Novel applications of materials in small dimensions are emerging in areas ranging from electronics, computers, health technologies, laser and fiber optics, to energy harvesting and storage. The presence of interfaces, surfaces and geometrical constraints in small scale structures causes change in material behavior through activation of various inelastic deformation mechanisms. Irrespective of the functionality, a fundamental understanding of material response at smaller scales is essential from the standpoint of performance and reliability during service. In this thesis, the interplay between diffusion, deformation and fracture in small scale structures is dealt with in the following two topics: (i) compressive stress evolution during Volmer-Weber growth of a thin film of high mobility materials and (ii) crack nucleation in Lithium-alloy battery electrodes during charging-discharging cycles. In the former, by coupling the constrained grain boundary (GB) diffusion model to the mechanism of excess surface chemical potential during deposition which drives adatoms into GBs, we study the effect of inhomogeneous GB diffusivity on the formation of GB diffusion wedges and evolution of compressive stress during film growth. In the limit of infinite surface and GB mobility, closed form analytical expressions for stress evolution during deposition cycles are derived and are successfully compared with the existing experimental data on Tin film growth. The effects of film thickness, deposition rate and GB mobility on transient stress-evolution and thickness and steady state stress compare well with experimental observations. In the latter, we have developed a cohesive model of crack nucleation in an initially crack-free electrode under galvanostatic intercalation and deintercalation processes for both 2D (strip) and axisymmetric (cylindrical) geometries with solute transport during diffusion induced stresses. The analysis identifies a critical characteristic dimension below which crack nucleation becomes impossible, suggesting that nanostructured electrodes are highly promising and viable option for applications in high capacity batteries. In a fundamental study of dislocation shielding of a Dugdale cohesive crack, we have derived closed form asymptotic solutions in the limits of high and low cohesive strengths. An important outcome of the study is a transition in dislocation shielding behavior depending on the cohesive strength; while the cohesive crack behaves as a singular crack at very high cohesive strengths (~7GPa), significant deviations from the singular crack behavior arise at cohesive strengths around 1GPa.
Bhandakkar, Tanmay K.,
"Some Coupled Deformation, Diffusion and Fracture Problems in Small Scale Structures"
(2011).
Mechanics of Solids Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0891431
