In this paper,a methodology integrating crystal plasticity(CP),the eXtended finite element method(XFEM)and the cohesive zone model(CZM)is developed for an Al-Cu-Mg alloy to predict fatigue crack propagation(FCP)across...In this paper,a methodology integrating crystal plasticity(CP),the eXtended finite element method(XFEM)and the cohesive zone model(CZM)is developed for an Al-Cu-Mg alloy to predict fatigue crack propagation(FCP)across grain boundary(GB)of Al-Cu-Mg alloy during stageІІ.One GB model is incor-porated into FCP constitutive law to describe grain interaction at GB.A bicrystal containing GB is built up to simulate FCP behavior through L participated GBs.Modelling features including GB characteristic,cumulative plastic strain(CPS)distribution and crystal slipping evidence can be identified.The numer-ical results are compared with published experimental data to check the accuracy of model.This work demonstrates that the combination of CP containing GB constitutive laws,XFEM and CZM is a promising methodology in predicting twist angle-controlled crack deflection through GBs.展开更多
The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenome...The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenomenon remains not fully understood.This study derives the equilibrium distribution of vacancies analytically by following thermodynamics and the micromechanics of crystal defects.This derivation suggests that vacancies cluster in regions under hydrostatic compression to minimize the elastic strain energy.Subsequently,a finite element model is developed for examining more general scenarios of interaction between vacancies and grain boundaries.This model is first verified and validated through comparison with some available analytical solutions,demonstrating consistency between finite element simulation results and analytical solutions within a specified numerical accuracy.A systematic numerical study is then conducted to investigate the mechanism that might govern the micromechanical interaction between grain boundaries and the profuse vacancies typically generated during plastic deformation.The simulation results indicate that the reduction in total elastic strain energy can indeed drive vacancies toward grain boundaries,potentially facilitating void nucleation in ductile fracture.展开更多
Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonl...Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.展开更多
A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate th...A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate the propagation of cracks at grain boundary. Simulation results show that the crystallographic orientation of PFZ has significant influence on crack propagation, which includes the crack growth direction and crack growth velocity. The fracture strain of soft orientation is larger than that of hard orientation due to the role of reducing the stress intensity at grain boundary in intergranular brittle fracture. But in intergranular ductile fracture, the fracture strain of soft orientation may be smaller than that of hard orientation due to the roles of deformation localization.展开更多
Based on the experimental results of the work-hardening processes of single crystals,the ac- commodation processes of polycrvstal deformation and the assumption of idealized polycrystal,the stress-strain relation of e...Based on the experimental results of the work-hardening processes of single crystals,the ac- commodation processes of polycrvstal deformation and the assumption of idealized polycrystal,the stress-strain relation of elasto-plastic deformation crystal was derived.The effect of orientation difference on the mechanical properties of the bicrvstalline specimens of aluminum was simulated by means of the finite element method(FEM)of elasto-plastic crystal.The results are in good agreement with the experimental results made by Clark and Chalmers in 1954.展开更多
The microscopic analyses of polycrystalline material at high temperature were carried out. The crystal plasticity model proposed by Asaro and Needleman was applied to a polycrystal model in the finite element simulati...The microscopic analyses of polycrystalline material at high temperature were carried out. The crystal plasticity model proposed by Asaro and Needleman was applied to a polycrystal model in the finite element simulation and the crystal slip system was randomly provided for each crystal. The grain boundary sliding, which was characteristic at high temperature, was also taken into account. It was shown that the inhomo-geneous deformation develops over the polycrystal and that the strain concentration appears around the triple point of crystal grain boundary.展开更多
This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality pro...This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality problem.We solve a small Navier-Stokes problem on the coarse mesh with mesh size H and solve a large linearized Navier-Stokes problem on the fine mesh with mesh size h.The error estimates derived show that if we choose h=O(|logh|^(1/2)H^(3)),then the two-level method we provide has the same H1 and L^(2) convergence orders of the velocity and the pressure as the one-level stabilized method.However,the L^(2) convergence order of the velocity is not consistent with that of one-level stabilized method.Finally,we give the numerical results to support the theoretical analysis.展开更多
Spalling is a typical tensile failure that results from the coupling evolution of microstructure and microdamage under high strain-rate loading.To understand the spalling damage behavior of polycrystalline materials a...Spalling is a typical tensile failure that results from the coupling evolution of microstructure and microdamage under high strain-rate loading.To understand the spalling damage behavior of polycrystalline materials at mesoscale,this paper develops a spalling model by integrating the crystal plasticity theory and the microvoid growth theory.The model is implemented in ABAQUS simulation via the VUMAT subroutine to simulate a planar impact process of copper,and the results are compared with experimental data.Due to the inhomogeneity of crystal plastic slip,the local stress fluctuates severely near the grain boundary.Therefore,without introducing the fluctuation in the threshold stress for microdamage evolution,this model can simulate the heterogeneous feature of microvoid nucleation,growth,and coalescence in materials.The results show that microvoids tend to nucleate at 25°–50°misorientation angle grain boundaries,which undergo a high probability of stress fluctuation.展开更多
基金supported by the National Natural Science Foun-dation of China(51901073).Qi Zhao was Visiting Scholar to the Soete Laboratory at Ghent University and supported by China Scholarship Council when this work is done.The authors wish to express their gratitude to Van Lang University,Vietnam for finan-cial support for this research.
