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Constitutive relation of an orthorhombic polycrystal with the shape coefficients

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Acta Mechanica Sinica 2005年第6期21卷 608-618页

作者： mojia huang Zhiwen Lan Huiling Liang Civil Engineering College Nanchang University. Nanchang 330029 China

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.

关键词： Crystalline mean shape Constitutive relation Orthorhombic polycrystal The shape coefficients The texture coefficients

Constitutive relation of weakly anisotropic polycrystal with microstructure and initial stress

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Acta Mechanica Sinica 2007年第2期23卷 183-198页

作者： mojia huang Hua Zhan Xiuqiao Lin Hai Tang Institute of Engineering Mechanics Nanchang UniversityNanchang 330029 China

Man （Nondestr Test Eval 15：191-214, 1999） derived the constitutive relation of a weakly-textured orthorhombic aggregate of cubic crystallites with effects of microstructure and initial stress. In this paper, a computational expression on the integration ∫SO（3） Q^× D^1m0dg is given. Then, by means of the computational expression, the general constitutive relation of a weakly-textured anisotropic polycrystal with the consideration of microstructure and initial stress is derived. As special cases of our general constitutive relation, two constitutive relations are given for an isotropic polycrystal and a weakly-textured anisotropic aggregate of cubic crystallites. The acoustoelastic tensor of the reference cubic crystal is derived to determine the material constants of the polycrystal. Two examples are given for understanding the physical meaning of the texture coefficients and the constitutive relations.

关键词： Generalconstitutive relation of weakly-textured polycrystal .Microstructure Initial stress .Cubic crystallites

GREEN’S FUNCTION AND EFFECTIVE ELASTIC STIFFNESS TENSOR FOR ARBITRARY AGGREGATES OF CUBIC CRYSTALS

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Acta Mechanica Solida Sinica 2004年第4期17卷 337-346页

作者： huang mojia Zheng Chaomei Institute of Engineering Mechanics Nanchang UniversityNanchang 330029China Computer Center Nanchang UniversityNanchang 330029China

A closed but approximate formula of Green’s function for an arbitrary aggregate of cubic crystallites is given to derive the e?ective elastic sti?ness tensor of the polycrystal. This formula, which includes three elastic constants of single cubic crystal and ?ve texture coe?cients, accounts for the e?ects of the orientation distribution function (ODF) up to terms linear in the tex- ture coe?cients. Thus it is expected that our formula would be applicable to arbitrary aggregates with weak texture or to materials such as aluminum whose single crystal has weak anisotropy. Three examples are presented to compare predictions from our formula with those from Nishioka and Lothe’s formula and Synge’s contour integral through numerical integration. As an applica- tion of Green’s function, we brie?y describe the procedure of deriving the e?ective elastic sti?ness tensor for an orthorhombic aggregate of cubic crystallites. The comparison of the computational results given by the ?nite element method and our e?ective elastic sti?ness tensor is made by an example.

关键词： Green’s function aggregates of cubic crystallites texture coeffcients, effective elastic stiffness tensor

Elasticity tensor and ultrasonic velocities for anisotropic cubic polycrystal

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Science China(Physics,Mechanics & Astronomy) 2008年第8期51卷 1097-1105页

作者： huang mojia CHEN MengCheng ZHENG TengLong huang WeiFu Institute of Advanced Study Nanchang UniversityNanchang 330031China East China Jiaotong University Nanchang 330013China

The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are called the texture coefficients. In this paper,we use the Clebsch-Gordan expression to derive an explicit expression of the elasticity tensor for an anisotropic cubic polycrystal. The elasticity tensor contains three material constants and nine texture coefficients. In order to measure the nine texture coefficients by ultrasonic wave,we give relations between the nine texture coefficients and ultrasonic propagation velocities. We also give a numerical example to check the relations.

关键词： elasticity tensor anisotropic cubic polycrystals texture coefficients ultrasonic velocities Clebsch-Gordan expression

PREDICTION OF YIELD FUNCTIONS ON BCC POLYCRYSTALS

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Acta Mechanica Solida Sinica 2006年第1期19卷 75-85页

作者： huang mojia Fu Mingfu Zheng Chaomei Institute of Engineering Mechanics Nanchang University Nanchang 330029 China Computer Center Nanchang University Nanchang 330029 China

By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill＇s criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs＇ model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function （ODF）, and the single BCC crystal＇s plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor＇s model in order to compare the expression with that of the macroscopic yield function.

