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Thermomechanical fatigue and aging of cast aluminum alloy : A link between numerical modeling and microstructural approach
Temperature-Fatigue Interaction L. Remy and J. Petit (Eds.) © 2002 Elsevier Science Ltd. and ESIS. All rights reserved
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THERMOMECHANICAL FATIGUE AND AGING OF CAST ALUMINUM ALLOY : A LINK BETWEEN NUMERICAL MODELING AND MICROSTRUCTURAL APPROACH I. Guillot*, B. Barlas**, G. Cailletaud**, M. Clavel*, D. Massinon*** * Universite de Technologie de Compiegne, Laboratoire Roberval, UMR CNRS 6066, HP 20529 - 60205 Compiegne cedex France ^ Centre des Materiaux de TEcole Nationale Superieure des Mines de Paris, UMR CNRS 7633 BP 87 - 91003 Evry France *** Fonderie Montupet, 67 rue J. de la Fontaine, 60181 Nogent-sur-Oise France
ABSTRACT The present paper is devoted to the modeling of the stress-strain behaviour of a cast aluminum alloy for cylinder heads (AISI 319), which is studied from the initial state T5 to saturated aging (320°C). The evolution of the microstructure during heating corresponds to the sequence : 6' -^ 0 (AI2CU). The effect of transformations and coarsening can be characterized either by mechanical testing or by hardness measurements and by coarsening model using TEM image analysis. The observed coarsening of spherical 6 precipitates is in good agreement with the Lifshitz-Slyozov-Wagner (LSW) theory. The use of these data in precipitation hardening theories provides a "microstructural" evaluation of the strength evolution. A mechanical model is written in a viscoplasticframework,since viscous effects play an important role in this temperature range. Constitutive equations include the description of Bauschinger effect and of aging, through a scalar internal variable a. A careful comparison is made between the two approaches, allowing us to present a physically supported mechanical behaviour, which can be extrapolated to other metalluigical compositions.
KEYWORDS Aluminum alloy, viscoplastic modeling, aging effect, transmission electron microscopy (TEM), image analysis, particle coarsening.
INTRODUCTION Over the past decade, the automotive industry has increasingly employed cast aluminum alloys as a replacement for cast iron in the production of engine components. Improvements in engine performance have caused the temperatures in aluminum cylinder heads to increase, especially in the inter valve zone, from below 170°C in earlier engines to peak temperatures above 300°C in recent engines [1]. The 319 aluminum family is commonly used in casting cylinder heads, due to
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its low density, good thermal conductivity and good casting properties. This class of material exhibits mechanical properties that depend strongly on microstructural features such as secondary dendritic arm spacing (SDAS), porosity, intermetallic compounds, hardening precipitates [2,3,4] . . . The effects of porosity [5,6,7], intermetallics [8,9,10,11], grain refinement [12,13], silicon concentration [14,15] are well established and the performance of these alloys has also been improved by modeling casting processes and the thermal treatments [12,16]. Previous studies have been performed on the same subject by some of the present authors [17,18] or other groups [3,1]. The purpose of these works was to obtain a mechanical model to define viscoplastic behavior in presence of a microstructural evolution. Well-selected mechanical experiments, which expose the material behavior under various loading and temperature histories, are an essential requirement to identify the coefficients of these models, which are purely phenomenological, so that a new experimental data base must be built if a new chemical composition is considered. On the other hand, the use of structural hardening models, including the effect of precipitate size distribution is still rare for the aluminum casting alloys. One of the reasons is that a good knowledge of the precipitate coarsening law during aging is needed in order to build a physically supported model of the mechanical behavior. The purpose of the present paper, which wants to bridge the gap between mechanics and metallurgical models, is therefore to gather careful mechanical testing and microstructural observations.
IVIATERIALS AND EXPEMIMDENTAL PROCEDURE The material of the study is a cast aluminum 319 alloy with a T5 heat treatment (24 hours at room temperature and 5 hours at 210°C). Its chemical composition is shown in table 1. All specimens used for microstructural characterization and mechanical testing were cast in a metallic die and provided by Montupet S.A. as 20 mm diameter rods. The T5 specimens were then aged at 100, 200, 250, 280 and 320°C, under various aging time up to 1000 hours and air-cooled in order to obtain the corresponding hardness values. The samples for TEM observations and mechanical testing were 100 h heat-treated at various temperatures. Element Wt (pet)
Si Cu Mg Fe 8.2 3.3 0.3 0.47
Mn
Zn
0.24
0.24
Ti Ca 0.2 0.0005
Sr 0.010
Table 1: Material composition in weight percent.
