Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials
We present that crystallographic slip in hexagonal metals involves a number of geometrically distinct slip families characterized by their slip direction and slip plane (basal, prismatic, and pyramidal). Owing to the low symmetry of hexagonal lattices, each of these slip families only have a few symmetrically equivalent slip systems (family members). Furthermore, different slip families become active at different resolved shear stress, i.e., they have different critical resolved shear stress values (CRSS). The plastic anisotropy of hexagonal materials makes the numerical prediction of their plastic behavior challenging and depends critically on the knowledge of CRSS values. The present contribution assesses the reliability of three proposed methods (with additional variations) to quantify CRSS values of the different hexagonal slip families. Those methods (a to c) rely on: (a) the statistics of observed surface slip traces in a (slightly) deformed polycrystal; (b) an iterative adjustment of CRSS values until a simulated single crystal indentation matches the corresponding experiment in terms of load–displacement response and residual surface topography of the indent; (c) in-situ high-energy X-ray diffraction to measure the evolution of resolved stress (from lattice strains) in grains for which single-family slip is probable based upon specific lattice reorientation conditions. Virtual experiments are performed on synthetic microstructures such that the (extracted) CRSS values resulting from simulating the different methodologies can be rigorously compared against the (target) CRSS values that are installed in the phenomenological constitutive material description used in the simulations. The resulting CRSS values of methods (a) exhibit a strong dependence on, and deterioration with, decreasing level of slip trace observability, which is an uncertain quantity in experimental measurements. For the inverse indentation method (b), the predicted CRSS values are within 8 % of their reference CRSS values for the two investigated cases. Lastly, the high-energy X-ray diffraction method (c) most reliably determines CRSS values for basal and prism slip, but lacks a strict grain selection criterion to assess pyramidal slip.