Date of Award

12-2008

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mechanical Engineering

Advisor

Joseph, Paul F

Committee Member

Thompson , Lonny L

Committee Member

Biggers , Sherrill B

Committee Member

Blouin , Vincent Y

Committee Member

Grujicic , Mica

Abstract

In this dissertation, research in two parallel directions is presented; the first involves the prediction of the final size and shape of a glass lens during a precision glass lens molding process and the second introduces a method to compute and quantify the importance of higher order terms in fracture mechanics for different modes of fracture.
The process of precision lens molding has received attention in recent years due to its potential to mass produce aspherical lenses. Aspherical lenses have significantly better optical properties and conventional lens making techniques are limited to manufacturing of spherical lenses only. The conventional technique involves an iterative procedure of grinding, lapping and polishing to obtain a desired surface profile. However in precision molding, the glass raw material or preform is placed between dies and heated until it becomes soft and molten. Then the dies are pressed against each other to deform the molten glass to take the shape of the dies. After this stage glass is cooled to room temperature by the use of nitrogen gas. Thus, in a single process the lens is made unlike the traditional approach. Although the molding process appears to a better alternative, there are shortcomings that need to be addressed before using the process for mass production. From the point of view of the current study, the shortcomings include both surface profiles and center thickness of the final lens.
In the expensive process of mold preparation, the mold surfaces are first machined to be exact negatives of the required surface profile of the lens. One of the main issues is the deviation of the surface profile of the final molded lens from that of the molds due to the complex, time and temperature dependent stress state experienced by the lens during the approximately 15 minute process of heating, pressing and then cooling. In current practice the deviation of manufactured lenses is as high as 20 microns, approximately 20 times the allowable deviation according to the optical design specifications. The empirical approach to solving this problem is to compensate the molds by trial and error based on practical experience which is very time-consuming and costly. Usually it takes 3-4 months and a considerable amount of money to compensate the molds to meet current specifications. This has motivated the development of computational solutions to arrive at a compensated mold shape which requires the prediction of the lens deviation within micron level accuracy taking into account process parameters and the complex material behavior of glass.
In this research, ABAQUS, a commercial FEM solver, is used to simulate the process and predict the final size/shape of the lens. The computational study of final size and shape includes a sensitivity analysis of the various material and process parameters. The material parameters include viscoelasticity, structural relaxation and the thermo-rheological behavior of the glass; friction and gap dependent heat transfer at the interface; and the thermo-mechanical properties of the molds. This comprehensive study will not only eliminate some of the parameters which have the least effect on the final size/shape, but also identify the key material properties and substantiate the need to obtain them more accurately through experimentation. At this time it should be mentioned that the material properties of the molding glasses considered are not available.
Friction coefficient at the mold/glass interface is one of the important input parameters in the model. A ring compression test was used in the current research to find the friction coefficient. In this test, a 'washer' or a ring shaped specimen is compressed between two flat dies at the molding temperature and the change in internal diameter is correlated to a friction coefficient. The main strength of this test is the sensitive nature of the inner diameter change during pressing for different friction conditions at the interface. In addition to friction coefficient, approximate viscoelastic material properties and the TRS behavior were also found out using this test from the experimental force and displacement data.
After validating the model to well within one micron, it was determined that the deviation of the lens profile with respect to the molds is primarily caused by structural relaxation of glass, thermal expansion behavior of the molds, friction at the glass/mold interface and time-temperature dependence of the viscoelastic material behavior of glass. Several practical examples/numerical studies that clearly show the cause for the deviation are presented. It is also shown that the deviation in the molded lens is affected by its location with respect to the molds. Finally the process of mold compensation is demonstrated using the computational tool.
In the other parallel direction, a method to determine higher order coefficients in fracture mechanics from the solution of a singular integral equation is presented. In the asymptotic series the stress intensity factor, k0 is the first coefficient, and the T-stress, T0 is the second coefficient. For the example of an edge crack in a half space, converged values of the first twelve mode I coefficients (kn and Tn, n=0,...,5) have been determined, and for an edge crack in a finite width strip, the first six coefficients are presented. Coefficients for an internal crack in a half space are also presented. Results for an edge crack in a finite width strip are used to quantify the size of the k-dominant zone, the kT-dominant zone and the zones associated with three and four terms, taking into account the entire region around the crack tip. Finally, this method was also applied to fracture problems with Mode-II loading.

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