An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystal...An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.展开更多
The effect of the laser processing parameters on the composition uniformity and shape coefficient of fusion zone with laser surface alloyed Cr plated on medium carbon low alloy steel has been studied.It was found that...The effect of the laser processing parameters on the composition uniformity and shape coefficient of fusion zone with laser surface alloyed Cr plated on medium carbon low alloy steel has been studied.It was found that the composition uniformity depends on the shape coefficient of fusion zone,and the later is a function of both power density and interaction time.If the power density is fixed to a certain value,the shape coefficient is directly,propor- tional to the interaction time.A completely,uniform molten pool can be obtained,when the shape coefficient is between 1.6 and 3.0.展开更多
This study focused on hydraulic characteristics around a gear-shaped weir in a straight channel. Systematic experiments were carried out for weirs with two different gear heights and eight groups of geometrical parame...This study focused on hydraulic characteristics around a gear-shaped weir in a straight channel. Systematic experiments were carried out for weirs with two different gear heights and eight groups of geometrical parameters. The impacts of various geometrical parameters of gear-shaped weirs on the discharge capacity were investigated. The following conclusions are drawn from the experimental study:(1) The discharge coefficient(m_c) was influenced by the size of the gear: at a constant discharge, the weir with larger values of a/b(a is the width of the gear, and b is the width between the two neighboring gears) and a/c(c is the height of the gear) had a smaller value of m_c. The discharge capacity of the gear-shaped weir was influenced by the water depth in the weir.(2) For type C1 with a gear height of 0.01 m, when the discharge was less than 60m^3/h and H_1=P < 1.0(H_1 is the water depth at the low weir crest, and P is the weir height), m_c significantly increased with the discharge and H_1=P; with further increases of the discharge and H_1=P, m_cshowed insignificant decreases and fluctuated within small ranges. For type C2 with a gear height of 0.02 m, when the discharge was less than 60m^3/h and H_1=P < 1.0, m_csignificantly increased with the discharge and H_1=P; when the discharge was larger than 60m^3/h and H_1=P > 1.0, m_c slowly decreased with the increases of the discharge and H_1=P for a=b 1.0 and a=c 1.0, and slowly increased with the discharge and H_1=P for a=b > 1.0 and a=c > 1.0.(3) A formula of m_cfor gear-shaped weirs was established based on the principle of weir flow, with consideration of the water depth in the weir, the weir height and width, and the height of the gear.展开更多
Shape coefficient is a significant factor accounting for building energy consumption. In order to decrease the building energy consumption of rural residence in severe cold regions,this paper from the perspective of r...Shape coefficient is a significant factor accounting for building energy consumption. In order to decrease the building energy consumption of rural residence in severe cold regions,this paper from the perspective of regulating the shape coefficient limit value,applies the field survey method to statistic and analyze the shape,width and depth of rural residence in severe cold regions and concludes the distribution characteristics and scope of building area. On this basis,though calculating and analyzing the relations between shape coefficient and length-width ratio under different building areas,meanwhile comprehensive considering the building function,farmers' living mode and requirements etc,it put forward that the shape coefficient of rural residence in severe cold regions should below 0. 8. It has important significance for guiding the rural energy-saving house design and construction of severe cold regions.展开更多
This study addresses the challenge of directly determining the elastic modulus of complex shaped ceramic products—such as gas turbine combustor tiles—using conventional standardized methods,which are limited by spec...This study addresses the challenge of directly determining the elastic modulus of complex shaped ceramic products—such as gas turbine combustor tiles—using conventional standardized methods,which are limited by specimen geometry.A rapid,non-destructive testing method based on the impulse excitation technique(IET)and a shape factor coefficient was proposed.Three types of shaped ceramic tiles were selected.The elastic modulus of standard rectangular specimens obtained by destructive sampling was used as the reference value,and the shape factor coefficient for each tile type was calibrated by combining the mass and fundamental frequency of the whole tile.Using this coefficient,the elastic modulus of whole tiles was calculated solely from non-destructively measured mass and frequency.The results show that the deviation between the elastic modulus derived from the proposed method and that from destructive testing is less than 5%,confirming the accuracy and reliability of the approach.The method overcomes the shape restrictions inherent in traditional testing,offering a fast,non-destructive solution suitable for onsite quality assessment and process control during the production of shaped ceramic components.展开更多
