含与不含晶界空穴的双晶体蠕变行为研究

基于晶体滑移理论,建立了各向异性镍基合金双晶体的蠕变本构模型和蠕变寿命预测模型,通过MARC用户子程序CRPLAW将上述本构模型进行了有限元实现,并对双晶体蠕变行为进行了计算分析,考虑了:(1)晶体取向的影响;(2)垂直、倾斜和平行于外载方向的三种位向晶界情况;(3)晶界处引进空间空穴的影响。结果表明,双晶体上特别是微空穴和晶界附近区域的蠕变应力应变呈现不同的变化规律,对此晶粒晶体取向和晶界位向有较大的影响;微空穴的存在削弱了双晶体的承载能力,显著地影响了双晶体蠕变持久寿命;相同条件下,垂直晶界对双晶体模型的蠕变损伤影响最为强烈,倾斜晶界次之,平行晶界最小;微空穴的生长与晶界位向和晶体取向有强烈的依赖关系,其中垂直晶界更有利于晶体滑移和微空穴生长。     

分析力学由广义坐标到作用-角变量--分析力学札记之六

简述分析力学描述运动的变量由广义坐标到作用-角变量的变化过程, 来看分析力学研究的不断深化.     

一维固液介质准周期结构声子晶体的传输特性

针对一维固液介质的Fibonacci序列准周期声子晶体,利用传输矩阵法研究了弹性纵波在准周期结构中的透射特性。计算结果表明：准周期结构具有比周期结构更宽的禁带,并伴随带边谐振;序列越高,带边谐振越强,并在较低序列的禁带中心出现谐振模;弹性波以0.1rad斜入射时,透射谱向高频方向移动;当固液介质波阻抗接近时,出现等间距的谐振模,同时禁带消失。     

各向异性双重介质垂直裂缝井两相流体渗流

建立了各向异性双重介质中垂直裂缝井两相渗流数学模型,用有限差分法求得了其解,进行了算例分析。得到了含水饱和度沿径向、最大及最小渗透率方向的分布和水驱油前缘等饱和度面随时间的变化,分别讨论了各向异性、吸渗作用对这种介质中两相流体渗流的影响。结果表明：渗透率较在的方向,前缘推进速度较快,油井见水较早;吸渗使前缘推进速度减慢,使油井见水晚。注水开发这种油藏时,见水前注入率不能太大以充分发挥吸渗作用,存在最佳注入率。这对于水力压裂垂直裂缝井注水开发碳酸盐岩裂缝性油藏有指导意义。     

Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.The project supported by the National Natural Science Foundation of China(10272009 and 10472030) and the Natural Science Foundation of Hunan Province(02JJY2014)     

近代塑性力学发展概况

经典塑性理论研究在50年代已经成熟,主要结果已总结在Hill的名著“塑性数学理论和Prager & Hodge的名著“理想塑性的固体理论”中。近15年来,非经典塑性理论突破了经典理论的先验限制,在下述六个方面有独特的发展:①由微小变形向有限变形发展,确立了有限塑性变形理论;②由宏观唯象理论向细观深度发展,确立了塑性细观力     

T应力对立方准晶中含十字交叉型裂纹的影响

论文研究了立方准晶中含十字交叉型裂纹尖端附近的T应力.采用了积分变换法,将相关边值问题转换为求解奇异积分方程,得到声子场和相位子场的T应力,且可以表示为裂纹张开位移和施加在无穷远处的载荷之和.裂纹张开位移在确定声子场和相位子场的T应力中起着主导作用.同时强调了T应力在立方准晶脆性断裂中的作用.此外,还研究了裂纹臂长度比...     

基于自适应交叉近似边界元法的快速声学灵敏度分析

基于自适应交叉近似边界元法构造一组快速声学灵敏度分析方法,其中,声学灵敏度分析分别采用直接微分法和伴随变量法;而自适应交叉近似算法被用以克服常规边界元法的高计算量和高存储量的固有缺点。自适应交叉近似算法在迭代求解之前对边界元系数矩阵进行压缩存储,可以在降低存储量的同时提高求解效率。在声学灵敏度分析中,通过直接使用求解未知边界状态值时保存的压缩系数矩阵,可以进一步提高求解效率。数值算例验证了所构造的方法的计算精度和求解效率,以及在大规模声场问题的最优化分析中的应用潜力。     

Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips

The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.     

带双裂纹的椭圆孔口问题的应力分析

利用复变方法,通过构造新的保角映射,研究了带双裂纹椭圆孔口的平面弹性问 题,得到了I型与II型裂纹问题应力强度因子的解析解.在极限情形下, 不仅可以还原经典的Griffith裂纹的结果,而且可模拟出十字裂纹和带双裂纹的圆 形孔口问题.     

双压电材料内含椭圆孔孔边界面裂纹的反平面问题

利用复变函数方法,研究了横观各向同性压电双材料中椭圆孔孔边界面裂纹的反平面问题．首先,利用保角变换函数将椭圆孔保角变换到一直线裂纹;其次,基于孔边及裂纹表面均电不可穿透并且自由的假设,利用Stroh公式分别得到了本问题的复势函数、裂尖场集中系数的解析表达式;最后,在面内电载荷及面外机械载荷的作用下,分析了椭圆孔尺寸、裂纹长度和外载对裂尖场集中系数的影响,并得到了一个有意义的结论：椭圆孔一边裂纹长度的改变对另一边裂纹裂尖场的影响有限,然而一旦椭圆孔退化为竖直裂纹,该影响将变得非常显著．     

一维六方准晶中星形静态裂纹和运动裂纹的解析解

利用复变函数方法研究了一维六方准晶中星形静态裂纹和运动裂纹的反平面剪切问题,得到了星形裂纹尖端处应力强度因子和动应力强度因子的解析解.当裂纹条数给定时,由此可得到直线裂纹,Griffith裂纹,共点均匀分布三裂纹,对称十字形裂纹,米字型裂纹(对称八裂纹)静力学和动力学问题的解析解.当k=4时,用数值算例讨论了声子场-相位子场耦合系数和裂纹运动速度对动应力强度因子的影响.当速度趋于0时,运动裂纹的解可以退化为静态裂纹的解.     

