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Dilute Mg alloys based upon earth-abundant elements, e.g., Al, Ca, and Zn have attractive combinations of strength, ductility, and workability. Even higher strength can be obtained in work-hardened material without the heat treatments required to induce Guinier-Preston zone strengthening of previously studied versions of these alloys. This stems from a slightly stronger crystallographic texture than is present after solutionizing, a high dislocation density, and to a lesser degree, a fine distribution of globular Zn-rich precipitates. The anisotropic plastic response of sheet material is described using an elasto-viscoplastic self-consistent (EVPSC) polycrystal model. Strain partitioning between grains during rolling-induced strain hardening is held responsible for the yield strength, ductility, and especially, strain hardening anisotropy. Texture-induced plastic anisotropy is well- known, but the effect of strong partitioning of strain between variously oriented grains is critical to explain what may be classified as a sort of strain path change (generalized Bauschinger) effect.