Eğilme momentine maruz içi boş silindirik yapılarda dönmüş dış yüzey çatlaklarının karışık mod kırılma analizleri = Mixed mode fracture analyses of deflected external surface cracks in hollow cylindrical structures under bending moment

Abstract

Tasarlanan mühendislik yapılarının ve makine parçalarının hasara uğraması sıklıkla karşılaşılan sorunlardan biridir. Karşılaşılan bu sorunlar çoğunlukla üretim yöntemine ve malzemenin iç yapısındaki kusurlara bağlı olarak ele almak mümkün olabilmektedir. Çoğunlukla malzemedeki bu kusurlar, yüzeyde veya iç yapıda meydana gelen mikro çatlaklar sonucu oluşabilmektedir. Bu mikro çatlaklar mühendislik yapılarının ve makine parçalarının üretim yöntemine bağlı olarak da meydana gelebilmektedir. Parçaların servis ömrü boyunca maruz kaldığı yükler altında, malzemenin iç yapısında veya yüzeyinde bulunan mikro çatlakların ilerlemesi sonucu kırılma hasarı meydana gelebilmektedir. Hasara uğramış yapıların incelenmesi sonucunda, nasıl hasara uğradığı çoğunlukla tespit edilebilmektedir. Bu tespite göre hasara uğramış parça bölgesel olarak; içinde veya yüzeyinde çatlak barındıran levha, içi boş silindir ve dolu silindir gibi daha küçük geometrik modellere indirgenebilmektedir. Elde edilen bu geometrik modeller için, kırılma mekaniği yöntemleri kullanılarak gerilme şiddet faktörleri hesaplanabilmektedir. Bu çalışmaların sonucunda meydana gelebilecek hasarları en aza indirgemek mümkün olabilmektedir. Malzemelerin yükleme durumuna bağlı olarak çatlakların üç farklı kırılma modu vardır. Karışık modlu gerilme şiddet faktörleri ; Mod-I (açılma modu), Mod-II (düzlem içi kayma modu), Mod-III (düzlem dışı kayma modu) olarak ifade edilmektedir. Karışık mod gerilme şiddet faktörlerinin elde edilme yöntemlerinden biri de zenginleştirilmiş sonlu elemanlar yöntemidir. Bu tez çalışması kapsamında, eğilme momentine maruz içi boş silindirik yapılarda dönmüş dış yüzey çatlaklarının karışık modlu gerilme şiddet faktörlerinin problem parametrelerine olan etkisi incelenmiştir. Problemi tanımlayan parametreler şunlardır; çatlak şekil oranı (a/c), çatlak derinliği/silindir et kalınlığı (a/t), silindir iç yarıçapı/silindir dış yarıçapı (Ri/Ro), çatlak dönme açısı (α)'. ANSYS APDL'de problem parametreleri ile modeller oluşturulmuştur. Bu modellere eğilme yükü ve sınır şartları uygulanarak FCPAS programında kullanılmak üzere çıktılar elde edilmiştir. FCPAS'den elde edilen sonuçlar, normalize edilerek gerilme şiddet faktörleri elde edilmiştir. Bu elde edilen gerilme şiddet faktörleri her bir parametre için karşılaştırmalı olarak grafik halinde sunulmuştur. Gerilme şiddet faktörleri ve problem parametrelerine bağlı olarak; serbest yüzey noktası ve çatlak ucu derinlik noktası için empirik denklemler geliştirilmiştir. Geliştirilen bu empirik denklemler, ara değer parametre analizlerinin sonuçları ile doğrulanarak uyum içinde olduğu sonucuna varılmıştır.

