A method for manufacturing a cutting tool includes: the cutting tool comprising a tool body made of a sintered alloy, a hard coating which is disposed on an outer surface of the tool body and has at least a layer formed of any of a carbide, a nitride, and a carbonitride, or a composite compound thereof, and a cutting edge which is formed at a ridge portion of the tool body and includes a portion of the hard coating located at the ridge portion, a laser peening step of directly irradiating the hard coating with a pulsed laser having a pulse width of 100 ps or less to apply compressive residual stress to the hard coating and a surface region of the tool body.

A turning insert has two opposite main surfaces and a peripheral surface which extends therebetween and has N side surfaces, where 2<N<9. The insert has mirror symmetry about a mid-plane and 360/N degree rotational symmetry about a central axis perpendicular to the mid-plane. The insert has two main edges which each have N main cutting edges and N corner cutting edges. Each main cutting edge has two raised edge portions and a lowered edge portion. Each main surface has N main rake surfaces and N corner rake surfaces. Each main surface further has at least N convex island protrusions and N at least partially convex peninsula protrusions, any and all island protrusions associated with a given main rake surface being located between two adjacent peninsula protrusions, each pair of adjacent peninsula protrusions having at least one island protrusion located therebetween.

A turning insert has two opposite main surfaces and a peripheral surface which extends therebetween and has N side surfaces, where 2<N<9. The insert has mirror symmetry about a mid-plane and 360/N degree rotational symmetry about a central axis perpendicular to the mid-plane. The insert has two main edges which each have N main cutting edges and N corner cutting edges. Each main cutting edge has two raised edge portions and a lowered edge portion. Each main surface has N main rake surfaces and N corner rake surfaces. Each main surface further has at least N convex island protrusions and N at least partially convex peninsula protrusions, any and all island protrusions associated with a given main rake surface being located between two adjacent peninsula protrusions, each pair of adjacent peninsula protrusions having at least one island protrusion located therebetween.

A turning tool has a cutting element for a lathe that uses metal-cutting technology, wherein the cutting element has a tool blade, wherein the tool blade of the cutting element has a curvature, in a top view, in which the tool blade intersects a tool axis of the cutting element at a perpendicular angle, in which the cutting element has an opening angle with reference to a center point, wherein the cutting element has asymmetry, in such a manner that the tool axis intersects the opening angle outside the center, and in which, in a top view of the cutting element, the curvature of the tool blade has a constant change in radius.