The samples used for TEM observations were cut with a low-speed cutting saw, mechanically rounded and thinned down to 3 mm and 120 /im respectively. The thin disks were electropolished in a double-jet Tenupol using a 33% nitric acid in methanol solution maintained at -30°C and 12 V. Thin foils were observed using a TEM operated at 100 kV. The particle dimensions were measured in two ways. In the case of the 0' precipitates, the length and thickness were measured from dark-field TEM micrographs of the particles viewed edge-on in the [001]AI zone axis. The measurements were made on 3.5-time magnification blow-ups of the negatives. The measured lengths of the 9' precipitates are the projected lengths in the (001 )^j directions. In fact, the precipitate plates have a somewhat irregular shape and the measured length, close to the plate diameter, (d = L), corresponds to the big axis of the ellipse with the same surface of the circled precipitate. Therefore, the thickness is equal to the small ellipse diameter. The non-coherent 0 precipitates exhibit quite a globular morphology and can be con-
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
11
sidered as spheres. The radii, (f = 5/2), were measured from bright-field TEM micrographs of the particles performed on zero tilt. The measurements were made on 2.5-time magnification blow-ups of the negatives. The geometrical parameters of the precipitates, 9' or 6, are obtained with populations of about 1000 particles. All data are obtained from a two-dimensional projection of three-dimensional volume elements in a thin foil of finite thickness, z. The conversion of the particle size distributions from planar to volumetric distributions was performed according to Shah and Altstetter analysis [19] with the Schwartz-Saltykov method [20, 21]. Vickers macrohardness was carried out with a 10 kg weight at room temperature. Each data point represents an average of five measurements. The scatter is approximately 2 Hv. Vickers microhardness measurements were performed on the a-phase with a 3 g weight. Each data point represents an average value of twenty measurements. The low cycle fatigue experiments were conducted until failure under strain control on a servohydraulic machine using cylindrical specimens, the strain being adjusted at each cycle to keep the plastic strain amplitude constant. The axial strain was determined using an extensometer located on the gauge length. Thermomecanical fatigue tests are also performed by adapting a setup previously developed at ONERA [22]. This experiment is described in detail elsewhere [23].
IWaCROSTRUCTURAL OBSERVATIONS The microstructure of the as-received materials consists of a dendritic aluminum structure containing Cu and an aluminum-silicon eutectic with intermetallic compounds between dendritic arms (fig. 1). The cooling rate control during solidification gives a SDAS (fig. la) around 20 //m and a grain size around 0.4 mm. Figure lb depicts silicon particles and intermetallic compounds. The amount and morphology of silicon particles were determined using image analysis. The value of the elongation factor, corresponding to the ratio of the maximum/minimum segments of the silicon particles, is close to 2. Therefore silicon eutectic can be described as pseudo-globular particles resulting from the eutectic structure modification related to Sr additions.
^^^•:li!-:SIBiiiiiiiiif| 1 M.i%^Liin^Bw^^0 50 ^m
1
^-^-^-^.-T, ^Sll'V.^-.l^.Sy
Figure 1: (a) SEM micrograph showing 319-T5 with SDAS = 20 fim. (b) Microstructure of the as-received 319-T5 alloy.
Figure 2a shows a dark-field TEM image of the precipitates (T5) viewed edge-on in the [001] AI
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78
zone axis. From the analysis of diffraction patterns, it was found that the disc shaped precipitates were all B'. As shown in figure 2, the evolution of the precipitate features in the annealed specimens corresponds to the sequence : d' —> 9 (AI2CU). Below 200°C, the only microstructural change is the coarsening of the 0' phase, which is well known for the Al-4wt% Cu binary alloy [24, 25, 26, 27, 28]. The subsequent growth of non-coherent 0 precipitates takes place for higher temperatures. As previously indicated, the particle dimensions were determined using image analysis. These results are summarized in table 2. Following the Lifshitz-SlyozovWagner [29, 30] theory (LSW theory), the volume fraction of particles is expected to remain constant during coarsening under steady-state condition. The mean value obtained is close to 3.8%, in agreement with the results due to Cerri et al. [31]. Aging conditions
Precipitates
d = L (nm)
5 = 2r (nm)
T5
e' e' e' e e
18.2 ± 3
-
20.8 ± 3.5
-
30.9 ± 4.5
-
-
39.4 ± 5.5
-
107.0 ± 8
T5 + 100hatlOOX T5 4-100hat200°C T5 + 100 h at 250°C T5 + 100 h at 320°C
Table 2: Mean volumetric precipitate diameters from TEM image analysis.
