A model for thermal fatigue in an aluminium casting alloy

Int. J. Fatigue Vol. 17, No. 6, pp. 399-406, 1995 Copyright © 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0142-1123/95/$10.00

I"~UTTERWO RT H lillE I N E M A N N

0142-1123(95)00009-7

A model for thermal fatigue in an aluminium casting alloy E. Velasco, R. Col~s, S. Valtierra* and J.F. Mojica* Facultad de Ingenier(a Mec~nica y Eldctrica, Universidad Aut6noma de Nuevo Le6n, AP 149-F, 66452 San Nicolas de los Garza, N.L. M6xico *Nemak, SA de CV, AP A-100, 64000 Monterrey, N.L. M~xico (Received October 1994; accepted February 1995) A model for simulating the constrained thermal fatigue of an aluminium casting alloy is presented in this work. The specimen being tested has its ends fixed to a given length while its centre is subjected to thermal cycling. The thermal gradients developed within the test are calculated by an explicit finite difference technique, and with them, the strain and stress gradients are calculated. The agreement between the predicted and measured values of stress is good enough to consider that the model reflects the behaviour of the material. It is found that the predicted life of the specimen is higher than that experimentally observed, an effect that might be due to overageing of the material as the specimen is being tested. (Keywords: thermal fatigue; modelling; casting; aluminium alloy 356; computer simulation)

The successful development and use of structrual parts made from aluminium castings requires the combination of properties such as high strength and ductility through the whole piece, regardless of changes in thickness, cross-sectional area or geometry of the piece. The microstructural characteristics required to attain these properties in aluminium castings have been determined through years of experience, research and development 1-3, in such a way that it is common knowledge that the performance required in a material depends on its microstructure. Some aluminium casting alloys, such as the ones belonging to the 300 series, can be heat-treated to obtain the required combination of high strength and ductility. These alloys are subjected to solution treatments at temperatures around 550 °C, in order to dissolve magnesium in the aluminium matrix, and upon quenching and subsequent ageing at temperatures between 150 and 200 °C Mg2Si precipitates to produce a fine dispersion of particles, which results in substantial strengthening and hardening 1-6. Although the toughness of an alloy can be altered by the time and temperature employed for ageing, this property is enhanced by modification of the silicon-rich phase of the eutectic; addition of Sr or Na to the alloy prior to pouring changes the morphology of the eutectic from a coarse dispersion to a fine, fibrous aspect 1-3,6. The alloys employed in the manufacture of automotive engines should also exhibit superior thermal fatigue resistance and elevated temperature strength, as certain elements in the engine, such as the valve

bridge in the cylinder head, are rigidly constrained in such a way that the expansions and contractions arising from thermal cycling result in the development of large thermal stresses, whose magnitude depends on the physical properties of the alloy and on the temperature range of the cycle. Catastrophic failure of the piece may occur after a small number of cycles owing to the high strain values that are involved7-1°. Thermal fatigue resistance of metals and alloys can be studied with the aid of devices such as the one shown in Figure 1. This particular apparatus was originally designed to evaluate thermal fatigue resistance of cast irons, and it is nowadays employed for the same purpose in aluminium alloysllA2. As the total length of the specimen is fixed, the test measures the influence of constrained (axial) expansion and contraction during thermal cycling. As temperature increases, the material may undergo yielding, which will result in the development of tensile stresses during cooling, as a shortened specimen will be strained. The aim of this work is to present a model developed to simulate the thermal fatigue to which an aluminium casting alloy is subjected as it is tested in a device such as the one shown in Figure 1. MODELLING The simulation was carried out for a 356 aluminium casting alloy (6.36 Si, 0.37 Mg, 0.07 Fe, 0.04 Mn wt%) subjected to the thermal cycling produced by induction heating of the central portion of a 91.4 mm

399

400

E. Velasco et al Data related to the mechanical properties of the alloy as a function of temperature (Figure 3) were obtained from different sources 2,3A1. The values of stress were normalized to a dimensionless parameter, X: X_

o'-

OrO

(])

where tr and tro are respectively the individual and the high-temperature values of stress, and Atr is the total stress range. Values of tro and Atr for both yield and tensile strength are reported in Table 1. The temperature dependence of both stresses is then adjusted to equations of the type tr = fro -

A41

- exp(cT")]

(2)

where a and c are the best-fit coefficients, which are given in Table 1 for both yield and tensile strength. It is reasonable to assume that the deformational behaviour of the alloy at any temperature can be described by equations of the type

Figure 1 Diagram of the device employed for fatigue testing

(3)

= k @

where E is the strain and n and k are temperaturedependent coefficients. The strain at the yield point is calculated with the aid of the temperature-dependent modulus of elasticity, E: 2"3

long specimen; during the test, both ends are water cooled, in order to avoid damaging the load cell and other sensing devices. A typical cycle consists in heating from 66 °C to 288 °C in 180 s, holding for 120 s, and cooling down to the original temperature (66°C) in 150 s, where it will remain for 60 s before starting a new cycle 11 (Figure 2). Heat conduction within the testpiece is calculated with a finite difference explicit model that divides half the length of the specimen into small nodes, as it is assumed that the heat flowing to the specimen ends is symmetrical and, therefore, it is only necessary to compute conduction from the centre to one end. The thermal gradient determined is then employed to calculate the deformational behaviour at each node or element, and to analyse the effect of the thermal fatigue in the piece.

