This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
Barium titanate[BaTiO_(3)(BT)]-based ceramics are typical ferroelectric materials.Here,the discontinuous grain growth(DGG)and relevant grain size effect are deeply studied.An obvious DGG phenomenon is observed in a pa...Barium titanate[BaTiO_(3)(BT)]-based ceramics are typical ferroelectric materials.Here,the discontinuous grain growth(DGG)and relevant grain size effect are deeply studied.An obvious DGG phenomenon is observed in a paradigmatic Zr^(4+)-doped BT-based ceramic,with grains growing from∼2.2–6.6 to∼121.8–198.4μm discontinuously near 1320℃.It is found that fine grains can get together and grow into large ones with liquid phase surrounding them above eutectic temperature.Then the grain boundary density(D g)is quantitatively studied and shows a first-order reciprocal relationship with grain size,and the grain size effect is dependent on D g.Fine grains lead to high D g,and then cause fine domains and pseudocubic-like phase structure because of the interrupted long-range ferroelectric orders by grain boundary.High D g also causes the diffusion phase transition and low Curie dielectric peak due to the distribution of phase transition temperature induced by internal stress.Local domain switching experiments reveal that the polarization orientation is more difficult near the grain boundary,implying that the grain boundary inhibition dominates the process of polarization orientation in fine-grain ceramics,which leads to low polarization but a high coercive field.However,large-grain ceramics exhibit easy domain switching and high&similar ferroelectricity.This work reveals that the grain boundary effect dominates the grain size effect in fine-grain ceramics,and expands current knowledge on DGG and grain size effect in polycrystalline materials.展开更多
The microstructures and mechanical properties of the directionally solidified Cu-15Ni-8Sn alloy were investigated at solidification rates ranging from 100 to 3000μm/s.The results showed that the solidification rate s...The microstructures and mechanical properties of the directionally solidified Cu-15Ni-8Sn alloy were investigated at solidification rates ranging from 100 to 3000μm/s.The results showed that the solidification rate significantly affects the phase distribution of the as-cast Cu-15Ni-8Sn alloy.The primary and secondary dendritic spacing reduces and eventually becomes stable as the solidification rate increases.Meanwhile,the size of the primary phase decreases,and its distribution becomes more uniform.The most severe segregation problem of this alloy has been greatly improved.Upon solidification at 100μm/s,the as-cast Cu-15Ni-8Sn alloy consists of the α-Cu matrix,γ-CuNi_(2)Sn phase,discontinuous precipitation structure,modulated structure,and DO_(22) ordered phases.However,as the solidification rate increases,the discontinuous precipitation structure,modulated structures,and DO_(22) ordered phases decrease and even disappear,reducing hardness.As the solidification rate increases,after homogenization treatment,the composition and microhardness distributions of Cu-15Ni-8Sn alloy become more uniform.The time for homogenization is also shortened.It reduces production energy usage and facilitates further mechanical processing.展开更多
The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fati...The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fatigue life has made certain progress. According to the law of thermodynamics, a new damage evolution equation is developed in the present study to predict the fatigue life of geometrically discontinuous structure under tension-torsion loading based on damage mechanics and the critical plane method. The essence of this approach is tha t the st rain parame ter of the uniaxial nonlinear fatigue damage model is replaced with the equivalent strain, which consists of the releva nt parame ters of the critical plane. However, it is difficult to calculate the stress-strain status and the critical plane position of geometrically dis? continuous structure by theoretical methods because of the existence of stress concentration and the multiaxial nonproportional characteristics. Therefore, a new numerical simulation method is proposed to determine the critical plane of geometrically discontinuous structure under multiaxial loading by means of the finite element method and MATLAB software. The fatigue life of notched specimens subjected to combined bending and torsion is predicted using the proposed met hod, and the result is compared with t hose from the experimen ts and the Manson-Cfiffin law. The comparisons show that the proposed method is superior to the Manson-Coffin law and is capable of reproducing the experimental results reasonably when the geometry of the structure is complex. It completely meets the needs of engineering practice.展开更多
We explored such issues as the formation mechanism,structure and propriety of the solid solutions of anthracene(ANT)-phenanthrene(PHE).Solution crystallization and solid-state grinding were employed to prepare solid s...We explored such issues as the formation mechanism,structure and propriety of the solid solutions of anthracene(ANT)-phenanthrene(PHE).Solution crystallization and solid-state grinding were employed to prepare solid solutions under different conditions.The thermal behavior and PXRD scanning results revealed the formation of discontinuous solid solutions,whose melting points and crystal lattices varied linearly with mixed ratio.Combing with Materials Studio,the formation possibility of solid solutions were investigated by evaluating the change of the energy.The crystal morphology of the solid solutions have a positive correlation with the change of the major part.Finally,the solution crystallization process of solid solution were studied using the population balance model.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金financially supported by the National Natu-ral Science Foundation of China(Nos.12104093,52072075,and 52102126)the Natural Science Foundation of Fujian Province(Nos.2021J05122,2021J05123,2022J01087,and 2022J01552)+2 种基金the Sichuan Province Science and Technology Support Program(No.2021YJ0560,22ZDYF3306,2022NSFSC1970,and 2022YFG0099)the Qishan Scholar Financial Support from Fuzhou University(No.GXRC-20099)the Fundamental Research Funds for the Central Universities,Southwest Minzu University(No.2020NTD03).
