Analysis of residual stresses and cracking of γ-TiAl castings

lntermetallics 2 (1994) 89-94

Analysis of residual stresses and cracking of y-TiAl castings J. Guan, G. W. Dieckhues* & P. R. Sahm Foundry-Institute, R WTH, Aachen, Germany (Received 28 May 1993: accepted 5 July 1993)

A coupled thermo-mechanical model has been developed to calculate the residual stresses upon cooling, the resulting distortions and cracking sensitivity as a function of the casting conditions. The developed programme module was used to carry out investigations on thermal stresses and cracking behaviour of 3'TiA1 investment castings. Special ring geometries with various casting moduli were chosen for the determination of the cracking sensitivity of TiAI castings. A criterion function that describes the cracking sensitivity has been derived from the temperature and stress history. The calculated results were compared to the real TiAI castings.

Keywords: T-TiA1, numerical modelling, FEM, residual stress, cracking sensitivity. investment casting.

dimensional stability. In application, these stresses will overlap with load stresses and may then cause a complete destruction of the cast part. The primary causes for such stresses are nonuniform cooling and allotropic transformations. Besides, the development of stresses is influenced by the geometry of the casting and by shrinkage hindrance. In order to make an optimal use of a material and to avoid the resulting casting defects it is essential to quantitatively determine the development of residual stresses. In this paper a coupled thermo-mechanical model is described which calculates the residual stresses upon cooling, the resulting distortions and cracking sensitivity as a function of the casting conditions. Utilising this FEM-programme module, investigations on TiA1 castings with special geometries were carried out to determine the effects of geometry on thermal stresses and cracking. To validate the simulation these calculations are compared to experimental results.

1 INTRODUCTION Alloys based on y-titanium aluminides (6-TiA1) exhibit a great potential to become a novel aerospace material because of their low density, high melting temperature (around 1460°C), good elevated-temperature strength and modulus retention, good resistance to oxidation and hydrogen absorption as well as acceptable creep properties. The TiA1 alloys are expected to replace the common Ti- and Ni-base superalloys in certain parts of turbines and engines. The resulting high specific strength promises a prominent position in aerospace applications. ~ While carrying out basic studies on the casting properties, the TiA1 alloys showed remarkable cracking sensitivity, particularly in areas where geometrical shrinkage hindrance occurs. Presumably, the castings had already cracked during solidification. The material obviously cannot withstand the developing thermal stresses because of its reduced strength at elevated temperatures and its intrinsic brittleness at temperatures below the ductile-brittle transient. Such thermal stresses cannot only cause cracking of castings during solidification, but also remain in the casting after cooling as internal stresses that may cause distortions and affect

2 TEMPERATURE-DEPENDENT PLASTIC FLOW During a solidification process the change of temperature and the allotropic transformations lead to different material properties. As shown schematically in Fig. l(a), not only the elasticity

* To whom correspondence should be addressed 89

Intermetallics 0966-9795/94/$7.00 © 1994 Elsevier Science Limited, England. Printed in Great Britain

90

J. Guan, G. W. Dieckhues, P. R. Sahm {0}.

for e - gy(T, gp) < 0 AT

TI
{Ao-0} = i_1,r + {~F/~{o'} } r[D]e~F/~{g}:

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-- F ({~1 ¢o Ts)

T

%(r, gp) = 0

(4)

flow o

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e,)

Fig. 1. Influences to temperature on the plastic flow of materials. (a) Schematic illustration of the temperature effects on the material's behaviour; (b) temperature effects on the von Mises yield surface (see text).

modulus and the yielding point change with temperature but also the hardening behaviour of the material. While hardening of the material at low temperatures increases with plastic deformation, the material shows a nearly ideal plastic behaviour at elevated temperatures. Due to this fact the yield condition depends not only on the plastic strain but also on temperature. The position of the yield surfaces also changes with temperature (see Fig. l(b)). To take these temperature effects into account, the normal general relation between the increments of strain and stress is modified by adding the initial stress {Ag0}:2 {Ao-} : [D] x ({Ae} - {Ae0}) + {Ago}

3 METHOD OF THE COUPLED SIMULATION Thermal stresses in cast parts are characterized by the mutual influences of the predominant thermal, metallurgical and mechanical conditions during solidification. In order to facilitate this problem and to reduce CPU time it is generally assumed that these complicated interactions within a casting system can be uncoupled. 5'6 Experience shows that influences of the mechanical conditions during the casting and cooling process back on the thermal and the metallurgical conditions are negligible. By simplifying the problem in this way the calculation of stresses and deformations can be carried out separately after the determination of temperatures and microstructures (Fig. 2). The temperature distribution during solidification processes is calculated by the FEM-programme CASTS developed at the Foundry-Institute of the