350

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E=7.36×104-46T

(4)

where the modulus is expressed in MPa and the temperature in °C, and given that the strain at which the tensile strength is achieved is 85% of the total one, n and k can be calculated from data available in the literature 2,3,i°. Figure 4 shows the temperature dependence of both coefficients as they were calculated with the above-mentioned assumptions. Once the temperature dependence of the different parameters is known, it is possible to construct stress-strain curves for different temperatures (Figure 5). The strain at any node or element due to the change

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Table 1 Parameters of Equation (2) Yield stress

Tensile strength

% (MPa)

315

420

Aa (MPa) c a

295 -3.56 2.38

395 -1.94 2.48

× 10 6

change in temperature; once the strain and temperature at each node are known, the stress can be calculated with the aid of Equation (3) if yielding has been achieved, or with the modulus of elasticity if not. It is worth noticing that, as the total length of the specimen is fixed, compressive stresses will be developed in heating and tensile stresses while cooling l°,u. Stress relaxation takes place during the holding period that follows the heating (Figure 2). Such an effect is incorporated within the model assuming that the time-dependent stress decay follows the relationship

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where t is the time and p and n are temperature dependent. Such a behaviour for specimens relaxed at two different temperatures is shown in Figure 6, where the dotted lines are the best-fit adjustment (see Table 2), whereas the points correspond to experimental data 11. It is possible to interpolate the relaxation coefficients in order to compensate for intermediate temperatures, as shown in Figure 7, which was constructed assuming a lineal dependence of p and r/ with the inverse of the absolute temperature; although the interpolation might lack a physical basis, it can be considered to be valid for the present purpose of modelling.

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in temperature, during either heating or cooling, can be calculated by • = ln(1 + aAT)

(6)

(5)

where a is the lineal expansion coefficient and AT the

whole specimen during the first fatigue cycle. The thermal gradients are calculated by the assumption that the centre of the specimen is heated and cooled at the rates shown in Figure 2, whereas the ends of the specimen are cooled by water. For the sake of clarity, the centre of the specimen is considered to be a zero distance in Figure 8.

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as its temperature changes. The centre of the specimen is reversed in this graph with respect to the previous one for the sake of clarity. No changes in strain were assumed to occur during the holding period at the higher temperature, as the relaxation can be considered to be equivalent to creep at constant strain 9,13, and therefore only the stress changes. The stresses to which each node was subjected to during the first cycle are shown in Figure 10; it was assumed that the strain and temperature dependences of the stress are given by Equations (1)-(6). The centre of the specimen is considered to be in the same position as in Figure 8. As the values of stress shown in Figure 10 are the local ones, the average ones were employed when comparing the predictions of the model with the measurements conducted during testing 11. Figure 11 shows the first three cycles of stress, as were measured during a test 11, together with the predictions produced by the present model for the first cycle, whereas the correlation between both sets of data is shown in Figure 12.

(s)

DISCUSSION Figure 6

Table 2

Stress relaxation at two different temperatures

Parameters of Equation (6)

Temperature °C r/ p

232 309.0 -0.135

288 293.8 -0.247

Figure 9 shows the strain gradients produced during the thermal cycling; the calculations were made with the aid of Equation (5), assuming that the strain is due only to the expansion or contraction of each node

Although the models developed for calculating the deformation and relaxation of the aluminium alloy are quite simple, and might lack a physical basis, the agreement obtained between measurements and predictions, shown in Figures 11 and 12, is indicative of their validity in the simulation of thermal fatigue. Thermal fatigue is associated with the failure of the component or piece after a low number of cycles have been accomplished, and it is related to the amount of plastic deformation involved in the test:

AepN b = C

(7)

where Aep is the total plastic range, N is the number of cycles to failure, C is a material constant and b is

403

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Thermal gradients during the first cycle of fatigue

a material-independent constant that ranges from 0.5 to 0.7. 9'14'15 The total deformation to which the specimen is subjected during the cycling can be obtained from Figure 9, where it can be seen that the maximum compressive strain, which is achieved at the centre of the sample, is around -0.005, which is higher in magnitude than the maximum tensile one, which is around 0.003 and is also achieved at the same position.