IVIECHANICAL BEHAVIOR The precipitate coarsening effect can be characterized either by mechanical testing (fig. 3) or by means of hardness measurements (fig. 4). Figure 3 describes the cyclic behavior at room temperature of the alloy after several aging conditions in plastic strain controlled tests at Ae^/2 = 0.3%. The evolution of the peak stress amplitude, A(T/2, (the average of the tensile and the compressive peak stresses) versus cumulated plastic strain clearly shows the effect of aging on mechanical properties. The total amount of softening represents about 100% of the initial stress (T5) for specimen aged at 320° C. Figure 4 illustrates the evolution of hardening versus time. Macrohardness measurements (fig. 4a) were found to be correlated with yield stress values, and give a good view of the transformation rate. The measurements confirm that the maximum softening occurs for aging at 320°C. A two-level test at 200°C then 320°C demonstrates that the asymptotic value obtained during the preheating at 200°C is forgotten at the second level, and that the asymptotic value at 320°C is reached. Other tests [18] show that, in a complex temperature history, the final asymptotic value depends first on the maximum temperature. Microhardness measurements (fig. 4b) show that the softening is supported by the a-phase due to the coarsening of the AI2CU precipitates.
PRESENTATION OF THE IVIACROSCOPIC MODEL The model is fiilly described in a companion paper in this conference [33]. Since the purpose of this work is to show that the microstructural evolution of the alloy determines its mechanical response, a short summary is given here.
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
79
Figure 2: Growth of AI2CU precipitates during 100 h agingfromthe T5 Treatment (a) T5 (b) T5 + 100hatlOO°C(c)T5 + 100hatl75°C(d)T5 + 100hat200°C(e)T5 + 100hat250°C(f)T5 + 100 h at 320°C. (a-d) darkfieldTEM micrographs, g = [002]^/, (e,f) brightfieldTEM image performed on zero tilt. 240 220
A A D
D
200 180
+ Acr/2 160 (MPa) 140
1
+ + 0
0
+ + + + -H-M III I I I ++-1- ++-H-I-+-H. 0 0 0 0
120 -0 100
0000000000 0 0 0 0 0 ^ T5 + 320C * lOOh T5 + 250C * lOOh T5 + 200c * lOOh T5 + 1750 * lOOh T5
O + D X A
-
0.1
Figure 3: Effect of aging on mechanical properties : stress amplitude at room temperature after several aging conditions versus cumulated plastic strain rate.
The model is an extension of a classical unified viscoplastic model for cyclic loadings [34],
80
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(a)
temps (h)
Figure 4: Aging at different temperatures (a) Macrovickers hardness evolution of the alloy (10 kg) (b) Microvickers hardness evolution of the cv-phase (3 g). with additional terms to take into account the aging of the alloy. Indeed, the physical properties of this material are very sensitive to the thermomechanical loading history. The kinematic variable is the tensor X and the isotropic variable is the scalar R. The yield criterion is defined with a von Mises function: f= with
J(A) = ((3/2)A^ : A'')''''
J{cr-X)~R-k and A'' deviatoric part of
A
(1) (2)
The normality rule is applied to compute viscoplastic strain rate as a power function of / as :
p=uy -d f=pg
(3)
where p is the cumulated plastic strain rate, g^ the plastic strain rate and (x) the positive part of X. The aging part is represented by a scalar mtemal variable a, starting from zero, and tending to an asymptotic value Ocx? (when the maximum aging state is reached, Ooo = 1), depending on temperature and describing the precipitate growth. Its evolution is exponential, with a temperature dependent time constant r :
(4)
The model can thus describe softening related to overheating. It has been identified on isothermal LCF tests and validated on anisothermal TMF tests using an original device given elsewhere [18]. For monotonic onedimensional loadings, explicit expressions are available for A", /?, the elastic part k and the viscous part a„ :
R = Q(l- e-'^') A; = flo + iiS(l - a)
(5) (6) (7) (8)
Finally, in a tension test: a(e'',i'',a,T) = X+R+k+a^ , where each parameter is a function of temperature except Di and Dj which are chosen to be constant. These parameters are identified
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
81
with experimental data and define the material file to be implemented in the code. The model has been implemented in the general finite element code ZeBuLon [35], having the numerical simulation of automotive cylinder head in view.
