PERTURBED NONLINEAR EVOLUTION INCLUSIONS IN BANACH SPACES

In this paper we discuss tLhe existence results of the integral solutions to nonlinear evolution inclusion: u' (t) ∈ Au(t) +F(t,u(t)), where A is m-dissipative and F is a set valued map in separable Banach spaces, and extend the relative results in references.

Existence Results for Impulsive Neutral Stochastic Evolution Inclusions in Hilbert Space

This paper is concerned with the existence of mild solutions of a class of impulsive neutral stochastic evolution inclusions in Hilbert space in the case where the right hand side is convex or nonconvex-valued. The results are obtained by using two fixed point theorems for multivalued mappings and evolution system theory.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.

Evolution and deformability of inclusions in Al-killed steel with rare earth-alkali metals(Ca or Mg) combined treatment

The quality of stainless steel is closely related to the deformability of inclusions,which is significantly affected by their compositions.The present study first inve stigated the evolution of inclusion compositions in AI-killed steel with rare earth-alkali metals(Ca or Mg)combined treatme nt through four laboratory-scale experiments.The Ce contents in the final steel are 0.0080 wt%,0.015 wt%,0.016 wt%and 0.010 wt%,respectively.The Mg content is 0.0014 wt%in Ce-Mg combined treated steel,and the Ca content is0.0015 wt%in Ce-Ca combined treated steel.The deformability of inclusions in both Ce_(2)O_(3)-Al_(2)O_(3)-CaO and Ce_(2)O_(3)-Al_(2)O_(3)-MgO systems was subsequently evaluated by calculating their Young's modulus at low temperature.The results show that irregular Al_(2)O_(3)and MgAl_(2)O_(4)with poor deformability are modified to CeAlO_(3)and Ce_(2)O_(3)by Ce treatment,resulting in the decrease of Young's modulus of inclusions.The deformability of inclusions is further improved due to the transformation from lumped-like CeAlO_(3)to spherical CaO-Al_(2)O_(3)-Ce_(2)O_(3)caused by Ca treatment,and some of these inclusions are the ones with low liquidus temperature.Thermodynamic analysis was used to discuss the control condition of the formation and evolution of inclusions.Accordingly,the appropriate addition amounts of Al,Mg,Ce,and Ca are expected to control inclusion compositions and properties,including deformability and liquidus temperature,thereby improving the steel performance.

Effect of Transverse Static Magnetic Field on Droplets Transient and Inclusions Evolution During the Electroslag Remelting Process of GCr15 Ingots

The voltage was recorded to investigate the influence of the static magnetic field on droplet evolution during the mag-netically controlled electroslag remelting （MC-ESR） process. MC-ESR experiments were carried out under differentremelting current, and transverse static magnetic fields （TSMF） of 85 mT, 130 mT and 160 mT were superimposed.Statistical work was performed to obtain the quantitative data of the droplets. The ASPEX Explorer was utilized toinvestigate the inclusions evolution of GCr15 ingots. The number of the droplets was 31 in 20 s during the traditional ESRprocess and reached 50 and 51 under the MC-ESR process with the TSMF of 85 mT and 130 mT, respectively. Whencompared the traditional ESR process with the MC-ESR process, the inclusions amount reduced 67%.

Evolution of Al2O3 inclusions by cerium treatment in low carbon high manganese steel

The influence of cerium（Ce）treatment on the morphologies,size and distributions of Al_2O_3 inclusions in low carbon high manganese steel was investigated by OM,SEM-EDS and theoretical calculation.The results showed that Ce can modify the morphologies and types of Al_2O_3 inclusions.After Ce treatment,the irregular Al_2O_3 inclusions were replaced by smaller and dispersive spherical cerium oxysulfides.The effects of treatment time and Ce content on the evolution of Al_2O_3 inclusions were examined.It indicated that Al_2O_3 inclusions were wrapped by rare earth inclusions to form a ring like shape Ce-enriched band around the inclusions.Model was established to elucidate the evolution mechanism of Al_2O_3 inclusions.Evolution kinetics of inclusions was discussed qualitatively to analyze the velocity controlled step.It was found that diffusion of Ce^（3＋）and Al^（3＋）in solid inclusion core and the formed intermediate layer would be the limited step during the evolution process.