(1)

where {Ae} is the total increment of strain, {Ae0} is the initial strain consisting of the thermal strain {Ae}t h and the strain {Ae}p h caused by the phase transformation: {A•0} : {Ae}t h + {Ae}p h

(2)

Depending on whether the yield condition is satisfied at a particular time, a distinction is made between the elasticity matrix [D]e and the elasticplastic matrix [D]ep"3'4 [D]e:

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t

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for ~ -

O-y(T, gp) = 0

[Analysisby usingcriterionfunctions fiT,1",{¢r},microsU-ucture, ~

(3)

The initial stress {Ago} presents an additional fictitious stress which is caused by the change of the yield condition with temperature. Therefore, it occurs only during plastic deformations and can be determined from the following equation:

- porosity - cracking and distortion - mechanical

properties

- solidification parameters

Fig. 2. Flow chart of the coupled thermo-mechanical simulation.

Residual stresses and cracking of 7-TiAI castings R W T H (Aachen, Germany). This programme package takes the heat transfer between interfaces of materials into account, 7 includes temperatureand structure-dependent thermophysical properties and incorporates the specific initial conditions of the casting processes and different boundary conditions such as insulation, radiation and conveclion) ~ The results from the calculation are stored at each time step and are used subsequently for the calculation of stresses. The development of stresses during the casting processes can be influenced by the structural transformation in several ways. On the one hand, :he thermo-mechanical properties of the casting are influenced by the structural transformations which on the other hand, change the specific volume of the phases involved. Moreover, the ~tress evolution is affected by the transformation plasticity. Using the calculated temperatures and structures as input data, the simulation of deformations and stresses can then be performed. In this process the specific casting conditions, such as shrinkage hindrance caused by moulding material and core behaviour, are taken into consideration. Finally, using certain criterion functions, various informations may be obtained from the calculations: • • • •

91

Da=32mm

Di = 30, 29, 28, 27, 26, 25 [ram]

Fig. 3. Geometry of TiA1 rings.

cracking sensitivity of TiA1 castings. A ring geometry is particularly suitable for the determination of the cracking sensitivity because it would shrink symmetrically on the core. This causes uniform stresses within the casting. First experiments have shown that a critical inner diameter has to be defined here, it varied between 25

shrinkage sensitivity and porosity, cracking behaviour and deformation, microstructural conditions, and mechanical properties.

4 EXPERIMENTAL AND NUMERICAL INVESTIGATIONS The developed programme module was used to carry out investigations on thermal stresses and cracking behaviour of TiA1 castings. The castings were made using the investment casting technique with ceramic shell moulds. In order to improve the cavity filling capacity and influence the structure transformations, ceramic shell moulds were preheated before the casting process. Because the moulding material shows high mechanical strength, it causes definite shrinkage hindrance. 4.1 Geometry of the casting, initial conditions, and boundary conditions Rings with a constant thickness of 2 mm, constant external diameter of 32 mm and variable inner diameter were chosen for the determination of

(a) 550

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350~

i

240

J 480

i 720 Time

960

1200

1440

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(b) Fig. 4. Utilising the ceramic shell mould in (a) the temperature development as measured in (b) was used as the boundary condition for the temperature calculations.

92

J. Guan, G. W. Dieckhues, P. R. Sahm

and 30 mm. The associated casting modulus (volume/surface ratio) assumes values between 0.33 and 0.64 (Fig. 3). The simulation of solidification and the calculation of stresses were based upon an experiment that was carried out with a pouring temperature of 1520°C (TiAI) and a preheating temperature of the ceramic shell mould of 520°C as initial conditions. During solidification and cooling of the casting the development of temperature on the surface of the ceramic shell mould was measured and recorded (Fig. 4). These data are then used as boundary conditions in the CASTS programme for the calculation of the temperature fields.

(a) 1,200 1,000 800 v~

600

.E

400

d:

4.2 Results

200

The rings' solidification time is relatively small. Because of the narrow solidification range of TiA1 alloys (c. 15 K) and the small casting modulus, the basically short solidification time varies only slightly with increasing casting modulus. Nevertheless different cooling rates were still observed. In all cases, however, a metal-mould equilibrium temperature was finally reached. Afterwards, the cooling continues slowly, for fixed radiation and convection (Fig. 5).

M=Modulus(V/A)[mini 5

I

0

15

20

25

30

35

40

45

50

Time[sec1

(b) Fig. 6, Development of the principal stresses in TiA1 rings upon cooling.

The calculation of temperatures is followed by a determination of thermal stresses. Figure 6(a) shows the calculated principal stresses at three time steps. The time sequence of the principal stresses is presented as a function of the casting modulus in Fig. 6(b). The figure shows that the principal stresses decrease with increasing modulus (or decreasing inner diameter) of the rings. The stresses approach a maximum which is reached at a temperature of approximately 600°C. At this temperature TiA1 alloys show a sharp ductile-brittle transition (Fig 7). The plastic

(a)

brittle-ductile-transRion regime

1.600

1

100

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800

600

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4

6

8

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14

16

18

20

(b) Fig. 5. Calculated cooling of the TiA1 rings: (a) temperature distribution; (b) cooling curves.