DISCUSSION Following [36], it is now interesting to compare the macroscopic stress model developed above with the stress resultingfi-ommicroscopic investigations. Indeed, both models are supposed to be linked by a classical relation between the apparent yield strength variation and the microscopic strength variation due to precipitate coarsening. Macroscopic level The stress amplitude can be obtained analytically [34] for a model using isotropic and nonlinear hardening variables. Since aging only affects the isotropic part and the second kinematic hardening, its variation will be simply : A
+ g t h ( D 2 ^ ) ) (1 - a)
(9)
Microscopic level Particles are big enough to be looped following the well-known Orowan looping mechanism. For impenetrable hard particles, the Orowan expression is given by : 2r
2p^ih
with r = j^/x6^, the tension line where ^ is a parameter close to 0.5, /x the alloy shear modulus at room temperature and b the Burgers vector lenght (2.86.10"^° m). The previous expression as to be corrected by a-phase volumefi-actioncontaining the precipitates (/« = 73%) as follows : Wlib rOro=-^fa
(11)
According to [36], the interparticle spacing is assumed to be :
-m
1/2
(12)
where f is the mean radius of the precipitates (cf tab 2) and fe the volumefi-actionof particles in the a-matrix (3.8%). Since the macroscopic model reference state corresponds to the alloy at maximum aging (100 hours at 320°Cand a - 1), the variation AT to be considered for the microscopic model is: ^'TOro = T{T) - 7'(320'>C)
(13)
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Comparison A transition rule must be introduced to go from the granular scale in the microscopic models to the macroscopic scale. Two crude assumptions may be first considered for that purpose. The static model assumes that all the grains have the same stress (no intergranular residual stresses), and provides a lower bound of the solution. On the other hand, Taylor's model [37] assumes that each grain will present the same plastic strain. The result of both models can be written as : Aa„
=
MATOTO
(14)
In texture-free FCC material, the static model gives M = 2.24, and Taylor's model predicts a value of 3.07. Self-consistent approaches provide more precise descriptions, which are valid for disordered microstructures, with varying values of M. The result of this study is given infigure5. Each value is presented with its error bar, keeping in mind that the larger error comes from the measurement of r in equation (12). The point (0,0) obtained for maximum aging has to belong to the lines. The value of M is found to be close to 2.5, which means that the present model is intermediate but tend to a static model. This value could change with plastic strain range.
A(7„iocro 80 (MPa) 60
20
30
40 50 Aroro (MPa)
Figure 5: Comparison between macroscopic and microscopic models.
CONCLUSION The behaviour of a cast aluminum alloy for cylinder head (AISI 319) has been investigated between its initial state T5 and saturated aging (320°C). Variations of physical properties due to microstructure evolution during heating have been exhibited, using micro and macro hardness measurements, TEM image analysis and mechanical testing. It has been found that the coarsening of precipitates follows the Lifshitz-Slyozov-Wagner theory. A numerical macroscopic model, written in a viscoplasticframeworkand taking into account the description of aging and Bauschinger effect, has been developed. In this model, aging is represented by a scalar internal variable a depending on temperature and time. A comparison can be made between the macroscopic mechanical model and the microscopic approach (Orowan theory). There is a good agreement between the two classes of theories, since the value of the apparent factor between the shear variation in the microscopic models and the variation of the macroscopic yield limit is close to 2.5.
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
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References [1] SMITH T.J., MAIER H.J., SEHITOGLU H., FLEURY E., ALLISON J. MetalL Mater. Trans.,
30A(1): 133-146,1999. [2] CATON M.J., JONES J.W., BOILEAU J.M., ALLISON J.E. Metall. Mater Trans.,
30A(12):3055-3068,1999. [3] SEHITOGLU H., QING X., SMITH T., MAIER H.J., ALLISON J.A. Metall. Mater Trans.,
31A(1):139-151,2000. [4] STOLARZ J., MADELAINE-DUPUICH O., MAGNIN T. Mater Sci. Eng, A299:275-286,
2001. [5] CACERES C.H., DJURDJEVIC M.B., STOCKWELL T.J., SOKOLOWSKI J.H. Scripta met-
all. mater, 40(5):63l-631,1999. [6] ROY N . , SAMUEL A.M., SAMUEL F.H. Metall. Mater Trans., 21 A{2):415^29,1996. [7] SAMUEL A.M., SAMUEL F.H. Metall. Mater Trans., 26A(9):2359-2372, 1995. [8] CACERES C.H., DAVIDSON C.J., GRIFFITHS J.R., WANG Q.G. Metall. Mater Trans.,
30A(10):2611-2618,1995. [9] GUSTAFSSON G., THORVALDSSON T., DUNLOP G . L . Metall. Trans., 17A(l):45-52,
1986. [10] HiROSAWA S., SATO T., KAMIO A., FLOWER H . M . Acta mater, 48:1797-1806,2000. [11] SAMUEL A.M., GAUTHIER J., SAMUEL F.H. Metall. Trans., 21A:\1S5-\19^, 1996. [12] GREER A.L., BUNN A.M., TRONCHE A., EVANS R V . , BRISTOW D.J.
Acta mater,
47(17):4253-4262,1999. [13] MOHANTY R S . , GRUSZLESKI J.E. Acta mater, 44(9)3149-3160, 1996. [14] PLAZA D . , ASENSIO J., PERO-SANZ J.A., VERDEJA J.I. Materials Characterization,
40:145-158,1998. [15] VELDMAN N.L.M., DAHLE A . K , ST. JOHN D.H., ARNBERG L. Metall. Mater Trans.,
32A(1):147-155,2001. [16] NASTAC L. Acta mater, 41ill):4253-^262,1999. [17] CAILLETAUD G . , DEPOID C , MASSINON D . , NICOULEAU-BOURLES E . In MAUGIN
et al, editor. Continuum thermodynamics : the art and science of modeling material behaviour. Kluwer, 2000. [18] NICOULEAU-BOURLES E. These de doctorat de TEcole Nationale Superieure de Mines de Paris, 1999. [19] SHAH D., ALTSTETTER C. Mater Sci. Eng, 26:175-183, 1976.