文摘Barium titanate[BaTiO_(3)(BT)]-based ceramics are typical ferroelectric materials.Here,the discontinuous grain growth(DGG)and relevant grain size effect are deeply studied.An obvious DGG phenomenon is observed in a paradigmatic Zr^(4+)-doped BT-based ceramic,with grains growing from∼2.2–6.6 to∼121.8–198.4μm discontinuously near 1320℃.It is found that fine grains can get together and grow into large ones with liquid phase surrounding them above eutectic temperature.Then the grain boundary density(D g)is quantitatively studied and shows a first-order reciprocal relationship with grain size,and the grain size effect is dependent on D g.Fine grains lead to high D g,and then cause fine domains and pseudocubic-like phase structure because of the interrupted long-range ferroelectric orders by grain boundary.High D g also causes the diffusion phase transition and low Curie dielectric peak due to the distribution of phase transition temperature induced by internal stress.Local domain switching experiments reveal that the polarization orientation is more difficult near the grain boundary,implying that the grain boundary inhibition dominates the process of polarization orientation in fine-grain ceramics,which leads to low polarization but a high coercive field.However,large-grain ceramics exhibit easy domain switching and high&similar ferroelectricity.This work reveals that the grain boundary effect dominates the grain size effect in fine-grain ceramics,and expands current knowledge on DGG and grain size effect in polycrystalline materials.
基金supported by the National Key Research and Development Program of China(Grant No.2020YFA0714400)Science and Technology Projects of Jiangxi Provincial Department of Education(Grant Nos.GJ210843 and GJJ200873)+2 种基金Scientific Research Starting Foundation for Advanced Talents of Jiangxi University of Science and Technology(Grant No.205200100570)the Project of the Key Scientific and Technological of Jiangxi Province(Grant No.20181BCB19003)Ningbo Enterprise Innovation Consortium Special Project(Grant No.2021H003).
文摘The microstructures and mechanical properties of the directionally solidified Cu-15Ni-8Sn alloy were investigated at solidification rates ranging from 100 to 3000μm/s.The results showed that the solidification rate significantly affects the phase distribution of the as-cast Cu-15Ni-8Sn alloy.The primary and secondary dendritic spacing reduces and eventually becomes stable as the solidification rate increases.Meanwhile,the size of the primary phase decreases,and its distribution becomes more uniform.The most severe segregation problem of this alloy has been greatly improved.Upon solidification at 100μm/s,the as-cast Cu-15Ni-8Sn alloy consists of the α-Cu matrix,γ-CuNi_(2)Sn phase,discontinuous precipitation structure,modulated structure,and DO_(22) ordered phases.However,as the solidification rate increases,the discontinuous precipitation structure,modulated structures,and DO_(22) ordered phases decrease and even disappear,reducing hardness.As the solidification rate increases,after homogenization treatment,the composition and microhardness distributions of Cu-15Ni-8Sn alloy become more uniform.The time for homogenization is also shortened.It reduces production energy usage and facilitates further mechanical processing.
基金the National Natural Science Foundation of China (Grant No. 51605212)the Natural Science Foundation of Gansu Province (Grant No. 17JR5RA122)the Project of Hongliu First-class Disciplines Development Program of Lanzhou University of Technology.
文摘The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading. Meanwhile, the application of critical plane method in the prediction of multiaxial fatigue life has made certain progress. According to the law of thermodynamics, a new damage evolution equation is developed in the present study to predict the fatigue life of geometrically discontinuous structure under tension-torsion loading based on damage mechanics and the critical plane method. The essence of this approach is tha t the st rain parame ter of the uniaxial nonlinear fatigue damage model is replaced with the equivalent strain, which consists of the releva nt parame ters of the critical plane. However, it is difficult to calculate the stress-strain status and the critical plane position of geometrically dis? continuous structure by theoretical methods because of the existence of stress concentration and the multiaxial nonproportional characteristics. Therefore, a new numerical simulation method is proposed to determine the critical plane of geometrically discontinuous structure under multiaxial loading by means of the finite element method and MATLAB software. The fatigue life of notched specimens subjected to combined bending and torsion is predicted using the proposed met hod, and the result is compared with t hose from the experimen ts and the Manson-Cfiffin law. The comparisons show that the proposed method is superior to the Manson-Coffin law and is capable of reproducing the experimental results reasonably when the geometry of the structure is complex. It completely meets the needs of engineering practice.
文摘We explored such issues as the formation mechanism,structure and propriety of the solid solutions of anthracene(ANT)-phenanthrene(PHE).Solution crystallization and solid-state grinding were employed to prepare solid solutions under different conditions.The thermal behavior and PXRD scanning results revealed the formation of discontinuous solid solutions,whose melting points and crystal lattices varied linearly with mixed ratio.Combing with Materials Studio,the formation possibility of solid solutions were investigated by evaluating the change of the energy.The crystal morphology of the solid solutions have a positive correlation with the change of the major part.Finally,the solution crystallization process of solid solution were studied using the population balance model.
