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.     

孔洞裂纹问题的一种数值方法

研究孔洞与裂纹的相互作用问题,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来解决,而利用笔者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孔洞与裂纹的相互作用既简单又有效.     

界面主裂纹和微裂纹之间的干涉

采用复势函数的位错解方法，通过对奇异积分方程的建立和数值求解，研究了界面主裂纹同界面及基体微裂纹之间的干涉．结果表明远场载荷角ψ同Ｄｕｎｄｅｒ’ｓ参数α对界面微裂纹及基体中水平微裂纹同主裂纹干涉的影响都很显著，而ψ对屏蔽区的影响则远小于α对其的影响     

次表面微裂纹对偏折主裂纹扩展行为的分布位错理论研究

为研究在拉伸载荷作用下包含一条埋置偏折裂纹和一条任意位置微裂纹的半无限大平面问题.论文基于连续分布位错法,建立相应的位错密度积分方程,并采用GAUESS-CHEBSHEV数值积分法得到其力学参量.通过有限元法对理论结果进行了验证.埋置深度、微裂纹中心到主裂纹尖端的距离将对主裂纹尖端的应力强度因子产生影响;结果表明相比于无微裂纹的情况,在某些方位处微裂纹对主裂纹尖端的扩展起到促进作用,而在其他方位的微裂纹对主裂纹尖端的扩展起到抑制作用;主裂纹尖端的扩展方向和等效应力强度因子相比于倾斜微裂纹而言受水平微裂纹的影响更大.     

含中心裂纹压电体的二维精确解

解析地研究了含中心裂纹的压电体，它在无穷远处承受机电载荷，并在裂面上满足由Parton和Kudryavtsev以及Hao和Shen提出的绝对电边界条件。在平面应变假设下，给出其二维精确解，并提供了机械应变能释放率和裂尖能量释放率等数值结果。考虑工业应用范围之内常用的远场载荷时，由绝对电边界条件得出的能量释放率表现出明显的非线性特征及载荷相关性，而不是完全与电场无关，这一结论与Xu和Rajapakse在较小载荷下得到的规律不同。     

双轴载荷作用下源于椭圆孔的分支裂纹的一种边界元分析

利用一种边界元方法来研究双轴载荷作用下无限大板中源于椭圆孔的分支裂纹.该边界元方法由Crouch 与 Starfied 建立的常位移不连续单元和笔者提出的裂尖位移不连续单元构成.在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界.文中算例说明本数值方法对计算平面弹性裂纹的应力强度因子是非常有效的.该文对双轴载荷作用下无限大板中源于椭圆孔的分支裂纹的数值结果进一步证实本数值方法对计算复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示双轴载荷及裂纹体几何对应力强度因子的影响.     

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。     

含圆孤裂纹系的压电材料反平面应变问题

应用复变函数解析延展原理，并通过求解Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题，得到了含圆弧裂纹压电材料反平面应变问题的一般解，对单个圆弧裂纹的情形，给出了封闭形式的复函数解和场强度因子，结果表明，当无限远处或裂纹表面同时受机械载荷（应力τ＾∞或Ｔｚ）和电载荷（电位移Ｄ＾∞或电荷ｑ）联合作用时，应力强度因子仅与机械载荷有关，而电位移动强度因子仅与电载荷有关。     

纳米晶体铝在单轴拉伸下的位错堆积对微裂纹扩展的影响

摘要：针对纳米晶体材料,研究了单轴拉伸载荷作用下纳米晶体铝中的裂纹与裂纹尖端发射的位错所形成的滑移面之间的相互作用。通过分布位错法,将裂纹和滑移面等效为均匀分布的连续位错,获得了裂纹面上应力场。并引入裂纹尖端的无位错区,研究了裂纹尖端无位错区对微裂纹的萌生和主裂扩展之间的影响。结果表明,不考虑裂纹尖端无位错区时,裂纹长度较短,会先在晶界处形成微裂纹,主裂纹较长时,主裂纹会直接穿晶扩展。滑移面与裂纹尖端夹角较大时,会增加裂纹尖端发射的位错个数,从而抑制主裂纹的扩展。考虑裂纹尖端无位错区时,无位错区先于晶界处出现微裂纹,通过主裂纹与微裂纹之间位错的相互发射,导致裂纹与尖端处微裂纹汇合,有效加速了主裂纹的扩展。     

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.     

带微裂纹物体的有效断裂韧性

按照等效介质的思想，引进有效表面能密度的概念，建立了带微裂纹物体有效断裂韧性的公式．具体计算了微裂纹群分别平行和垂直于宏观裂纹两种情况的减韧比．表明微裂纹群在产生应力屏蔽（或反屏蔽）效应的同时，也降低了材料的有效断裂韧性，减小了对宏观裂纹的扩展阻力．     

Modified model of macro–microcrack interaction

The general asymptotic solution of macrocrack interaction with an arbitrary field of microcracks is modified to the case where microcracks are located around a main crack. A comparison with the solution for a semi-infinite crack is discussed. The shielding-amplification zones are identified in terms of the distance from the microcrack to the main crack of finite size.     