[20] DE HOFF R.T., RHINES F.N. Microscopic quantitative. Masson, Paris, 1972.
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[21] UNDERWOOD E.E. Quantitative stereology. Addison-Wesley Publishing Co., Reading, MA, 1970. [22] CAILLETAUD G., CULIE J.R, KACZMAREK H. La Recherche Aerospatiale, 2:85-97,
1981. [23] NicouLEAU-BouRLES E., EL-MAYAS N . , MASSINON D . , CAILLETAUD G.
In
SKRYPEK J.J., HETNARSKI R.B., editor, Thermal stress '99, pages 241-244, Cracow, June 2000. [24] AARONSON H.I., CLARK J.B., LAIRD C. Met. Sc. y., 2:155-158,1968.
[25] BOYD J.D., NICHOLSON R.B. ActaMetalL, 19(10):1101-1109,1971. [26] MERLE R , FOUQUET R ActaMetalL, 29:\9\9-\921,
1981.
[27] MERLE R, FOUQUET R , MERLIN J., GOBIN RR Phys. Stat. Sol., 35:213-222,1976.
[28] SANKARAN R., LAIRD C. Acta mater, 22(8):957-969,1974. [29] LiFSCHITZ LM., SLYOZOV V.V. J. phys. Chem. Solids, 19(l/2):35-50,1961. [30] WAGNER C. Z Elektrochem., 65(7/8):581-591,1961. [31] CERRI E., EVANGELISTA E., RYUM N . Metall. Mater Trans., 27A(2):257-263,1997. [32] DICKSON J.L, BOUTIN J., HANDFIELD L. Mater Sci. Engng, 64:L7-L11,1984.
[33] NiCOULEAU-BoURLES E., FEYEL R , QUILICI S., CAILLETAUD G. In TemperatureFatigue interaction, Paris, 29-31 May 2001. ESIS-Elsevier. [34] LEMAITRE J., CHABOCHE J.L. Mecanique des materiaux solides. Dunod, Paris, 1988. [35] BESSON, J. AND LE RICHE, R. AND FOERCH, R. AND CAILLETAUD, G. Revue Eu-
ropeenne des Elements Finis, 7(5):567, 1998. [36] CULIE J.R, CAILLETAUD G., LASALMONIE A. La Recherche Aerospatiale, 2:109-119, 1982. [37] TAYLOR, G. I. J. Inst. Metals, 62:307, 1938.
75
THERMOMECHANICAL FATIGUE AND AGING OF CAST ALUMINUM ALLOY : A LINK BETWEEN NUMERICAL MODELING AND MICROSTRUCTURAL APPROACH I. Guillot*, B. Barlas**, G. Cailletaud**, M. Clavel*, D. Massinon*** * Universite de Technologie de Compiegne, Laboratoire Roberval, UMR CNRS 6066, HP 20529 - 60205 Compiegne cedex France ^ Centre des Materiaux de TEcole Nationale Superieure des Mines de Paris, UMR CNRS 7633 BP 87 - 91003 Evry France *** Fonderie Montupet, 67 rue J. de la Fontaine, 60181 Nogent-sur-Oise France
ABSTRACT The present paper is devoted to the modeling of the stress-strain behaviour of a cast aluminum alloy for cylinder heads (AISI 319), which is studied from the initial state T5 to saturated aging (320°C). The evolution of the microstructure during heating corresponds to the sequence : 6' -^ 0 (AI2CU). The effect of transformations and coarsening can be characterized either by mechanical testing or by hardness measurements and by coarsening model using TEM image analysis. The observed coarsening of spherical 6 precipitates is in good agreement with the Lifshitz-Slyozov-Wagner (LSW) theory. The use of these data in precipitation hardening theories provides a "microstructural" evaluation of the strength evolution. A mechanical model is written in a viscoplasticframework,since viscous effects play an important role in this temperature range. Constitutive equations include the description of Bauschinger effect and of aging, through a scalar internal variable a. A careful comparison is made between the two approaches, allowing us to present a physically supported mechanical behaviour, which can be extrapolated to other metalluigical compositions.
KEYWORDS Aluminum alloy, viscoplastic modeling, aging effect, transmission electron microscopy (TEM), image analysis, particle coarsening.
