By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three hig...By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three high symmetry directions and four oft-symmetry directions, and then simulate the phonon dispersion curves of Cu at high pressures of 50, 100, and 150 GPa. The results show that the shapes of dispersion curves at high pressures are very similar to that at zero pressure. All the vibration frequencies of Cu in all vibration branches at high pressures are larger than the results at zero pressure, and increase correspondingly as pressure reaches 50, 100, and 150 GPa sequentially. Moreover, on the basis of phonon dispersion, we calculate the values of specific heat of Cu at different pressures. The prediction of thermodynamic quantities lays a significant foundation for guiding and judging experiments of thermodynamic properties of solids under high pressures.展开更多
The electronic state and potential data of U2 molecules are performed by first principle calculations with B3LYP hybrid exchange-correlation functional, the valence electrons of U atom are treated with the （5s4p3d4f...The electronic state and potential data of U2 molecules are performed by first principle calculations with B3LYP hybrid exchange-correlation functional, the valence electrons of U atom are treated with the （5s4p3d4f）/[3s3p2d2f] contraction basis sets, and the cores are approximated with the relativistic effective core potential. The results show that the ground electronic state is x^9∑g＋. The pair potential data are fitted with a Murrell-Sorbie analytical potential function. The U-U embedded atom method （EAM） interatomic potential is determined based on the generalized gradient approximation calculation within the framework of the density functional theory using Perdew-Burke-Ernzerhof exchange-correlation functional at the spin-polarized level. The physical properties, such as the cohesive energy, the lattice constant, the bulk modulus, the shear modulus, the sc/fec relative energy, the hep/fce rela- tive energy, the shear modulus and the monovacaney formation energy are used to evaluate the EAM potential parameters. The U-U pair potential determined by the first principle calculations is in agreement with that defined by the EAM potential parameters. The EAM calculated formation energy of the monovacancy in the fee structure is also found to be in close agreement with DFT calculation.展开更多
To understand the atomistic mechanisms of tension failure of Ni-based superalloy,in this study,the classical molecular dynamics(MD)simulations were used to study the uniaxial tension processes of both the Ni/Ni3 Al in...To understand the atomistic mechanisms of tension failure of Ni-based superalloy,in this study,the classical molecular dynamics(MD)simulations were used to study the uniaxial tension processes of both the Ni/Ni3 Al interface systems and the pure Ni and Ni3 Al systems.To examine the effects of interatomic potentials,we adopted embedded atom method(EAM)and reactive force field(ReaxFF)in the MD simulations.The results of EAM simulations showed that the amorphous structures and voids formed near the interface,facilitating further crack propagation within Ni matrix.The EAM potentials also predicted that dislocations were generated and annihilated alternatively,leading to the oscillation of yielding stress during the tension process.The ReaxFF simulations predicted more amorphous formation and larger tensile strength.The atomistic understanding of the defect initiation and propagation during tension process may help to develop the strengthening strategy for controlling the defect evolution under loading.展开更多
Molecular dynamics simulation was used to simulate the thermodynamic properties of three binary alloys,Pb-Ag （1：1）,Pb-Ag （4：1）,and Pb-Ag （9：1）.The energy functions,such as excess free energy,cohesive energy,a...Molecular dynamics simulation was used to simulate the thermodynamic properties of three binary alloys,Pb-Ag （1：1）,Pb-Ag （4：1）,and Pb-Ag （9：1）.The energy functions,such as excess free energy,cohesive energy,and formation energy,were calculated.The calculated values agree well with the experimental ones.The atomic interactions were analyzed in macroscopic and microcosmic views and both are consistent well.展开更多
The modified embedded atom method (MEAM) is an empirical extension of the embedded atom method (EAM) that includes angular forces. By fitted to the lattice constants, the cohesive energy, the APE (anti-phase boundary)...The modified embedded atom method (MEAM) is an empirical extension of the embedded atom method (EAM) that includes angular forces. By fitted to the lattice constants, the cohesive energy, the APE (anti-phase boundary) energy, and the vacancy formation energy of TiAl, an accurate MEAM potential is obtained for the TiAl system with L10 structure. The calculation results of the properties of TiAl are in good agreement with experiments and the results of first principle (F.P.) calculations.展开更多