Further investigation of interaction between interface macrocrack and parallel microcracks in bimaterial anisotropic solids

In this paper, with the aid of superimposing technique and the Pseudo Traction Method (PTM), the interaction problem between an interface macrocrack and parallel microcracks in the process zone in bimaterial anisotropic solids is reduced to a system of integral equations. After the integral equations are solved numerically, a conservation law among three kinds ofJ-integrals is obtained which are induced from the interface macrocrack tip, the microcrack and the remote field, respectively. This conservation law reveals that the microcrack shielding effect in such materials could be considered as the redistribution of the remoteJ-integral. The project supported by the National Natural Science Foundation of China, and the Doctorate Foundation of Xi'an Jiaotong University     

A heuristic approach to microcracking and fracture for ceramics with statistical consideration

Microcracking damage and toughening are examined for ceramics. These effects have been found to depend on the material microstructure and macrocrack growth. Isotropic damage, attributed to random distribution of microcrack location, length and orientation can be associated with a disordered microstructure and a non-uniform residual stress field. When the applied stress is the main cause of cracking, the microcrack distribution is no longer random such as a system of quasi-parallel cracks. To highlight the effect of crack interaction, discrete models are advanced where damage is simulated by a distribution of microcracks. The dilute concentration assumption is invoked to simplify the analysis.The two-dimensional discrete model is based on a phenomenological approach that is statistical in character. Interactions of microcracks and with a macrocrack are considered by means of a boundary element technique (A. Brencich, A. Carpinteri, Int. J. Fracture 76 (1996) 373–389; A. Brencich, A. Carpinteri, Eng. Fract. Mech. 59 (1998) 797–814) where both isotropic and anisotropic damage could be treated. Comparisons with other results are made to show that the model can be applied to analyse the fracture behaviour of different materials.     

Thermal fracture of macrocrack with closure as influenced by microcracks

The fracture stability of macrocracks under uniform heat flux is analyzed to include the effect of a system of microcracks. The interaction of cracks leads to full or partial closure of crack surfaces. The boundary problem is stated and a solution is obtained. The domains where microcracks are closed and/or affect partial closing of the macrocrack are found. Evaluated is the macrocrack tip stress intensity factor accounting for closure.     

M-integral analysis for a two-dimensional metal/ceramic bimaterial solid with extending subinterface microcracks

Summary  The problem of the extension of subinterface microcracks in an infinite metal/ceramic bimaterial solid is studied. For the microcrack growth, the values of the M-integral are calculated under the assumption of a self-similar growth. First, the role that the M-integral plays in a metal/ceramic bimaterial solid with growing subinterface cracks is analyzed. It is concluded that an inherent relation exists between the value of the M-integral and the decrease of the effective elastic moduli for a bimaterial solid with growing subinterface microcracks. Second, it is concluded that mutual amplification and shielding effects exist during the microcrack extension, while they are substantially dependent on the increment of the microcrack length as well as the geometry of the microcrack arrangement under given loads. This strong mutual shielding effect of interacting microcracks makes the microcrack extension become increasingly difficult, and may stop the growth of the microcracks even under constant loads. Also, it is concluded that for a certain microcrack growth, the value of the M-integral in metal/ceramic bimaterial solid is always larger than that in homogeneous brittle solid for the same crack configuration. This means that the same microcrack growth in the former case shows lower stability than that in the latter one, due to the existence of a ductile phase. Received 3 May 2001; accepted for publication 27 June 2002 This work was supported by the Chinese National Nature Science Foundation (Grant 19472053) and supported by the Doctorate Foundation of Xi'an Jiaotong University (Grant DFXJU2000-15).     

干涉问题中T应力与各向异性的作用

采用离散模型（包括半无限主裂纹和近尖微裂纹）研究了各向异性材料主微裂纹干涉问题中T应力对主裂尖参数的影响,并且与相同情况下各向同性材料的结果进行了比较,比较结果列于文中各图。研究结果表明,在各向异性材料和各向同性材料中T应力对主裂尖应力强度因子的影响趋势是相似的,但是由于T应力与材料各向异性性质的共同作用,使两种情况下T应力对主裂尖参数的影响结果存在着明显的偏差。     

On collinear microcrack–inclusion arrays interaction and related problems

Investigated is a crack problem for an array of collinear microcracks in composite matrix. Inclusions are situated in between the neighbouring microcracks tips and exhibit different elastic properties than matrix. The problem is solved using the technique of distributed dislocations. A developed approximate fundamental solution for a single dislocation lying in a general point between inclusions is employed in the distribution of continuously distributed dislocation to cracks modelling. Stress intensity factor is calculated for various cracks/inclusions geometries and elastic moduli mismatches. Stability and/or instability of the straight microcrack paths is investigated for slowly growing microcracks with inclusions located in between the neighbouring microcracks tips. Applications to periodic microcrack tunnelling and microcracks weakening ahead of the main crack are discussed.     

Interaction between an interface crack and subinterface microcracks in metal/piezoelectric bimaterials

The J-integral analysis is presented for the interaction problem between a semi-infinite interface crack and subinterface matrix microcracks in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack subjected to different loads and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is deduced to a system of singular integral equations with the aid of a superimposing technique. The integral equations are then solved numerically and a conservation law among three values of the J-integral is presented, which are induced from the interface crack tip, the microcracks and the remote field, respectively. The conservation law not only provides a necessary condition to confirm the numerical results derived, but also reveals that the microcrack shielding effect in such materials could be considered as a redistribution of the remote J-integral. It is this redistribution that does lead to the phenomenological shielding effect.     

压电材料中的微裂纹屏蔽问题分析

分析当主裂纹与一个微裂纹在远场I型力（KI）和远场电位移（Ke)作用下的相互干涉问题,得出了在微裂纹的位置角和方向角周时独立变化时,微裂纹对主裂纹的屏蔽作用的全局使命主裂纹扩展,通过电算还发现Ortiz在各向同性材料和各向异性材料中得出的“微裂纹群对主裂纹最大屏蔽效应产生在微裂纹方向与最大主应力垂直的方向”在压电材料中不再成立,进而提出除Hutchinson指出微裂纹屏蔽效应两个来源（即：材料有效刚度的降低和残余应力的释放）外的另一个来源,微裂纹对主裂砂电场的扰动,在对主微裂纹J积分分析时发现J2积分与J1积分具有同等重要的地位。