INTRODUCTION Over the past decade, the automotive industry has increasingly employed cast aluminum alloys as a replacement for cast iron in the production of engine components. Improvements in engine performance have caused the temperatures in aluminum cylinder heads to increase, especially in the inter valve zone, from below 170°C in earlier engines to peak temperatures above 300°C in recent engines [1]. The 319 aluminum family is commonly used in casting cylinder heads, due to
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its low density, good thermal conductivity and good casting properties. This class of material exhibits mechanical properties that depend strongly on microstructural features such as secondary dendritic arm spacing (SDAS), porosity, intermetallic compounds, hardening precipitates [2,3,4] . . . The effects of porosity [5,6,7], intermetallics [8,9,10,11], grain refinement [12,13], silicon concentration [14,15] are well established and the performance of these alloys has also been improved by modeling casting processes and the thermal treatments [12,16]. Previous studies have been performed on the same subject by some of the present authors [17,18] or other groups [3,1]. The purpose of these works was to obtain a mechanical model to define viscoplastic behavior in presence of a microstructural evolution. Well-selected mechanical experiments, which expose the material behavior under various loading and temperature histories, are an essential requirement to identify the coefficients of these models, which are purely phenomenological, so that a new experimental data base must be built if a new chemical composition is considered. On the other hand, the use of structural hardening models, including the effect of precipitate size distribution is still rare for the aluminum casting alloys. One of the reasons is that a good knowledge of the precipitate coarsening law during aging is needed in order to build a physically supported model of the mechanical behavior. The purpose of the present paper, which wants to bridge the gap between mechanics and metallurgical models, is therefore to gather careful mechanical testing and microstructural observations.
IVIATERIALS AND EXPEMIMDENTAL PROCEDURE The material of the study is a cast aluminum 319 alloy with a T5 heat treatment (24 hours at room temperature and 5 hours at 210°C). Its chemical composition is shown in table 1. All specimens used for microstructural characterization and mechanical testing were cast in a metallic die and provided by Montupet S.A. as 20 mm diameter rods. The T5 specimens were then aged at 100, 200, 250, 280 and 320°C, under various aging time up to 1000 hours and air-cooled in order to obtain the corresponding hardness values. The samples for TEM observations and mechanical testing were 100 h heat-treated at various temperatures. Element Wt (pet)
Si Cu Mg Fe 8.2 3.3 0.3 0.47
Mn
Zn
0.24
0.24
Ti Ca 0.2 0.0005
Sr 0.010
Table 1: Material composition in weight percent.
The samples used for TEM observations were cut with a low-speed cutting saw, mechanically rounded and thinned down to 3 mm and 120 /im respectively. The thin disks were electropolished in a double-jet Tenupol using a 33% nitric acid in methanol solution maintained at -30°C and 12 V. Thin foils were observed using a TEM operated at 100 kV. The particle dimensions were measured in two ways. In the case of the 0' precipitates, the length and thickness were measured from dark-field TEM micrographs of the particles viewed edge-on in the [001]AI zone axis. The measurements were made on 3.5-time magnification blow-ups of the negatives. The measured lengths of the 9' precipitates are the projected lengths in the (001 )^j directions. In fact, the precipitate plates have a somewhat irregular shape and the measured length, close to the plate diameter, (d = L), corresponds to the big axis of the ellipse with the same surface of the circled precipitate. Therefore, the thickness is equal to the small ellipse diameter. The non-coherent 0 precipitates exhibit quite a globular morphology and can be con-
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
11
sidered as spheres. The radii, (f = 5/2), were measured from bright-field TEM micrographs of the particles performed on zero tilt. The measurements were made on 2.5-time magnification blow-ups of the negatives. The geometrical parameters of the precipitates, 9' or 6, are obtained with populations of about 1000 particles. All data are obtained from a two-dimensional projection of three-dimensional volume elements in a thin foil of finite thickness, z. The conversion of the particle size distributions from planar to volumetric distributions was performed according to Shah and Altstetter analysis [19] with the Schwartz-Saltykov method [20, 21]. Vickers macrohardness was carried out with a 10 kg weight at room temperature. Each data point represents an average of five measurements. The scatter is approximately 2 Hv. Vickers microhardness measurements were performed on the a-phase with a 3 g weight. Each data point represents an average value of twenty measurements. The low cycle fatigue experiments were conducted until failure under strain control on a servohydraulic machine using cylindrical specimens, the strain being adjusted at each cycle to keep the plastic strain amplitude constant. The axial strain was determined using an extensometer located on the gauge length. Thermomecanical fatigue tests are also performed by adapting a setup previously developed at ONERA [22]. This experiment is described in detail elsewhere [23].
IWaCROSTRUCTURAL OBSERVATIONS The microstructure of the as-received materials consists of a dendritic aluminum structure containing Cu and an aluminum-silicon eutectic with intermetallic compounds between dendritic arms (fig. 1). The cooling rate control during solidification gives a SDAS (fig. la) around 20 //m and a grain size around 0.4 mm. Figure lb depicts silicon particles and intermetallic compounds. The amount and morphology of silicon particles were determined using image analysis. The value of the elongation factor, corresponding to the ratio of the maximum/minimum segments of the silicon particles, is close to 2. Therefore silicon eutectic can be described as pseudo-globular particles resulting from the eutectic structure modification related to Sr additions.
