【作者】 刘宝良；

【导师】 闫相桥；

【作者基本信息】 哈尔滨工业大学 ， 工程力学， 2010， 博士

【摘要】 本文开展线弹性体缺陷-裂纹问题研究源于下列事实:（1）实际工程结构（材料）中总是不可避免地存在着各种不同形式的缺陷（如孔洞）;（2）由于应力集中,孔边很可能起源裂纹。关于本课题的来源、研究的目的和意义、研究现状及主要研究内容见本论文的绪论,即第1章。对于三维缺陷-裂纹问题,本文对三种典型模型进行了研究。1、对应于文献中广泛报道的表面半圆形裂纹问题,本文建立了表面半球形缺陷（孔洞）-裂纹问题。事实上本模型研究是激发我们展开广泛的线弹性缺陷-裂纹问题研究的源泉。详细的研究见第2章。2、对应于文献中广泛报道的棱角角点裂纹问题,本文建立了棱角缺陷（孔洞）-裂纹问题。对这一裂纹问题,在研究方法上与第2章研究表面半球形缺陷-裂纹问题一样,都是利用ANSYS有限元分析软件建立缺陷-裂纹问题的有限元分析模型,详细地计算裂纹尖端应力强度因子,并与对应的表面裂纹问题的结果进行比较,以揭示缺陷的存在对裂纹尖端应力强度因子的影响。详细的研究见第3章。表面裂纹通常作为三维力学问题处理,这无疑是非常复杂的,对于表面缺陷-裂纹问题更是如此。在第4章,我们研究的是这样一类表面缺陷-裂纹问题,它们都具有相同的深度,称为类平面裂纹问题。这类表面缺陷-裂纹问题在工程中是客观存在的,但尚未见报道其研究成果。在第4章,基于先前对于无限大体中矩形裂纹问题、表面矩形裂纹问题的研究以及杂交位移不连续法（一种平面弹性裂纹问题的边界元法）,我们提出了一种求解类平面裂纹问题的数值方法,在本质上它是一种平面边界元方法,数值例算说明了本数值方法的有效性和准确性。进而利用这种数值方法求解了表面圆孔-裂纹问题和表面方孔-裂纹问题,所获得的数值结果一方面进一步证实本数值方法的有效性和准确性,另一方面可以揭示裂纹体几何参数对裂纹尖端应力强度因子的影响。对于二维缺陷-裂纹问题,本文利用杂交位移不连续法对下列几种典型模型进行了研究。1、对应于文献中广泛报道的矩形拉伸板单边裂纹问题,我们研究了矩形拉伸板单边缺陷裂纹问题,包括单边裂纹问题、单边半圆孔裂纹问题、和单边半方孔裂纹问题,详见第5章。2、对应于文献中广泛报道的矩形拉伸板双边裂纹问题,我们研究了矩形拉伸板双边缺陷裂纹问题,包括双边裂纹、双边半圆孔裂纹问题和双边半方孔裂纹问题,详见第6章。在这里顺便指出,第6章的矩形拉伸板双边缺陷裂纹问题研究与第5章的矩形拉伸板单边缺陷裂纹问题研究是平行的。3、对应于文献中广泛报道的矩形拉伸板中心裂纹问题,我们研究了矩形拉伸板中心缺陷裂纹问题,包括中心裂纹问题、中心圆孔裂纹问题和中心方孔裂纹问题,详见第7章。由于孔边应力集中,孔边很可能起源裂纹。因此,很多研究者专注于孔边裂纹问题。在第8章我们再次十分关注此类无限大板中孔-裂纹问题,重点研究三种孔边裂纹问题,即椭圆孔-裂纹问题、菱形孔-裂纹问题和三角孔-裂纹问题。为此,通过把Bueckner原理普遍化,我们提出了一种求解远方载荷(σ_xx^∞,σ_yy^∞,σ_xy^∞)作用下无限大板中孔边裂纹问题的数值方法:通过把适于单一裂纹的Bueckner原理[112]扩充到远方载荷作用下无限大板中孔边裂纹问题,将原问题分解为承受远方载荷不含孔边裂纹的均匀问题,和在远方不承受载荷但在裂纹面上和孔的表面上承受面力的问题。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Yan[3]最近提出的杂交位移不连续法,这种孔边裂纹问题是很容易数值求解的。算例说明本数值方法对分析无限大板中孔边裂纹问题既简单又非常有效。进而利用这种数值方法研究了三种孔-裂纹问题,包括两种载荷情况:（1）远方均匀拉伸载荷,即σ_xx^∞=0,σ_yy^∞=σ,σ_xy^∞=0;（2）裂纹表面和孔的表面承受均匀压缩载荷p。我们通过改变孔的几何形状和几何参数,通过与无限大板中心裂纹问题的应力强度因子比较,揭示了孔的几何形状和几何参数对应力强度因子的影响。发现孔对源于它的裂纹的应力强度因子具有屏蔽影响和放大影响。这种屏蔽影响和放大影响随着孔的几何形状和几何参数的变化而变化。这种发现在工程上或许具有重要意义。通常作为断裂试件的矩形拉伸板中心裂纹问题是断裂力学中最常见的裂纹问题之一。在第9章,针对这种试样的机械加工问题（如加工切槽、预制疲劳裂纹）,我们提出了中心切槽裂纹板拉伸试样,包括两个模型,即中心切槽圆弧根部裂纹板拉伸试样和中心切槽角形根部裂纹板拉伸试样。利用Yan[3]最近提出的杂交位移不连续法,对中心切槽裂纹板拉伸试样进行了详细的分析。通过改变切槽根部的几何形状和几何参数,通过与中心裂纹板拉伸试样的应力强度因子比较,揭示了切槽根部的几何形状和几何参数对应力强度因子的影响,获得了一些有价值的数据。这些数据对中心裂纹板拉伸试样的机械加工有一定的指导作用。通常作为断裂试件的矩形拉伸板双边裂纹问题是断裂力学中最常见的裂纹问题之一。在第9章,类似于对中心裂纹板拉伸试样所做的,我们提出了双边切槽裂纹拉伸试样并进行了详细的分析。本文的研究揭示出,孔洞对源于它的裂纹尖端应力强度因子具有屏蔽影响和放大影响。这种屏蔽影响和放大影响随着孔洞的几何形状和几何参数的变化而变化。本文通过引入一些几何特征参量,详细地揭示这种影响性。这些研究无论对于丰富断裂力学的成果,还是对指导含孔洞结构的设计与安全性评价都具有重要意义。尤其是,我们提出的缺陷对源于缺陷的裂纹尖端应力强度因子的屏蔽影响和放大影响的概念在工程上具有重要意义。工程技术人员可以利用孔洞的屏蔽效应,设计孔洞（包括孔洞的形状及其大小）以最大限度地提高含裂纹结构的承载能力,或者类似地利用孔洞的放大效应,设计孔洞以最大限度地降低含裂纹结构的破坏载荷（用于爆破试验中）。更多还原

【Abstract】 In this dissertation, a cavity crack problem is investigated based on the following facts: （1） There are inevitably some flaws, such as crack, cavity, inclusions,etc, in engineering materials; （2） Due to the stress concentration effect around the hole, cracks are likely to initiate at the hole under the action of fatigue loading.The origin, aim and significance of the research subject and the investigation status quo are described in the Introduction of the dissertation, i.e., Chapter One. In addition, the main investigation problems are presented.For a three dimensional cavity crack problem, the following three typical models are investigated:One is a surface semi-spherical cavity crack which corresponds to a surface semi-circualr crack reported widely in literature. In fact, it is the study of the model that activates us to deal with a wide of cavity cracks in linear