Anisotropy can be characterized at dierent scales. At a microscopic level, anisotropy is present in the microstructure, as pores and particles may have a preferred orientation.
At a macroscopic level, anisotropy is evidenced by the dierence of shrinkage and viscous properties in the dierent directions. Both scales are related to each other. Anisotropy can be induced into the compact body from dierent ways: green bodies can already be anisotropic from processing, porous bodies can become anisotropic during sintering when stresses are either applied or induced by constraining conditions.
2.4.1 Anisotropy in the green body
2.4.1.1 Die pressing
Giess132 observed dierent shrinkage in the axial and radial direction for glass compacts composed of non spherical crushed glass particles. Particle orientation during pressing is believed to be the source for anisotropy during sintering: at sides of the particles tend to align horizontally.33 Exner and Giess133 found a correlation between the shrinkage anisotropy factor k and the degree of orientation of the pore/solid interface. k is dened as following:
k = ∆L/L0
∆D/D0 = εz
εr (2.37)
Irrespective of particle size or shape, the shrinkage is always smaller in the pressing direction. Indeed, Olevsky134 showed that the sintering stress is larger in the direction of the larger pore axes because of the smaller value of the radius of curvature in this direction.
2.4 Anisotropy 33 Shrinkage anisotropy could also arise from other factors such as particle rearrangement and inhomogeneous density distribution in the green compact.
2.4.1.2 Tape casting and lamination
Anisotropy in the plane induced by tape casting was studied by Raj and Cannon135. Tape cast substrates exhibit large sintering shrinkage anisotropy in the plane. Shrinkage in the transverse direction is always higher than that in the casting direction. The anisotropy is higher in the initial stages of sintering and decreases as sintering progresses. High shear rates, obtained with increased casting speed and smaller doctor blade gap, resulted in increased anisotropy. Image analysis of the surface of green tapes showed signicant correlation between particle orientation and shrinkage anisotropy: shrinkage was found to be higher in the transverse direction, though the particles were oriented in the casting direction. While the Laplacian pressure in the direction of larger pore axis is higher, the viscosity will be larger in the same direction, thereby reducing the overall anisotropy eect.
Lamination without a die press increases strongly the anisotropy in the plane per-pendicular to the axial direction.136 For alumina, it was found that the nal in-plane shrinkage is in any case higher than the axial shrinkage.63;136 It was related to the packing structure being denser in the axial direction136 and pores oriented parallel to the plane.63
2.4.2 Anisotropy under uniaxial load during sintering
Gravity has to be taken into account and provides an external stress inducing anisotropy.
Olevsky137;138 elaborated a mathematical model showing the gravity eect. It resulted in isosceles trapezoid shaped samples. At the beginning of sintering (when density is lower than 72%) greater intensity of shrinkage anisotropy is provided by diusional creep mechanism than by viscous ow. On the other hand, the viscous ow mechanism causes higher anisotropy at higher densities (72%<ρ<100%).
Boccaccini and Olevsky139 plotted qualitatively the anisotropy factor, k (eq. 2.37), for dierent cases of glass-powder compacts under a constant uniaxial load. They distin-guished two dierent cases:
The viscous deformation induced by sintering is initially higher than the viscous deformation induced by the external uniaxial stress (gure 2.17(a)).
The viscous deformation induced by the external uniaxial stress is initially higher than the viscous deformation induced by sintering (gure 2.17(b)).
In both cases, k is dependent on time and after a certain time the anisotropy factor reaches a limit which corresponds to the inverse of the eective Poisson's ratio. In the rst case, the load is smaller than the sintering stress only initially (I). The sintering stress
(I) (II) (III) Time
Time
Time
σz
σ0
εr
k
k k0
0 0
0 Time
Time
Time σ0
k -1/ν
0 0 0
(a) (b)
σz
εr
εz
εz
-1/ν
Figure 2.17: Schematic diagram showing the evolution of the relevant variables during sintering of glass-powder-compacts under a constant uniaxial load. (a) The viscous defor-mation induced by sintering is initially higher than the viscous defordefor-mation induced by the external uniaxial stress, (b) the viscous deformation induced by the external uniaxial stress is initially higher than the viscous deformation induced by sintering.139
further decreases as densication proceeds and the applied load becomes larger than the sintering stress. It is then corresponding to the rst case.
To measure the sintering parameters, whatever the technique used, an external load is applied. This load will have an eect on the shrinkage anisotropy, microstructure and density. Isotropic equations used during the experiment may be not valid anymore. The goal is to get rid of these eects. One envisaged solution is to use loads smaller than the sintering stress. However, for glass based systems, even small loads can result in signicant shear due to low intrinsic shear viscosity of the glass phase139;140(nevertheless, if the load is kept below∼5 kPa, the shrinkage anisotropy factor will be hardly dependent on stress).
In order to avoid this problem, optical dilatometers could be used.141 Another envisaged solution is to reduce the time when the load is applied. Bordia58;92 and Zuo72;74 noticed the importance of the microstructural verication such as pore size and orientation as well as grain growth. In the case of continuous sinter forging (the load is applied for a large increase of density), it was observed that pores elongate along the loading direction as the externally applied load promotes neck growth, whereas, for free sintering no preferred pore orientation was observed.72 Both eects change the values of the uniaxial viscosity and the viscous Poisson's ratio. To avoid microstructural modications, Zuo performed discontinuous sinter-forging.74Free sintering takes place up to various predened densities and subsequent sintering at various constant uniaxial loads for a small increase of densities
2.4 Anisotropy 35
Free film sintering
a)
b)
1
1 1
2
2
Constrained film sintering 2
z x
Figure 2.18: Schematic diagram of particle morphology of free (a) and constrained (b) polycrystalline lms during sintering.
(= 5% in the case of alumina74). Cai et al.56 proposed cyclic dilatometry to measure the viscosities and eliminate the stress history eects. The stress history eect (changes in shrinkage anisotropy and sample microstructure) is minimized as between the loading regimes, unloading regimes take place and allow the material to recover toward a stress-free state. It was shown that a constant load test overestimates the viscosity by an order of magnitude compared with the cyclic loading test.142 Grain size of a loaded specimen and a freely sintered specimen were compared and did not show any variation.56
2.4.3 Constrained sintering of laminates
Macroscopically, this is a boundary case as the layer cannot shrink in the plane and the anisotropy factor tends to innity. An orientation of the pores may result during sintering (gure 2.18).63 Considering four particles, the probability of neck formation at the position 1 and 2 for a lm freely sintered is the same, whereas, when the lm is constrained, the neck formation in position 1 is favored to the neck formation in position 2 as the particles in thexdirection cannot approach each other. As indicated in gure 2.18, pores elongate along thez direction. This was experimentally observed by Guillon et al.63 Moreover, densication retardation and preferential pore orientation were found to be more important for thinner lms. The authors dene two levels of geometrical constraint:
in the vicinity of the substrate, a lower density and ner microstructure were observed compared to the center of the layer. The presence of this interface layer is suggested to result from hindered particle rearrangement.63
2.4.4 Sintering with rigid inclusions
Non-sintering particles in a glass matrix inuence also anisotropy. For glass-ceramics, Boccaccini and Olevsky130 showed that sintering anisotropy decreases as content of inclu-sions increases compared to the sintering behavior of the glass. In any case, samples were found to shrink more in the radial than in the axial direction. However, if the inclusions are oriented, anisotropic shrinkage is intensied.130 Shrinkage anisotropy can be also in-uenced by partial or total crystallization: the new crystallites are playing the same role as non-sintering particles.