Coarsening of γ′ in Ni–Al alloys aged under uniaxial compression: I. Early-stage kinetics
Introduction
Coarsening under applied stress often produces what has come to be known as directional coarsening of the precipitate microstructure. In Ni-base alloys directional coarsening refers to the tendency of the γ′ precipitate phase (based on Ni3Al, L12 crystal structure) to form either plates or rods at very long aging times. In unstressed specimens, the spatial distribution of small γ′ particles is initially random, but strong elastic interactions among the precipitates introduce significant alignment, or anisotropy, in the microstructure at longer aging times [1]. In binary Ni–Al alloys, the anisotropy manifests itself in the formation of plates of γ′, the broad faces of which are randomly distributed among the three cube planes. In binary Ni–Ga alloys the anisotropy produces plates of γ′ (in this case Ni3Ga), similar to those in Ni–Al alloys, but also rods with axes parallel to the cube directions [2]. Aging under applied stress significantly biases the microstructure. In monocrystalline or directionally solidified alloys subjected to a uniaxial stress parallel to, say, [1 0 0] during aging, the γ′ microstructure takes the form of plates or rods which lie parallel to the stress direction or plates with the faces normal to the stress direction depending on the sign of the applied stress; these manifestations of directional coarsening are generally referred to as rafting [3]. The theoretically predicted preference for plates or rods in a rafted microstructure depends on the state of strain in the alloy. When the deformation is purely elastic, the preference depends on the sign of the applied stress, the difference between the lattice constants of the matrix (γ) phase and the γ′ phase (the lattice mismatch) and on the elastic constants C11 and C12 of the γ and γ′ phases via the parameter △C11–△C12, where △C11 and △C12 are the differences between C11 and C12, respectively, for the γ′ and γ phases [4], [5], [6].
The earliest observations of rafting were made on Ni-base superalloys subjected to considerable plastic deformation under creep conditions [7]. Since the initial observations of rafting, there have been many other experiments on the evolution of γ′ precipitate morphology in Ni-base alloys aged under applied stress; the results reported in Refs. [8], [9], [10], [11], [12], [13], [14], [15], [16], [17] are representative, though by no means exhaustive. The kinetics of rafting have also been investigated, albeit sparingly [18], [19], [20]. In all this work, the specimens were initially aged under stress-free conditions to produce large γ′ precipitates. The stress was then applied and evolution of the precipitate microstructure investigated. Moreover, the stresses were large enough to plastically deform the alloys; evolution of the γ′ precipitate microstructure under conditions of purely elastic deformation has not been previously investigated.
Only recently have there been serious attempts to evaluate the kinetics of directional coarsening under applied stress using computer simulation experiments. The 2D simulations of Laberge et al. [21], [22] reproduce many of the microstructural aspects of rafting observed experimentally, and predict that the average particle size increases as t1/3 long after the shapes become non-equiaxed and the spatical distributions become highly anisotropic. The kinetics of coarsening under applied stress in their simulations are in this sense similar to those predicted by the classic theories of Lifshitz and Slezov [23] and Wagner [24] (the LSW theory) for coarsening of precipitates under stress-free conditions. However, the most recent 3D simulation experiments of Sagui et al. [25], Orlikowski et al. [26] and Gupta et al. [27] suggest somewhat different kinetic behavior. The simulations of Orlikowski et al. [26] predict significant departures of the time exponent from n=1/3 when the dispersed phase is the majority phase and coalescence events dominate the growth process. When the dispersed phase is the minority phase, however, t1/3 kinetics are observed even though the shapes of the precipitates change with time. On the other hand, the simulations of Gupta et al. [27] indicate a deceleration of the rate of coarsening and a departure from t1/3 kinetics when the volume fraction is small. While the microstructural anisotropy evolves differently under tension and compression in the simulations of Gupta et al., the kinetics of particle growth under reversal of the applied stress are nearly indistinguishable. The results of Gupta et al. also show that t1/3 kinetics are observed at shorter Monte Carlo aging times, and depart from this behavior at around the same times that the microstructure begins to become anisotropic (i.e. when rafting becomes significant).
In this paper, we present the results of experiments on coarsening under applied stress, using experimental conditions which differ in three important ways from previous work: (1) all the specimens were initially in the solution treated condition prior to aging under stress; (2) the stresses were small enough and the temperatures low enough to ensure that deformation was elastic for all aging times; (3) the kinetics of coarsening of the γ′ precipitates were the primary focus of the work, rather than the kinetics of rafting. All the work was done on single crystal specimens stressed in compression, with the axis of the applied stress parallel to [1 0 0]. In a companion paper [28], we present data on the characterization of the shapes of the particles as functions of aging time and applied stress. In nearly all our work, we have examined the microstructures in the (1 0 0) plane, i.e. the plane normal to the axis of the applied stress. This choice might not appear to be ideal, since the formation of both plates and/or rods would appear to be best evaluated by examination of either of the other two cube planes. However, there are quite practical reasons for this choice, and we believe that the kinetics of coarsening are best evaluated in this section, especially in the early stages, where the shapes are expected to remain nearly equiaxed, irrespective of whether the applied stress ultimately induces the formation of rods or plates.
The evolution of morphology during coarsening was another principal objective of the research. That work involved detailed measurements of the shapes of individual precipitates, including measurements of the extent to which the precipitates become cuboidal and the extent to which their shapes depart from being equiaxed. The results of those investigations and their implications are described in Part III of this series of papers. In Part II [29], we present a model for diffusion under applied stress which we believe provides a partial explanation for one of the main findings of the work on the kinetics, namely the retardation of coarsening kinetics in specimens aged under compression.
Section snippets
Aging under applied stress
The experiments were performed on cylindrically symmetric specimens with the axis of the applied compressive stress parallel to [1 0 0]. The geometries employed included doubly tapered (DT) specimens ~10 mm long with diameters varying from ~3 to 6 mm and right cylindrical (RC) specimens ~4 mm in diameter and ~3 mm in length. The DT geometry is advantageous because microstructural evolution under stress can be investigated without requiring a unique specimen for each stress. We chose to vary the
Doubly tapered specimens
The γ′ precipitate microstructures observed in all the specimens aged under applied stress are essentially identical to published microstructures observed in specimens aged under stress-free conditions [1]. Any differences are subtle and impossible to observe by visual examination for the aging conditions used in this investigation. The average radius of the precipitates, 〈r〉, is plotted vs. the applied stress, σ, in Fig. 3 for all the aging times used in the experiments on the DT specimens;
Discussion
The possible roles of several obvious experimental factors were thoroughly investigated in order to ascertain whether there is truly an effect of stress gradient on the kinetics of coarsening. It was not possible to measure the temperature gradient along the length of the DT specimens accurately, so we cannot exclude the possibility that the temperature profiles in the longer DT specimens were as uniform as we would have liked. The magnification calibration of the TEM was checked routinely
Summary
The kinetics of coarsening of γ′ precipitates in monocrystalline Ni–Al alloys aged at 640 °C under applied compressive stress have been investigated. For the most part, an applied compressive stress tends to slow down the growth rate of the average precipitate by 20–25%. At the same time the stress induces an increase in the width of the particle size distributions. We believe that the apparent effect of stress gradient is not real, but an artifact of the experimental set-up associated with
Acknowledgments
The authors are grateful to the Department of Energy for their financial support of this research under grant No. DE-FG03-96ER45573.
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