Using the Gleeble-1500 D simulator, the hot deformation behavior and dynamic recrystallization critical conditions of the 10%Ti C/Cu-Al2O3(volume fraction) composite were investigated by compression tests at the tempe...Using the Gleeble-1500 D simulator, the hot deformation behavior and dynamic recrystallization critical conditions of the 10%Ti C/Cu-Al2O3(volume fraction) composite were investigated by compression tests at the temperatures from 450 °C to 850 °C with the strain rates from 0.001 s-1 to 1 s-1. The results show that the softening mechanism of the dynamic recrystallization is a feature of high-temperature flow true stress-strain curves of the composite, and the peak stress increases with the decreasing deformation temperature or the increasing strain rate. The thermal deformation activation energy was calculated as 170.732 k J/mol and the constitutive equation was established. The inflection point in the lnθ-ε curve appears and the minimum value of-(lnθ)/ε-ε curve is presented when the critical state is attained for this composite. The critical strain increases with the increasing strain rate or the decreasing deformation temperature. There is linear relationship between critical strain and peak strain, i.e., εc=0.572εp. The predicting model of critical strain is described by the function of εc=1.062×10-2Z0.0826.展开更多
The NiAl–TiC–TiB2 composites were processed by self-propagating high-temperature synthesis（SHS） method using raw powders of Ni, Al, Ti, B4 C, TiC, and TiB2, and their microstructure and micro-hardness were investi...The NiAl–TiC–TiB2 composites were processed by self-propagating high-temperature synthesis（SHS） method using raw powders of Ni, Al, Ti, B4 C, TiC, and TiB2, and their microstructure and micro-hardness were investigated. The TiC–TiB2 in NiAl matrix, with contents from 10 to 30 wt%, emerged with the use of two methods： in situ formed and externally added. The results show that all final products are composed of three phases of NiAl, TiC, and TiB2. The microstructures of NiAl–TiC–TiB2 composites with in situ-formed TiC and TiB2 are fine, and all the three phases are distributed uniformly. The grains of NiAl matrix in the composites have been greatly refined, and the micro-hardness of NiAl increases from 381 HV100 to 779 HV100. However, the microstructures of NiAl–TiC–TiB2 composites with externally added TiC and TiB2 are coarse and inhomogeneous, with severe agglomeration of TiC and TiB2 particles. The samples containing externally added 30 wt% TiC–TiB2attain the micro-hardness of 485 HV100. The microstructure evolution and fracture mode of the two kinds of NiAl–TiC–TiB2 composites are different.展开更多
Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is ...Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions（PTBCs,also known as traction continuity conditions）are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element（FE）analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional（UD）fiber-reinforced composites.展开更多
The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wa...The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.展开更多
This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls...This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls(2020)and the one by Zhou(2020),respectively.The proofs in this paper are much simpler than the previous ones.展开更多
基金Project(51101052) supported by the National Natural Science Foundation of China
文摘Using the Gleeble-1500 D simulator, the hot deformation behavior and dynamic recrystallization critical conditions of the 10%Ti C/Cu-Al2O3(volume fraction) composite were investigated by compression tests at the temperatures from 450 °C to 850 °C with the strain rates from 0.001 s-1 to 1 s-1. The results show that the softening mechanism of the dynamic recrystallization is a feature of high-temperature flow true stress-strain curves of the composite, and the peak stress increases with the decreasing deformation temperature or the increasing strain rate. The thermal deformation activation energy was calculated as 170.732 k J/mol and the constitutive equation was established. The inflection point in the lnθ-ε curve appears and the minimum value of-(lnθ)/ε-ε curve is presented when the critical state is attained for this composite. The critical strain increases with the increasing strain rate or the decreasing deformation temperature. There is linear relationship between critical strain and peak strain, i.e., εc=0.572εp. The predicting model of critical strain is described by the function of εc=1.062×10-2Z0.0826.
基金financially supported by the National Natural Science Foundation of China(Nos.51072104 and 51272141)Tai Shan Scholars Project of Shandong Province,China(No.ts20110828)
文摘The NiAl–TiC–TiB2 composites were processed by self-propagating high-temperature synthesis（SHS） method using raw powders of Ni, Al, Ti, B4 C, TiC, and TiB2, and their microstructure and micro-hardness were investigated. The TiC–TiB2 in NiAl matrix, with contents from 10 to 30 wt%, emerged with the use of two methods： in situ formed and externally added. The results show that all final products are composed of three phases of NiAl, TiC, and TiB2. The microstructures of NiAl–TiC–TiB2 composites with in situ-formed TiC and TiB2 are fine, and all the three phases are distributed uniformly. The grains of NiAl matrix in the composites have been greatly refined, and the micro-hardness of NiAl increases from 381 HV100 to 779 HV100. However, the microstructures of NiAl–TiC–TiB2 composites with externally added TiC and TiB2 are coarse and inhomogeneous, with severe agglomeration of TiC and TiB2 particles. The samples containing externally added 30 wt% TiC–TiB2attain the micro-hardness of 485 HV100. The microstructure evolution and fracture mode of the two kinds of NiAl–TiC–TiB2 composites are different.
文摘Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions（PTBCs,also known as traction continuity conditions）are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element（FE）analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional（UD）fiber-reinforced composites.
基金Supported by National Natural Science Foundation of China (10775148,10975146,11035006)
文摘The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.
基金Supported by NSFC(Grant Nos.12171491 and 12071006)。
文摘This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls(2020)and the one by Zhou(2020),respectively.The proofs in this paper are much simpler than the previous ones.
