Dislocation and grain boundary have great influence on helium behavior in materials. In this paper, the helium bubble coalescence in titanium with dislocations was simulated using molecular dynamics method. The result...Dislocation and grain boundary have great influence on helium behavior in materials. In this paper, the helium bubble coalescence in titanium with dislocations was simulated using molecular dynamics method. The results show that, when the second helium bubble nucleates near the slip plane, it grows toward the first helium bubble which lies at the dislocation core till they coalesce with each other. However, it is not easy for the coalescence to occur if the two helium bubbles lie in different atomic layers in (001) plane. If the second helium bubble is nucleated on the side of the slip plane with full atomic layers, the second helium bubble growth could lead to the movement of the first helium bubble toward the other sides of the slip plane. The growth rate and direction of the second helium bubble are closely related to the pressure around it.展开更多
The helium bubble structure and growth modes near dislocations in titanium are studied using the molecular dynamics method. A helium crystal with an HCP structure in titanium is found to have a lattice constant of 1.9...The helium bubble structure and growth modes near dislocations in titanium are studied using the molecular dynamics method. A helium crystal with an HCP structure in titanium is found to have a lattice constant of 1.977 A？ at 0 K. On either side of the slip plane, helium bubbles form in the（001） plane, but they are in different growth modes. On the side of the slip plane with full atomic layers, helium bubbles grow toward the slip plane and easily cross the slip plane. In the growth process, the position of the top surface of the helium bubble remains almost unchanged. On the other side of the slip plane,the helium bubble grows initially toward the dislocation core, but it is difficult to cross the slip plane, which results in growth in the opposite direction upon reaching the slip plane.展开更多
It is an important mechanical parameter for fracture toughness that affects hydraulic fracturing.Some methods such as indoor test core and logging data interpretation are commonly used to obtain fracture toughness.The...It is an important mechanical parameter for fracture toughness that affects hydraulic fracturing.Some methods such as indoor test core and logging data interpretation are commonly used to obtain fracture toughness.These methods,however,have their own limitations.Liu's method has focused the mechanical properties of shale including fracture toughness based on micro-/nano-indentation experiments.Zeng's method has pointed that the former method of calculating fracture toughness ignores the maximum holding stage in the indentation-displacement curves,they point out and correct the fracture stress intensity factor model,but the final calculation of the fracture toughness of the numerical difference is of two orders of magnitude.In this paper,micro-indentation experiments were carried out to further analyze and correct the model by collecting and analyzing Longmaxi shale cuttings.After Zeng and Liu's methods are combined,the irreversible elastic energy by energy area actually was measured.To some extent,the difference between the two kinds of fracture toughness is reduced.展开更多
Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by definin...Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.展开更多
基金supported by the National Natural Science Foundation of China(No.22038011,No.22078257,No.22108213,No.52176142)the China Postdoctoral Science Foundation(2021M692548)+1 种基金the Joint Fund of the Yulin University and the Dalian National Laboratory for Clean Energy(Grant YLU-DNL Fund 2022001)the Young Talent Support Plan of Shaanxi Province。
文摘Dislocation and grain boundary have great influence on helium behavior in materials. In this paper, the helium bubble coalescence in titanium with dislocations was simulated using molecular dynamics method. The results show that, when the second helium bubble nucleates near the slip plane, it grows toward the first helium bubble which lies at the dislocation core till they coalesce with each other. However, it is not easy for the coalescence to occur if the two helium bubbles lie in different atomic layers in (001) plane. If the second helium bubble is nucleated on the side of the slip plane with full atomic layers, the second helium bubble growth could lead to the movement of the first helium bubble toward the other sides of the slip plane. The growth rate and direction of the second helium bubble are closely related to the pressure around it.
基金supported by the National Natural Science Foundation of China(Grant No.11505120)the Project of Innovative Talents of North China University of Water Resources and Electric Power,China(Grant No.70483)
文摘The helium bubble structure and growth modes near dislocations in titanium are studied using the molecular dynamics method. A helium crystal with an HCP structure in titanium is found to have a lattice constant of 1.977 A？ at 0 K. On either side of the slip plane, helium bubbles form in the（001） plane, but they are in different growth modes. On the side of the slip plane with full atomic layers, helium bubbles grow toward the slip plane and easily cross the slip plane. In the growth process, the position of the top surface of the helium bubble remains almost unchanged. On the other side of the slip plane,the helium bubble grows initially toward the dislocation core, but it is difficult to cross the slip plane, which results in growth in the opposite direction upon reaching the slip plane.
基金This work is supported by the National Natural Science Foundation of China(Grant No.51604230)the Young Elite Scientists Sponsorship Program by CAST(2017QNRC001)the Scientific Research Foundation of International Cooperation and Exchanges of Sichuan Province(Grant Nos.2017HH0061&2016HH0001).
文摘It is an important mechanical parameter for fracture toughness that affects hydraulic fracturing.Some methods such as indoor test core and logging data interpretation are commonly used to obtain fracture toughness.These methods,however,have their own limitations.Liu's method has focused the mechanical properties of shale including fracture toughness based on micro-/nano-indentation experiments.Zeng's method has pointed that the former method of calculating fracture toughness ignores the maximum holding stage in the indentation-displacement curves,they point out and correct the fracture stress intensity factor model,but the final calculation of the fracture toughness of the numerical difference is of two orders of magnitude.In this paper,micro-indentation experiments were carried out to further analyze and correct the model by collecting and analyzing Longmaxi shale cuttings.After Zeng and Liu's methods are combined,the irreversible elastic energy by energy area actually was measured.To some extent,the difference between the two kinds of fracture toughness is reduced.
基金Supported by the Natural Science Foundation of Hebei Province(61203142)
文摘Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.
