Peierls框架与裂纹尖端位错行为

本文在Peieris框架下对裂纹尖端位错成核与发射问题进行了严格的数学分析。在修正Rice设想的基础上;建立了一组新的控制方程。应力场与位错密度场分别表示成第一类与第二类切比雪夫多项式的级数。相应的张开位移与滑错位移可以用三角级数表示。通过离散的方法;控制方程转化为一组非线性代数方程。用Newton—Raphson方法求解这组方程;得到远场为纯剪、纯拉及两者复合情况下的解答。计算结果清楚地揭示了裂纹尖端位错成核与发射过程

晶体塑性理论的极值原理

本文基于晶体塑性增量理论,讨论了给定应力率或给定应变率的情况下,滑移剪切率的确定方法;提出了相应的多变量函数的极值原理;把问题归结为二次凸规划问题. 对于晶体在外力作用下塑性响应问题,本文提出了两个新的与边值问题等价的极值原理.在这些极值原理中,滑移剪切率将作为独立宗量,通过变分方程求得

On the effect of an out-of-plane constraint on the three-dimensional crack front fields in a thin elastic plate

Two-dimensional theories of fracture are still applied widely today and provide theoretical foundations for solutions to many practical problems. These two-dimensional theories are based on the plane strain or plane stress assumption. However, strictly speaking, for a thin elastic plate with a through-thickness crack under tension, plane strain conditions can be met only at the crack front (except the corn point) and plane stress conditions exist at a distance of about one half of the plate thickness from the crack front in the mid-plane. What are the stress fields in the region where both plane strain and plane stress conditions cannot be met? In this paper, further investigations into the problem are carried out. Three-dimensional Maxwell stress functions, the principle of minimum complementary potential energy and three-dimensional J-integrals are employed to obtain an analytical solution to depict the relationship among out-of-plane constraints, three-dimensional J-integrals and stress intensity factors. Three-dimensional finite element simulations with fine meshes are carried out to verify the analytical results. Compared with the corresponding plane strain solution, the solution proposed is valid in a larger region

非线性弹塑性问题的数学分析和有限元公式

本文将国际上流行的两点张量法及 Lagrange 描写方法统一起来。运用虚功原理及张量变换得到了 Lagrangian 坐标系及 Euler 坐标系中的应力率平衡方程以及与之等价的变分方程;同时推导出塑性大变形三维有限元公式。作为特例又导出二维平面应变及平面应力的有限元公式

扩展裂纹尖端弹塑性场的仿真模拟

通过对紧凑拉伸试样裂纹扩展实验的有限元仿真模拟以及对中心裂纹试样和三点弯曲试样的精细有限元计算和分析;证实了稳态扩展裂纹尖端附近环形区内应力场三参数J-k_2-Q表征的有效性。研究结果进一步表明:在扩展裂纹尖端附近的环形区域内;因试样几何类型的不同;存在着不同类型的双参数主导区。对紧凑拉伸试样和弯曲裂纹试样;在裂关附近环形区内存在着J-k_2主导区;而对中心裂纹试样;在裂尖附近环形区内则存在着J-Q主导区。在一般情况下;应由J-k_2-Q三参数表征

A New GE-3 Parallel Algorithm for the Parabolic Equation

利用SAul’yEV格式和它的对称格式及一个绝对稳定的隐格式,构造了一个求解抛物型方程的分组显式(gE-3)并行算法,该算法的截断误差为O(τ+H2),条件稳定.数值例子验证了理论分析的有效性。Using a scheme,its symmetric scheme and an implicit differencing scheme of absolute stability,we construct group explicit scheme(GE-3) parallel algorithm for solving parabolic equation.The truncation error of this algorithm is O(τ+h2) with stability conditions.A numerical example shows that the schemes are effective.贵州省科技厅资金项目(黔科合J字[2008]2122号)资

Size Effects in the Particle-Reinforced Metal-Matrix Composites

Many experimental observations have shown the influences of particle size on the mechanical properties of the particle-reinforced metal-matrix composite. However. the conventional theory cannot explain the phenomena because no length scale parameters are included in the conventional theory. In the present paper, the strain gradient theory proposed by Chen and Wang [32] is used, and a systematic research of the particle size effect in the particle-reinforced metal-matrix composite is carried out. Many composite factors, such as the particle size, the particle aspect ratio, the Young's modulus ratio of the particle to the matrix material, particle volume fraction and the strain hardening exponent of the matrix material, are investigated in detail. Two kinds of particle shapes, spheroidal particle and cylindrical particle, are considered to check the strength dependence of the particle shapes. Calculation to the special materials used by Ling [9] has been done, and the calculation results are consistent with the experimental results in Ling [9]. The material length scale parameter is predicted

Effective elastic moduli of inhomogeneous solids by embedded cell model

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional tyro-phase composites

Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks