The Taylor factor analyses can predict the yield response of a grain to the induced stress state, based on the family of active slip systems. Taylor factor is used to analyze the level of plastic deformation of individual grain. On the other hand, the activation of slip systems depends on the crystallographic orientation and local stress differences near grain boundaries between adjacent grains. Therefore, is there any correlation between crystallographic orientation or texture and Taylor factor, for example in a rolled sheet?
Taylor's method does not directly permit to predict the deformation textures due to the indeterminacy of the crystal rotation. However, as you pointed out, this method is assumed to predict the deformation state rather than the one of the stresses (instead of what you mentioned); this can be done through consideration of the energy that can help determine the polycrystals tensile curves from those of single crystals (oriented in multiple slips), and this from Taylor factor “M”. For a polycrystal, the Taylor factor is the average of the ratio of the Taylor factors (for each single crystal) on the number of grains. The resulting value is commonly assumed as “upper bound” which is opposed to the “lower bound” associated with Sachs model that is based on the assumption that each grain of a polycrystal is subjected to the same stress state that the aggregate (here there is no continuity of deformation at the grain boundaries). It is worth noting that in many practical cases, neither deformation nor strain are completely imposed, so that the boundary conditions of deformation are intermediate (known as “mixed conditions”)
In fact, Taylor's method (when introducing Taylor factor) assumes that each grain deforms in the same manner as the polycrystalline aggregate by respecting the deformation continuity through the grain boundaries. This implies that five terms of each grain strain tensor should be imposed. Besides, according to von Mises, to accommodate the plastic deformation (that is fully imposed, case of rolled sheet for instance) requires at least 5 active slip systems that will be chosen from the 12 systems {111} (as well as their opposites) (CFC case). Among all combinations of five slip systems that can accommodate the imposed deformation, Taylor considered a criterion relating to minimal work by proposing that the active combinations for a plastic strain increment are those that minimize internal work for active slips.
For these common concepts, you can consider the following articles:
J.H. Driver. A. Skalli, Revue Phys. Appl. 17, 447 (1982)
J.H. Driver. A. Skalli and M. Wintenberger, Phil Mag. 49A, 505 (1984)
R. Fortunier and J.H Driver, Acta Metall, 35 309 (1987)
However, some authors had calculated deformation textures using Taylor's method by calculating the crystal rotations, taking either “random solutions” [1] or “an average solution” among all the possible solutions [2].
[1] J.S. Kallend and G.J. Davies, Phil. Mag., 25(2), 471-490 (1972)
[2] P. van Houtte and E. Arnoudt, Z. Metallk, 66, 367 (1975)
In fact you answered your question already by your explanation. "The Taylor factor analyses can predict the yield response of a grain ..., based on the family of active slip systems. ... On the other hand, the activation of slip systems depends on the crystallographic orientation ..."
Therefore, there must be a correlation between Taylor factor and crystal orientation,
Taylor's method does not directly permit to predict the deformation textures due to the indeterminacy of the crystal rotation. However, as you pointed out, this method is assumed to predict the deformation state rather than the one of the stresses (instead of what you mentioned); this can be done through consideration of the energy that can help determine the polycrystals tensile curves from those of single crystals (oriented in multiple slips), and this from Taylor factor “M”. For a polycrystal, the Taylor factor is the average of the ratio of the Taylor factors (for each single crystal) on the number of grains. The resulting value is commonly assumed as “upper bound” which is opposed to the “lower bound” associated with Sachs model that is based on the assumption that each grain of a polycrystal is subjected to the same stress state that the aggregate (here there is no continuity of deformation at the grain boundaries). It is worth noting that in many practical cases, neither deformation nor strain are completely imposed, so that the boundary conditions of deformation are intermediate (known as “mixed conditions”)
In fact, Taylor's method (when introducing Taylor factor) assumes that each grain deforms in the same manner as the polycrystalline aggregate by respecting the deformation continuity through the grain boundaries. This implies that five terms of each grain strain tensor should be imposed. Besides, according to von Mises, to accommodate the plastic deformation (that is fully imposed, case of rolled sheet for instance) requires at least 5 active slip systems that will be chosen from the 12 systems {111} (as well as their opposites) (CFC case). Among all combinations of five slip systems that can accommodate the imposed deformation, Taylor considered a criterion relating to minimal work by proposing that the active combinations for a plastic strain increment are those that minimize internal work for active slips.
For these common concepts, you can consider the following articles:
J.H. Driver. A. Skalli, Revue Phys. Appl. 17, 447 (1982)
J.H. Driver. A. Skalli and M. Wintenberger, Phil Mag. 49A, 505 (1984)
R. Fortunier and J.H Driver, Acta Metall, 35 309 (1987)
However, some authors had calculated deformation textures using Taylor's method by calculating the crystal rotations, taking either “random solutions” [1] or “an average solution” among all the possible solutions [2].
[1] J.S. Kallend and G.J. Davies, Phil. Mag., 25(2), 471-490 (1972)
[2] P. van Houtte and E. Arnoudt, Z. Metallk, 66, 367 (1975)
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