Shape has an undeniable impact on particle behaviour,and the shapes of naturally occurring granular matter are typically irregular.Computational studies of irregularly shaped particles are challenging but necessary to...Shape has an undeniable impact on particle behaviour,and the shapes of naturally occurring granular matter are typically irregular.Computational studies of irregularly shaped particles are challenging but necessary to gain a better understanding of the flow of particulate matter.This study focuses on the behaviour of irregular sinter particles and applies the discrete element method to examine the effects of static and rolling friction coefficients and particle shape on the angle of repose and porosity of sinter piles.A three-dimensional model of an irregular sinter particle reconstructed by close-range photogrammetry served as the template for generating multi-sphere particles with varying numbers of sub-spheres(1,3,7,22,and 135)and sphericity ranging from 1 to 0.69.Simulations of particle piles were conducted for a range of values of the coefficients of static and rolling friction.The results indicate that the angle of repose increases with static friction and also increases with rolling friction coefficient when it is lower than the static coefficient.The angle of repose shows clear dependence on particle shape,particularly for lower rolling friction coefficients.The friction coefficients for particles of five different shapes were individually determined through bulk calibration,and irregularly shaped particles in DEM were found to require lower friction coefficients.Porosity was marginally affected by the static and rolling friction coefficients for spherical particles,while non-spherical particles showed porosity increasing with the rolling friction coefficient.The relationship between particle sphericity and porosity was nonlinear:as sphericity decreases from 1.00 to 0.69,the porosity first decreases to a minimum and then increases.The findings confirmed that both friction and particle shape have a significant influence on the structure of sinter piles,with implications for material handling and processing in industrial applications.展开更多
基金The project supported by the National Natural Science Foundation of China(10562004)the Oversea Returning Grant of China.
文摘An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.
文摘The effect of the laser processing parameters on the composition uniformity and shape coefficient of fusion zone with laser surface alloyed Cr plated on medium carbon low alloy steel has been studied.It was found that the composition uniformity depends on the shape coefficient of fusion zone,and the later is a function of both power density and interaction time.If the power density is fixed to a certain value,the shape coefficient is directly,propor- tional to the interaction time.A completely,uniform molten pool can be obtained,when the shape coefficient is between 1.6 and 3.0.
基金supported by the National Natural Science Foundation of China(Grant No.51409155)
文摘This study focused on hydraulic characteristics around a gear-shaped weir in a straight channel. Systematic experiments were carried out for weirs with two different gear heights and eight groups of geometrical parameters. The impacts of various geometrical parameters of gear-shaped weirs on the discharge capacity were investigated. The following conclusions are drawn from the experimental study:(1) The discharge coefficient(m_c) was influenced by the size of the gear: at a constant discharge, the weir with larger values of a/b(a is the width of the gear, and b is the width between the two neighboring gears) and a/c(c is the height of the gear) had a smaller value of m_c. The discharge capacity of the gear-shaped weir was influenced by the water depth in the weir.(2) For type C1 with a gear height of 0.01 m, when the discharge was less than 60m^3/h and H_1=P < 1.0(H_1 is the water depth at the low weir crest, and P is the weir height), m_c significantly increased with the discharge and H_1=P; with further increases of the discharge and H_1=P, m_cshowed insignificant decreases and fluctuated within small ranges. For type C2 with a gear height of 0.02 m, when the discharge was less than 60m^3/h and H_1=P < 1.0, m_csignificantly increased with the discharge and H_1=P; when the discharge was larger than 60m^3/h and H_1=P > 1.0, m_c slowly decreased with the increases of the discharge and H_1=P for a=b 1.0 and a=c 1.0, and slowly increased with the discharge and H_1=P for a=b > 1.0 and a=c > 1.0.(3) A formula of m_cfor gear-shaped weirs was established based on the principle of weir flow, with consideration of the water depth in the weir, the weir height and width, and the height of the gear.
