From the Classical Schmid Factor to Tensor-Based Global Measures: A Critical Review and Practical Advice for...

The Schmid factor provides a compact link between an applied load and the resolved shear stress on a selected crystallographic system. For uniaxial loading, m=cosφcosλ, and its maximum magnitude is 0.5. This familiar result is conditional on the uniaxial stress model rather than a universal bound. Under a symmetric Cauchy stress tensor σ, the corresponding projection is τRSS=bTσn. A dimensionless global Schmid factor (GSF) further requires a stated reference stress. When the von Mises equivalent stress σeq=32s:s is used, with orthogonal unit vectors b and n and σeq>0, |GSF|≤13, the uniaxial limit is recovered as a special case. This review separates the tensor projection from effective or modified factors defined for particular loading conditions. SF and GSF describe the favorability of a crystallographic system under a prescribed stress, but they are neither intrinsic material properties nor complete activation criteria. Magnesium alloys are used to examine slip-system competition, twinning polarity, texture, local stress redistribution, and differences in critical resolved shear stress. In addition to calculation procedures, limiting cases, reporting requirements, and research directions, common learning difficulties and a progressive route for interpreting Schmid-based measures are discussed.