The constant C in Equation (7) can be evaluated by considering that the upper limit of the fatigue test is failure in a tension test, where A% ~ ~ and N = 0.25. Figure 13 shows the number of cycles to failure as b ranges from 0.5 to 0.7; data from the literature 2,3 establish that ~f at the higher temperature for the aluminium alloy is between 0.4 and 0.5. If the total strain value is taken to be 0.008, the expected number of cycles to failure should vary between 625 and 975

404

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and from 67 to 92 (depending on whether b takes the value of 0.5 or 0.7), whereas the experimental values range from 536 to 644 cycles to failure 11. An interesting point to notice in Figure 5 is that the curve corresponding to the higher temperature is readily adjusted to the parameters shown in Table 2, but the one for the lower temperature is not. An attempt was made in order to adjust this particular

curve to two portions, yielding the results shown in Figure 14, where a better fit is accomplished when total relaxation is divided into two different regions, the first one corresponding to times shorter than 700 s and the second one to longer times. This behaviour can be explained by considering the heat treatment to which the specimens used in the relaxation and thermal cycling were subjected to, which is artificial ageing to

A mode/for thermal fatigue in an aluminium casting alloy

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peak hardness (T6), which produces a fine dispersion of Mg2Si particles. It is possible that during relaxation some of the particles will grow at the expense of the smaller ones, resulting in the overageing of the specimen, and the consequent reduction of strength of the specimen. It should be mentioned that the curve adjusted to the short-time data was obtained from the analysis 16 of a relaxation test carried out on a stabilized aluminium cast alloy 12, in which no overageing is expected to occur. Strain localization on a peak-hardened heat-treatable aluminium alloy can readily occur during fatigue testing, with the negative consequences of reducing the ductility of the alloy 17-m, a feature that might explain the reduction of cycles of

406

E. Velasco et al

fatigue observed 11, in comparison with those predicted from tensile tests. CONCLUSIONS The fatigue testing of an aluminium casting alloy is simulated by modelling the deformational and relaxation behaviours of the alloy; the models were deduced using data available in the open literature. The good agreement between predicted and measured values of stress certifies the validity of the models employed in the simulation. The fatigue life of the specimen is overestimated when results from tensile tests are employed in conjunction with the strain range predicted by the model, but this lack of agreement can be explained when the reduction in ductility, due to the occurrence of strain localization in a microstructure containing a fine dispersion of particles, is taken into account.

10

11 12

ACKNOWLEDGEMENTS The authors would like to thank the support and facilities provided by CONACYT and Nemak, S.A. de C.V.

13 14 15

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REFERENCES 1 2 3

Mondolfo, L. 'Aluminium Alloys: Structure and Properties', Butterworth, London, 1986 Hatch, J.E. 'Aluminum: Properties and Physical Metallurgy', ASM, Metals Park, 1984 'ASM Handbook, Vol. 2: Properties and Selection: Non-

17 18 19

Ferrous Alloys and Special-Purpose Materials', ASM International, Materials Park, 1990 Campbell, J. 'Castings', Butterworth-Heinemann, London, 1991 'ASM Handbook, Vol. 4: Heat Treating', ASM International, Materials Park, 1991 Altenpohl D. 'Aluminum Viewed from Within', AluminiumVerlag, Diisseldorf, 1982 Swanson, S.R. 'Handbook of Fatigue Testing', ASTM STP 566, American Society for Testing and Materials, Philadelphia, 1974 Krempl, E. and Wundt, B.M. 'Hold-Time Effects in HighTemperature, Low Cycle Fatigue', ASTM STP 489, American Society for Testing and Materials, Philadelphia, 1971 Spera, D.A. In 'Thermal Fatigue of Materials and Components', (Eds D.A. Spera and D.F. Mowbray), ASTM STP 612, American Society for Testing and Materials, Philadelphia, 1976, p. 3 Hopkins, S.W. In 'Thermal Fatigue of Materials and Components', (Eds D.A. Spera and D.F. Mowbray), ASTM STP 612, American Society for Testing and Materials, Philadelphia, 1976, p. 157 Hetke A., Gundlach, R.B. and Rossetto, M.A. 'Aluminum Casting Quality in Alloy 356 Engine Components', Intermet Corporation & Climax Research Services, 1993 Gundlach, R.B. 'Thermal Fatigue Resistance of Aluminum Alloy 319', Climax Research Services, 1993 Feltham, P. J. lnst Met. 1960-61, 89, 210 Coffin, L.F. Met. Eng. Q. 1963, 3, 15 Coffin, L.R. In 'Thermal Fatigue of Materials and Components', (Eds D.A. Spera and D.F. Mowbray), ASTM STP 612, American Society for Testing and Materials, Philadelphia, 1976, 227 Velasco, E. PhD Research, Universidad Aut6noma de Nuevo Le6n, 1994 Starke, E.A. and Liitjering G. In 'Fatigue and Microstructure', (Ed. M. Meshii), ASM, Metals Park, 1979, p. 205 Wells, C.H. In 'Fatigue and Microstructure', (Ed. M. Meshii), ASM, Metals Park, 1979, p. 307 Colfis, R. and Grinberg A. Mater. Sci. Eng. 1993, A161, 201