The Discrete Dislocation Dynamics-Extended Finite Element Coupling Algorithm And Its Application In The Polycrystalline Materials

There are many internal discontinuities in the actual material,such as cracks,holes,inclusions,grain boundaries,phase boundaries.When dealing with these discontinuous interface problems,the traditional finite element method requires a local mesh encryption or some repartition of the grid near the discontinuous interface.The traditional finite element method still has many inconveniences in the calculation of the discontinuous interface problem.The extended finite element method(XFEM)is based on the traditional finite element function with the addition of an extended discontinuous shape function to represent the discontinuous surface.It is not necessary to repartition the mesh in the calculation.The description of the discontinuous field is completely independent of the model grid boundaries.And the method has a great advantage when dealing with the discontinuous problems.A dislocation is one of the carriers of the crystal plasticity.It is of great significance to directly simulate the plastic deformation of the materials through the dynamic evolution of the discrete dislocations.Since a dislocation can also be viewed as a discontinuous surface,the extended finite element method can be used to study the dislocation related problems.At present,there are mainly three existing dislocation research methods: the traditional discrete dislocation dynamics-finite element superposition algorithm(DDD-FEM),the discrete-continuous method(DCM),and the discrete dislocation dynamics-extended finite element coupling algorithm(DDD-XFEM)studied in this paper.Because the existing algorithms still have some limitations in the calculation of the dislocation related problems,this paper improves the existing traditional DDD-XFEM algorithm which includes the dislocation core enrichment and independently develops an improved DDD-XFEM algorithm.The algorithm can more accurately and efficiently consider the interaction between a large number of dislocations and a large number of interfaces.The main contents and the main research results of this paper are as follows::(1)In this paper,a new improved DDD-XFEM algorithm is developed independently,and the related Fortran program is compiled.The accuracy and the efficiency of the algorithm are verified by the practical examples,and the paper illustrates the advantages of the algorithm when calculating a large number of dislocations and interface problems.Compared with the traditional DDD-FEM superposition algorithm,this algorithm can better deal with the grain boundary and the phase boundary problems,without calculating the socalled polarization stress,and the computational efficiency is significantly improved.Compared with the DCM coupling algorithm,this algorithm avoids the so-called plastic strain distribution,and it is more accurate when dealing with the interface problems.Compared with the traditional DDD-XFEM algorithm,the computational efficiency of the algorithm is improved by times,and it does not have a strong grid size dependence.(2)Based on the improved DDD-XFEM algorithm,this paper studies the size effect(the Hall-Petch effect)of the two-dimensional polycrystalline materials under the monotonic loading.The reason for the size effect is explained from the dislocation movement level.A large number of dislocations on the rigid grain boundary are captured,and the discrete slip bands of the dislocations in the polycrystalline material are observed.(3)Based on the improved DDD-XFEM algorithm,this paper studies the mechanical response of the two-dimensional polycrystalline materials under the cyclic loading.The calculated result is analyzed and the size effect of the stress relaxation of the polycrystalline materials under the cyclic loading is discovered for the first time.And the paper explains its inherent dislocation mechanism.