Assessing the combined effects of hold time and overload on crack propagation and implications for failure analysis

Abstract

Fracture Mechanics is an engineering field that deals with defects that may occur when materials are exposed to stresses exceeding their strengths. The fundamentals of fracture mechanics date back to 1920 when British engineer A. A. Griffith investigated the fracture of glass fibers. During and after World War II, efforts to understand the cracks in aircraft parts accelerated research on fracture mechanics. In later years, approaches for the plastic region formed at the crack tip and the stress intensity factor developed by George R. Irwin and his colleagues have made significant progress in this field. The Stress Intensity Factor (SIF) is an important parameter in Crack Mechanics that measures the intensity of the stress field at the crack tip. It varies depending on three main parameters. These three parameters are crack length, crack geometry factor, and the stress causing the crack to open. Different opening modes have been developed to examine the crack opening situations in more detail. These types of openings are Mode I, Mode II, and Mode III opening type. Mode I opening type is characterized by a stress applied perpendicular to the direction of the crack opening. This stress causes the crack tips to separate. Mode I is seen as the most common and generally the most dangerous crack mode because it is known that the possible cracks usually progress in this mode and grow rapidly, damaging the piece. Mode II opening type refers to the situation where cracks grow under a shear stress parallel to the crack plane and along the crack. This is usually seen when a torque is applied to a material or there is friction on a material. Mode III, also known as the tearing mode, is caused by out-of-plane shear stresses. It is a type of opening that is less frequently seen compared to the other two modes. The scope of the work done in this thesis starts here. In this study, the algorithm developed and the calculations made have been made considering the mod-1 opening type. During these calculations, a process that went step by step was followed. Firstly, the initial crack length was determined considering the probability of crack formation in a part and the part quality processes. This length was taken into account and a semi-elliptical surface crack, which can generally be used in the initial evaluations in parts, was chosen. There are different solutions in the literature for stress intensity factor calculations to be made for this crack type. In this study, equations developed by Newman and Raju were used to calculate the stress intensity factor. After these calculations, da/dN-$\Delta$K graphs are needed to decide on the possibility of a crack progressing. After the first stress intensity factor is calculated for a crack, three different situations will be in question. If the calculated value is lower than the threshold value obtained from material tests, the crack will not progress and the part will remain safe. As the second case, if the crack is larger than the threshold value, it will progress and how many cycles it will be able to carry out this progress is the main subject of this study. Thirdly, if a calculation exceeding the fracture toughness value obtained from material tests is made, it is assumed that the part has suffered direct damage. In order to mathematically express the da/dN-$\Delta$K curves obtained from material tests, various equations have been developed in the literature. Paris, Sigmoidal, and Forman equations can be given as examples of these equations. Each of the three equations has its own advantages. In this study, the sigmoidal equation was used in the calculations as it better reflected the behavior that could occur in the first and third regions. The Walker model, one of the approaches developed to include the effect of the average stress in the calculations, was used. With this model, the effect of loads with an R ratio different from zero on the crack progression rate was included. In this model, the "m" parameter, which depends on the material, was obtained from the literature. When calculating crack progression, it is not possible to directly use these loadings in parts exposed to complex loads. Therefore, complex loads can be simplified by cycle counting methods. In this study, the given loads were filtered and converted into cyclic loads using the rainflow cycle counting method. It is assumed that stresses at the crack tips go to infinity. Therefore, plastic deformation zones form at the crack tip. Since these zones show a growing behavior as the crack progresses, they can reduce the part life in the life calculations to be made. There are different approaches to model these areas. In this study, models developed by Irwin and Douglas were explained. The Irwin model considers the plastic zone forming around the crack tip as a symmetrical distribution. In this model, the plastic zone around the crack tip expands in an elliptical shape. The Douglas model proposes that the plastic zone has an asymmetrical distribution around the crack tip. In this model, the plastic zone expands more intensively under high stress on the side of the crack tip. The main difference between these two models is related to the symmetry or asymmetry of the plastic zone. While the Irwin model considers the plastic zone symmetrical, the Douglas model suggests that the plastic zone is asymmetric. In this study, equations proposed by Irwin were used when making calculations. Another topic related to the plastic zone is the Retardation effect, which slows down the crack progression rate. In some mission profiles, a larger plastic zone is formed in the next step at the places where the stresses peak. There is a certain slowdown in the crack progression rate until the crack overcomes the plastic zone formed at the peak of the stress, and this situation increases the part life. Various approaches have been developed to model this situation. In this study, the Willenborg, Generalized Willenborg, and Modified Generalized Willenborg approaches were explained. The Modified Generalized Willenborg method was used in the calculations as it provides a more robust approach and gives more accurate results in life determinations. In this method, there are four coefficients related to material tests. These coefficients are represented by $\phi$, $\chi$ , $\lambda$ and $\rho$. These coefficients are available for INCO718 material at different temperatures in the literature and calculations were made on this material in this study and these coefficients were used. In crack progression calculations, in addition to cyclic loads, if the crack stays for a long time under one load, time-dependent effects also have an effect on progression. For example, in flight profiles, this situation is also included in the total life calculation when the crack remains stable at a certain load for long periods. In this regard, the superposition method and interpolation method have been developed to calculate the combined effects of cyclic and time-dependent loads. In the scope of this thesis, time-dependent effects were addressed with the superposition method and included in the calculation. As a result, in this study, fatigue life calculations were made using the factors affecting the crack progression mechanism and the effects of these factors were examined in detail. For these examinations, crack progression analyses were made under the conditions of cyclic loading, cyclic loading with overload, cyclic loading with overload with negative R ratio, time-dependent loading, and time-dependent loading under overload, and the results were reported and validated with commercial software.