of materials for the mould were used: homogenous silica sand mould (Q-Q) anddoublematerial made ofhigh insulation material (HI) and copper chill (Ch) which was located in the bottom side of casting. The parametersof the obtained structure ( solid solution exclusively) have been described, considering the position of columnar-to-equiaxed (CET) transition zone.
Fig. 2. Scheme of moulds: a) experimental, b) virtual, c) location of thermocouples
In the simulation calculations it was used the variations of selected thermo-physical and microstructure formation values parameters. Theirs values and units were presented in Table1 for casting which solidified in homogenous silica sand mould and for casting which the mould contains the chill. It should be mentioned that introducing in Calcosoft (CAFE) module the parameters to castings crystallization modeling which allow the segregation of solute which is very important feature. In order to generate the latent heat (heat of crystallization) it was used the reference to actual liquidus temperature in function of local solute concentration according to Scheil model (10). It is assumed in this model there is no solute diffusion in solid phase while in liquid phase there is full distribution of solute (infinite intensity of diffusion).
Table 1. Parameters ranges used to simulation.
Parameter / Name / Value / UnitVariable Parameters
homogenous silica sand mould
λQ / thermal conductivity / 0.5÷1.5 / W/mK
αcast-mould / heat transfer coefficient / 500÷20 000 / W/m2K
ΔTm-s-Q / undercooling on silica sand mould surface / 2÷5 / K
ΔTm-v-Q / undercooling in bulk of liquid volume / 2÷5 / K
ns-Q / nucleation density on silica sand mould surface / 1e4÷1e8 / 1/m2
nv-Q / nucleation density in the bulk of liquid volume / 1e5÷1e10 / 1/m3
a3 / kinetics coefficient / 1.49e-8÷1.49e-5 / ms-1K-2
high insulation mould with chill
λHI / thermal conductivity / 0.3÷1.5 / W/mK
αcast-chill / heat transfer coefficient / 50÷1000 / W/m2K
ΔTm-s-HI / undercooling on high insulation mould surface / 2.5÷10 / K
ΔTm-s-ch-HI / undercooling on chill surface / 5÷20 / K
ΔTm-v-HI / undercooling in bulk of liquid volume / 0.5÷8 / K
ns-HI / nucleation density on surface of mould / 1e5÷1e8 / 1/m2
ns-Ch / nucleation density on surface of chill / 1e5÷1e8 / 1/m2
nv-HI / nucleation density in the bulk of liquid volume / 1e7÷1e10 / 1/m3
a3 / kinetics coefficient / 6.5e-8÷6.5e-5 / ms-1K-2
Variable parameters taken as constant values
αcast-mould / heat transfer coefficient cast-mould / 10 000 / W/m2K
αmould-ambient. / heat transfer coefficient cast-mould mould-external / 20 / W/m2K
CpQ / heat capacity of silica sand mould / 1500 / kJ/m3K
CpHI / heat capacity of high insulation mould / 587 / kJ/m3K
ΔTsσ / standard deviation on mould surface / 0.4 / K
ΔTchill-σ / standard deviation on chill surface / 0.4 / K
ΔTv-σ / standard deviation in bulk of liquid volume / 0.4 / K
EXPERIMENTAL AND VIRTUALSTUDIES
The analysis and selection of thermo-physical coefficients and the values of parameters needed in the empirical relations (nucleation and growth) required to the simulation in order to obtain good conformity of the virtual crystalline microstructure with the experiment one are easier when their impact on the virtual microstructure is known. The model sensibility is decisive in this case. The series of simulation tests (Table 2 and Table 3) in case of investigate the sensitivity of model on the changing of particular values parameters were made. In each test only one value was changed.
The results of model parameters values influence study on CET zone are shown in Table 4 for the castings solidifying in the conditions of the homogenous silica sand mould(Q-Q) and in Table 5 and fig.3 for the mould with the chill (HI-Ch). According to the fig.3 it indicates that in the range of investigations the biggest influence on CET zone increase has the increase of mould, also ΔTm-v and kinetics coefficient a3. Values of simulation parameters have higher influence on the CET zone in casting part submitted to intensive cooling where appear the higher thermal gradients.
Table 2. Parameters used in simulation for casting realizedin silica sand mould.
