A Triple-Scale Crystal Plasticity Modeling and Simulation on Size Effect due to Fine-Graining

Abstract

In this paper ， a triple − sca 】 e crystal plastic 重 ty nlodel bridging three hierarchical lnateriai str しlc ． tures ， 正 ． e ， ， dislocatiQn structure ， grain aggregate and practical macroscopic s 亡ructure is devclopcd ， Geometrically necessary ( GN ) dislocation density and GN incompatibility are employed so as tQ describe isolated dislocations and dislocation pairs in a grain ， respectively ． Then the homogenization rnethod is hユtroduced into the GN dislocation − cTystal plasticity model for derivation of 亡 he governillg equatiQn of macroscopic structure w ｛ tb the mathematical and physical c ｛ msistencies ． Using the prcscnt Inodel ， a triple − scale FE simulation briclging the abc )ve tllree hierarchical structures is carried out for f ． c ． c ， polycrystals with djffere 飢 mean grain size ． It is shown that the present model can qualitatively reproduce size effects of Inacroscopic specimen with u 畫 trafine grain ， i ・ e ・ ， the i1 ユerease Qf initial yield stress ， the decrease of hardening ratiQ after reachil19 且 e τ lsile strellgth alld the reductioll of tensile ducUlity with decrease of its grain size ． MQreQver， the relationship between macroscopic yielding of specimen and microscopic grain yielding is discussed and the mechanism of the poor tcnsile ductility due to 且ne graining is clarified

A Triple-Scale Crystal Plasticity Simulation on Yield Behavior of Annealed FCC Fine-Grained Metals

“…Using Eq. ( 10) and the formulation of the conventional homogenization method with the rate form constitutive law [8], the elastoviscoplastic constitutive equation of the macroscopic structure for crystal plasticity theory is obtained [4].…”

“…In order to clarify the utility of UFGM numerically, it is important to investigate size effects of metallic materials that depend on the initial grain size. In our previous work [4], the homogenization method is introduced into a geometrically necessary (GN) dislocation-crystal plasticity model [5] so as to develop an extended multiscale model bridging the three hierarchical material structures, i.e., dislocation structure, grain aggregate and macroscopic structure. In this paper, we discuss about the size effects of UFGM such as increase of initial yield stress, decrease of hardening ratio causing plastic instability and reduction of tensile ductility.…”