含孔扁薄球壳的复变函数解法

本文建立了含孔扁薄球壳的复变函数求解方法,从而为这一类问题的求解提供了一条有效而规范的途径.     

压电效应下一维六方准晶双材料孔边裂纹的反平面问题研究

利用复变函数方法和保角变换技术研究了压电效应下一维六方准晶双材料中圆孔边单裂纹的反平面问题．考虑电不可渗透型边界条件,运用保角变换和Stroh公式得到了弹性体受远场剪切力和面内电载荷作用下裂纹尖端应力强度因子和能量释放率的解析解. 数值算例分析了几何参数、远场受力、电位移载荷对能量释放率的影响．结果表明：裂纹长度、耦合系数和远场剪切力的减小可以抑制裂纹的扩展．不考虑电场时,声子场应力对能量释放率的影响较小．本文的研究结果可作为研究一维六方压电准晶双材料孔边裂纹问题的理论基础,同时为压电准晶及其复合材料的设计、制备、优化和性能评估提供理论依据．     

DECAGONAL QU ASICRYSTALLINE ELLIPTICAL INCLUSIONS UNDER THERMOMECHANICAL LOADING

In this work, an elegant method is proposed to derive the thermoelastic field in- duced by thermomechanical loadings in a decagonal quasicrystalline composite composed of an infinite matrix reinforced by an elliptical inclusion. The thermomechanical loadings include a uniform temperature change, remote uniform in-plane heat fluxes and remote uniform in-plane stresses. The corresponding boundary value problem is ultimately reduced to the solution of two independent sets of four coupled linear algebraic equations, each of which involves four complex constants characterizing the internal stress field. The solution demonstrates that a uniform tem- perature change and remote uniform stresses will induce an internal uniform stress field, and that uniform heat fluxes will result in a linearly distributed internal stress field within the elliptical inclusion. The induced uniform rigid body rotation within the inclusion is given explicitly.     

求解含孔边裂纹各向异性板应力强度因子的复变—广义变分方法

本文提供了一个求解含孔边裂纹正交各向异性板应力强度因子的复变一广义变分方法.首先建立满足所有弹性力学基本方程式和裂纹表面边界条件的应力与位移级数表达式.然后应用广义变分原理满足其余边界条件从而确定应力强度因子.计算表明,级数收敛迅速,结果与有限元法非常一致,而所需机时较少.     

The anti-plane solution for the edge cracks originating from an arbitrary hole in a piezoelectric material

In this paper, a general and simple way was found to solve the problem of an arbitrary hole with edge cracks in transversely isotropic piezoelectric materials based on the complex variable method and the method of numerical conformal mapping. Firstly, the approximate mapping function which maps the outside of the arbitrary hole and the cracks into the outside of a circular hole is derived after a series of conformal mapping process. Secondly, based on the assumption that the surface of the cracks and hole is electrically impermeable and traction-free, the approximate expressions for the complex potential, fields intensity factors and energy release rates are presented, respectively. Thirdly, under the in-plane electric loading together with the out-plane mechanical loading, the influences of the hole size, crack length and mechanical/electric loading on the fields intensity factors and energy release rates are analyzed. Finally, some particular holes with edge cracks are studied in numerical analysis. The result shows that, the mechanical loading always promotes crack growth, while the electric loading may retard crack growth.     

压电压磁复合材料中正六边形孔边裂纹的反平面断裂问题

基于线性磁电弹性理论,利用Schwarz-Christoffel(CS)变换技术和Stroth公式,首次系统研究了压电压磁复合材料中含带两个不对称裂纹的正六边形孔口问题在部分渗透磁电边界条件下的解析解.当忽略磁场时,磁电非渗透裂纹和磁电渗透裂纹两种极端情况下的解析解答可退化为文献已有研究结果.数值结果揭示了正六边形孔口尺寸、裂纹长度以及力电载荷和磁载荷对能量释放率的影响规律.研究结果表明：减小孔口边长和裂纹长度可以提高材料的可靠性;机械载荷总是促进裂纹扩展;在磁电非渗透和磁电部分渗透边界条件下,负电场和负磁场会延缓裂纹的扩展,而正电场可以增强或阻碍裂纹的扩展,这取决于所施加的电场和磁场的强度以及机械载荷的水平;在磁电渗透边界条件下,电场和磁场对裂纹的扩展没有影响.     

点群10mm十次对称二维准晶中的两类接触问题

采用复变函数法探讨了在一个刚性压头作用下十次对称二维准晶材料的两类接触问题,即具有有限摩擦的接触问题以及粘结接触问题. 特别地对于平底压头,获得了表征声子场和相位子场的全纯函数的显式表达式,以及在压头上的接触应力分布. 结果显示,对于具有有限摩擦的接触问题,接触应力在接触区边缘具有实指数奇异性$-1/2pm beta$, 其中$beta$由准晶体的材料常数及静摩擦系数确定;而对于粘结接触问题,接触应力在接触区边缘具有振荡型奇异性$-1/2pm {rm i}v$, 其中$varepsilon $由准晶体的材料常数确定.