Lp. / λQ / αcast-Q / ΔTm-s / ns / ΔTm-v / nv / a3
1 / 1.5 / 10000 / 2 / 1e6 / 5 / 1e7 / 1.49e-7
2 / 0.5 / 10000 / 2 / 1e6 / 5 / 1e7 / 1.49e-7
3 / 1.0 / 10000 / 5 / 1e6 / 2 / 1e7 / 1.49e-7
4 / 1.0 / 10000 / 5 / 1e6 / 2 / 1e7 / 1.49e-6
5 / 1.0 / 10000 / 5 / 1e6 / 2 / 1e7 / 1.49e-8
6 / 1.0 / 10000 / 5 / 1e4 / 2 / 1e5 / 1.49e-7
7 / 1.0 / 10000 / 5 / 1e8 / 2 / 1e9 / 1.49e-7
8 / 1.0 / 10000 / 5 / 1e4 / 2 / 1e6 / 1.49e-7
9 / 1.0 / 10000 / 5 / 1e6 / 2 / 1e8 / 1.49e-7
10 / 1.0 / 10000 / 5 / 1e8 / 2 / 1e10 / 1.49e-7
11 / 1.0 / 5000 / 5 / 1e6 / 2 / 1e7 / 1.49e-7
12 / 1.0 / 1000 / 5 / 1e6 / 2 / 1e7 / 1.49e-7
13 / 1.0 / 500 / 5 / 1e6 / 2 / 1e7 / 1.49e-7
14 / 1.0 / 20000 / 5 / 1e6 / 2 / 1e7 / 1.49e-7
15 / 1.0 / 10000 / 5 / 1e7 / 2 / 1e8 / 1.49e-7
16 / 1.0 / 10000 / 5 / 1e6 / 2 / 1e7 / 1.49e-5
Table3. Parameters used in simulation for casting realizedin high insulation mould with chill.
Lp. / λHI / αcast-chill / ΔTm-s / ns / ΔTm-s-ch-HI / ns-chill / ΔTm-v / nv / a3
1 / 0.5 / 1000 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
2 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
3 / 0.5 / 100 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
4 / 0.5 / 50 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
5 / 0.3 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
6 / 0.8 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
7 / 1.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
8 / 0.5 / 500 / 2.5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
9 / 0.5 / 500 / 7.5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
10 / 0.5 / 500 / 10 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
11 / 0.5 / 500 / 5 / 1e5 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
12 / 0.5 / 500 / 5 / 1e7 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
13 / 0.5 / 500 / 5 / 1e8 / 10 / 1e7 / 2 / 1e8 / 6.5e-6
14 / 0.5 / 500 / 5 / 1e6 / 5 / 1e7 / 2 / 1e8 / 6.5e-6
15 / 0.5 / 500 / 5 / 1e6 / 15 / 1e7 / 2 / 1e8 / 6.5e-6
16 / 0.5 / 500 / 5 / 1e6 / 20 / 1e7 / 2 / 1e8 / 6.5e-6
17 / 0.5 / 500 / 5 / 1e6 / 10 / 1e5 / 2 / 1e8 / 6.5e-6
18 / 0.5 / 500 / 5 / 1e6 / 10 / 1e6 / 2 / 1e8 / 6.5e-6
19 / 0.5 / 500 / 5 / 1e6 / 10 / 1e8 / 2 / 1e8 / 6.5e-6
20 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 4 / 1e8 / 6.5e-6
21 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 6 / 1e8 / 6.5e-6
22 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 8 / 1e8 / 6.5e-6
23 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e7 / 6.5e-6
24 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e9 / 6.5e-6
25 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e10 / 6.5e-6
26 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-8
27 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2 / 1e8 / 6.5e-7
28 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 1.5 / 1e8 / 6.5e-6
29 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 2.5 / 1e8 / 6.5e-6
30 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 3.5 / 1e8 / 6.5e-6
31 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 3.0 / 1e8 / 6.5e-6
32 / 0.5 / 500 / 5 / 1e6 / 10 / 1e7 / 4.5 / 1e8 / 6.5e-6
Table 4.Virtual structures for cylindrical casting realizedin silica sand mould.
