We discuss a constitutive model describing the permanent densification of fused silica under large applied pressures and shear stresses. The constitutive law is assumed to be rate‐independent and uses a yield function coupling hydrostatic pressure and shear stress, a flow rule describing the evolution of permanent strains after initial densification, and a hardening rule describing the dependence of the incremental densification on the levels of applied stresses. Normality, or lack thereof, of the permanent strain increments to the current yield surface in stress space allows for various relative contributions of densification and shear flow in the ensuing deformation. The constitutive law accounts for multiaxial states of stress, since during polishing and grinding operations complex stress states, with large shear components due to friction and abrasion, occur in a thin surface layer due to the action of abrasive particles. We apply the constitutive law in estimating the extent of the densified layer during the mechanical interaction of an abrasive grain and a flat surface under polishing and grinding conditions. The grain is assumed to be spherical and in Hertz contact with the surface, or sharp and in point contact. The effect on the densified depth of stress relaxation due to densification is discussed.
A direct reading thermal comparator has been used to measure the thermal conductivity of dielectric thin-film coatings. In the past, the thermal comparator has been used extensively to measure the thermal conductivity of bulk solids, liquids, and gases. The technique has been extended to thin-film materials by making experimental improvements and by the application of an analytical heat flow model. Our technique also allows an estimation of the thermal resistance of the film/substrate interface which is shown to depend on the method of film deposition. The thermal conductivity of most thin films was found to be several orders of magnitude lower than that of the material in bulk form. This difference is attributed to structural disorder of materials deposited in thin-film form. The experimentation to date has primarily centered on optical coating materials. These coatings, used to enhance the optical properties of components such as lenses and mirrors, are damaged by thermal loads applied in high-power laser applications. It has been widely postulated that there may be a correlation between the thermal conductivity and the damage threshold of these materials.
In the last 10 years, freeform optics has enabled compact and
high-performance imaging systems. This article begins with a brief
history of freeform optics, focusing on imaging systems, including
marketplace emergence. The development of this technology is motivated
by the clear opportunity to enable science across a wide range of
applications, spanning from extreme ultraviolet lithography to space
optics. Next, we define freeform optics and discuss concurrent
engineering that brings together design, fabrication, testing, and
assembly into one process. We then lay out the foundations of the
aberration theory for freeform optics and emerging design
methodologies. We describe fabrication methods, emphasizing
deterministic computer numerical control grinding, polishing, and
diamond machining. Next, we consider mid-spatial frequency errors that
inherently result from freeform fabrication techniques. We realize
that metrologies of freeform optics are simultaneously sparse in their
existence but diverse in their potential. Thus, we focus on metrology
techniques demonstrated for the measurement of freeform optics. We
conclude this review with an outlook on the future of freeform
optics.
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