Combining with the low temperature material properties and the boiling heat transfer coefficient of specimen immersed in the liquid nitrogen, a numerical model based on metallo-thermo-mechanical couple theory was esta...Combining with the low temperature material properties and the boiling heat transfer coefficient of specimen immersed in the liquid nitrogen, a numerical model based on metallo-thermo-mechanical couple theory was established to reproduce the deep cryogenic treatment （DCT） process of a newly developed cold work die steel Cr8Mo2SiV （SDC99）. Moreover, an experimental setup for rapid temperature measurement was designed to validate the simulation results. The investigation suggests that the differences in temperature and cooling rate between the surface and core of specimen are very significant. However, it should be emphasized that the acute temperature and cooling rate changes during DCT are mainly concentrated on the specimen surface region about 1/3 of the sample thickness. Subjected to DCT, the retained austenite of quenched specimen continues to transform to martensite and finally its phase volume fraction reduces to 2.3%. The predicted results are coincident well with the experimental data, which demonstrates that the numerical model employed in this study can accurately capture the variation characteristics of temperature and microstructure fields during DCT and provide a theoretical guidance for making the reasonable DCT procedure.展开更多
Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much ...Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much simpler than it was, meanwhile the nonstandard characteristics of convergence with respect to u.c. topology is given.展开更多
A local Hankel transformation of order 1/2 is defined for every finite place of the field of rational numbers.Its inversion formula and the Plancherel type theorem are obtained.A Connes type trace formula is given for...A local Hankel transformation of order 1/2 is defined for every finite place of the field of rational numbers.Its inversion formula and the Plancherel type theorem are obtained.A Connes type trace formula is given for each local Hankel transformation of order 1/2.An S-local Connes type trace formula is derived for the S-local Hankel transformation of order 1/2.These formulas are generalizations of Connes' corresponding trace formulas in 1999.展开更多
基金The National Natural Science Foundation of China(11701134)The National Natural Science Foundation of Shandong Province,China(ZR2017JL008)The Science and Technology Plan Project of the Educational Department of Shandong Province,China(J16LI12,J15LI54)
基金Project (51171104) supported by the National Natural Science Foundation of China
文摘Combining with the low temperature material properties and the boiling heat transfer coefficient of specimen immersed in the liquid nitrogen, a numerical model based on metallo-thermo-mechanical couple theory was established to reproduce the deep cryogenic treatment （DCT） process of a newly developed cold work die steel Cr8Mo2SiV （SDC99）. Moreover, an experimental setup for rapid temperature measurement was designed to validate the simulation results. The investigation suggests that the differences in temperature and cooling rate between the surface and core of specimen are very significant. However, it should be emphasized that the acute temperature and cooling rate changes during DCT are mainly concentrated on the specimen surface region about 1/3 of the sample thickness. Subjected to DCT, the retained austenite of quenched specimen continues to transform to martensite and finally its phase volume fraction reduces to 2.3%. The predicted results are coincident well with the experimental data, which demonstrates that the numerical model employed in this study can accurately capture the variation characteristics of temperature and microstructure fields during DCT and provide a theoretical guidance for making the reasonable DCT procedure.
基金Supported by the Speaial Science Foundation of the Edneational Committee of Shaanxi Province(oojk207).
文摘Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much simpler than it was, meanwhile the nonstandard characteristics of convergence with respect to u.c. topology is given.
文摘A local Hankel transformation of order 1/2 is defined for every finite place of the field of rational numbers.Its inversion formula and the Plancherel type theorem are obtained.A Connes type trace formula is given for each local Hankel transformation of order 1/2.An S-local Connes type trace formula is derived for the S-local Hankel transformation of order 1/2.These formulas are generalizations of Connes' corresponding trace formulas in 1999.
