Static tensile test and tensile-tensile fatigue test of medium carbon steel sheet specimens with surface crack precut were performed on MTS810 hydraulic testing machine to clear the meaning of the point of Hp(y) value...Static tensile test and tensile-tensile fatigue test of medium carbon steel sheet specimens with surface crack precut were performed on MTS810 hydraulic testing machine to clear the meaning of the point of Hp(y) value zero. Magnetic memory signals were measured during the test process. The results show that only one point of Hp(y) zero value exists in all measured magnetic signal curves during the loading process, which should be a sign of intersection of positive-negative magnetic poles after magnetic ordered state appears and does not indicate the position of surface crack precut. The analysis shows that the surface crack precut can not interrupt the magnetic ordered state occurred during the test completely, hence its Hp(y) value is not zero. However, the crack extending to a penetrated defect at the instant of specimen′s fracture leads to the discontinuance of magnetic ordered state.展开更多
Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite a...Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite and can be attained.This partially generalizes a well-known work of Chang and Yang(1988)who have obtained the inequality whenβ=0.展开更多
基金This work was financially supported by the National Natural Science Foundation of China (No.50235030, 50505052).
文摘Static tensile test and tensile-tensile fatigue test of medium carbon steel sheet specimens with surface crack precut were performed on MTS810 hydraulic testing machine to clear the meaning of the point of Hp(y) value zero. Magnetic memory signals were measured during the test process. The results show that only one point of Hp(y) zero value exists in all measured magnetic signal curves during the loading process, which should be a sign of intersection of positive-negative magnetic poles after magnetic ordered state appears and does not indicate the position of surface crack precut. The analysis shows that the surface crack precut can not interrupt the magnetic ordered state occurred during the test completely, hence its Hp(y) value is not zero. However, the crack extending to a penetrated defect at the instant of specimen′s fracture leads to the discontinuance of magnetic ordered state.
基金supported by National Natural Science Foundation of China(Grant Nos.11721101 and 11401575)。
文摘Let Ω■R^(2) be a smooth bounded domain with 0∈■Ω.In this paper,we prove that for anyβ∈(0,1),the supremum u∈W^(1,2(Ω)),∫_(Ω)^(sup) udx=0,∫_(Ω)|▽u|^(2)dx≤1∫_(Ω)e^(2π(1-β)u^(2))/|x|^(2β)dx is finite and can be attained.This partially generalizes a well-known work of Chang and Yang(1988)who have obtained the inequality whenβ=0.
