microstructures. Light gray indicates the weaker phase and dark gray/black indicates the stronger phase. During deformation of the interconnected weak layer microstructure (c), strain is partitioned into the weaker phase and strong inclusions remain relatively undeformed. Stresses in the two phases will be similar but large strain heterogenaity is induced in the weak phase as the weaker material must flow around the rigid inclusions. During deformation of the load‐bearing framework microstructure (d) strain is distributed ~homogeneously as the strong matrix imposes its strain and strain rate on the weaker inclusions. Stresses will be lower in the weaker phase as it flows at lower stress than the stronger matrix.
In contrast, when a LBF microstructure exists, the soft phase is not interconnected and the rheology of the aggregate is controlled by the harder phase. Stress is supported primarily by the stronger phase and the stronger phase imposes its strain rate on the softer phase (Figure 2.6d). In this case, stress levels in the two phases diverge. Although local heterogeneous strain rate occurs at phase boundaries, the aggregate as a whole behaves in a manner very close uniform strain rate in the two phases.
Determining conditions where IWL versus LBF are stable depends on phase proportions, strength contrast and total strain. Strength contrast will be determined by the contrast in parameters in the flow laws for the phases (e.g., activation energy and volume and stress exponent). Larger strength contrasts between the phases and a lower volume fraction of the softer phase promotes stability of a LBF. Generally speaking IWL dominates when the volume fraction of the weak phase exceeds ~30–40% (i.e., percolation threshold). However, large strains also tend to favor IWL microstructures as the weaker inclusions coalesce to form interconnected microstructures resulting in a transition from LBF to IWL behavior (Handy, 1990, 1994).
2.5.2 Differential Stresses in High Pressure Studies of Polyphase Aggregates
Given the discussion above, the difficulty in interpreting stress data from high pressure experiments on polyphase materials becomes clear. Unless one knows if a material deforms in an IWL or LBF style, interpretation of stresses measured in individual phases becomes problematic. In high‐pressure experiments that use lattice strain to calculate stresses, the stresses are measured in the individual phases and there is not currently a technique that is used to independently measure the bulk strength of the material. Looking at the two deformation experiments on Brg and Fp that are shown in Figures 2.2 and 2.3, a large discrepancy is observed. Miyagi & Wenk (2016) find room‐temperature strength of Brg to be ~1.4 times that of Fp, while in contrast Girard et al. (2016) find Brg to be about four times stronger. Notable differences exist between these two experiments, primarily that the work of Girard et al. (2016) is performed at high temperature and under steady‐state conditions. Computations by Kraych et al. (2016) find the strength contrast to be ~4 at 30 GPa and room temperature, but find that this decreases at high temperatures. Although the calculated strength of Brg in this study is similar to those of experiments at room temperature and high temperature, the strength contrast trend is inconsistent with the two‐phase experiments. However, in the experiments this may be due to microstructure and the effect of IWL versus LBF‐style deformation. Miyagi & Wenk (2016) did not recover samples for microstructural analysis; however, the larger sample in Girard et al. (2016) is amenable to documentation of microstructure. Microstructural analysis from this experiment seems to indicate that although Brg appears to be interconnected, as would be expected for LBF behavior, strain seems to be largely partitioned into the softer Fp, which is expected for IWL behavior. Based on the description of Handy, an LBF should result in large differences in stresses measured in each phase whereas the stresses measured in each phase for IWL should be close. One possibility for this discrepancy is that the samples in Girard et al. (2016) are transitioning between LBF and IWL, and if this is the case this transition would occur at strains greater than 60–70%. Indeed, this study concluded that at high strains shear weakening and strain localization is expected to occur. In contrast to Girard et al. (2016), a study on 72% CaGeO3 Pv + 28% MgO as an analog for Brg + Fp found a strength contrast of ~2 and found that the stresses in CaGeO3 in the two‐phase experiments were higher than in single‐phase experiments. Based on this, it was concluded that a LBF behavior dominates (Y. Wang et al., 2013). Another analog study on NaMgF3 Pv + NaCl analogs with a strength contrast of ~10 found systematically lower stresses in NaMgF3 with the addition of 15‐70% NaCl (Kaercher et al., 2016). In contrast to NaMgF3, stress levels remained ~ constant in NaCl independent of volume fraction. Deformation behavior of samples with volume fractions of NaCl > 50% were consistent with an IWL. Samples with less than 50% NaCl were not consistent with either an IWL or an LBF and it was concluded that the behavior of the samples were somewhere intermediate to IWL and LBF.
There are several reasons why high‐pressure experiments may not match stress levels expected for either IWL or LBF microstructures. IWL and LBF are bounds on stress and strain partitioning, so it is not surprising that experiments may deviate from these two end‐member behaviors. In Handy’s formulation, constant volume deformation is assumed, and this may not necessarily be the case for high pressure (and high temperature) experiments, particularly if pressure or temperature changes occur during deformation, such as in DAC experiments and to a lesser extent in large volume deformation. Although nonlinearity of deformation is accounted for, the behavior predicted by Handy (1990, 1994) assumes plastically isotropic phases. This is not strictly true for most minerals particularly those deforming via dislocations. Finally, given that the percolation threshold for a phase is ~30–40% by volume, there is a range of phase proportions where interconnectedness of both phases occurs. Although simultaneous interconnectedness of phases may not be stable to higher strains, it may be stable over relatively small strains experienced in experiments, and one would expect that this would result in stress and strain partitioning that is intermediate to IWL and LBF end members.
2.5.3 Texture Development in Polyphase Materials
Texture development in polyphase materials is also complex. Experimental texture studies in polyphase earth materials are fairly limited, however, in material science deformation and texture development in composites has been studied more extensively. The following discussion will focus on composites with large strength contrasts, as this is more relevant to the discussion of lower mantle aggregates. One class of materials that have a large strength contrast is metal matrix composites. These materials are composed of a ductile metal matrix that has been reinforced with hard carbides, borates, or oxides and thus present a composite with a large strength contrast. It is commonly observed that the inclusion of hard particles results in modification of texture type or a reduction in texture strength in the metal matrix (e.g., Garcés et al., 2005, 2006; Poudens et al., 1995; S. C. Xu et al., 2011; Zhang et al., 2004). In these materials, high strength particles induce complex strain fields around these nearly undeformed inclusions, resulting in texture strength reduction in the metal matrix. In Al+SiC composites, SiC concentrations >10% show decreased texture strength in the Al matrix (Poudens et al., 1995; Zhang et al., 2004). Likewise Garcés et al. (2006) found that in Mg+Y2O3 composites, the addition of yittria particles lowers texture strength in the softer Mg phase due to complex deformation patterns around the hard ceramic particles. In aluminum borate reinforced 6061 aluminum alloy, texture development in the aluminum matrix is quite different when compared to pure phase 6061 alloys (S. C. Xu et al., 2011). These cases are extreme examples where the hard phase does not deform and so the matrix must flow around the particles. A less extreme example is a study on extrusion of Al‐Pb composites containing 20%, 40%, 60%, and 80% volume fractions of Al (Brokmeier et al., 1988). This study found that in both phases, increasing the volume fraction of a phase resulted in a decrease in texture strength of the other phase. The texture decrease in the harder Al phase is attributed to increased strain partitioning into the softer phase (i.e., there is less internal deformation of Al grains as the volume fraction of Pb increases). In the softer Pb phase, the decrease in texture strength with addition of Al is attributed to heterogeneous strain induced in the Pb phase by the hard Al grains. The authors term this effect “turbulence of flow”