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The remarkable crystallographic plastic anisotropy of magnesium and its alloys reflects in its polycrystal response via texture. While texture-strength linkages have been studied, the role of textural variability on damage remains elusive. The challenge is to obtain relevant metrics that relate the net plastic anisotropy to macroscopic modes of damage. A possible approach is to adopt mechanistic descriptions of the damage. Motivated by the recent experimental and theoretical works in this direction, here we appeal to the Hill yield function to characterize the net plastic anisotropy of polycrystalline magnesium via the Hill plastic anisotropy tensor h. Metrics based on the components of h offer a way to predict damage as a possible damage predictor. Using the results from our recent extensive three-dimensional crystal plasticity simulations for a wide range of textures, we map the net plastic anisotropy onto the coefficients of h, separately for the tensile and compressive responses. Metrics based on these coefficients serve as indicators for the propensity of textured polycrystals to damage by: (i) porosity evolution, or (ii) shear instability. An attempt is made to understand the potential roles textural variability and crystallographic plastic anisotropy play in damage under different loading conditions.