In general, when the one-dimensional heat conduction equation is solved by the method of separation of variables, we need to know the governing equations, two boundary conditions and initial condition. Because the thermophysical parameters in different layers of laminated materials are different, the heat conduction model cannot be expressed by the same governing equation. For each layer of laminated material, the boundary condition is unknown. That equation can-not be solved directly by the general separation variable method. In this work the separation of variable method is extended. The temperature field of laminated material's heat transfer is divided into many minute time intervals on the time axis. Based on differential conception, in a minimum time interval, the temperature at the junction of laminated materials can be considered to be proportional to time. Assume that the slope coefficient makes the boundary condition known, then for each layer of laminated materials, the general separation of variables method will be used to solve the temperature field. According to the same temperature and the energy continuity at the junction of laminated materials, one can solve the slope coefficient. The temperature field in the whole time domain can be obtained through cycling. Then the three-layer insulation materials are analyzed by the extended separation variable method. The correctness of the method is verified by comparing the calculated results with those from the finite element method. The influences of the type and thickness of heat insulation layer, heat transfer coefficient, air temperature on the heat insulation are studied. It is found that the thermal conductivity of the thermal insulation layer has a great influence on the insulation. The material with low heat conduction coefficient can enhance the heat insulation effect. The thicker the thickness of the insulation layer, the more slowly the surface temperature of the heat insulation material rises, and the lower the final temperature, the better the insulation effect is. The thicker the thickness of the insulation layer, the smaller the heat flux density of the heat insulation material shell is, and the better the heat insulation effect when the heat transfer reaches a stable state. All calculation results are consistent with physical phenomena. In this work, the analytical method is used to solve the heat transfer problem of laminated materials. Compared with the general numerical methods, the analytical method presents clear physical meaning and high efficiency of operation as well.
By means of optical microscope, SEM and EDS, the microstructure of laser cladding layer under 1200W laser heat input was analyzed. Through the research, the relationship between precipitate characteristics and properties of the cladding layer was studied, and failure reason was found. The results show that Co, Cr and W elements have the tendency of short-range diffusion in the surface region in Stellite 6 alloy with a jagged shape. In this area, Co-Cr-W-Fe precipitated and hardened layer formed with high hardness and abrasive resistance but a lower ductility. Meanwhile, intergranular phase M23C6 precipitated. Some parts the big temperature gradient and overheat accelerated the precipitation process, led to the incomplete fusion of dendritic crystal, crack initiation and propagation on account of the integrated factors. Some solutions were put forward to reduce the failure risk.
Multiferroics, can simultaneously exhibit multiple ferroic orders, including magnetic order, electric order and elastic order. Among these orders there exist intimately coupling effects. Multiferroics is significant for technological applications and fundamental research. The interplay between ferroelectricity and magnetism allows a magnetic control of ferroelectric properties and an electric control of magnetic properties, which can yield new device concepts. Recent experimental research shows that the Fe/BaTiO<sub>3</sub> compound exhibits a prominent magnetoelectric effect, which originates from a change in bonding at the ferroelectric-ferromagnet interface that changes the interface magnetization when the electric polarization reverses, and thus offering a new route to controlling the magnetic properties of multilayer compound heterostructures by the electric field. Motivated by recent discoveries, in this paper we investigate theoretically the thermodynamics of a finite ferroelectric-ferromagnetic chain. A microscopic Heisenberg spin model is constructed to describe magnetoelectric properties of this composite chain, in which electric and magnetic subsystem are coupled through interfacial coupling. However, this vector model is not integrable in general. Therefore, one has to resort to numerical calculations for the thermodynamic properties of such a system. A uniform discrete spin vector is adopted here to approximate the original continuous one, and then the transfer-matrix method is employed to derive the analytical expression. To verify its rationality and effectiveness, the zero-field specific heat of a classical spin chain is solved based on this simplified model, and compared with the exact solution. It demonstrates that the main characteristics obtained by previous research are well reproduced here, and the whole variant trend is also identical. And then the quantities concerned in this paper are calculated, including the magnetization, polarization, magnetoelectric susceptibility, and specific heat. The influence of interfacial coupling, external field, and single-ion anisotropy on the magnetoelectric effect of the composite chain are examined in detail. The results reveal that the interfacial coupling enhances the magnetization and polarization. And in the magnetic field driven magnetoelectric susceptibility, the large magnetoelectric correlation effects are observed, indicating that the magnetic behaviors can be effectively controlled by an external electric field. Meanwhile, it is also found that the external field and single-ion anisotropy both suppress the magnetoelectric susceptibility. In addition, interestingly, the specific heat of system presents a three-peak structure under high electric field, which stems from the thermal excitation of spin states as well as dipole moment caused jointly by electric field and temperature.
As one of the widely used materials for hydro turbine runners, 13Cr4Ni martensitic stainless steels (13/4 MSS) manufactured by forging and wire arc additive manufacturing (WAAM), respectively, were selected for high-cycle fatigue tests, and the effects of microstructures and defect characteristics on fatigue mechanism were investigated. The results indicate that compared to the forged 13/4 MSS, the microstructure of the WAAM test piece is very fine, and the martensite units, consequently, are smaller in size. The yield strength and ultimate tensile strength are 685 MPa and 823 MPa for the forged specimen and 850 MPa and 927 MPa for the WAAM specimens, respectively. The fatigue strength of 107 cycles at room temperature is 370 MPa for forged specimens and 468 MPa for WAAM specimens. The predominant defect of the forged 13/4 MSS specimen is inclusion, and the fatigue initiates mainly at the surface and subsurface. While for the WAAM specimen, the most commonly found defects are pores, and the fatigue initiation is internal and at the subsurface. In addition, the fine microstructure, as well as the high strength and hardness, enable the WAAM material to have higher fatigue strength. In order to assess the effect of defects on fatigue performance, the stress intensity factor and El-Haddad model were adopted in the present study. It was found that the forged specimens with fish-eye (FIE) zones and the WAAM specimens with granular bright facet (GBF) zones have longer fatigue life. The fatigue strengths of the forged 13/4 MSS were therefore predicted by defect size. In contrast, the fatigue strengths of the WAAM 13/4 MSS were predicted by both defect and GBF sizes.
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