NUMERICAL MODELING OF FATIGUE BEHAVIOUR OF POLYCRYSTALLINE MATERIALS

Abstract

Polycrystalline materials find applications across various industries and technologies such as aircraft, bridges, pressure vessel, cranes, etc. due to their unique mechanical and physical properties. For many years, the fatigue failure of components made from polycrystalline material has been a major problem, sometimes resulting in loss of life and financial costs. Fatigue is a complex material degradation process which occurs over a number of successive loading cycles. The fatigue damage progresses through different stages. Microscopic internal defects, like microcracks and microvoids, can either be present in the material due to manufacturing processes or nucleate within the initially defect-free material during fatigue loading due to the microstructural changes. The merging of microcracks leads to the macrocrack initiation. This is followed by the stable propagation of the macrocrack and the sudden fracture of the component with continued cycling. It has been found that the conditions for fatigue crack initiation and propagation are strongly influenced by various microstructural parameters. A significant scatter is observed in the fatigue lives of polycrystalline materials due to variations in microstructural parameters i.e. microstructure topology, grain size and shape, elastic anisotropy, the volume fraction of phases, etc. Hence, many research efforts have been undertaken to predict the fatigue behaviour of polycrystalline materials under the influence of microstructural variations. The continuum damage mechanics (CDM) provides an effective methodology for characterizing the fatigue damage evolution and predicting the fatigue life of the components. In CDM approach, a scalar or tensorial damage variable is incorporated into the material constitutive model to describe the load reduction capability of the material. Using a damage variable, CDM can seamlessly describe the crack initiation and propagation stages of fatigue failure. To simulate the fatigue life of the components, CDM is combined with finite element method. The CDM is also used for microstructure based fatigue life prediction in a few studies. However, one of the major challenges in the microstructure based CDM simulations is to effectively incorporate the essential features of a real microstructure of the polycrystalline materials. Additionally, the computational time required for simulating the microstructure-based fatigue life poses a significant challenge. Recent advancements in numerical simulation techniques such as the polygonal finite element method (PFEM), smoothed finite element method (SFEM), and extended finite element method (XFEM), have opened new avenues for fatigue life simulations. The convex polygonal elements with random shape and size can effectively treated in the PFEM.In this thesis, a CDM based computational framework has been developed to predict the fatigue life of polycrystalline material under the influence of microstructural variations and mean stresses. The Voronoi and Laguerre tessellation techniques have been utilized to generate the numerical model with microstructural details. The CDM based fatigue life prediction framework is established for both high cycle fatigue and low cycle fatigue regimes. Initially, the CDM is combined with the PFEM to efficiently predict the high cycle fatigue life and its scatter in two phase (𝛼/𝛽 ) duplex microstructure titanium alloys. Using several realizations of the microstructure models with different parameters, the scatter in high cycle fatigue is quantitatively analyzed. The effect of different sources of randomness in microstructures i.e., topology of microstructure, grain size, volume fraction of alpha phase, inhomogeneity in elastic modulus and internal voids, on the fatigue life is investigated. Further, the CDM and PFEM based computation framework is extended to determine the low cycle fatigue life of two phase titanium alloys under the influence of microstructural variations. In the low cycle fatigue loading, the damage is primarily governed by the plastic strains. The evolution of damage and plastic strains is dependent on each other. Hence, damage coupled elasto-plastic constitutive equations are implemented to accurately capture the fatigue behaviour the material. A new strain-based damage evolution law is proposed to predict the effect of mean grain size on the LCF life. The simulated stress-strain response and fatigue lives show good agreement with experimental data. Next, the CDM based computational framework is developed to predict the microstructure-based fatigue crack initiation life of 3D specimens. A methodology is developed to generate complex 3D polycrystalline microstructure RVEs at the desired critical locations of a large-scale component. To enhance the capabilities of the proposed computational framework, it has been implemented in the commercial finite element software Abaqus. The damage coupled constitutive equations and jump in cycles algorithm are implemented in user defined subroutines UMAT and UEXTRENALDB, respectively. The fatigue crack initiation lives of notched specimens are analyzed using the developed framework. Finally, a new strain-based fatigue life model is proposed to efficiently predict the fatigue life under the influence of mean stresses. The model is validated with extensive experimental data.