Insert, cutting tool, and method for cutting workpiece using the cutting tool

A cutting insert, comprising:

• an upper surface;
• a lower surface positioned at a side opposite to the upper surface;
• a lateral surface connected to the upper surface and the lower surface;
• and
• a cutting edge positioned at an intersection of the lateral surface and the upper surface;
• wherein the upper surface comprises
• a corner portion defined by a boundary between the upper surface and the lateral surface, the corner portion having a shape of a curved line that is outwardly convex in a plan view of the upper surface,
• a side portion directly connected to the corner portion and forming the cutting edge together with the corner portion,
• a rake face that extends along the side portion and the corner portion and extends downward with increasing distance from the side portion and the corner portion,
• a first rising face that is separated from the cutting edge with the rake face disposed therebetween and extends upward with increasing distance from the rake face, and
• a second rising face that is connected to an upper portion of the first rising face and extends upward with increasing distance from the first rising face,
• wherein the first rising face comprises
• a first sub-face that extends along the corner portion, and
• a second sub-face that extends along the side portion,
• wherein the second rising face comprises
• a third sub-face that extends along the corner portion, and
• a fourth sub-face that extends along the side portion,
• wherein an inclination angle of the first sub-face is greater than an inclination angle of the third sub-face in a first sectional view taken along a bisector of the corner portion,
• wherein an inclination angle of the second sub-face is greater than an inclination angle of the fourth sub-face in a second sectional view taken in a direction orthogonal to the side portion,
• wherein an entirety of a first boundary, which is a boundary between the first sub-face and the third sub-face, is positioned above the cutting edge along the corner portion,
• wherein a second boundary, which is a boundary between the second sub-face and the fourth sub-face, includes
• a first portion positioned above the cutting edge along the side portion, and
• a second portion positioned below the cutting edge along the side portion, and
• wherein a height of the second boundary decreases from the first portion to the second portion in a direction along the side portion and away from the corner portion.