An Analysis of Anisotropic Material Failure under Shear and Tension

Upon mechanical loading, the true stress-strain response of a polycrystalline
metallic material traverses key stages, which include (i) an elastic-to-plastic
transition, (ii) occurrence of peak stress, followed by (iii) gradual stress soft-
ening, and (iv) degradation culminating into a complete loss of load carrying
capacity that is synonymous with ultimate failure or ductility. Predicting how
the macroscopic failure process (stages (ii)-(iv)) is connected to the multiscale
mechanics of anisotropic plasticity remains a thorny challenge. From a mecha-
nistic standpoint, a challenging question is: What determines the ductility of a
polycrystalline material – void coalescence or material instability? The former
refers to a local failure process whereby generic mechanisms of void nucleation,
growth and link-up operate. Material instability here refers to the formation of
shear bands, which manifests in the form of intense localization of plastic deformation in thin bands. In this work, we aim to address the following questions by
means of three-dimensional unit cell finite element calculations of voided unit
cells
• How does material plastic anisotropy of the matrix affect the the two
failure modes?
• Beyond plastic anisotropy, what roles do crystallographic deformation
mechanisms (slip and twinning) play in determining the failure modes?
• Are the failure modes cooperative or competitive?
We adopt a computational methodology based on static condensation to efficiently compute the loss of ellipticity of the macroscopic tangent modulus that
enables on-the-fly evaluation of strain localization. The efficacy of this method is
assessed for isotropic and anisotropic materials under various controlled tensile
and shear stress states.