平面弹性介质多孔多裂纹问题的一种数值方法

提出了平面弹性介质中多孔洞多裂纹相互作用问题的一种数值计算方 法. 通过把适于单一裂纹的Bueckner原理扩充到含有多孔洞多裂纹的一般体系，将原问题 分解为承受远处载荷不含裂纹不含孔洞的均匀问题，和在远处不承受载荷但在裂纹面上和孔 洞表面上承受面力的多孔洞多裂纹问题. 于是，以应力强度因子作为参量的问题可以通过考 虑后者(多孔洞多裂纹问题)来解决，而利用提出的杂交位移不连续法，这种多孔 洞多裂纹问题是容易数值求解的. 算例说明该数值方法对分析平面弹性介质中多孔洞多裂纹 相互作用的问题既简单又有效.     

主裂纹与微裂纹相互作用问题的有效数值计算方法

提出了平面弹性介质中主裂纹与微裂纹相互作用问题的有效数值计算 方法. 通过把适于单一裂纹的Bueckner原理扩充到含有多裂纹的一般体系，将原问题分解 为承受远处载荷不含裂纹的均匀问题，和在远处不承受载荷但在裂纹面上承受面力的多裂纹 问题. 于是，以应力强度因子作为参量的问题可以通过考虑后者(多裂纹问题)来解决，而 利用提出的杂交位移不连续法，这种多裂纹问题是容易数值求解的. 列举 Cai和 Faber为评价主裂纹与微裂纹相互作用问题的近似方法而列举的算例，说明 该数值方法对分析平面弹性介质中主裂纹与微裂纹相互作用问题既简单又非常有效.     

磁电弹性体中纳米孔边任意位置贯穿裂纹的解析解

本文研究了反平面机械载荷、面内电载荷和面内磁载荷作用下磁电弹材料中含有纳米尺度孔边任意位置贯穿裂纹的Ⅲ型断裂力学性能.基于Gurtin-Murdoch表面弹性理论考虑纳米缺陷(孔洞和裂纹)的表面效应,利用磁电弹理论和复变弹性理论获得了纳米缺陷表面为磁电不可通条件下磁电弹场的精确解,给出了贯穿裂纹两端裂尖的磁电弹场强因子的解析表达.所得结果与已有研究比较说明了本文方法的有效性.讨论了裂纹位置、裂纹相互作用与施加多物理场载荷对无量纲磁电弹场强因子的影响.结果表明：贯穿裂纹裂尖的无量纲磁电弹场强因子尺寸效应显著;缺陷表面效应对裂纹耦合尖端场的影响受裂纹位置的制约;无量纲磁电弹场强因子受贯穿裂纹两端的裂纹长度比与施加力电磁载荷的显著影响.     

应力梯度不均匀时平板表面裂纹的应力强度因子

本文采用考虑裂纹面上具有任意分布载荷的线弹簧模型,在Kirchhoff板弯曲理论的假设下,将含半椭圆型表面裂纹的平板问题化为一组耦合的积分方程组进行求解,对均匀拉伸和纯弯曲两种载荷作用下的应力强度因子数值解,同经典线弹簧模型和有限元解进行了比较,并给出了经典线弹簧模型不能得到的、裂纹面上承受幂次不均匀应力分布时应力强度因子的数值解.     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

缺陷孔对平面裂纹应力强度因子的影响

带有裂纹和缺陷孔洞的板的问题是一个多连域的边值问题，这类问题适合用边界元法所具有的高精度特性来求解．采用子域边界元法，在平面应变的条件下对存在中心裂纹的平面板受远处拉伸和剪切裁荷的作用进行了数值分析．研究了圆形孔洞对Ⅰ型和Ⅱ型应力强度因子的影响，与有限元法进行了对比，求解结果更加精确．计算了椭圆形孔对Ⅰ型应力强度因子的影响，得到了一些有意义的结果，并对移动接触弹性体作用下的带裂纹板进行了钻孔研究．     

