A cutting insert according to one aspect has a flat plate shape including a first main surface having a polygonal shape, a second main surface located opposite to the first main surface, and an outer peripheral surface located between the first main surface and the second main surface. The cutting insert includes a cutting portion located in regions including at least a corner portion of the first main surface, and a main body portion located in a region other than the corner portion. A thickness of the main body portion is larger than a thickness of the cutting portions, and the main body portion includes a recessed portion or a protruding portion located in the outer peripheral surface thereof.

A hard film formed on/above a substrate has a composition represented by the following formula (1): Cr.sub.1−aMg.sub.a(B.sub.xC.sub.yN.sub.1−x−y) (1). In the formula (1), a is the atomic ratio of Mg, x is the atomic ratio of B, and y is the atomic ratio of C; and a, x, and y satisfy the following relationships: 0.05≦a≦0.30, 0≦x≦0.20, and 0≦y≦0.30.

A cutting tool having a cutting edge member which forms at least one corner part, wherein a material for the cutting edge member is selected from either diamond, an ultrahigh-pressure sintered body containing cubic boron nitride or a PVD or CVD coating applied to a surface of the ultrahigh-pressure sintered body. At least part of an intersecting edge between an end surface of the cutting edge member and a peripheral side surface thereof is provided with a cutting edge. A chip breaker comprising a breaker wall surface is formed in the end surface of the cutting edge member. The breaker wall surface has at least one projected surface part which bulges outwardly from the cutting tool. As viewed from the end surface, the recessed surface part is arranged so as to be apart from a virtual plane A which is defined so as to divide the corner part into halves.

A cutting tool having a cutting edge member which forms at least one corner part, wherein a material for the cutting edge member is selected from either diamond, an ultrahigh-pressure sintered body containing cubic boron nitride or a PVD or CVD coating applied to a surface of the ultrahigh-pressure sintered body. At least part of an intersecting edge between an end surface of the cutting edge member and a peripheral side surface thereof is provided with a cutting edge. A chip breaker comprising a breaker wall surface is formed in the end surface of the cutting edge member. The breaker wall surface has at least one projected surface part which bulges outwardly from the cutting tool. As viewed from the end surface, the recessed surface part is arranged so as to be apart from a virtual plane A which is defined so as to divide the corner part into halves.

A cutting element, which is configured for the machining of a non-metallic composite material composed of a matrix and particles held together by the matrix, has a flank face, a rake face and a cutting edge which is coated with an edge coating and via which the flank face and the rake face are connected to one another, with which the non-metallic composite material can be machined in an improved fashion. The cutting edge within a cutting edge section thereof is curved in such a way that the cutting edge immediately beneath the edge coating in a section in a section plane that is perpendicular to the cutting edge has, at every point of the cutting edge section, a local radius of curvature which is greater than or equal to 10 μm and less than or equal to 80 μm.

A coated tool includes a base body and a diamond coating. The coated tool has a cutting edge. The first surface comprises a first region close to the cutting edge and a second region further away from the cutting edge than the first region. The diamond coating comprises an outer surface having dome-shaped protrusions. The protrusions include first protrusions having an equivalent circle diameter of 6 .Math.m or more located in the first region, and second protrusions having an equivalent circle diameter of 6 .Math.m or more located in the second region. A number of the first protrusions per 1 mm.sup.2 is a first protrusion number. A number of the second protrusions per 1 mm.sup.2 is a second protrusion number. The first protrusion number is 30 or less, and the second protrusion number is larger than the first protrusion number.

A coated tool in a non-limiting embodiment of the present disclosure includes a base and a coating layer located on the base. The coated tool includes a first surface, a second surface adjacent to the first surface, and a cutting edge located on at least a part of a ridge part of the first surface and the second surface. The coating layer includes a Ti-based coating layer. If a fracture toughness value of the Ti-based coating layer is measured on a surface of the coating layer parallel to a surface of the base, the Ti-based coating layer includes a first region where the fracture toughness value is 10 MPa.Math.m.sup.0.5 or more.

A coated tool in a non-limiting embodiment of the present disclosure includes a base and a coating layer located on the base. The coated tool includes a first surface, a second surface adjacent to the first surface, and a cutting edge located on at least a part of a ridge part of the first surface and the second surface. The coating layer includes a Ti-based coating layer. If a fracture toughness value of the Ti-based coating layer is measured on a surface of the coating layer parallel to a surface of the base, the Ti-based coating layer includes a first region where the fracture toughness value is 10 MPa.Math.m.sup.0.5 or more.

Provided is a holder of a cutting insert that performs turning on a work by feeding a cutting edge in a Y axis direction which is different from a longitudinal direction (X axis) of a tool holder installed in a tool rest, and that can easily adjust the projection amount without contacting a part of the holder to the tool rest. A Y axis holder holds the cutting insert including a cutting edge to perform turning on a work that moves along the Z axis, and is installed in a state where relative movement in the X axis direction with respect to the tool rest is possible, such that a projection amount of the cutting insert along the X axis is changeable. The Y axis holder performs turning on the work using the cutting insert when the holder moves in the Y axis direction which is different from the X axis direction. The Y axis holder has a shape in which an end portion thereof in the X axis direction is projected from the cutting edge of the cutting insert, and a positioning portion to determine the projection amount of the cutting insert from the tool rest is disposed on the end portion.

A cutting tool includes a substrate and a coating film, wherein the coating film has a first layer formed from a plurality of hard grains, the hard grains are made of TiSiCN having a cubic crystal structure, the hard grains have a lamellar structure in which a layer having a relatively high silicon concentration and a layer having a relatively low silicon concentration are alternately stacked, and a maximum value of percentage of number A.sub.Si of silicon atoms to a sum of the number A.sub.Si of silicon atoms and number A.sub.Ti of titanium atoms in a grain boundary region between the hard grains, {A.sub.Si/(A.sub.Si+A.sub.Ti)}×100, is larger than an average value of percentage of number B.sub.Si of silicon atoms to a sum of the number B.sub.Si of silicon atoms and number B.sub.Ti of titanium atoms in the first layer, {B.sub.Si/(B.sub.Si+B.sub.Ti)}×100.