P W. Dondl, J. Zimmer/J. Mech. Phys. Solids 52(2004)2057-2077 Table 2 Elastic Moduli (in GPa) Orthorhombic Monoclinic CCG 33.0 The values for the tetragonal and monoclinic phases are, except for rounding errors, the same as in Fadda et al.(2002, Tables ll(b), Iv(b))(orthorhombic data seem to be e). Note also the re-labeling of the indices in the monoclinic phase in Table IV in Fadda et alL. Here, the tetragonal phase labeling is always used. In the two-dimensional setting considered her trigonal and the orthorhombic configurations have the same independent moduli. However, C11- C22 holds only for the tetragonal phase, and not for the orthorhombic one Table Location of the breaks for the mesh on the 0.035 0.012 0.0000450.00002-0.0000050.000025 0.000225 0.007 0.05 0.0015 0.0005 0.0001 0.0125 0.06 This is a general property of orbit spaces, see, e.g., Zimmer(2004a). Table 1 lists the location of the other minima We turn towards the construction of a function on the orbit space such that p (p is a phenomenological energy function modeling the relevant mechanical properties of Zirconia at the t-o-m triple point. Since the Hilbert map identifies exactly the symmetry related variants as one point in the orbit space, can be an arbitrary function. It will be chosen to be a piecewise function. In this way, all available experimental and theoretical data of the elastic moduli can be fitted accurately. The values for the elastic moduli and the locations of the minima are taken from Fadda et al.(2002). No experimental data were available for the orthorhombic phase, so orthorhombic data of a similar agnitude as at the other phases were chosen before fitting the energy function. See Table 2 for the elastic moduli The definition of is done in two steps. First, a mesh on the orbit space is created The breaks are the locations where different pieces of the function will be joined. They form boxes in a natural way. The breaks are listed in Table 3. A comparison with the location of the minima on the orbit space in Table 1 shows that every minimum is2066 P.W. Dondl, J. Zimmer / J. Mech. Phys. Solids 52 (2004) 2057 – 2077 Table 2 Elastic Moduli (in GPa) Tetragonal Orthorhombic Monoclinic C11 340 300 312 C22 340 350 350 C66 95.0 90.0 66.3 C12 33.0 33.0 35.2 C16 0 0 3.2 C26 0 0 4.3 The values for the tetragonal and monoclinic phases are, except for rounding errors, the same as in Fadda et al. (2002, Tables II(b), IV(b)) (orthorhombic data seem to be unavailable). Note also the re-labeling of the indices in the monoclinic phase in Table IV in Fadda et al. (2002). Here, the tetragonal phase’s labeling is always used. In the two-dimensional setting considered here, the tetragonal and the orthorhombic con3gurations have the same independent moduli. However, C11 = C22 holds only for the tetragonal phase, and not for the orthorhombic one. Table 3 Location of the breaks for the mesh on the orbit space 1 −0.05 −0.035 −0.02 −0.0025 0.0025 0.005 0.0075 0.0125 0.03 0.05 0.056 0.07 0.085 0.1 2 −0.0005 −0.000045 −0.00002 −0.000005 0.000025 0.00005 0.000075 0.000225 0.001 0.002 0.0026 0.004 0.0055 0.007 3 −0.05 −0.0015 −0.001 −0.0005 0.0001 0.0125 0.02 0.03 0.045 0.06 This is a general property of orbit spaces, see, e.g., Zimmer (2004a). Table 1 lists the location of the other minima. We turn towards the construction of a function  on the orbit space such that () is a phenomenological energy function modeling the relevant mechanical properties of Zirconia at the t-o-m triple point. Since the Hilbert map identi3es exactly the symmetry related variants as one point in the orbit space,  can be an arbitrary function. It will be chosen to be a piecewise function. In this way, all available experimental and theoretical data of the elastic moduli can be 3tted accurately. The values for the elastic moduli and the locations of the minima are taken from Fadda et al. (2002). No experimental data were available for the orthorhombic phase, so orthorhombic data of a similar magnitude as at the other phases were chosen before 3tting the energy function. See Table 2 for the elastic moduli. The de3nition of  is done in two steps. First, a mesh on the orbit space is created. The breaks are the locations where diIerent pieces of the function will be joined. They form boxes in a natural way. The breaks are listed in Table 3. A comparison with the location of the minima on the orbit space in Table 1 shows that every minimum is