界面裂纹问题中的通用权函数法

热载荷和机械载荷共同作用下复合材料中的裂纹扩展往往发生在界面处.传统求解热冲击及机械载荷共同作用下界面裂纹尖端的应力强度因子的数值方法(如有限元、边界元法等),计算工作量大、效率低.通用权函数与时间无关,运用通用权函数法可以免除对每个时刻的应力分析,计算效率可得到很大提高.本文将通用权函数法推广到求解热载荷和机械载荷共同作用下界面裂纹尖端的应力强度因子过渡过程的问题中,推导出求解平面双材料界面裂纹问题应力强度因子的通用权函数法计算格式.基于此格式,计算热载荷和机械载荷共同作用下界面裂纹尖端的应力强度因子.通过实例计算比较,表明此方法得到的结果可以达到与相互作用积分法相当的工程应用精度.最后,应用此方法研究了热障涂层受热冲击及表面力共同作用时裂纹长度以及涂层厚度对应力强度因子的影响.结果表明:在一定边界条件下,当热障涂层中存在边缘裂纹时,随着涂层厚度的增加,更容易导致裂纹的扩展和涂层的剥落.     

一维六方压电准晶三角形孔边裂纹反平面问题

通过引入合适的数值保角映射,利用Stroh型公式研究一维六方压电准晶中正三角形孔边裂纹的反平面问题,给出在电非渗透边界条件下三角形孔边裂纹尖端的场强度因子和能量释放率。通过数值算例,讨论场强度因子和能量释放率随缺陷几何尺寸和力电荷载的变化规律。结果表明:随孔边裂纹长度的增加,场强度因子先急剧增加后减小,并趋于定值1,正三角形孔洞的尺寸对其影响可忽略不计;声子场和相位子场机械载荷总是促进裂纹扩展,而电位移对裂纹的扩展极大地依赖于声子场和相位子场载荷的大小。     

微小缺口/孔洞的激光衍射无损检测

基于裂纹和孔洞的小尺寸特征,提出了微小缺口/孔洞的激光衍射无损探测技术,给出了解析表达式.通过这一技术,对单向拉伸试件中所含单边缺口和中心孔洞在外载作用下的演化过程进行了实时原位检测,获得了缺口/孔洞孔径随载荷的变化曲线及模拟裂纹时裂纹的张开位移、裂纹开裂长度及应力强度因子等一系列断裂参数.     

特征距离和扩充无网格法分析多裂纹相互作用

提出特征距离这一概念对内部基扩充无网格法进行修正,并数值模拟了多裂纹之间的相互作用。特征距离法用于选择内部基扩充无网格Galerkin法的奇异基函数,该方法仅对传统的内部基扩充无网格Galerkin法作了很小的改进,即可方便地应用于求解多裂纹问题;给出了相互作用能量积分计算混合型模式下的应力强度因子,数值模拟了三条内部裂纹和六条边裂纹问题,并与杂交位移不连续边界元法的计算结果进行比较。数值结果表明:修正的内部基扩充无网格法可以方便、有效地求解多裂纹问题,在不增加附加节点和自由度的情况下与杂交位移不连续方法的计算精度非常接近。     

Automated numerical simulation of the propagation of multiple cracks in a finite plane using the distributed dislocation method

In this paper, an automated numerical simulation of the propagation of multiple cracks in a finite elastic plane by the distributed dislocation method is developed. Firstly, a solution to the problem of a two-dimensional finite elastic plane containing multiple straight cracks and kinked cracks is presented. A serial of distributed dislocations in an infinite plane are used to model all the cracks and the boundary of the finite plane. The mixed-mode stress intensity factors of all the cracks can be calculated by solving a system of singular integral equations with the Gauss–Chebyshev quadrature method. Based on the solution, the propagation of multiple cracks is modeled according to the maximum circumferential stress criterion and Paris' law. Several numerical examples are presented to show the accuracy and efficiency of this method for the simulation of multiple cracks in a 2D finite plane.     

