Boundary element formulations for fracture mechanics problems

In this thesis, we study the advanced boundary element method for fracture mechanics, including static and dynamic problems. Static problems are solved by using the dual boundary element method, that the dual equations are the displacement and the traction boundary integral equations. An efficient integral equation formulation is proposed with the displacement equation being used on the outer boundary and the traction equation being used on one of the crack faces, which bases on the works in the paper Dual boundary integral formulation for 2-d linear elastic crack problems (Submitted to Journal of Computational Mathematics). Discontinuous quarter point elements are used to correctly model the displacement in the vicinity of crack tips. Using this formulation a general crack problem can be solved in a single-region formulation, and only one of the crack faces needs to be discretised. Once the relative displacements of the cracks are solved numerically, physical quantities of interest, such as crack tip stress intensity factors can be easily obtained. Normally, the stress intensity factor is obtained by using discontinuous quarter point element method. Because quadratic boundary elements do not correctly describe the behaviour of displacement near the crack tips, special crack tip elements are needed to model the displacement in the vicinity of crack tips. In this work, we present a special crack tip element method, which provides similar accuracy as that of quarter point element method, but a much easier discretisation of the crack face for evaluating stress intensity factors. Further, a new subregion boundary element technique is presented to solve composite material problems, which bases on the work in the paper A new subregion boundary element method (Published by 15th International Conference on Boundary Element Technology 2003). Similar composite problems are also solved by using domain decomposition method, which based on the work in the paper A new subregion boundary element technique based on the domain decomposition method (Submitted to Engineering Analysis with Boundary Elements). The technique is more efficient than traditional methods because it significantly reduces the size of the final matrix. This is advantageous when a large number of elements need to be used, such as in crack analysis. Also, as the system of equations for each subregion is solved independently, parallel computing can be utilized. Further, if the boundary conditions are changed the only equations required to be recalculated are the ones related to the regions where the changes occur. This is very useful for cases where crack extension is modelled with new boundary elements or where crack faces come to contact. Dynamic fracture mechanics problems are solved by using the dual reciprocity boundary element method, which based on the work in the paper A subregion DBEM formulation for dynamic analysis of two dimensional cracks (Accepted by Mathematical and Computer Modelling). The dual reciprocity boundary element method employing the step by step time integration technique is developed to analyse two-dimensional dynamic crack problems. In this method the equation of motion is expressed in boundary integral form using elastostatic fundamental solutions. In order to transform the domain integral into an equivalent boundary integral, a general radial basis function is used for the derivation of the particular solutions. The dual reciprocity boundary element method is combined with an efficient subregion boundary element method to overcome the difficulty of a singular system of algebraic equations in crack problems. Dynamic stress intensity factors are calculated using the discontinuous quarter point elements

Fracture Characteristics Analysis of Pressured Pipeline with Crack Using Boundary Element Method

Metal materials can inevitably show deteriorated properties by the factors of stress, temperature, and environmental erosion in distinct operating environments. Without proper protection, the service life would be shortened or even deadly danger would be caused. This study aims to apply Finite Element Method and Boundary Element Method to analyzing the effects of corroded petrochemical pipes on the fatigue life and the fracture form. The research results of nondestructive testing and software analyses show that cracked oil pipes with uniform corrosion bear larger stress, mainly internal pressure, on the longitudinal direction than the circumferential direction. As a result, the maximal fatigue loading cycle of a circumferential crack is higher than that of a longitudinal one. From the growing length and depth of a crack, the final aspect ratio of crack growth appears in 2.42–3.37 and 2.71–3.42 on the circumferential and longitudinal direction, respectively. Meanwhile, the ratios of loading cycles of circumferential and longitudinal crack are 26.23 on uncorroded and 20.54 on general metal loss oil pipe. The complete crack growth and the correspondent fatigue loading cycle could be acquired to determine the service life of the oil pipe being operated as well as the successive recovery time

Modeling of hydraulic fracturing in rocks: A multiscale and fluid-solid coupling approach.

This dissertation investigates the implications of the fluid flow on the behaviour of the particle-scale structure of a porous hard rock, based on the Discrete Element Method (DEM). This project is driven by the need to contribute towards a better understanding of the mechanical behaviour of porous rock formations under intense injection conditions and the influence of natural pre-existing rock damage to the hydraulic fracturing mechanism. The proposed numerical scheme incorporates different methods for computing both the solid and co-existing fluid phases. The solid phase (rock sample) has been characterized as a collection of discrete interacting particles, bound by spring-like contacts according to the DEM. Meanwhile, the fluid phase has been modelled by discretising the Navier-Stokes equations for porous media, utilising the fluid coupling algorithm embedded in the Particle Flow Code (PFC3D) software by Itasca. The outcome of this dissertation suggests that the DEM approach is an advanced computational method that can reproduce accurate rock models, adequately describe the inter-particle dynamics and thus contribute towards direct numerical and experimental comparisons, and interpret the geo-mechanical behaviour of the rock materials. Furthermore, this study identifies the importance of shear cracking in the hydraulic fracturing models, whereas conventional theory relates hydraulic fracturing with tensile cracking. Finally, this study focuses on the influences of various parameters, such as the external stress regime, fluid viscosity and pre-existing fractures, on the mechanical behaviour of the rock material in the particle-scale and the hydraulic fracturing process as a whole. This work is in an early stage and it aims to simulate hydraulic fracturing experiments with the use of a 3D modelling and the DEM approach, and to investigate the micromechanical response of the rock. Further research may include areas such as the 3D modelling of pre-cracked rocks using a larger variety of fracture angles