Eksenel gerilmeye 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 tension loading

Abstract

Tasarım ve analizlerde geleneksel yaklaşım, malzemelerin mukavemeti konseptini kullanarak hesaplamalar yapmaktır. Bu yaklaşımda uygulanan yüklemeye bağlı olarak parçada oluşan gerilmeler hesaplanır. Malzemede oluşan gerilmenin, hasar kriterine bağlı olarak akma veya çekme dayanımını aşmasıyla hasar meydana gelir. Fakat malzemelerde çatlak gibi kusurların varlığı özellikle çatlak etrafındaki gerilmeleri arttırır ve bu malzemeler geleneksel yöntemler kullanılarak tahmin edilen ömürden daha önce hasara uğramaktadır. Bunun sonucunda ağır can ve mal kaybına sebebiyet verilebilir. Kırılma mekaniği bir çatlak veya kusuru olan bir parçanın mevcut şartlarda hasara uğrayıp uğramayacağını teşhis edip maruz kaldığı yükleme durumuna göre ömrünü tahmin etmektedir. Kırılma mekaniği yaklaşımında parçanın maruz kaldığı gerilmenin, çatlak boyutunun ve parça geometrisinin bir fonksiyonu olarak gerilme şiddet faktörü hesaplanmaktadır. Gerilme şiddet faktörü (GŞF), bir malzeme özelliği olan kırılma tokluğunu (Kc) aştığında ani kırılma meydana gelmektedir. Bu sebeple GŞF'lerinin önceden bilinmesi gerekli bir durumdur. Bu tez çalışmasında eksenel çekme gerilmesine maruz içi boş silindirlerde dönmüş eliptik yüzey çatlaklarının; çatlak derinliği/çatlak genişliği (a/c), çatlak derinliği/silindir et kalınlığı (a/t), silindir iç yarıçapı/silindir dış yarıçapı (Ri/Ro), çatlak dönme açısı (α) parametrelerine göre FCPAS programı kullanılarak karışık mod kırılma analizleri gerçekleştirilmiştir. Tez kapsamındaki analizlere başlamadan önce literatürdeki çalışmalarla kıyaslamalar yapılıp paralel sonuçlar elde edilmiştir. Çatlak ucu bölgesinde eleman boyutu ve çatlak önü bölüntüleme sayısı için yakınsama çalışmaları yapılmıştır. Karışık mod kırılma analizleri sonucunda her model için KI, KII, KIII GŞF'leri dağılımları elde edilmiştir. Çatlak önü boyunca elde edilen GŞF dağılımları normalize edilerek dönme açısının değişimine bağlı olarak her bir senaryo için grafiklerde gösterilmiştir. α dönme açısının artmasıyla KI değerinin azaldığı, KII ve KIII değerlerinin ise arttıkları gözlemlenmiştir. Dönme açısı parametresi dışında a/c arrtıkça KI ve KII'nin azaldığı, çatlak ucu dip noktasında sıfır değerini alan KIII'ün serbest yüzey noktalarına gidildikçe arttığı gözlemlenmiştir. a/t ve Ri/Ro artışı ise KI'i arttırmış, KII ve KIII'e neredeyse hiç etki etmemiştir. Paylaşılan grafiklerle GŞF'lerinin ilgili parametrelere göre grafikten kolayca okunması amaçlanmıştır. Ayrıca problem için ele alınan parametre değerleri arasında kalan tüm olası modellerin çatlak ucu dip ve serbest yüzey noktalarında GŞF'lerini hesaplayabilecek empirik denklemler, çoklu regresyon analizi ile geliştirilmiştir. Denklem sağlamaları için ara değer modelleri oluşturulup bu modellerden elde edilen GŞF'leri, empirik denklem sonuçlarıyla karşılaştırılılıp sonuçlar grafiklerde paylaşılmıştır.