In this paper, thermoelastic problem of onedimensional copper rod under thermal shock is simulated using molecular dynamics method by adopting embedded atom method potential. The rod is on axis x, the left outermost s...In this paper, thermoelastic problem of onedimensional copper rod under thermal shock is simulated using molecular dynamics method by adopting embedded atom method potential. The rod is on axis x, the left outermost surface of which is traction free and the right outermost surface is fixed. Free boundary condition is imposed on the outermost surfaces in direction y and z. The left and right ends of the rod are subjected to hot and cold baths, respectively. Temperature, displacement and stress distributions are obtained along the rod at different moments, which are shown to be limited in the mobile region, indicating that the heat propagation speed is limited rather than infinite. This is consistent with the prediction given by generalized thermoelastic theory. From simulation results we find that the speed of heat conduction is the same as the speed of thermal stress wave. In the present paper, the simulations are conducted using the large-scale atomic/molecular massively parallel simulator and completed visualization software.展开更多
Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can b...Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can be applied to other metals. The dislocation emission from a crack tip has been simulated successfully using molecular dynamics method, the result is in good agreement with the elastic solution.展开更多
The parameters of embedded atom method for elements Ce, Th and Yb were determined by fitting the lattice constants, the cohesive energy, the monovacancy formation energy and the bulk modulus of elements. The alloy pot...The parameters of embedded atom method for elements Ce, Th and Yb were determined by fitting the lattice constants, the cohesive energy, the monovacancy formation energy and the bulk modulus of elements. The alloy potential was taken as the form of Johnson′s. The formation enthalpies of Th-Ce, Th-Yb and Ce-Yb binary alloys systems and Ce-Th-Yb ternary alloy were calculated with the present embedded atom potentials. The calculations for binary alloys are in good agreement with the results calculated with Miedema′s theory. As for the ternary alloy, the calculated formation enthalpies are in good agreement with those extrapolated from the formation enthalpies of constitutive binary alloys by Toop′s model.展开更多
This paper studies the coalescence of heteroclusters Au767 and Ag767 by using molecular dynamics with the embedded atom method, where layer atomic energy is employed to describe the potential energy variation of per a...This paper studies the coalescence of heteroclusters Au767 and Ag767 by using molecular dynamics with the embedded atom method, where layer atomic energy is employed to describe the potential energy variation of per atom in different layers along radial direction. The results show that the coalescence is driven by releasing the atomic energy of the coalesced zone. The deformation, which is induced by substitutional and vacancy diffusion during the coalescence, makes the coalesced cluster disorder. If the summation of the thermal energy and the released atomic energy is large enough to keep the disorder state, the clusters form a metastable liquid droplet; otherwise, the clusters coalesce into a solid cluster when the coalesced cluster reaches the equilibrium state, and the coalesced cluster experiences liquid to solid ordering changes during the coalescence of a solid Au767 with a liquid Ag767 and a liquid Au767 with a liquid Ag767. The centre of figure of the cluster system is shifted during the coalescence process, and higher coalescence temperature causes larger shift degree.展开更多
The modified embedded atom method proposed by authors has been applied to calculating the enthalpies of formation of random alloys and the ordered intermetallic compounds for noble metal binary systems bearing Rh or I...The modified embedded atom method proposed by authors has been applied to calculating the enthalpies of formation of random alloys and the ordered intermetallic compounds for noble metal binary systems bearing Rh or Ir. The present results are in good agreement with those of Miedema theory, available experiments and the first-principles quantum mechanics calculations. The present results indicate that Cu-Rh, Cu-lr, Ag-Rh, Ag-lr, Au-Rh, Au-lr, Pd-Rh and Pd-lr systems are repulsive, however, IMi-Rh, Ni-lr, Pt-lr, Pt-Rh and Rh-lr systems form solid solutions and Ni-Rh, Ni-lr and Pt-Rh show ordering tendency.展开更多