关键词： yield function the ODF BCC polycrystal single BCC crystals anisotropy

输电铁塔主材内力与基础水平位移关系式的研究

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南昌大学学报（理科版） 2024年第3期48卷 231-240页

作者：过浩川吴松吴昊李强黄模佳樊晨旭杨垂玮南昌大学工程建设学院江西南昌330031 国网安徽省电力有限公司安徽合肥230061 中国能源建设集团安徽省电力设计院有限公司安徽合肥230601

铁塔基础在遭遇地质灾害的情况下会发生垂直和水平位移;相比于水平位移,人们多关注基础垂直位移对塔构件内力的影响,但水平位移对杆件内力影响同样不可忽略,研究输电铁塔基础水平位移与铁塔安全性的关系具有重要意义。为了推导基础水平... 详细信息

铁塔基础在遭遇地质灾害的情况下会发生垂直和水平位移;相比于水平位移,人们多关注基础垂直位移对塔构件内力的影响,但水平位移对杆件内力影响同样不可忽略,研究输电铁塔基础水平位移与铁塔安全性的关系具有重要意义。为了推导基础水平位移与铁塔主材内力的解析式,运用梁和杆的刚度等效方法和能量法,给出了单腿水平位移作用下四个塔腿承受弯矩的比例关系,推导出主材在第一横格面处的最大弯矩,通过简化模型推导出单腿基础水平位移作用下铁塔各塔腿主材最大轴力表达式,并通过有限元计算对最大轴力表达式进行修正。输电铁塔受上部荷载在主材中主要产生轴向拉(压)应力,而基础水平位移主要产生弯矩应力。本文给出的主材内力与塔腿位移表达式可作为输电线路塔腿基础发生水平位移后铁塔的安全评估的依据。

关键词：输电铁塔基础水平位移内力计算式有限元分析

维普期刊数据库博看期刊

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立方晶粒正交板材瑞利波速与织构系数的关系

固体力学学报 2014年第6期35卷 527-533页

作者：吴萍黄模佳南昌大学工程力学研究所南昌330031

正交板材是由大量微小晶粒组成的正交多晶体材料,而多晶体中晶粒的取向分布(可通过取向分布函数中的织构系数来描述)影响着多晶体材料的力学性能,也必然影响着瑞利波的传播速度.将多晶体材料的织构系数引入到弹性张量中,通过特征值办法... 详细信息

正交板材是由大量微小晶粒组成的正交多晶体材料,而多晶体中晶粒的取向分布(可通过取向分布函数中的织构系数来描述)影响着多晶体材料的力学性能,也必然影响着瑞利波的传播速度.将多晶体材料的织构系数引入到弹性张量中,通过特征值办法,采用线性化处理,推导出立方晶粒正交板材的瑞利波速与织构系数的关系式,并通过对正交板材瑞利波速的测量获得织构系数,其结果与超声横波纵波测量结果相吻合.

关键词：织构系数瑞利波弹性张量正交板材超声波测量

16Mn低合金60°角钢轴压构件嵌固系数的取值研究

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铸造技术 2015年第9期36卷 2187-2190页

作者：程华虎黄模佳南昌大学工程力学实验中心江西南昌330031 南昌大学高等研究院江西南昌330031

研究了轴心受压状态下16Mn低合金60°角钢构件嵌固系数的取值。结果表明,16Mn低合金60°角钢的嵌固系数与90°角钢的嵌固系数两者都接近于1.0,这表明角钢两肢之间的嵌固作用很小。相对于90°角钢,16Mn低合金60°角钢的嵌固系数较小。主... 详细信息

研究了轴心受压状态下16Mn低合金60°角钢构件嵌固系数的取值。结果表明,16Mn低合金60°角钢的嵌固系数与90°角钢的嵌固系数两者都接近于1.0,这表明角钢两肢之间的嵌固作用很小。相对于90°角钢,16Mn低合金60°角钢的嵌固系数较小。主要是因为随着角钢两肢夹角的减小,两构件的相互约束作用即嵌固作用会减弱。建议在规定16Mn低合金60°角钢轴心受压构件宽厚比限值时,嵌固系数取为1.0。

关键词： 16Mn低合金60°角钢轴心受压嵌固系数临界荷载有限元仿真

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梯形重力坝的应力函数解及其有限元验证

力学与实践 2023年第1期45卷 113-118页

作者：肖先志肖奉英黄模佳南昌大学工程力学系南昌330031

弹性力学教材中通过取三次多项式应力函数给出三角形横截面的重力坝应力场,但工程中重力坝的横截面几乎均为梯形,其坝顶并非三角形尖顶。将应力函数的半逆解法与锲形体的应力函数相结合,寻找出适用于梯形重力坝的应力函数,根据梯形重力... 详细信息

弹性力学教材中通过取三次多项式应力函数给出三角形横截面的重力坝应力场,但工程中重力坝的横截面几乎均为梯形,其坝顶并非三角形尖顶。将应力函数的半逆解法与锲形体的应力函数相结合,寻找出适用于梯形重力坝的应力函数,根据梯形重力坝力的边界条件,并利用圣维南原理,给出了梯形重力坝的应力场解析式。用有限元计算给出了梯形重力坝应力场的数值仿真结果。应力场解析式与有限元仿真结果非常吻合,说明了梯形重力坝应力场解析式的正确性。梯形重力坝应力场解析式对水利工程中重力坝的结构强度及设计具有重要的理论指导意义和应用价值。

关键词：梯形重力坝应力场应力函数求解有限元仿真比较