^^^•:li!-:SIBiiiiiiiiif| 1 M.i%^Liin^Bw^^0 50 ^m
1
^-^-^-^.-T, ^Sll'V.^-.l^.Sy
Figure 1: (a) SEM micrograph showing 319-T5 with SDAS = 20 fim. (b) Microstructure of the as-received 319-T5 alloy.
Figure 2a shows a dark-field TEM image of the precipitates (T5) viewed edge-on in the [001] AI
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78
zone axis. From the analysis of diffraction patterns, it was found that the disc shaped precipitates were all B'. As shown in figure 2, the evolution of the precipitate features in the annealed specimens corresponds to the sequence : d' —> 9 (AI2CU). Below 200°C, the only microstructural change is the coarsening of the 0' phase, which is well known for the Al-4wt% Cu binary alloy [24, 25, 26, 27, 28]. The subsequent growth of non-coherent 0 precipitates takes place for higher temperatures. As previously indicated, the particle dimensions were determined using image analysis. These results are summarized in table 2. Following the Lifshitz-SlyozovWagner [29, 30] theory (LSW theory), the volume fraction of particles is expected to remain constant during coarsening under steady-state condition. The mean value obtained is close to 3.8%, in agreement with the results due to Cerri et al. [31]. Aging conditions
Precipitates
d = L (nm)
5 = 2r (nm)
T5
e' e' e' e e
18.2 ± 3
-
20.8 ± 3.5
-
30.9 ± 4.5
-
-
39.4 ± 5.5
-
107.0 ± 8
T5 + 100hatlOOX T5 4-100hat200°C T5 + 100 h at 250°C T5 + 100 h at 320°C
Table 2: Mean volumetric precipitate diameters from TEM image analysis.
IVIECHANICAL BEHAVIOR The precipitate coarsening effect can be characterized either by mechanical testing (fig. 3) or by means of hardness measurements (fig. 4). Figure 3 describes the cyclic behavior at room temperature of the alloy after several aging conditions in plastic strain controlled tests at Ae^/2 = 0.3%. The evolution of the peak stress amplitude, A(T/2, (the average of the tensile and the compressive peak stresses) versus cumulated plastic strain clearly shows the effect of aging on mechanical properties. The total amount of softening represents about 100% of the initial stress (T5) for specimen aged at 320° C. Figure 4 illustrates the evolution of hardening versus time. Macrohardness measurements (fig. 4a) were found to be correlated with yield stress values, and give a good view of the transformation rate. The measurements confirm that the maximum softening occurs for aging at 320°C. A two-level test at 200°C then 320°C demonstrates that the asymptotic value obtained during the preheating at 200°C is forgotten at the second level, and that the asymptotic value at 320°C is reached. Other tests [18] show that, in a complex temperature history, the final asymptotic value depends first on the maximum temperature. Microhardness measurements (fig. 4b) show that the softening is supported by the a-phase due to the coarsening of the AI2CU precipitates.
PRESENTATION OF THE IVIACROSCOPIC MODEL The model is fiilly described in a companion paper in this conference [33]. Since the purpose of this work is to show that the microstructural evolution of the alloy determines its mechanical response, a short summary is given here.
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
79
Figure 2: Growth of AI2CU precipitates during 100 h agingfromthe T5 Treatment (a) T5 (b) T5 + 100hatlOO°C(c)T5 + 100hatl75°C(d)T5 + 100hat200°C(e)T5 + 100hat250°C(f)T5 + 100 h at 320°C. (a-d) darkfieldTEM micrographs, g = [002]^/, (e,f) brightfieldTEM image performed on zero tilt. 240 220
A A D
D
200 180
+ Acr/2 160 (MPa) 140
1
+ + 0
0
+ + + + -H-M III I I I ++-1- ++-H-I-+-H. 0 0 0 0
120 -0 100
0000000000 0 0 0 0 0 ^ T5 + 320C * lOOh T5 + 250C * lOOh T5 + 200c * lOOh T5 + 1750 * lOOh T5
O + D X A
-
0.1
Figure 3: Effect of aging on mechanical properties : stress amplitude at room temperature after several aging conditions versus cumulated plastic strain rate.