文摘In this paper,a methodology integrating crystal plasticity(CP),the eXtended finite element method(XFEM)and the cohesive zone model(CZM)is developed for an Al-Cu-Mg alloy to predict fatigue crack propagation(FCP)across grain boundary(GB)of Al-Cu-Mg alloy during stageІІ.One GB model is incor-porated into FCP constitutive law to describe grain interaction at GB.A bicrystal containing GB is built up to simulate FCP behavior through L participated GBs.Modelling features including GB characteristic,cumulative plastic strain(CPS)distribution and crystal slipping evidence can be identified.The numer-ical results are compared with published experimental data to check the accuracy of model.This work demonstrates that the combination of CP containing GB constitutive laws,XFEM and CZM is a promising methodology in predicting twist angle-controlled crack deflection through GBs.
基金supported by the National Key Research and Development Program of China under Grant No.2023YFB3712401the National Natural Science Foundation of China under Grant Nos.12102254 and 12327802.
文摘The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenomenon remains not fully understood.This study derives the equilibrium distribution of vacancies analytically by following thermodynamics and the micromechanics of crystal defects.This derivation suggests that vacancies cluster in regions under hydrostatic compression to minimize the elastic strain energy.Subsequently,a finite element model is developed for examining more general scenarios of interaction between vacancies and grain boundaries.This model is first verified and validated through comparison with some available analytical solutions,demonstrating consistency between finite element simulation results and analytical solutions within a specified numerical accuracy.A systematic numerical study is then conducted to investigate the mechanism that might govern the micromechanical interaction between grain boundaries and the profuse vacancies typically generated during plastic deformation.The simulation results indicate that the reduction in total elastic strain energy can indeed drive vacancies toward grain boundaries,potentially facilitating void nucleation in ductile fracture.
基金supported by the National Natural Science Foundation of China(10901122)Zhejiang Provincial Natural Science Foundation (Y6090108)supported by the National Natural Science Foundation of China(10971165)
文摘Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.
基金Projects(51475162,51405153)supported by the National Natural Science Foundation of ChinaProject(14JJ5015)supported by the Hunan Provincial Natural Science Foundation,China
文摘A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate the propagation of cracks at grain boundary. Simulation results show that the crystallographic orientation of PFZ has significant influence on crack propagation, which includes the crack growth direction and crack growth velocity. The fracture strain of soft orientation is larger than that of hard orientation due to the role of reducing the stress intensity at grain boundary in intergranular brittle fracture. But in intergranular ductile fracture, the fracture strain of soft orientation may be smaller than that of hard orientation due to the roles of deformation localization.
文摘Based on the experimental results of the work-hardening processes of single crystals,the ac- commodation processes of polycrvstal deformation and the assumption of idealized polycrystal,the stress-strain relation of elasto-plastic deformation crystal was derived.The effect of orientation difference on the mechanical properties of the bicrvstalline specimens of aluminum was simulated by means of the finite element method(FEM)of elasto-plastic crystal.The results are in good agreement with the experimental results made by Clark and Chalmers in 1954.
基金supported by the Ministry of Education,Japan,as 21st Century COE program on Sustainable Energy System(E-3)as grant-in-aid for scientific research(No.15360053)
文摘The microscopic analyses of polycrystalline material at high temperature were carried out. The crystal plasticity model proposed by Asaro and Needleman was applied to a polycrystal model in the finite element simulation and the crystal slip system was randomly provided for each crystal. The grain boundary sliding, which was characteristic at high temperature, was also taken into account. It was shown that the inhomo-geneous deformation develops over the polycrystal and that the strain concentration appears around the triple point of crystal grain boundary.
基金funded by the National Natural Science Foundation of China under Grant No.10901122 and No.11001205by Zhejiang Provincial Natural Science Foundation of China under Grant No.LY12A01015.
文摘This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality problem.We solve a small Navier-Stokes problem on the coarse mesh with mesh size H and solve a large linearized Navier-Stokes problem on the fine mesh with mesh size h.The error estimates derived show that if we choose h=O(|logh|^(1/2)H^(3)),then the two-level method we provide has the same H1 and L^(2) convergence orders of the velocity and the pressure as the one-level stabilized method.However,the L^(2) convergence order of the velocity is not consistent with that of one-level stabilized method.Finally,we give the numerical results to support the theoretical analysis.
基金supported by the NSFC(Nos.12172367,11790292,11988102,and U2141204)the Strategic Priority Research Program(Nos.XDB22040302 and XDB22040303).
文摘Spalling is a typical tensile failure that results from the coupling evolution of microstructure and microdamage under high strain-rate loading.To understand the spalling damage behavior of polycrystalline materials at mesoscale,this paper develops a spalling model by integrating the crystal plasticity theory and the microvoid growth theory.The model is implemented in ABAQUS simulation via the VUMAT subroutine to simulate a planar impact process of copper,and the results are compared with experimental data.Due to the inhomogeneity of crystal plastic slip,the local stress fluctuates severely near the grain boundary.Therefore,without introducing the fluctuation in the threshold stress for microdamage evolution,this model can simulate the heterogeneous feature of microvoid nucleation,growth,and coalescence in materials.The results show that microvoids tend to nucleate at 25°–50°misorientation angle grain boundaries,which undergo a high probability of stress fluctuation.