elastic body. The study detail is described in Chapter Two.Two is a corner cavity crack which corresponds to a three-dimensional corner crack reported widely in literature. For the crack problem, as done in Chapter Two in research technique, a finite element model for a cavity crack is set up by using the ANSYS finite element software. The SIFs of the cavity crack are calculated in detail and are compaered with those of a corresponding surface crack to reveal the effect of the cavity on the SIFs. The study detail is described in Chapter Three.A surface crack is usually treated with as a three-dimensional problem, which is no doubt very complicated. For a surface cavity crack problem, it is so. Chapter Four is concerned with such a kind of surface crack with an approximately same depth, which is called a liked-plane crack. Such a liked-plane crack is objective existence in engineering. To our knowledge, however, its solution has not been obtained. Based on the previous investigations on internal rectangular crack and surface rectangular crack in infinite solid in tension and a hybrid displacement discontinuity method （a boundary element method） proposed recently by Yan, a numerical approach for the liked-plane crack problem is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the SIFs of a liked-plane crack. Specifically, a surface circular hole crack problem and a surface square hole crack problem are investigated in detail.For a two dimensional cavity crack problem, the following typical models are investigated by a hybrid displacement discontinuity method.One is single defect crack in rectangular plate in tension which corresponds to Single Edge Crack reported widely in literature. It includes Single Edge Crack, single semi-circualr hole crack and single semi-square hole crack. The study detail is described in Chapter Five.Two is double defect cracks in rectangular plate in tension which corresponds to a Double Edge Cracks reported widely in literature. It includes Double Edge Cracks, double semi-circualr hole cracks and double semi-square hole cracks. The study detail is described in Chapter Six. By the way, it is pointed out that the double defect cracks in rectangular plate in tension in Chapter Six is parallel to the single defect crack in rectangular plate in tension in Chapter Five.Three is a center defect crack in rectangular plate in tension which corresponds to a center crack in rectangular plate in tension reported widely in literature. It includes a center crack, a circualr hole crack and a square hole crack. The study detail is described in Chapter Seven.Due to the stress concentration effect around the hole, cracks are likely to initiate at the hole under the action of fatigue loading. Consequently, a number of papers dealing with hole edge crack problems. This dissertation deals again with crack（s） emanating from a hole in infinite plate. Three kinds of hole cracks （an elliptical hole crack, a rhombus hole crack and a triangle hole crack） are emphasized. By extending Bueckner’s principle suited for a crack to a hole crack problem in infinite plate subjected to remote loadsσ_xx^∞,σ_yy^∞,σ_xy^∞, in Chapter Eight, the original problem (the hole crack problem in infinite plate subjected to remote loadsσ_xx^∞,σ_yy^∞,σ_xy^∞) is divided into a homogeneous problem （the one without hole crack） subjected to remote loads and a hole crack problem in an unloaded body with applied tractions on the surfaces of hole and crack. Thus, the results in terms of the SIFs can be obtained by considering the latter problem, which is analyzed easily by means of a hybrid displacement discontinuity method. Numerical examples are included to illustrate that the numerical approach is very simple and effective for analyzing the hole crack problem in infinite plate.By using the numerical approach, further, three hole crack problems are analyzed in detail. Two loads are considered: （1） remote tension:σ_xx^∞=0,σ_yy^∞=σ,σ_xy^∞=0; （2） pressure load p on the surface of hole and crack. By changing hole geometry form and hole geometry parameters and by comparing the SIFs of the hole crack problem with those of the center crack problem, the effect of the hole geometry form and hole geometry parameters on the SIFs is revealed. It is found that a hole has a shielding and an amplifying effect on the SIFs of crack（s） emanating from the hole. The shielding and amplifying effects are varied with hole geometry form and hole geometry parameters. These findings perhaps have an important meaning in engineering.A model frequently used in fracture mechanics, as we know, is a center cracked plate tension specimen （CCT）. According to mechanical machining of the specimen （i.g., mechanical machining of notch and fatige crack）, in Chapter Nine, this dissertation presents a center notch root crack in rectangular plate in tension. It includes two models: a center notch circular arc root crack and a center notch angle root crack. By using a hybrid displacement discontinuity method, the effect of the notch root geometry forms and geometry parameters on the SIFs of the center cracked plate tension specimen is studied in detail. Some valuable numerical results are obtained, which perhaps have some guidance role for mechanical machining of the center cracked plate tension specimen.A model frequently used in fracture mechanics, as we know, is a double edge cracked plate tension specimen （DECT）. As done in Chapter Nine for a center cracked plate tension specimen （CCT）, this dissertation presents double notch crack model in rectangular plate in tension. The notch crack model are analyzed in detail in Chapter Nine.It is found from the this dissertation research that a cavity has a shielding effect and an amplifying effect on the SIFs of crack（s） emanating from the cavity. The shielding and amplifying effects are varied with with the cavity geometry form and cavity geometry parameters. By introducing some geometric characteristic quantities, in this dissertation, these effects are revealed in detail. This research is very importance for enriching fracture mechanics and for design and safe evaluation of structure with cavity crack. Especially, the concepts of the shielding and amplifying effects presented here perhaps have an important meaning in engineering. An engineer can make use of the“shielding effect”to enhance the carrying capacity of a structure with a crack by cutting a cavity with a proper size in the structure. Similarly, an engineer can make use of the“amplifying effect”to reduce the failure load of a structure with a crack by cutting a cavity with a proper size in the structure.更多还原