When the designed engineering structures and machine parts are exposed to loads above a certain critical load value, damages may occur as a result of high deformation and collapse. These problems are mostly due to the production method and the defects in the internal structure of the material. Mostly, these defects in the material can occur as a result of microcracks on the surface or in the internal structure. These micro cracks can also occur depending on the production method of engineering structures and machine parts. If the parts are exposed to lower and repetitive loads throughout their service life, fracture damage may occur after a certain time or suddenly as a result of the progression of micro cracks in the internal structure or surface of the material. Therefore, the formation and propagation of cracks in structural parts should be prevented. The part must be replaced or repaired before the crack length reaches a critical value. In the process of examining the damaged structures, it can often be determined how they were damaged. According to this determination, the damaged piece can regionally be reduced to crack problems in more basic and smaller geometries such as plate with internal of surface cracks or solid or hollow cylinders containing surface cracks. These geometric models can be analyzed under various loads and the corresponding stress intensity factors can be calculated. In a structural part under stress, the magnitude of the stresses occurring in the tip region of the crack, which tend to go to infinity mathematically, in other words, rapidly approaching infinity towards the crack tip, is determined by the parameter called the stress intensity factor. It is denoted by the symbol K. When the K value exceeds a critical Kc value, which is a material characteristic, the crack grows suddenly and fracture occurs. This critical value is called fracture toughness and is expressed with the symbol Kc. Cracks have three different fracture modes depending on the loading condition of the materials. Mixed-mode stress intensity factors have three components, which are mode-I (opening mode), mode-II (in-plane shear mode), mode-III (out- of-plane shear mode). Within the scope of this thesis, the effects of different parameters on mixed-mode stress intensity factors of deflected outer surface cracks in hollow cylindrical structures subjected to bending moment were investigated. Parameters defining the problem are; crack shape ratio (a/c), crack depth/cylinder wall thickness (a/t), cylinder inner radius/cylinder outer radius (Ri/Ro), crack rotation angle (α). In all models created depending on the problem parameters in ANSYS APDL, a=1 was chosen as unit crack length. The height parameter of the cylinder (2H) was determined as 6 times the outer radius in all models. After these limitations are determined, the (a/c) ratios are 0.25, 0.5, 1, 2, respectively; ( a/t ) ratios are 0.05, 0.1, 0.25, 0.5, 0.8, respectively; The (α) angle values considered are 0°, 15°, 30°, 45°, xxxii 60°, 75°, respectively, and finite element models corresponding to all combinations of these values have been created. In the meshing process, 20-noded quadratic hexahedron solid elements were used in the crack tunnel volumes, and the use of prismatic elements was not allowed. For the remaining volumes, tetrahedron elements were used. Due to the existing symmetry in the problem, half models were obtained by dividing the cylinder volume into two equal parts along the height in order to make the mesh partition thinner by dividing the crack region into smaller elements in the models and to shorten the solution time. By applying bending load and symmetry displacement boundary conditions to this half model, the finite element mesh structure has been created, and outputs to be used in the FCPAS program have been obtained. The FCPAS (Fracture and Crack Propagation Analysis System) program calculates the stress intensity factors using the enriched finite element method. Elements adjacent to the crack tip and located along the crack front line are called the enriched elements. Elements adjacent to the enriched elements are the transition elements. Transition elements were formed by reducing the enriched element formulation from one to zero along the element thickness from the sides of enriched elements to the sides of regular elements. This yields a transition zone between enriched elements and normal elements. The fluctuations in the crack tip stress intensity factors are reduced by the transition elements and the calculation of the stress intensity factors can be made more accurate. The obtained fracture analysis results from FCPAS in terms of mode-I, mode-II and mode-III stress intensity factors were normalized. These obtained mixed-mode stress intensity factors are presented in graphs for each parameter comparatively. According to these results, it was observed that the maximum mode-I stress intensity factor occurred at 0°, and the mode-I stress intensity factor decreased with increasing α angle value. Since in-plane and out-of-plane shear stresses do not occur at 0°, mode-II and mode-III stress intensity factors do not occur. It has been observed that the maximum absolute values of mod-II and mod-III stress intensity factors occur at inclination angle of 45°. It was observed that the absolute values of mode-II and mode-III stress intensity factors decreased at 60°, 30°, 75° and 15° angle values, respectively. As the Ri/Ro ratio increased, the mode-I stress intensity factor value increased; It was concluded that the mode-I stress intensity factor value decreased with the increase of a/c and a/t ratios. Due to the large number of problem parameter variables, it is not possible to develop a single empirical equation that provides all the results. For this reason, a total of four equations are developed for mode-I and mode-II normalized SIFs (mode-III SIF is zero at the depth point) for the crack tip depth points, for two different ranges of 0.25 ≤ a/c ≤ 1 and 2 ≥ a/c ≥ 1. 10. Similarly, for the same two ranges of a/c, a total of six empirical equations are developed for mode-I, mode-II and mode-III SIFs of the free surface point. These empirical equations were compared with the analysis results of the models containing 24 randomly selected intermediate values of the problem's parameters and validation studies were carried out. It was observed that the difference between the crack tip depth point values and the empirical equation results for mode-I and mode-II remained below 10%. For mode-I, mode-II and mode-III SIFs at the free surface, it was observed that the difference between the values obtained from finite element analyses and those from the empirical equations remained below 15%, except for a few cases. Therefore, it wasconcluded that the values of the models and those from the empirical equations for both crack front points were in good agreement with each other.