The model is an extension of a classical unified viscoplastic model for cyclic loadings [34],
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(a)
temps (h)
Figure 4: Aging at different temperatures (a) Macrovickers hardness evolution of the alloy (10 kg) (b) Microvickers hardness evolution of the cv-phase (3 g). with additional terms to take into account the aging of the alloy. Indeed, the physical properties of this material are very sensitive to the thermomechanical loading history. The kinematic variable is the tensor X and the isotropic variable is the scalar R. The yield criterion is defined with a von Mises function: f= with
J(A) = ((3/2)A^ : A'')''''
J{cr-X)~R-k and A'' deviatoric part of
A
(1) (2)
The normality rule is applied to compute viscoplastic strain rate as a power function of / as :
p=uy -d f=pg
(3)
where p is the cumulated plastic strain rate, g^ the plastic strain rate and (x) the positive part of X. The aging part is represented by a scalar mtemal variable a, starting from zero, and tending to an asymptotic value Ocx? (when the maximum aging state is reached, Ooo = 1), depending on temperature and describing the precipitate growth. Its evolution is exponential, with a temperature dependent time constant r :
(4)
The model can thus describe softening related to overheating. It has been identified on isothermal LCF tests and validated on anisothermal TMF tests using an original device given elsewhere [18]. For monotonic onedimensional loadings, explicit expressions are available for A", /?, the elastic part k and the viscous part a„ :
R = Q(l- e-'^') A; = flo + iiS(l - a)
(5) (6) (7) (8)
Finally, in a tension test: a(e'',i'',a,T) = X+R+k+a^ , where each parameter is a function of temperature except Di and Dj which are chosen to be constant. These parameters are identified
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
81
with experimental data and define the material file to be implemented in the code. The model has been implemented in the general finite element code ZeBuLon [35], having the numerical simulation of automotive cylinder head in view.
DISCUSSION Following [36], it is now interesting to compare the macroscopic stress model developed above with the stress resultingfi-ommicroscopic investigations. Indeed, both models are supposed to be linked by a classical relation between the apparent yield strength variation and the microscopic strength variation due to precipitate coarsening. Macroscopic level The stress amplitude can be obtained analytically [34] for a model using isotropic and nonlinear hardening variables. Since aging only affects the isotropic part and the second kinematic hardening, its variation will be simply : A
+ g t h ( D 2 ^ ) ) (1 - a)
(9)
Microscopic level Particles are big enough to be looped following the well-known Orowan looping mechanism. For impenetrable hard particles, the Orowan expression is given by : 2r
2p^ih
with r = j^/x6^, the tension line where ^ is a parameter close to 0.5, /x the alloy shear modulus at room temperature and b the Burgers vector lenght (2.86.10"^° m). The previous expression as to be corrected by a-phase volumefi-actioncontaining the precipitates (/« = 73%) as follows : Wlib rOro=-^fa
(11)
According to [36], the interparticle spacing is assumed to be :
-m
1/2
(12)
where f is the mean radius of the precipitates (cf tab 2) and fe the volumefi-actionof particles in the a-matrix (3.8%). Since the macroscopic model reference state corresponds to the alloy at maximum aging (100 hours at 320°Cand a - 1), the variation AT to be considered for the microscopic model is: ^'TOro = T{T) - 7'(320'>C)
(13)
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Comparison A transition rule must be introduced to go from the granular scale in the microscopic models to the macroscopic scale. Two crude assumptions may be first considered for that purpose. The static model assumes that all the grains have the same stress (no intergranular residual stresses), and provides a lower bound of the solution. On the other hand, Taylor's model [37] assumes that each grain will present the same plastic strain. The result of both models can be written as : Aa„
=
MATOTO
(14)
In texture-free FCC material, the static model gives M = 2.24, and Taylor's model predicts a value of 3.07. Self-consistent approaches provide more precise descriptions, which are valid for disordered microstructures, with varying values of M. The result of this study is given infigure5. Each value is presented with its error bar, keeping in mind that the larger error comes from the measurement of r in equation (12). The point (0,0) obtained for maximum aging has to belong to the lines. The value of M is found to be close to 2.5, which means that the present model is intermediate but tend to a static model. This value could change with plastic strain range.
A(7„iocro 80 (MPa) 60
20
30
40 50 Aroro (MPa)
Figure 5: Comparison between macroscopic and microscopic models.
CONCLUSION The behaviour of a cast aluminum alloy for cylinder head (AISI 319) has been investigated between its initial state T5 and saturated aging (320°C). Variations of physical properties due to microstructure evolution during heating have been exhibited, using micro and macro hardness measurements, TEM image analysis and mechanical testing. It has been found that the coarsening of precipitates follows the Lifshitz-Slyozov-Wagner theory. A numerical macroscopic model, written in a viscoplasticframeworkand taking into account the description of aging and Bauschinger effect, has been developed. In this model, aging is represented by a scalar internal variable a depending on temperature and time. A comparison can be made between the macroscopic mechanical model and the microscopic approach (Orowan theory). There is a good agreement between the two classes of theories, since the value of the apparent factor between the shear variation in the microscopic models and the variation of the macroscopic yield limit is close to 2.5.
Thermomechanical Fatigue and Aging of Cast Aluminum Alloy:
83
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