1 / 2 / 3 / 4 / 5 / 6 / 7 / 89 / 10 / 11 / 12 / 13 / 14 / 15 / 16
Table 5. Virtual structures for cylindrical casting realizedin high insulation mould with chill.
1 / 2 / 3 / 4 / 5 / 6 / 7 / 89 / 10 / 11 / 12 / 13 / 14 / 15 / 16
Table 5 (continued)
17 / 18 / 19 / 20 / 21 / 22 / 23 / 24
25 / 26 / 27 / 28 / 29 / 30 / 31 / 32
a)
/ b)
c)
/ d)
Fig. 3.Model’s sensitivity diagrams on particular thermal and CAFE parameters influence (for high insulation mould casting – see Tables 3 and 5).
Fig.4. Comparison of obtained real and virtual structures for solidified casting: a) in homogenous silica sand mould (λQ=0.75, αcast-mould=10000, ΔTm-s=5, ns=1e6, ΔTm-v=2, nv=1e7, a3=1.49e7), b) in high insulation mould with Cu chill (λHI=0.2, αcast-chill=400, ΔTm-s=5, ns=1e6, ΔTm-s-ch-HI=10, nv=1e7, ΔTm-v=2, a3=1.49e7) for the best conformity.
The identification of thermal conditions influence was obtained using the measure of coolingcurves with the use of thermocouples type K and digital measurement equipment todata logging. The real and virtual thermocouples were fixed in the same points coordinates (fig.2c).The set of experimental and virtual cooling curves were shown adequately on the fig.5a-c for homogenous silica sand mould and on fig. 5d-f for high insulation mould with chill. The times of solidification in particular points and also the relative differences were shown in Table 6. The relative differences were determined using the following relationship: Δ%=[(texp-tsim)/texp] 100%. The differences in times of α-phase solidification tsim and texp for casting solidifying in homogenous silica sand mould are approximately from 0 to 9% whereas for mould with chill approximately6-7%.
The simulation investigation results concerning the CET (columnar-to-equiaxed) zone transition) were subjected todetailed analyze. The real and virtual microstructures obtained from simulation are shown in fig.4 for the best conformity. The CET zones transition (direction of measurement – in geometric axe of casting) were shown in Table 7.
Table 6. Estimated α-phase solidification times in particular points of cast (see fig. 5). / Table 7. CET zone transition and its relative differences (see fig. 4).Point
number / solidification time, s
Q-Q / HI-Ch
SIM. / EXP. / Δ% / SIM. / EXP. / Δ%
1 / 422 / 424 / ~0 / 266 / - / -
2 / 441 / 459 / ~4 / 710 / ~750 / ~6
3 / 445 / 487 / ~9 / 983 / 1050 / ~7
/ mould / CET
mm
Q-Q / SIM. / 3
EXP. / 3
HI-Ch / SIM. / 63
EXP. / 62
a)b)
c)d)
e)f)
Fig.5. Real (continuous line) and virtual (dotted line) cooling curves validated by
α-phase solidification curves: a), b), c) in homogenous silica sand mould in particular points, d), e),f)in high insulation mould with chill;obtained for the beststructures conformity (see Fig. 4).
FINAL REMARKS
The validation study of microstructure based on prediction effectiveness was analyzed and estimated with the use of CAFE–3D model. It gave after large number of parameters considering the model sensitivity tests the satisfactory conformity for both silica sand and high insulation mould castings with chill taking into consideration local solidification times and CET zone position.
Upon the validation of experimental-simulation study of structure it can be formulated the following conclusions:
1.Calcosoft 3D system with CAFE model requires the extended validation of parameters in order to bring to satisfactory conformity with results of experimental investigations (CET zone transition).
2.The practical analyze of the influence of thermal and CAFE model coefficients and parameters indispensable to complete the empirical interrelations used for simulation of crystalline structure formation (“soft” modeling) presented in this paper is useful. The new elements in this micro-modeling require the pre-describe validation tests. Calcosoft CAFE-3D model requires that kind of performance before its application in industry to predict the zone properties, grain sizes and orientation of structures incastings.
3.It is very important to consider the dynamic intensity of thermal process and influence of substitute thermal conductivity of mould material and of heat transfer coefficient on casting-chill boundary, both variable in temperature-time reality. It will be realized during next stage of planned researches.
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