The embedded atom method (EAM) was used to theoretically analyze the effect of the lattice parameter variation on the order-disorder transformation in binary alloys. Based on EAM, it is found that only one kind of ord...The embedded atom method (EAM) was used to theoretically analyze the effect of the lattice parameter variation on the order-disorder transformation in binary alloys. Based on EAM, it is found that only one kind of order-disorder transition (second-order transition) exists for AB alloy. Three groups of order-disorder transformation can be observed for the A(3)B or AB(3) compounds. For group I, the order-disorder is a completely first-order transition. For group II, the order-disorder transformation is a classical first-order transition. For group III, the order-disorder transformation is found to be a second-order transition. The lattice parameter variations have a significant effect on E-2 coefficient, which is related to the ordering energy. These results are in good agreement with experiments.展开更多
Molecular dynamics(MD) simulations are performed to investigate the effects of stress on generalized stacking fault(GSF) energy of three fcc metals(Cu, Al, and Ni). The simulation model is deformed by uniaxial tension...Molecular dynamics(MD) simulations are performed to investigate the effects of stress on generalized stacking fault(GSF) energy of three fcc metals(Cu, Al, and Ni). The simulation model is deformed by uniaxial tension or compression in each of [111], [11-2], and [1-10] directions, respectively, before shifting the lattice to calculate the GSF curve. Simulation results show that the values of unstable stacking fault energy(γusf), stable stacking fault energy(γsf), and unstable twin fault energy(γutf) of the three elements can change with the preloaded tensile or compressive stress in different directions.The ratio of γsf/γusf, which is related to the energy barrier for full dislocation nucleation, and the ratio of γutf/γusf, which is related to the energy barrier for twinning formation are plotted each as a function of the preloading stress. The results of this study reveal that the stress state can change the energy barrier of defect nucleation in the crystal lattice, and thereby can play an important role in the deformation mechanism of nanocrystalline material.展开更多
The Pu-He pair potential fitted by ab initio data, and the Pu-Pu and He-He modified embedded atom method (MEAM) poten-tials have been implemented to perform multi-scale simulations for the interactions of fracture wit...The Pu-He pair potential fitted by ab initio data, and the Pu-Pu and He-He modified embedded atom method (MEAM) poten-tials have been implemented to perform multi-scale simulations for the interactions of fracture with the self-interstitial atom(SIA), He interstitial atom and He-vacancy clusters. The simulation results indicate that Pu atoms around the fracture agglom-erate into an elliptic self-interstitial loop. Interstitial He atoms evolve into separate interstitial atoms, small He atom clustersand some substitutional He atoms. The He-vacancy cluster forms a spheric structure with a 1:1 He-to-vacancy ratio. Finally,the existence of self-interstitial atoms will lead to the local change of Pu lattice and an increasing disorder, and the wholesimulation cell shows a melting state at about 10.0 ps.展开更多
The modified embedded atom method(MEAM)with the universal form of embedding function and a modified energy term along with the pair potential has been employed to determine the potentials for alkali metals:Na,K,by fit...The modified embedded atom method(MEAM)with the universal form of embedding function and a modified energy term along with the pair potential has been employed to determine the potentials for alkali metals:Na,K,by fitting to the Cauchy pressure(C_(12)−C_(44))/2,shear constants Gv=(C_(11)−C_(12)+3C_(44))/5 and C_(44),the cohesive energy and the vacancy formation energy.The obtained potentials are used to calculate the phonon dispersions of these metals.Using these calculated phonons we evaluate the local density of states of neighbours of vacancy using Green’s function method.The local density of states of neighbours of vacancy has been used to calculate mean square displacements of these atoms and formation entropy of vacancy.The calculated mean square displacements of both 1st and 2nd neighbours of vacancy are found to be lower than that of host atom.The calculated phonon dispersions agree well with the experimental phonon dispersion curves and the calculated results of vacancy formation entropy compare well with the other available results.展开更多
