A discrete dislocation analysis of hydrogen-assisted mode-I fracture

© 2016 Elsevier LtdFracture of engineering alloys in the presence of hydrogen commonly occurs by decohesion along grain boundaries via a mechanism known as hydrogen induced decohesion (HID). This mechanism is investigated here by analysing the mode-I fracture of a single crystal with plastic flow in the crystal described by discrete dislocation plasticity (DDP) and material separation (decohesion) modelled using a cohesive zone formulation. The motion of dislocations is assumed to be unaffected by hydrogen diffusion. While the cohesive strength is assumed to be reduced proportional to the local hydrogen concentration. Two limiting cases are analysed: (i) the fast diffusion limit where the hydrogen within the material is assumed to be at chemical equilibrium throughout the loading so that there is a high hydrogen concentration in the regions of high hydrostatic stress around dislocations and near the crack tip and (ii) the slow diffusion limit where we assume that there is no appreciable hydrogen diffusion over the duration of loading and thus the hydrogen concentration remains spatially uniform as in a stress-free material. The lower cohesive strength at high hydrogen concentrations results in reduced dislocation activity around the crack tip and a reduction in the material toughness. In fact, at the highest hydrogen concentrations analysed here, crack growth primarily occurs in an elastic manner. However, surprisingly the calculations predicted that the toughness in the fast diffusion case was no more than 12% lower compared to the slow diffusion case suggesting that the stress concentrations due to the dislocation structures and the crack tip fields have only a minor effect on the toughness reduction in the presence of hydrogen. The DDP calculations are finally used to investigate the sensitivity of the material toughness to the grain boundary cohesive strength. The calculations show that the toughness of materials with a small cohesive opening at the peak cohesive traction are more sensitive to hydrogen loading. We speculate that this result might be used as a guide in grain boundary engineering to design alloys that are less sensitive to hydrogen embrittlement by the HID mechanism

Higher order numerical methods for singular perturbation problems

Philosophiae Doctor - PhDIn recent years, there has been a great interest towards the higher order numerical methods for singularly perturbed problems. As compared to their lower order counterparts, they provide better accuracy with fewer mesh points. Construction and/or implementation of direct higher order methods is usually very complicated. Thus a natural choice is to use some convergence acceleration techniques, e.g., Richardson extrapolation, defect correction, etc. In this thesis, we will consider various classes of problems described by singularly perturbed ordinary and partial differential equations. For these problems, we design some novel numerical methods and attempt to increase their accuracy as well as the order of convergence. We also do the same for existing numerical methods in some instances. We find that, even though the Richardson extrapolation technique always improves the accuracy, it does not perform equally well when applied to different methods for certain classes of problems. Moreover, while in some cases it improves the order of convergence, in other cases it does not. These issues are discussed in this thesis for linear and nonlinear singularly perturbed ODEs as well as PDEs. Extrapolation techniques are analyzed thoroughly in all the cases, whereas the limitations of the defect correction approach for certain problems is indicated at the end of the thesis.South Afric

Behavior of Metallic and Composite Structures (Second Volume)

Various types of metallic and composite structures are used in modern engineering practice. For aerospace, car industry, and civil engineering applications, the most important are thin-walled structures made of di erent types of metallic alloys, brous composites, laminates, and multifunctional materials with a more complicated geometry of reinforcement including nanoparticles or nano bres. The current applications in modern engineering require analysis of structures of various properties, shapes, and sizes (e.g., aircraft wings) including structural hybrid joints, subjected to di erent types of loadings, including quasi-static, dynamic, cyclic, thermal, impact, penetration, etc.The advanced metallic and composite structures should satisfy multiple structural functions during operating conditions. Structural functions include mechanical properties such as strength, sti ness, damage resistance, fracture toughness, and damping. Non-structural functions include electrical and thermal conductivities, sensing, actuation, energy harvesting, self-healing capability, electromagnetic shielding, etc.The aim of this SI is to understand the basic principles of damage growth and fracture processes in advanced metallic and composite structures that also include structural joints. Presently, it is widely recognized that important macroscopic properties, such as macroscopic sti ness and strength, are governed by processes that occur at one to several scales below the level of observation. A thorough understanding of how these processes influence the reduction of sti ffness and strength forms the key to the design of improved innovative structural elements and the analysis of existing ones