Abstract: An abrasive tool insert is formed from a substrate having an inner face that has a center, and annular face which annular face has a periphery. The inner face slopes outwardly and downwardly from the center at an angle ranging from between about 5° and 30° from the horizontal. The annular face surrounds by the inner face and terminates at the periphery. The annular face slopes downwardly and outwardly from the inner face at an angle of between about 20° and 75° from the horizontal. A continuous abrasive layer, having a center and a periphery forming a cutting edge, is integrally formed on the substrate and defines an interface therebetween.

Abstract: An abrasive tool insert includes (a) a substrate having a support face that includes (1) an inner support table, (2) an outer shoulder having a width, Sw, and (3) a downwardly sloping interface from the support table to the shoulder, which interface has a slope angle, Sa. A continuous abrasive layer, integrally formed on the substrate support face, includes (1) a center having a height, Dc, (2) a diameter, Dd, (3) a periphery having a height, Dp, in contact with the shoulder and which periphery forms a cutting edge. Sw:Dd ranges from between 0 and about 0.5. For each Sa and Sw:Dd, Dc:Dp is selected so as to diminish residual stress in the abrasive layer.