Study For A Cavity Crack Problem In Linear Elastic Body

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 loadsσxx∞,σyy∞,σxy∞, in Chapter Eight, the original problem (the hole crack problem in infinite plate subjected to remote loadsσxx∞,σyy∞,σxy∞) 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:σxx∞=0,σyy∞=σ,σxy∞=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.