The traditional approach in design and analysis is to make calculations using the concept of strength of materials. In this approach, the stresses generated in the part are calculated depending on the applied loading. Damage occurs when the stress generated in the material exceeds the yield or tensile strength, depending on the damage criterion. However, the presence of defects such as cracks in materials increases stresses, especially around cracks, and these materials are damaged earlier than predicted life using conventional methods. As a result of this, severe loss of life and property may be caused. Fracture mechanics diagnoses whether a part with a crack or defect will be damaged under existing conditions and estimates the service life of the material based on the loading condition to which it is subjected. In the fracture mechanics approach, the stress intensity factor (SIF) is calculated as a function of the stress to which the part is subjected, the crack size and the part geometry. Damage occurs when the stress intensity factor exceeds the fracture toughness (Kc), which is a material property. For this reason, it is a requirement to know the SIFs in advance. Although analytical, experimental and numerical methods are used to calculate SIFs, analytical methods cannot present the exact solution of a three-dimensional structure or a part, which has complicated geometry and subjected to multi loading. Difficulties in the supply of appropriate test equipment, proper environment and specimen in experimental methods, make numerical methods more preferable compared to other methods. Among the numerical methods, using the finite element method, the amount of energy that will cause the formation of cracks in materials, whether the crack will progress in the current situation, if the crack will progress, the growth rate of the crack and the profile it will follow in the next step can be estimated. In addition, calculation of crack propagation lives, which allow determination of how long the cracked part can be left in the structure or machine, can also be done. In this thesis, firstly the studies carried out about the cylinder containing cracks in the literature and their results have been mentioned. The energy balance approach and stress intensity factor approach used in fracture mechanics problems and fracture modes representing movements of crack surfaces in different directions are explained. The crack depth/width of the crack (a/c=0.25, 0.5, 1, 2), the depth of the crack/cylinder wall thickness (a/t=0.05, 0.1, 0.25, 0.5, 0.8), cylinder inner radius/cylinder outer radius (Ri/Ro=0.1, 0.3, 0.6, 0.9, 0.95) and crack deflection angle (α=0°, 15°, 30°, 45°, 60°, 75°) parameters define the problem of deflected elliptical surface cracks in a hollow cylinder under tension loading in the. Using ANSYS APDL, the first model was created according to the geometric parameters and the meshing process was xxxvi performed. After that, tensile stress was applied to the model from the lower and upper surfaces of hollow cylinder, restricting the free body movement of the part. The following finite element model data are transferred from ANSYS to FCPAS for mixed mode fracture analyses; the loads and boundary conditions at the node points; the node numbers of the finite elements, the coordinates of the nodal points forming elements, the elements and nodes located along the crack front. Until this stage, the log file containing the steps performed in APDL has been exported and the parameters have been converted into dynamic variables in the log file. Thus, a parametric macro file has been created that will be used to create all other models later automatically. The capabilities of the FCPAS system, in which mixed mode fracture analyses are performed, have been mentioned and the fracture analysis procedure has been explained. The enriched finite element formulation used by FRAC3D, which is the solver of FCPAS, is shared and the terms in the formulation are explained. Before starting the analyses within the scope of the thesis, comparisons were made with the studies in the literature, which investigated solid and hollow cylinders with surface cracks and under bending and tension loads. Convergence studies which is necessary for numerical methods to obtain accurate results were carried out for the element size at crack tip and the division number of crack front as well. After determining the crack tip element size to be used in the analyses and the number of divisions of the crack front line, all other models were created with the macro file that was created earlier. Thus, the time to be spent on repetitive operations has been saved. Mixed mode fracture analyses of the models within the scope of the thesis were carried out, which yielded a total of 600 different models. As a result of the mixed mode fracture analyses, KI, KII, KIII SIF distributions along crack fronts were obtained for each model. The SIF distributions obtained along the crack front are normalized and shown in the graphs for each scenario depending on the change in the deflection angle. According to shared graphs, it was observed that the KI value decreases with increasing deflection angle α, while the KII and KIII values increase. Apart from the deflection angle parameter, effects of a/c, a/t and Ri/Ro are also examined. Analysis results show that KI and KII decrease as a/c increases, and KIII, which takes the zero value at the crack tip deep point, increases as the free surface point is approached. The increase in a/t and Ri/Ro parameters increased KI, but has almost no effect on KI and KIII. It is intended that the SIFs can be easily read from the graph according to the related parameters with the shared graphs. After explaining regression analysis steps in MINITAB and its necessity for developing empirical equations, using normalized SIFs obtained from mixed mode fracture analyses of at the crack tip depth point and free surface point, empirical equations that can calculate the SIFs for these points of all possible intermediate values of the studied parameter have been developed by performing multiple-parameter regression analysis. In order to validate these empirical equations, additional 28 models, with combinations of the problem's parameters having intermediate values, were also created. In these models, mixed mode fracture analyses were performed with the FCPAS program and the results were compared with the values obtained from empirical equations.Comparison of results and the SIF distributions of the above validation problems were included. Percentage differences between empirical equations and the finite element solutions were also presented as a table for all modes as well.