Study On Nucleation And Propagation Of Twinning In Hexagonal Close-packed Crystals Through Crystal Plasticity Model

The deformation mechanism of metal materals is mainly divided into eastic and plastic deformation.It is very significant to investigate the mechanism of plastic deformation of the metal material,because plastic deformation plays an important role during the use of metal materials.Based on the crystal plasticity theory,this paper focus on a study for the metallic material typically HCP crystal structure,by modifying the theoretical formula for correction,and gives a new variation of the method to describing twinning of the crystal HCP structure during deformation hrough an incremental doformation gradient F?t,lattice transformation R??t and lattice shear stress S??.And for nucleation and process of bicrytals or polycrystals,we propose a rate-dependent Hadamard embedded crystal plastic grain boundary model.The main achievements are as follows:Firstly,we propose a new crystal plascity model through an incremental doformation gradient F?t,lattice transformation R??t and lattice shear stress S??.And lattice transformation R??t represent the Propagation of Twinning;S?? is the plascity stress.Because a recovery of the one-to-one relation between the continuum material point and its underlying lattice,we could show the process of twinning.Secondly,our formulation was applied to a Mg single crystal,which we loaded in compression at three different angles(Case A<0001>?Case B<1210>?Case C<1010>)to compare with the experiments(Kelley and Hosford,1968)and other evidence from the literature(Basu and Al-Samman,2015;Bian and Shin,2013).The modeled behavior of Mg up to moderate strain(ignoring re-twinning)proved in good agreement with experiments.In particular,the stress-strain curves traced by the Mg crystal in orientations A,B and C are in agreement with the experiments(Kelley and Hosford,1968),and the predicted evolution of twin volumes is consistent with the same.Moreover,the simulated cross-hatched twin patterns compare well with experiments in terms of twin plate size and spindle shape,the cross-hatch configurations and twin variant plurality.In addition,we disuss the rotation time of twinning,TwinSpan,and the larger the TwinSpan,the greater the advantage of the main variant of twinning(competing with othrer variants),the distincter the twin pattern,the less other twins'variants near the main variant.Thirdly,we propose a rate-dependent Hadamard embedded crystal plastic grain boundary model to expain the influence of grain boundary on twin and variant.Supposed a jumps in displacement[F](deformation gradient of grain boundary),and we obtain the parameters of grain boundary through the transition deformation gradient of grain boundary and the grain slip systems of both sides of grain boundary.So we build a polycrystalline crystal plasticity model.We verify the validity of grain boundary model by comparing the FCC single crystal and bicrystals with 0° grain boundary orientation defference.Then the new model is appled on simulation of Al bicrystals,Mg bicrysstals,and Mg polyscrystals.The results of Al bicrystals show the larger the orientation difference of the twin crystals,the greater the energy required for the sliding movement in the grains;as the orientation difference increases,the macro yield stress increases,and the equivalent Young's modulus of the grain boundary increases first and then decreases and compared with MD,further validated the model.The results of Mg bicrystals and polycrystals compared with results of EBSD and simulation by MD are very similar,and it is obtained that the twins first appear at the grain boundaries and the larger the difference angle between adjacent grains,the easier it is for the twins to expand in its direction.Lastly,prosed three nucleation criterions:press criterion,intercept criterion and hybrid criterion based the stress state of material point,the definition of twinning(tensile twin or compression twin)and the combination respectively.At the same time,the evolution law of the nucleation critical shear stress(NCRSS)of twin system is proposed,such as no evolution law,linear function evolution and exponential function evolution according to the relevant experiment phenomena.Through the numerical simulation,explain the influention of the evolution law of NCRSS and nuclearion criterions duiring the twinning deformation process.Those are shown that constraint conditions and nucleation criterions directly affects the varints of twinning,and nucleation function(evoliton of NCRSS)affects the propagation of twinning by orthogonal table and simulation.