Modeling of voids/cracks and their interactions

Numerical modeling of a two-dimensional elastic body containing multiple voids/cracks to study the interaction between these defects can be significantly simplified by developing special finite elements, each containing an internal circular/elliptic hole or a slit crack. These finite elements are developed using complex potentials and the conformal mapping technique. The elements developed can be divided into two categories, namely, the semi-analytic-type and hybrid-type elements. The latter element type is an improved version of the former due to the implementation of displacement continuity along the inter-element boundary. All the proposed elements can be easily combined with the conventional displacement elements, such as isoparametric elements, to analyze the above-mentioned problems without using complicated finite element meshes. Numerical examples have been employed to illustrate the modeling of voids/cracks and their interactions. The results obtained using the semi-analytic-type elements are in good agreement with the theoretical results, and the corresponding results obtained using the hybrid-type elements show an improvement of the agreement with the theoretical results. However, the former element type is much easier to construct.     

Interacting multiple cracks in piezoelectric materials

In this paper, a method is presented to calculate the plane electro–elastic fields in piezoelectric materials with multiple cracks. The cracks may be distributed randomly in locations, orientations and sizes. In the method, each crack is treated as a continuous distributed dislocations with the density function to be determined according to the conditions of external loads and crack surfaces. Some numerical examples are given to show the interacting effect among multiple cracks.     

Elastic fields of interacting elliptic inhomogeneities

This paper presents a method for the calculation of two-dimensional elastic fields in a solid containing any number of inhomogeneities under arbitrary far field loadings. The method called pseudo-dislocations method, is illustrated for the solution of interacting elliptic inhomogeneities. It reduces the interacting inhomogeneities problem to a set of linear algebraic equations. Numerical results are presented for a variety of elliptic inhomogeneity arrangements, including the special cases of elliptic holes, cracks and circular inhomogeneities. All these complicated problems can be solved with high accuracy and efficiency.     

On the asymptotics of the stress and strain fields near a crack tip

The problem is solved under the plane strain conditions for a crack of general form, which in general is neither a mode I nor a mode II crack. We assume that the strains are small and the material is nonlinearly elastic. The mathematical statement of the problem is reduced to the eigenvalue problem for a system of ordinary nonlinear differential equations. Its solution is obtained numerically. We show that, for an incompressible material with power-law relations between the stress and strain deviators, the solution (the well-known HRR-asymptotics [1, 2]) exists only for mode I and II cracks. In the general case, we can only speak of approximate solutions. A similar conclusion can be made for different-modulus materials. We analyze the results of the preceding papers [1–7], where specific cases of the problem were considered.     

大延伸非均匀介质中地震波全弹性散射理论Ⅰ--弹性波单次散射理论

所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究.应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解.这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础.在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论.该理论可包容小尺度非均匀体、大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论.     

Fissuration multiple par corrosion sous contrainte : Modélisation du comportement mécanique par une méthode d'homogénéisation

Stress Corrosion Cracking (SCC) phenomenon is characterised by initiation and propagation of surface cracks frequently multiple. In order to model the mechanical behaviour of such materials we propose, as for composites, the use of homogenization techniques. Two materials are considered, first one corresponding to the cracked external volume and the second to the internal safe material. The cracked volume is considered as a two phase material, i.e., elastic matrix containing elliptical voids. The overall behaviour of the equivalent material is obtained applying the usual homogenization rules. Comparison between simulations and experimental results is done.     

含单排周期微裂纹平板结构中的弹性波传播

受损伤固体中含有的微裂纹或微孔洞往往具有周期性，对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题，它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年。Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题。并推出显式分析结果。本文基于弹性动力学理论，分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况，可采用具有退化核第一类Fredholm积分方程方法分析求解，在求解中给出相应的无量纲数，例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。