Molecular dynamics simulations using embedded atom method (EAM) potential were performed to study nano-void growth and coalescence at grain boundary in face-centered cubic bicrystal copper. Thin-plate specimens subjec...Molecular dynamics simulations using embedded atom method (EAM) potential were performed to study nano-void growth and coalescence at grain boundary in face-centered cubic bicrystal copper. Thin-plate specimens subjected to uniaxial tension strain with one-void and two-void at the centered grain boundary were employed to analyze the effect of specimen size, temperature and applied strain rate on the stress-strain response, incipient yield strength and macroscopic effective Young's modulus. The evolutions of dislocations, twin bands and void shapes under different specimen sizes were also presented. The obtained results show that, regardless of the void numbers, the specimen sizes, temperature, the applied strain rate had significant influence on the void shape evolution, stress-strain curve and incipient yield strength, while negligible effects on the macroscopic effective Young's modulus except for the temperature. Moreover, the voids growth rate along the grain boundary was also found to be associated with the specimen sizes.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 61078057 and 11204227)the Scientific Research Program of Education Department of Shaanxi Province, China (Grant No. 12JK0958)
文摘By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three high symmetry directions and four oft-symmetry directions, and then simulate the phonon dispersion curves of Cu at high pressures of 50, 100, and 150 GPa. The results show that the shapes of dispersion curves at high pressures are very similar to that at zero pressure. All the vibration frequencies of Cu in all vibration branches at high pressures are larger than the results at zero pressure, and increase correspondingly as pressure reaches 50, 100, and 150 GPa sequentially. Moreover, on the basis of phonon dispersion, we calculate the values of specific heat of Cu at different pressures. The prediction of thermodynamic quantities lays a significant foundation for guiding and judging experiments of thermodynamic properties of solids under high pressures.
文摘The electronic state and potential data of U2 molecules are performed by first principle calculations with B3LYP hybrid exchange-correlation functional, the valence electrons of U atom are treated with the （5s4p3d4f）/[3s3p2d2f] contraction basis sets, and the cores are approximated with the relativistic effective core potential. The results show that the ground electronic state is x^9∑g＋. The pair potential data are fitted with a Murrell-Sorbie analytical potential function. The U-U embedded atom method （EAM） interatomic potential is determined based on the generalized gradient approximation calculation within the framework of the density functional theory using Perdew-Burke-Ernzerhof exchange-correlation functional at the spin-polarized level. The physical properties, such as the cohesive energy, the lattice constant, the bulk modulus, the shear modulus, the sc/fec relative energy, the hep/fce rela- tive energy, the shear modulus and the monovacaney formation energy are used to evaluate the EAM potential parameters. The U-U pair potential determined by the first principle calculations is in agreement with that defined by the EAM potential parameters. The EAM calculated formation energy of the monovacancy in the fee structure is also found to be in close agreement with DFT calculation.
基金financially supported by the National Key Research and Development Program of China(Grant Nos.2017YFB0701502 and 2017YFB0702901)the National Nature Science Foundation of China(Grant No.91641128)
文摘To understand the atomistic mechanisms of tension failure of Ni-based superalloy,in this study,the classical molecular dynamics(MD)simulations were used to study the uniaxial tension processes of both the Ni/Ni3 Al interface systems and the pure Ni and Ni3 Al systems.To examine the effects of interatomic potentials,we adopted embedded atom method(EAM)and reactive force field(ReaxFF)in the MD simulations.The results of EAM simulations showed that the amorphous structures and voids formed near the interface,facilitating further crack propagation within Ni matrix.The EAM potentials also predicted that dislocations were generated and annihilated alternatively,leading to the oscillation of yielding stress during the tension process.The ReaxFF simulations predicted more amorphous formation and larger tensile strength.The atomistic understanding of the defect initiation and propagation during tension process may help to develop the strengthening strategy for controlling the defect evolution under loading.
基金supported by the National Natural Science Foundation of China-Yunnan United Foundation (No. U0837604)
文摘Molecular dynamics simulation was used to simulate the thermodynamic properties of three binary alloys,Pb-Ag （1：1）,Pb-Ag （4：1）,and Pb-Ag （9：1）.The energy functions,such as excess free energy,cohesive energy,and formation energy,were calculated.The calculated values agree well with the experimental ones.The atomic interactions were analyzed in macroscopic and microcosmic views and both are consistent well.
基金the National Natural Science Foundation of China.
