Multiscale crystal plasticity modeling based on geometrically necessary crystal defects and simulation on fine-graining for polycrystal

A Dislocation-Crystal Plasticity Simulation on FCC Single Crystal Considering Geometrically Necessary Dislocation Density and Incompatibility

“…Expressing the density of dislocation pair consisting of the adjacent two dislocations by the second-order gradient of slip and comparing it with Eq. (3), the GN incompatibility (17) as a dislocation density is rewritten in the form…”

“…(2) and (4), dislocation densities on slip system α are written in the forms expressed in the same fashion to the previous paper (17) , such that…”

“…The plastic deformation rate p D and the plastic spin p W are kinematically defined as the symmetric and anti-symmetric parts of (17), (18) where subscript A denotes the anti-symmetric part of the second-order tensor. From the usual elastic constitutive equation and Eq.…”

“…However, three-stage hardening curves are not reproduced by calculations using the above conventional models. In order to work out these problems, in the previous paper (17) , we define a new GN dislocation density tensor and a new GN incompatibility tensor based on the dislocation density tensor and the incompatibility tensor proposed by Kröner (18) . The GN dislocation density tensor is represented by the first-order gradient of slip, and it can be regarded as a generalized GN dislocation density.…”

Dislocation-Based Crystal Plasticity Modeling and Simulation for HCP Metals Considering Evolution of Twin-Microstructure

“…Additionally, a new deformation twining model based on the phase-field theory is coupled with the above model through an order parameter and resolved shear stress. In this model, elastic strain energy on twin plane and anisotropic interfacial energy between matrix and twinned region are adopted in the Ginzburg-Landau free energy as the bulk energy and the gradient energy, (8) ．また，双晶変形が生じる領域はレンズ状や帯状になることが知られており (9) ，このような双晶組 織の近傍から動的再結晶によって微細化が開始すると報告されている (10) (11) ．さらに，再結晶の核生成サイトは転 位密度の高い領域であると言われているため (12) ，Mg の一連の微細化過程をモデル化する際には，双晶組織の形 成および転位密度の情報を考慮する必要がある． 転位の情報を取り入れた解析モデルとしては転位-結晶塑性モデル (13) (14) が挙げられる．これはすべりを塑性変 形の素過程とする結晶塑性モデル (15) (16) と，転位密度の上昇による加工硬化を表現した Bailey-Hirsch モデル …”