Degree Type

Dissertation

Date of Award

2007

Degree Name

Doctor of Philosophy

Department

Aerospace Engineering

First Advisor

Ambar Mitra

Abstract

Boundary element method (BEM) is an effective numerical technique to solve complex engineering problems. The fundamental solutions for both isotropic and anisotropic boundary element method are studied as the basic to develop elastostatic boundary integral equations.;The numerical implementation of BEM is described in a very detailed fashion. Multi zone BEM is introduced to calculate polycrystal grains structure. The connectivity between grains is modeled with a stiffness spring system. The sliding effect at grain boundaries is simulated by a non linear sliding model.;After anisotropy and grain sliding are implemented with BEM, the information on the grain boundaries can be calculated effectively. Inside the grains, the dislocation theory is discussed. For multiple dislocations stress field, two calculation methods are introduced: discrete dislocation method and dislocation density tensor method. For the dislocation density tensor method, the domain integral involved are transformed into boundary integral to save the runtime and be compatible with the BEM formulation. To control the total error and save time, a combined method with those two is developed to calculate multiple dislocations stress field. The new mixed method reduce the run time from the order O(n2) to O(n) and keep the error within 2%.;With dislocation stress field, the dislocation dynamics are generated with the dislocation calculation and the superposition with the boundary conditions. The size effect for yielding is shown and satisfies the Hall-Petch law. The results with grain sliding and anisotropy are also shown and analyzed.

DOI

https://doi.org/10.31274/rtd-180813-16831

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Dun Leng

Language

en

Proquest ID

AAI3289424

OCLC Number

213362891

ISBN

9780549336945

File Format

application/pdf

File Size

127 pages

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