Peridynamic modelling of fatigue damage in polycrystalline materials

Student thesis: Doctoral Thesis

Abstract

Fracture of structures and materials can bring great threat to human life, environment and finance. Among all types of fracture mechanisms, one of the most important ones to be considered is fatigue fracture. Although many studies have carried out on macroscopic point of view, only few studies are focus on crystal level. The main objective of this study is to find an alternative way to simulate microscopic fatigue cracks. Engineers have developed various of techniques (continuum mechanics) and numerical methods (Finite Element Method) to study fracture of structures. However, majority of these numerical techniques are based on partial differential equations and will become invalid when there are discontinuities (cracks and sharp concentration gradients) occurring inside the body. To overcome this limitation, a continuum mechanics theory based on integro-differential equations, Peridynamics (PD), was developed and used for both fracture and fatigue analysis. Since the study is focus on crystal level, an ordinary state-based polycrystal PD formulation is developed to analyse cubic polycrystalline materials to overcome the constraint condition on material constants brought by Bond-based (BB) PD theory. The formulation is validated by first considering static analyses and comparing the displacement fields obtained from the finite element method and Ordinary State-based (OSB) PD. As a result, the OSB PD polycrystal model can provide accurate displacement fields by comparing it with finite element method. Then, dynamic analysis is performed to investigate the effect of grain boundary strength, crystal size, and discretization size on fracture behaviour and fracture morphology. In the past decades, several different methods (Stress - Life, Strain - Life and Paris Law etc.) have been developed to assist researchers on studying fatigue crack propagations, which also have been combined with PD theory by researchers. For instance, studies on stress energy release rate of a crack tip (for instance J-integral) have been carried out, but few methods are available to calculate the Stress Intensity Factor (SIF) which is directly related to a widely used formula to evaluate crack propagation rate in fatigue analysis - Paris' Law. However, using J-integral can sometime be quite tricky, due to which path has been chosen for analyse. In this study, Displacement Extrapolation Method (DEM) is used to calculate SIF in PD framework more conveniently. In DEM, only crack surface needs to be checked each time when crack propagates, so the detection of the position of crack tip becomes rather important. Although several methods combined with Cohesive Zone Model (CZM) have been used to find crack tip in fracture analysis, few studies on crack tip tracking technique have been done in PD framework. In this thesis, a new automatic crack tip tracking method is discovered and accurately validated by comparing the crack growth speed with the existing study. In the end, all the above methods, including the implemented polycrystal OSB PD formulation, new approach of calculating SIF using DEM under PD framework and the all-new crack tip tracking method, are combined with the PD fatigue model to provide an alternative way to simulate fatigue crack propagation of polycrystalline material.
Date of Award31 Aug 2021
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorErkan Oterkus (Supervisor) & Nigel Barltrop (Supervisor)

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