An approximate yield criterion for porous single crystals

Abstract

This study is devoted to the derivation of an approximate yield function for voided single crystals deforming by crystallographic slip. By making use of a regularized form of the Schmid law and solving approximately the hydrostatic case with a limit-analysis calculation, a Gurson-type yield criterion is proposed. It is obtained by a heuristic extension of existing limit-analysis results for a matrix obeying a quadratic Hill-type criterion. The proposed yield function is successfully compared with numerical results from the literature for face-centered cubic crystals.

A model for porous single crystals with cylindrical voids of elliptical cross-section

“…At this point, it is perhaps relevant to make contact with the corresponding three-dimensional models proposed by Han et al (2013) and Paux et al (2014). In these models-which have been assessed for an FCC crystal (near equiangular case in our notation)-even though the deviatoric response includes the effect of the crystal anisotropy (i.e., number of slip systems and orientations), the corresponding response under purely hydrostatic stressing is independent of the orientation of the systems in Han et al (2013) and independent of the number and orientation of slip systems in Paux et al (2014).…”

A rate-independent crystal plasticity model with a smooth elastic–plastic transition and no slip indeterminacy

“…This approach was successfully applied to the deformation of polycrystals by Darrieulat and Piot (1996); 25 Montheillet et al (1985), to the simulation of texture evolution (Gambin and Barlat, 1997) and, more recently, to ductile fracture of single crystals (Paux et al, 2015). The drawback of this single criterion formulation is that it is more difficult to introduce interaction between slip systems and latent hardening effects.…”

A porous crystal plasticity constitutive model for ductile deformation and failure in porous single crystals

“…For a given strain increment (∆ ), the increments of void growth (∆ ) is computed using ( 28 ) while the increments of shear strain (∆ ) in the slip systems are uniquely calculated by substituting equation ( 26 ), ( 27 ) and ( 28 ) into ( 25 ). Once ∆ and (∆ ) are known in terms of the strain increments (∆ ), all the other increments can be found through equations ( 26 ), ( 27 ) and ( 29 ).…”

“…There has been significant research performed in this area in the recent past, these works have been thoroughly reviewed and discussed in the literature, for example by incorporating crystallographic aspect for anisotropic behaviour ( [14], [22]- [26] and references there in) or anisotropy through phenomenological plasticity models (for details see [26]- [28]). These works are based on Gurson type approach (for details see [25]- [28] and references therein), and homogenisation approaches ( [14], [22]- [24]). In the proposed work, an approach similar to [1] has been used to incorporate the void growth and coalescence effect in a crystal plasticity based constitutive model in a phenomenological context.…”