Texture, hardening and non-proportionality of strain in BCC polycrystal deformation

• We investigated the effects of non-proportional strain paths on stress states and dislocation distributions in polycrystals.
• A range of hardening rules were investigated (self- and isotropic latent).
• We showed that straining non-proportionally to a known final strain-state can result in differing yield surface responses.
• Differing dislocation distributions formed under non-prop strain paths are more pronounced under isotropic-latent hardening.
• The effects of non-proportionality of strain on predicted ductility is also shown.

Non-proportionality of straining, initial texture and hardening has been investigated in single- and polycrystal BCC steel using a crystal plasticity finite element framework. The effect of hardening on achievable ductility is also predicted for a BCC polycrystal. Two extreme forms of hardening have been investigated; namely, isotropic latent hardening and anisotropic self-hardening. Dislocation density evolutions on all independent slip systems have been calculated in order to investigate the establishment of dislocation distributions and their dependence on non-proportionality, hardening and initial texture. Results for a BCC single crystal are considered first in order to provide insight into subsequent polycrystal investigations.The degree of non-proportionality during straining, whilst maintaining in all cases the identical, final strain state, has been shown to lead to moderately differing final stress states, with a higher degree of non-proportionality giving the largest divergence from the corresponding proportional stress states. The nature of the hardening is also found to influence the strength of the non-proportionality effect, with isotropic latent hardening leading to the development of greater non-proportionality effects on stress than those for anisotropic self-hardening in polycrystals. The polycrystal dislocation distributions established are found to depend on the degree of non-proportionality, particularly under uniaxial straining conditions (as opposed to biaxial straining), and very strongly on the nature of the hardening assumed, but less so on the initial texture. In addition, the predicted limit strain is moderately affected under non-proportional biaxial strain paths as opposed to more significant increases under non-proportional uniaxial strain paths. It has been shown that that non-proportionality plays a key role in the establishment of strain localization and hence on forming limits.