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Description
Commercially pure (CP) and extra low interstitial (ELI) grade Ti-alloys present excellent corrosion resistance, lightweight, and formability making them attractive materials for expanded use in transportation and medical applications. However, the strength and toughness of CP titanium are affected by relatively small variations in their impurity/solute content (IC), e.g., O,

Commercially pure (CP) and extra low interstitial (ELI) grade Ti-alloys present excellent corrosion resistance, lightweight, and formability making them attractive materials for expanded use in transportation and medical applications. However, the strength and toughness of CP titanium are affected by relatively small variations in their impurity/solute content (IC), e.g., O, Al, and V. This increase in strength is due to the fact that the solute either increases the critical stress required for the prismatic slip systems ({10-10}<1-210>) or activates another slip system ((0001)<11-20>, {10-11}<11-20>). In particular, solute additions such as O can effectively strengthen the alloy but with an attendant loss in ductility by changing the behavior from wavy (cross slip) to planar nature. In order to understand the underlying behavior of strengthening by solutes, it is important to understand the atomic scale mechanism. This dissertation aims to address this knowledge gap through a synergistic combination of density functional theory (DFT) and molecular dynamics. Further, due to the long-range strain fields of the dislocations and the periodicity of the DFT simulation cells, it is difficult to apply ab initio simulations to study the dislocation core structure. To alleviate this issue we developed a multiscale quantum mechanics/molecular mechanics approach (QM/MM) to study the dislocation core. We use the developed QM/MM method to study the pipe diffusion along a prismatic edge dislocation core. Complementary to the atomistic simulations, the Semi-discrete Variational Peierls-Nabarro model (SVPN) was also used to analyze the dislocation core structure and mobility. The chemical interaction between the solute/impurity and the dislocation core is captured by the so-called generalized stacking fault energy (GSFE) surface which was determined from DFT-VASP calculations. By taking the chemical interaction into consideration the SVPN model can predict the dislocation core structure and mobility in the presence and absence of the solute/impurity and thus reveal the effect of impurity/solute on the softening/hardening behavior in alpha-Ti. Finally, to study the interaction of the dislocation core with other planar defects such as grain boundaries (GB), we develop an automated method to theoretically generate GBs in HCP type materials.
ContributorsBhatia, Mehul Anoopkumar (Author) / Solanki, Kiran N (Thesis advisor) / Peralta, Pedro (Committee member) / Jiang, Hanqing (Committee member) / Neithalath, Narayanan (Committee member) / Rajagopalan, Jagannathan (Committee member) / Arizona State University (Publisher)
Created2014
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Description
In this paper, at first, analytical formulation of J-integral for a non-local particle model (VCPM) using atomic scale finite element method is proposed for fracture analysis of 2D solids. A brief review of classical continuum-based J-integral and anon-local lattice particle method is given first. Following this, detailed derivation for the

In this paper, at first, analytical formulation of J-integral for a non-local particle model (VCPM) using atomic scale finite element method is proposed for fracture analysis of 2D solids. A brief review of classical continuum-based J-integral and anon-local lattice particle method is given first. Following this, detailed derivation for the J-integral in discrete particle system is given using the energy equivalence and stress-tensor mapping between the continuum mechanics and lattice-particle system.With the help of atomistic finite element method, the J-integral is expressed as a summation of the corresponding terms in the particle system.

Secondly, a coupling algorithm between a non-local particle method (VCPM) and the classical finite element method (FEM) is discussed to gain the advantages of both methods for fracture analysis in large structures. In this algorithm, the discrete VCPM particle and the continuum FEM domains are solved within a unified theoretical framework. A transitional element technology is developed to smoothly link the 10-particles element with the traditional FEM elements to guaranty the continuity and consistency at the coupling interface. An explicit algorithm for static simulation is developed.

Finally, numerical examples are illustrated for the accuracy, convergence, and path-independence of the derived J-integral formulation. Discussions on the comparison with alternative estimation methods and potential application for fracture simulation are given. The accuracy and efficiency of the coupling algorithm are tested by several benchmark problems such as static crack simulation.
ContributorsZope, Jayesh (Author) / Liu, Yongming (Thesis advisor) / Oswald, Jay (Committee member) / Jiang, Hanqing (Committee member) / Arizona State University (Publisher)
Created2016
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Description
A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM)

A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM) in which the dislocations are modelled according to the Volterra dislocation model. Interior discontinuities are introduced across dislocation glide planes using enrichment functions and the resulting boundary value problem is solved through the standard finite element variational approach. The level set method is used to describe the geometry of the dislocation glide planes without any explicit treatment of the interface geometry which provides a convenient and an appealing means for describing the dislocation. A method for estimating the Peach-Koehler force by the domain form of J-integral is considered. The convergence and accuracy of the method are studied for an edge dislocation interacting with a free surface where analytical solutions are available. The force converges to the exact solution at an optimal rate for linear finite elements. The applicability of the method to dislocation interactions with inclusions is illustrated with a system of Aluminium matrix containing Aluminium-copper precipitates. The effect of size, shape and orientation of the inclusions on an edge dislocation for a difference in stiffness and coefficient of thermal expansion of the inclusions and matrix is considered. The force on the dislocation due to a hard inclusion increased by 8% in approaching the sharp corners of a square inclusion than a circular inclusion of equal area. The dislocation experienced 24% more force in moving towards the edges of a square shaped inclusion than towards its centre. When the areas of the inclusions were halved, 30% less force was exerted on the dislocation. This method was used to analyse interfaces with mismatch strains. Introducing eigenstrains equal to 0.004 to the elastic mismatch increased the force by 15 times for a circular inclusion. The energy needed to move an edge dislocation through a domain filled with circular inclusions is 4% more than that needed for a domain with square shaped inclusions.
ContributorsVeeresh, Pawan (Author) / Oswald, Jay (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Arizona State University (Publisher)
Created2016