基金Sponsored by the National Project of Scientific and Technical Supporting Programs Funded by Ministry of Science & Technology of China (Grant No.2011BAJ08B06)
文摘Shape coefficient is a significant factor accounting for building energy consumption. In order to decrease the building energy consumption of rural residence in severe cold regions,this paper from the perspective of regulating the shape coefficient limit value,applies the field survey method to statistic and analyze the shape,width and depth of rural residence in severe cold regions and concludes the distribution characteristics and scope of building area. On this basis,though calculating and analyzing the relations between shape coefficient and length-width ratio under different building areas,meanwhile comprehensive considering the building function,farmers' living mode and requirements etc,it put forward that the shape coefficient of rural residence in severe cold regions should below 0. 8. It has important significance for guiding the rural energy-saving house design and construction of severe cold regions.
基金National Key Research and Development Program of China(2023YFB3711200)Key Research and Development Project of Henan Province(231111230700).
文摘This study addresses the challenge of directly determining the elastic modulus of complex shaped ceramic products—such as gas turbine combustor tiles—using conventional standardized methods,which are limited by specimen geometry.A rapid,non-destructive testing method based on the impulse excitation technique(IET)and a shape factor coefficient was proposed.Three types of shaped ceramic tiles were selected.The elastic modulus of standard rectangular specimens obtained by destructive sampling was used as the reference value,and the shape factor coefficient for each tile type was calibrated by combining the mass and fundamental frequency of the whole tile.Using this coefficient,the elastic modulus of whole tiles was calculated solely from non-destructively measured mass and frequency.The results show that the deviation between the elastic modulus derived from the proposed method and that from destructive testing is less than 5%,confirming the accuracy and reliability of the approach.The method overcomes the shape restrictions inherent in traditional testing,offering a fast,non-destructive solution suitable for onsite quality assessment and process control during the production of shaped ceramic components.
基金funded by China Scholarship Council(grant No.202106890009).
文摘Shape has an undeniable impact on particle behaviour,and the shapes of naturally occurring granular matter are typically irregular.Computational studies of irregularly shaped particles are challenging but necessary to gain a better understanding of the flow of particulate matter.This study focuses on the behaviour of irregular sinter particles and applies the discrete element method to examine the effects of static and rolling friction coefficients and particle shape on the angle of repose and porosity of sinter piles.A three-dimensional model of an irregular sinter particle reconstructed by close-range photogrammetry served as the template for generating multi-sphere particles with varying numbers of sub-spheres(1,3,7,22,and 135)and sphericity ranging from 1 to 0.69.Simulations of particle piles were conducted for a range of values of the coefficients of static and rolling friction.The results indicate that the angle of repose increases with static friction and also increases with rolling friction coefficient when it is lower than the static coefficient.The angle of repose shows clear dependence on particle shape,particularly for lower rolling friction coefficients.The friction coefficients for particles of five different shapes were individually determined through bulk calibration,and irregularly shaped particles in DEM were found to require lower friction coefficients.Porosity was marginally affected by the static and rolling friction coefficients for spherical particles,while non-spherical particles showed porosity increasing with the rolling friction coefficient.The relationship between particle sphericity and porosity was nonlinear:as sphericity decreases from 1.00 to 0.69,the porosity first decreases to a minimum and then increases.The findings confirmed that both friction and particle shape have a significant influence on the structure of sinter piles,with implications for material handling and processing in industrial applications.