0,1 0

200

400 600 800 Temperature [~J

1000

Fig. 7. Influence of temperature on the rupture elongation of TiA1 alloy. I

93

Residual stresses and cracking of T-TiAl castings

7°°I

]

~600 e-.

i

I

500

(a) 0

100 200 300 400 500 600 700 800 9QO 1000

Temperature[°C ] Fig. 8. Temperature dependence of the ultimate strength of TiA1 alloy)2 deformability for stress relaxation decreases continuously below the transition temperature and finally disappears totally. Only elastic deformability remains. During cooling not only the stresses, but also the strength of the material changes with temperature, ~2 (Fig. 8). Therefore, the cracking criterion, the ratio of the maximum principal stress o-1 (see Fig. 6) and the tensile strength R m is crucial for the cracking behaviour of the material: 6 Cracking criterion - o-~ Rm

A large value indicates a large tendency to cracking. The calculated cracking criterion reaches its maximum values during the early stages of cooling, (see Fig. 9). With decreasing inner diameter of the rings, the maximum values shift to later times. In general, the maximum values for the cracking criterion are reached at around 900°C. This means that the maximum danger of cracking already occurs at temperatures above the ductilebrittle transition temperature. Moreover, one can see that the risk of cracking increases with the inner diameter of the rings. 3

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.

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.

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1

2

3

4

5

6

7

8

9

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Time [sec] Fig. 9. Influence of the geometry on the cracking criterion o-~/R m of TiAl-rings (see text).

(b) Fig, 10. Comparison between (a) the calculated cracking criteria, and (b) the observed crack locations.

Figure l0 shows the calculated cracking sensitivity compared to the experimental results of the castings. The predicted danger of cracking is particularly high in the gating area for all ring geometries because the sharp angle at the gate causes a large notch effect. This corresponds to experimental results which indicate cracks for all cast rings in the gating area. The cracking criterion values are also high on the perimeter of those rings which have a large inner diameter. In agreement with the calculations, the experimental results again show additional cracks on the perimeter of the three thin-walled rings.

5 SUMMARY

Intensified demands concerning the quality of castings increasingly require, among other things, detailed quantitative knowledge of the distribution of residual stresses during solidification and cooling. In this paper a coupled thermomechanical model for determining the thermal stresses and distortion of real castings was presented. Utilising this software, investigations on TiAI castings were performed. A criterion function that describes the cracking sensitivity has been derived from the temperature and stress history. Also the geometric effects were examined. The calculated and the experimental results of the castings have shown good agreement.

94

J. Guan, G. W. Dieckhues, P. R. Sahm

ACKNOWLEDGEMENTS The authors wish to thank the Otto JunkerStiftung and the Deutsche Forschungsgemeinschaft (DFG) for providing financial support to carry out this research.

REFERENCES 1. Kim, Y.-W., J. of Metals, 41(7) (1989) 24---30. 2. Hetnarski, R. B., Thermal Stresses III. Elsevier Science Publishers BV, Amsterdam, The Netherlands, 1989. 3. Zienkiewicz, O. C., Methode der finiten Elemente. Carl Hanser Verlag, Munich, Germany, 1984. 4. Fletcher, J. Thermal Stress and Strain Generation in Heat Treatment. The Materials Science Publisher, London, UK, 1989. 5. TOns, H. J., Thermoplastische Berechnung nach der

Methode der finiten Elementen. Dr-Ing thesis, University GHS Essen, Essen, Germany, 1985. 6. Guan, J. & Sahm, P. R., Giessereiforschung, 43(1) (1991) 10-17. 7. Sch~ifer, W., Hediger, F. & Btihrig-Polaczek, A., In Proceedings of the First European Conference on Materials and Processes Euromat 89, DGM Informationsgesellschaft, Oberursel, Germany, 1990, pp. 121-7. 8. Sahm, P. R., Richter, W. & Hediger, F., Giessereiforschung, 35(2) (1983) 3542. 9. Sahm, P. R. & Hansen, P. N., Numerical Simulation and Modelling of Casting and Solidification Processes for Foundry and Cast-house. International Committee of Foundry Technical Associations CIATF, Zurich, Switzerland, 1984. 10. Sturm, J. C. & Sahm, P. R., In Modeling of Casting and Welding Processes IV. The Minerals, Metals & Materials Society, USA, 1988, pp. 69--78. 11. Hofmann, N., Reske, U., Vor, H. & Sahm, P. R., Giesserei-Forschung, 43(3) (1991) 101-6. 12. Wunderlich, W., Kremser, T. & Frommeyer, G., Z. Metallkde, 81 (1990) 802-8.