Effects of Rare Earth elements on microstructure evolution and mechanical properties of 718H pre-hardened mold steel

718 H Pre-ha rdened mold steels with diffe rent Rare Earth(RE) contents were prepared to investigate the influence of RE on microstructure evolution and mechanical properties through a series of experiments and theoretical analysis.The results indicated that the toal oxygen(T.O) content decreased from 15 ppm to 6 ppm with 0.022 wt% RE addition,which is attributed to the active chemical properties of RE elements.For test steels,RE additions of 0.012 wt% and 0.022 wt% were significantly effective for refining inclusions by eliminating 11.5% large-sized inclusions with diameter exceeding 10 μm compared with that of ORE steel.RE addition contributed to modify irregular MnS and Al2 O3 inclusions into ellipsoidal RE-inclusions(RE2 O,RES,RE2 O2 S and REAlO3).The purification of molten steel and the modification of inclusions by RE treatment have significant effects on improvement of the fatigue crack growth tests(FCG) inhibition ability and impact energy as well as the isotropy.However,excessive addition of RE elements(0.07 wt%)seriously reduced the impact energy,ultimate tensile strength and FCG inhibition ability due to rapidly increase of the volume fraction of large-sized inclusions.In addition to the inclusions formed by RE treatment,trace solid solution RE atoms improve the stability of undercooled austenite,resulting in the transformation region of bainite and perlite of 0.07 RE steel shifting to the bottom right and prolonging the incubation period compared with that of ORE steel.

Inclusion evolution in 50CrVA spring steel by optimization of refining slag

In order to control the CaO-Al;O;-SiO;-MgO system inclusions in 50 CrVA spring steel in a lower melting temperature region,high temperature equilibrium experiments between steel and slag were performed in the laboratory,under the conditions of the initial slag basicity within 3-7and the content of Al;O;between 18-35mass%,to investigate the formation and evolution of this type of inclusion.The results indicate that the total oxygen content in the steel decreases with the increase of slag basicity and the decrease of Al;O;content in slags,and CaO-Al;O;-SiO2-MgO inclusions tend to deviate from the low melting point region with the increase of Al;O;content in slags.The most favorable composition for the refining slag is composed of 51-56mass% CaO,9-13mass% SiO;,20-25mass% Al;O;and 6mass% MgO.In this case,the inclusions in 50 CrVA spring steel are mostly in the low melting point regions,in which their plasticities are expected to improve during steel rolling.The MgO-based inclusions were observed in the steel matrix and the formation mechanism was theoretically and schematically revealed.It is also found that adding around 11mass% of MgO into the refining slags is beneficial to reducing the refractory corrosion.Further work should be carried out focusing on the evolution rates of MgO-based inclusions.

Reoxidation of liquid steel and evolution of inclusions during protective atmosphere electroslag remelting of Ce-containing heat-resistant stainless steel

The evolution of Ce-containing inclusions and its correlation with the reoxidation of liquid steel during protective atmosphere electroslag remelting(ESR)of heat-resistant steel were studied.The reoxidation of liquid steel took place during the ESR,resulting in the oxygen pickup from 0.0014 to 0.0053 wt.%.The inclusions in the consumable electrode,liquid metal pool and remelted ingot are Ce_(2)O_(2)S and Ce_(2)O,inclusions invariably.The inclusions in the remelted ingot are originated from three ways:(I)the original inclusions from the electrode;(Il)the newly formed Ce_(2)O_(2)S and Ce_(2)O_(3) inclusions in the liquid metal pool by reoxidation remaining still in remelted ingot;(IlI)the newly generated Ce2O2S and Ce_(2)O_(3) inclusions during cooling and solidification of liquid steel.The relative proportions of Ce_(2)O_(3) inclusions in liquid metal pool and remelted ingot are 41% and 76.5%,respectively.The inclusions ranging from 2 to 5μm in the remelted ingot take up 55%,followed by the inclusions smaller than 2μm(43%of total inclusions).The number proportion of the Ce_(2)0,inclusions in the liquid metal pool which were removed by floating up into slag is 1.96×10-5%.