文摘The modified embedded atom method (MEAM) is an empirical extension of the embedded atom method (EAM) that includes angular forces. By fitted to the lattice constants, the cohesive energy, the APE (anti-phase boundary) energy, and the vacancy formation energy of TiAl, an accurate MEAM potential is obtained for the TiAl system with L10 structure. The calculation results of the properties of TiAl are in good agreement with experiments and the results of first principle (F.P.) calculations.
基金supported by the National Natural Science Foundation of China (10872158)
文摘In this paper, thermoelastic problem of onedimensional copper rod under thermal shock is simulated using molecular dynamics method by adopting embedded atom method potential. The rod is on axis x, the left outermost surface of which is traction free and the right outermost surface is fixed. Free boundary condition is imposed on the outermost surfaces in direction y and z. The left and right ends of the rod are subjected to hot and cold baths, respectively. Temperature, displacement and stress distributions are obtained along the rod at different moments, which are shown to be limited in the mobile region, indicating that the heat propagation speed is limited rather than infinite. This is consistent with the prediction given by generalized thermoelastic theory. From simulation results we find that the speed of heat conduction is the same as the speed of thermal stress wave. In the present paper, the simulations are conducted using the large-scale atomic/molecular massively parallel simulator and completed visualization software.
基金The project supported by the National Natural Science Foundation of China
文摘Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can be applied to other metals. The dislocation emission from a crack tip has been simulated successfully using molecular dynamics method, the result is in good agreement with the elastic solution.
文摘The parameters of embedded atom method for elements Ce, Th and Yb were determined by fitting the lattice constants, the cohesive energy, the monovacancy formation energy and the bulk modulus of elements. The alloy potential was taken as the form of Johnson′s. The formation enthalpies of Th-Ce, Th-Yb and Ce-Yb binary alloys systems and Ce-Th-Yb ternary alloy were calculated with the present embedded atom potentials. The calculations for binary alloys are in good agreement with the results calculated with Miedema′s theory. As for the ternary alloy, the calculated formation enthalpies are in good agreement with those extrapolated from the formation enthalpies of constitutive binary alloys by Toop′s model.
基金supported by the National Natural Science Foundation of China (Grant No 50374027)the program for New Century Excellent Talents in University of China (Grant No NCET-06-0289)the 111 project of China (Grant No B07015)
文摘This paper studies the coalescence of heteroclusters Au767 and Ag767 by using molecular dynamics with the embedded atom method, where layer atomic energy is employed to describe the potential energy variation of per atom in different layers along radial direction. The results show that the coalescence is driven by releasing the atomic energy of the coalesced zone. The deformation, which is induced by substitutional and vacancy diffusion during the coalescence, makes the coalesced cluster disorder. If the summation of the thermal energy and the released atomic energy is large enough to keep the disorder state, the clusters form a metastable liquid droplet; otherwise, the clusters coalesce into a solid cluster when the coalesced cluster reaches the equilibrium state, and the coalesced cluster experiences liquid to solid ordering changes during the coalescence of a solid Au767 with a liquid Ag767 and a liquid Au767 with a liquid Ag767. The centre of figure of the cluster system is shifted during the coalescence process, and higher coalescence temperature causes larger shift degree.
基金This work is partly supported by The National Natural Science Foundation of China(59762001)Guangxi Natural Science Foundation(9811031)the Foundation of Ten-Hundred-Thousand Project of Personnel Department of Guangxi(2000209).
文摘The modified embedded atom method proposed by authors has been applied to calculating the enthalpies of formation of random alloys and the ordered intermetallic compounds for noble metal binary systems bearing Rh or Ir. The present results are in good agreement with those of Miedema theory, available experiments and the first-principles quantum mechanics calculations. The present results indicate that Cu-Rh, Cu-lr, Ag-Rh, Ag-lr, Au-Rh, Au-lr, Pd-Rh and Pd-lr systems are repulsive, however, IMi-Rh, Ni-lr, Pt-lr, Pt-Rh and Rh-lr systems form solid solutions and Ni-Rh, Ni-lr and Pt-Rh show ordering tendency.
基金the National Natural Science Foundation of China under contract No. 59895151-01.]
