Abstract: A method for conducting an abrasive operation can include providing a fixed abrasive article and separating a first part from a second part using the fixed abrasive article according to a deterministic process.

Abstract: An abrasive article comprising a substrate having an elongated body and abrasive particles attached to the elongated body, the content of the abrasive particles oscillates along the length of the body between a minimum and maximum value, and the minimum content is greater than 0.

Abstract: An abrasive article including a substrate having an elongated body, a tacking layer overlying the substrate, and a first type of abrasive particle overlying the tacking layer and defining a first abrasive particle concentration at least about 10 particles per mm of substrate.

Abstract: An abrasive article includes a substrate having an elongated body, a plurality of discrete tacking regions defining a discontinuous distribution of features overlying the substrate, where at least one discrete tacking region of the plurality of discrete tacking regions includes a metal material having a melting temperature not greater than 450° C., a plurality of discrete formations overlying the substrate and spaced apart from the plurality of discrete tacking regions, and a bonding layer overlying the substrate, plurality of discrete tacking regions, and plurality of discrete formations.

Abstract: An abrasive article comprising a substrate having an elongated body and abrasive particles attached to the elongated body, the content of the abrasive particles oscillates along the length of the body between a minimum and maximum value, and the minimum content is greater than 0.

Abstract: An abrasive article includes a substrate having an elongated body, a plurality of discrete tacking regions defining a discontinuous distribution of features overlying the substrate, where at least one discrete tacking region of the plurality of discrete tacking regions includes a metal material having a melting temperature not greater than 450° C., a plurality of discrete formations overlying the substrate and spaced apart from the plurality of discrete tacking regions, and a bonding layer overlying the substrate, plurality of discrete tacking regions, and plurality of discrete formations.

Abstract: An abrasive article includes a substrate having an elongated body, a plurality of discrete tacking regions defining a discontinuous distribution of features overlying the substrate, where at least one discrete tacking region of the plurality of discrete tacking regions includes a metal material having a melting temperature not greater than 450° C., a plurality of discrete formations overlying the substrate and spaced apart from the plurality of discrete tacking regions, and a bonding layer overlying the substrate, plurality of discrete tacking regions, and plurality of discrete formations.

Abstract: An abrasive article includes a substrate having an elongated body, a plurality of discrete tacking regions defining a discontinuous distribution of features overlying the substrate, where at least one discrete tacking region of the plurality of discrete tacking regions includes a metal material having a melting temperature not greater than 450° C., a plurality of discrete formations overlying the substrate and spaced apart from the plurality of discrete tacking regions, and a bonding layer overlying the substrate, plurality of discrete tacking regions, and plurality of discrete formations.

Abstract: An abrasive article includes a substrate comprising an elongated body, a first type of abrasive particle overlying the substrate, a bonding layer overlying the first type of abrasive particle, and a lubricious material overlying or integrated within the bonding layer.

Abstract: An abrasive article includes a substrate having an elongated body, a plurality of discrete tacking regions defining a discontinuous distribution of features overlying the substrate, where at least one discrete tacking region of the plurality of discrete tacking regions includes a metal material having a melting temperature not greater than 450° C., a plurality of discrete formations overlying the substrate and spaced apart from the plurality of discrete tacking regions, and a bonding layer overlying the substrate, plurality of discrete tacking regions, and plurality of discrete formations.

Abstract: An abrasive article including a substrate having an elongated body, a tacking layer overlying the substrate, and a first type of abrasive particle overlying the tacking layer and defining a first abrasive particle concentration at least about 10 particles per mm of substrate.

Abstract: An abrasive article including a substrate having an elongated body, a tacking layer overlying the substrate, and a first type of abrasive particle overlying the tacking layer and defining a first abrasive particle concentration at least about 10 particles per mm of substrate.

Abstract: An abrasive article including a substrate having an elongated body, a tacking layer overlying the substrate, a first type of abrasive particle overlying the tacking layer, a second type of abrasive particle different than the first type of abrasive particles overlying the tacking layer, and a bonding layer overlying at least a portion of one of the first type of abrasive particle and the second type of abrasive particle and the tacking layer.

Abstract: An abrasive article including a substrate having an elongated body, a tacking layer overlying the substrate, a first type of abrasive particle overlying the tacking layer, a second type of abrasive particle different than the first type of abrasive particles overlying the tacking layer, and a bonding layer overlying at least a portion of one of the first type of abrasive particle and the second type of abrasive particle and the tacking layer.

Abstract: An abrasive article includes a substrate having an elongated body, a plurality of discrete tacking regions defining a discontinuous distribution of features overlying the substrate, where at least one discrete tacking region of the plurality of discrete tacking regions includes a metal material having a melting temperature not greater than 450° C., a plurality of discrete formations overlying the substrate and spaced apart from the plurality of discrete tacking regions, and a bonding layer overlying the substrate, plurality of discrete tacking regions, and plurality of discrete formations.

Abstract: An abrasive article including a substrate made of a wire, abrasive particles affixed to the substrate, the abrasive particles having a first coating layer overlying the abrasive particles, and a second coating layer different than the first coating layer overlying the first coating layer. The abrasive article further including a bonding layer overlying the substrate and abrasive particles.

Abstract: An abrasive article including a substrate as an elongated member, a first layer overlying the substrate, abrasive particles overlying the first layer, fillets connecting the first layer and the abrasive particles, a bonding layer overlying the abrasive particles, the first layer and the fillets, and the fillets have a fillet characteristic relative to an abrasive application, the fillet characteristic selected from the group consisting of tacking factor (tfl/tf), a fillet-to-particle factor (tf/dab), a fillet-to-bonding layer factor (tf/tbl), a contact factor (Ab/Af), a fillet size variance (Vf), and a combination thereof.

Abstract: A grinding tool includes a shank having an axis, and at least two abrasive portions mounted directly to and in contact with the shank without a hub therebetween. Each of the abrasive portions has a substantially identical profile formed therein.

Abstract: An abrasive article including a substrate made of a wire, abrasive particles affixed to the substrate, the abrasive particles having a first coating layer overlying the abrasive particles, and a second coating layer different than the first coating layer overlying the first coating layer. The abrasive article further including a bonding layer overlying the substrate and abrasive particles.

Abstract: An abrasive article including a substrate having an elongated body, a tacking layer overlying the substrate, and a first type of abrasive particle overlying the tacking layer and defining a first abrasive particle concentration at least about 10 particles per mm of substrate.