FATIGUE AND CREEP CRACK GROWTH ANALYSIS USING XFEM

Abstract

Nowadays, the biggest challenge for scientists/designers is to increase the life of components/structures with minimum effect on their performance. The efficiency and reliability of these systems are directly related to the life of components/structures. Only efficient and reliable systems can fulfill the requirements of today’s advanced technologies to maximize the utilization of resources. These advanced technologies involve harsh operating conditions like high temperatures, corrosive atmosphere, nuclear radiation exposed environment, offshore conditions for components/structures. The chances of failure of components/structures in these conditions increase due to crack nucleation or rapid growth of pre-existing cracks. The crack nucleation or their growth drastically affects the overall fracture toughness and load-carrying capacity of components/structures. Thus, understanding the crack nucleation/growth is a topic of great interest to the research community. The accurate prediction of crack growth behavior in the design phase can increase the operational life of components/structures. Therefore, a new numerical methodology is needed to predict the crack growth behavior in harsh conditions to aid the design of components/structures. The finite element method (FEM) is the most commonly used numerical method to assist scientists/designers. However, FEM does not work efficiently for components/structures having pre-existing crack due to the conformal mesh requirement. The crack propagation makes the FEM more cumbersome because it needs remeshing after each crack growth. This process leads to data mapping from the old mesh to the new mesh, which eventually introduces errors in the solution. These modeling issues of FEM can be eliminated using advanced numerical methods such as meshfree method, extended FEM (XFEM) and many more. Among these methods, XFEM got a lot of recognition owing to its FE background. In XFEM, enrichment functions i.e. Heaviside and tip enrichment functions, are added in the displacement approximation through the partition of unity. The Heaviside enrichment functions mimic the displacement jump across the crack surface while tip enrichment functions produce the singularity effect at the crack tip/front. XFEM based numerical methodologies are developed in this thesis to predict the crack growth behavior in components/structures subjected to fatigue and creep conditions. Developed methodology for fatigue crack growth (FCG) includes the elasto-plastic behavior of materials in the mathematical formulation to account for the plasticity at the crack tip. The von Mises plasticity model, along with Ramberg-Osgood material behavior, is employed to model the material plasticity. The fatigue crack growth rate is estimated by the Paris law using the stress intensity factor (SIF). The J-integral decomposition approach is used to calculate the SIFs of individual modes in which field variables are decomposed about the crack plane into symmetric and antisymmetric parts. The crack growth direction is obtained by the maximum principal stress criterion. The developed methodology is validated by comparing the FCG for a compact tensile specimen with experimental observations. The capabilities of the developed methodology are shown by simulating various specimens and components. This methodology is further extended for elasto-plastically graded material where material properties have an exponential gradient in a particular direction. Since the gradation is continuous and piecewise differentiable thus, the crack tip singularity of graded material is similar to a homogeneous material. The developed methodology is independent of the gradation direction. The FCG behaviors of various specimens and components subjected to mode-I and mixed mode are estimated through this developed methodology. The predicted FCG behavior and crack paths are found consistent with the theoretical expectation. In the developed creep crack growth (CCG) methodology, the entire analysis is performed in two steps i.e. elasto-plastic analysis and creep analysis. The elasto-plastic analysis models the instantaneous effect of loading while the creep analysis estimates creep strains and their effects on the domain. The creep strains are calculated through the creep laws, which act like constitutive laws and depend on the state of the domain. The non-uniform distribution of creep strain leads to stress relaxation and redistribution that is incorporated in the formulation. The creep crack growth rate is calculated by Ct  -integral based relation that is analogous to Paris Law. The benefit of Ct  -integral is that it includes all the creep stages i.e. small scale creep, transition creep and extensive creep. The crack growth direction is decided by the maximum circumferential stress criterion. The developed methodology is validated for the creep strain and creep crack growth with experimental results. Various specimens and components are simulated to demonstrate the capabilities of the developed methodology. The developed CCG methodology is extended for elasto-plastically graded material where material properties vary exponentially in a particular direction. The creep strain response and CCG behavior of various specimens and components under mode-I and mixed mode are predicted by developed methodology. The consistency between the numerical results and theoretical expectations is found for all the simulations. All the simulations are performed using self-developed Matlab codes and validated with experimental results. The obtained results of the simulation are found consistent with theoretical expectations.