Brittle-ductile transition in shape adaptive grinding (SAG) of SiC aspheric optics

Silicon carbide is a ceramic material with a desirable combination of high thermal and mechanical stability, making it ideal for optical application in aerospace and next generation lithography. It is however notoriously difficult to machine down to super-fine finish when the shape is other than flat or spherical. In this paper, we describe the application of a "semi-elastic" machining method called shape adaptive grinding (SAG), in which an elastic tool is combined with rigid pellets made of nickel or resin, to which super abrasives are bonded. A comprehensive model of the physical interaction between SAG tool and workpiece is proposed, and used to understand the mechanics driving brittle-ductile transition on ceramic materials such as SiC. Machining parameters adequate for optical finishing are then derived from the model and demonstrated on an aspheric silicon carbide workpiece, which was manufactured by reaction bonding and coated with a layer of pure SiC by chemical vapour deposition (CVD). Through SAG processing and final polishing, this aspheric mirror was improved from an initial form error of 40 gm down to 112 nm Peak-to-Valley, with no residual damage visible on the surface.