文摘The embedded atom method (EAM) was used to theoretically analyze the effect of the lattice parameter variation on the order-disorder transformation in binary alloys. Based on EAM, it is found that only one kind of order-disorder transition (second-order transition) exists for AB alloy. Three groups of order-disorder transformation can be observed for the A(3)B or AB(3) compounds. For group I, the order-disorder is a completely first-order transition. For group II, the order-disorder transformation is a classical first-order transition. For group III, the order-disorder transformation is found to be a second-order transition. The lattice parameter variations have a significant effect on E-2 coefficient, which is related to the ordering energy. These results are in good agreement with experiments.
基金supported by Australia Research Council Discovery Projects(Grant No.DP130103973)financially supported by the China Scholarship Council(CSC)
文摘Molecular dynamics(MD) simulations are performed to investigate the effects of stress on generalized stacking fault(GSF) energy of three fcc metals(Cu, Al, and Ni). The simulation model is deformed by uniaxial tension or compression in each of [111], [11-2], and [1-10] directions, respectively, before shifting the lattice to calculate the GSF curve. Simulation results show that the values of unstable stacking fault energy(γusf), stable stacking fault energy(γsf), and unstable twin fault energy(γutf) of the three elements can change with the preloaded tensile or compressive stress in different directions.The ratio of γsf/γusf, which is related to the energy barrier for full dislocation nucleation, and the ratio of γutf/γusf, which is related to the energy barrier for twinning formation are plotted each as a function of the preloading stress. The results of this study reveal that the stress state can change the energy barrier of defect nucleation in the crystal lattice, and thereby can play an important role in the deformation mechanism of nanocrystalline material.
文摘The Pu-He pair potential fitted by ab initio data, and the Pu-Pu and He-He modified embedded atom method (MEAM) poten-tials have been implemented to perform multi-scale simulations for the interactions of fracture with the self-interstitial atom(SIA), He interstitial atom and He-vacancy clusters. The simulation results indicate that Pu atoms around the fracture agglom-erate into an elliptic self-interstitial loop. Interstitial He atoms evolve into separate interstitial atoms, small He atom clustersand some substitutional He atoms. The He-vacancy cluster forms a spheric structure with a 1:1 He-to-vacancy ratio. Finally,the existence of self-interstitial atoms will lead to the local change of Pu lattice and an increasing disorder, and the wholesimulation cell shows a melting state at about 10.0 ps.
文摘The modified embedded atom method(MEAM)with the universal form of embedding function and a modified energy term along with the pair potential has been employed to determine the potentials for alkali metals:Na,K,by fitting to the Cauchy pressure(C_(12)−C_(44))/2,shear constants Gv=(C_(11)−C_(12)+3C_(44))/5 and C_(44),the cohesive energy and the vacancy formation energy.The obtained potentials are used to calculate the phonon dispersions of these metals.Using these calculated phonons we evaluate the local density of states of neighbours of vacancy using Green’s function method.The local density of states of neighbours of vacancy has been used to calculate mean square displacements of these atoms and formation entropy of vacancy.The calculated mean square displacements of both 1st and 2nd neighbours of vacancy are found to be lower than that of host atom.The calculated phonon dispersions agree well with the experimental phonon dispersion curves and the calculated results of vacancy formation entropy compare well with the other available results.
基金supported by the Open Foundation of State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology (Grant No. KFJJ11-0Y)the National Basic Research Program of China (Grant No. 2010CB631005)the National Natural Science Foundation of China (Grant Nos. 11172148 and 51071094)
文摘Molecular dynamics simulations using embedded atom method (EAM) potential were performed to study nano-void growth and coalescence at grain boundary in face-centered cubic bicrystal copper. Thin-plate specimens subjected to uniaxial tension strain with one-void and two-void at the centered grain boundary were employed to analyze the effect of specimen size, temperature and applied strain rate on the stress-strain response, incipient yield strength and macroscopic effective Young's modulus. The evolutions of dislocations, twin bands and void shapes under different specimen sizes were also presented. The obtained results show that, regardless of the void numbers, the specimen sizes, temperature, the applied strain rate had significant influence on the void shape evolution, stress-strain curve and incipient yield strength, while negligible effects on the macroscopic effective Young's modulus except for the temperature. Moreover, the voids growth rate along the grain boundary was also found to be associated with the specimen sizes.
