多晶体中的晶粒取向分布可通过取向分布函数(orientation distribution function,ODF)表示.取向分布函数(ODF)可在Wigner D-函数基下展开,其展开系数称为织构系数.利用Clebsch-Gordan表达式推导出立方晶粒各向异性集合多晶体的弹性张量...多晶体中的晶粒取向分布可通过取向分布函数(orientation distribution function,ODF)表示.取向分布函数(ODF)可在Wigner D-函数基下展开,其展开系数称为织构系数.利用Clebsch-Gordan表达式推导出立方晶粒各向异性集合多晶体的弹性张量显表达式,该弹性张量表达式包含3个材料常数和9个织构系数.为了织构系数的超声波测定,给出了这9个织构系数与超声波速之间的关系式,并通过一个算例来验证这个关系式.展开更多
We present in this paper a numerical algorithm that couples the atomistic and continuum models for the thermal-mechanical coupled problem of polycrystalline aggregates.The key point is that the conservation laws shoul...We present in this paper a numerical algorithm that couples the atomistic and continuum models for the thermal-mechanical coupled problem of polycrystalline aggregates.The key point is that the conservation laws should be satisfied for both the atomistic and continuum models at the microscale.Compared with the traditional methods which construct the constitutive equations of the grain interiors and grain boundaries by continuum mechanics,our model calculates the continuum fluxes through molecular dynamics simulations,provided that the atomistic simulations are consistent with the local microstate of the system.For the grain interiors without defects,central schemes are available for solving the conservation laws and the constitutive parameters can be obtained via molecular dynamics simulations.For the grain boundary structures,the front tracking method is employed because the solutions of the conservation equations are discontinuous near the defects.Firstly,appropriate control volumes are chosen at both sides of the interface,then the finite volume method is applied to solve the continuum equations in each control volume.Fluxes near both sides of the interface are calculated via atomistic simulations.Therefore,all thermo-mechanical information can be obtained.展开更多
文摘多晶体中的晶粒取向分布可通过取向分布函数(orientation distribution function,ODF)表示.取向分布函数(ODF)可在Wigner D-函数基下展开,其展开系数称为织构系数.利用Clebsch-Gordan表达式推导出立方晶粒各向异性集合多晶体的弹性张量显表达式,该弹性张量表达式包含3个材料常数和9个织构系数.为了织构系数的超声波测定,给出了这9个织构系数与超声波速之间的关系式,并通过一个算例来验证这个关系式.
基金supported by the National Basic Research Program of China (Grant No. 2010CB832702)the National Natural Science Foundation of China (Grant Nos. 90916027 and 11202065)
文摘We present in this paper a numerical algorithm that couples the atomistic and continuum models for the thermal-mechanical coupled problem of polycrystalline aggregates.The key point is that the conservation laws should be satisfied for both the atomistic and continuum models at the microscale.Compared with the traditional methods which construct the constitutive equations of the grain interiors and grain boundaries by continuum mechanics,our model calculates the continuum fluxes through molecular dynamics simulations,provided that the atomistic simulations are consistent with the local microstate of the system.For the grain interiors without defects,central schemes are available for solving the conservation laws and the constitutive parameters can be obtained via molecular dynamics simulations.For the grain boundary structures,the front tracking method is employed because the solutions of the conservation equations are discontinuous near the defects.Firstly,appropriate control volumes are chosen at both sides of the interface,then the finite volume method is applied to solve the continuum equations in each control volume.Fluxes near both sides of the interface are calculated via atomistic simulations.Therefore,all thermo-mechanical information can be obtained.
