Cutting elements having cutting edges with continuous varying radii and bits incorporating the same

1. A shear cutter type cutting element comprising:

a substrate for mounting on a drag bit; and

an ultra hard material cutting layer over the substrate, said cutting layer comprising a surface portion for making contact with a material to be cut by said cutting element, said surface portion in cross-section having a varying curvature that is formed by a plurality of adjacent sections, each section having a different radius of curvature than its adjacent section, wherein the surface portion in cross-section comprises a first section adjacent to a second section which is adjacent a third section, wherein the first section is non-flat and comprises a first radius of curvature, wherein the third section is non-flat and comprises a third radius of curvature, wherein the second section is flatter than the first and third sections and wherein the third radius of curvature is greater than the first radius of curvature, wherein the cutting layer comprises a first surface interfacing with the substrate and a second surface opposite the first surface, wherein the first section extends from the second surface.

2. The cutting element as recited in claim 1 , wherein the first and third sections curve in the same direction in cross-section.

3. The cutting element as recited in claim 1 , wherein one of the first and third sections curves in a first direction, and wherein the other of the first and third sections curves in a second direction opposite the first direction.

4. The cutting element as recited in claim 1 , wherein the second section is flat.

5. The cutting element as recited in claim 1 , wherein the surface portion in cross-section defines a chamfer.

6. The cutting element as recited in claim 1 , wherein the surface portion extends from a peripheral surface of the cutting layer.

7. The cutting element as recited in claim 1 , wherein the cutting layer comprises a first surface interfacing with the substrate, a second surface opposite the first surface, and a peripheral surface between the first and second surfaces, wherein the third section extends from the peripheral surface.

8. The cutting element as recited in claim 1 , wherein the surface portion in cross-section comprises at least 35 sections, each section having a different radius of curvature than its adjacent section.

9. The cutting element as recited in claim 1 , wherein the second radius of curvature is greater than the third radius of curvature.

10. The cutting element as recited in claim 9 , wherein the second radius of curvature is greater than the first radius of curvature.

11. A shear cutter type cutting element comprising:

a substrate for mounting on a drag bit; and

an ultra hard material cutting layer over the substrate, said cutting layer comprising a surface portion for making contact with a material to be cut by said cutting element, said surface portion in cross-section having a varying curvature that is formed by a plurality of adjacent sections, each section having a different radius of curvature than its adjacent section, wherein the surface portion in cross-section comprises a first section adjacent to a second section which is adjacent a third section, wherein the first section is non-flat and comprises a first radius of curvature, wherein the third section is non-flat and comprises a third radius of curvature, wherein the second section is flatter than the first and third sections and wherein the third radius of curvature is greater than the first radius of curvature, wherein the cutting layer comprises a first surface interfacing with the substrate, a second surface opposite the first surface, and a peripheral surface between the first and second surfaces, wherein the third section extends from the peripheral surface.

12. The cutting element as recited in claim 11 , wherein the first and third sections curve in the same direction in cross-section.

13. The cutting element as recited in claim 11 , wherein one of the first and third sections curves in a first direction, and wherein the other of the first and third sections curves in a second direction opposite the first direction.

14. The cutting element as recited in claim 11 , wherein the second section is flat.

15. The cutting element as recited in claim 11 , wherein the surface portion in cross-section defines a chamfer.

16. The cutting element as recited in claim 11 , wherein the surface portion in cross-section comprises at least 35 sections, each section having a different radius of curvature than its adjacent section.

17. The cutting element as recited in claim 11 , wherein the second radius of curvature is greater than the third radius of curvature.

18. The cutting element as recited in claim 17 , wherein the second radius of curvature is greater than the first radius of curvature.

19. A shear cutter type cutting element comprising:

a substrate for mounting on a drag bit; and

an ultra hard material cutting layer over the substrate, said cutting layer comprising a surface portion for making contact with a material to be cut by said cutting element, said surface portion in cross-section having a varying curvature that is formed by a plurality of adjacent sections, each section having a different radius of curvature than its adjacent section, wherein the surface portion in cross-section comprises a first section adjacent to a second section which is adjacent a third section, wherein the first section is non-flat and comprises a first radius of curvature, wherein the third section is non-flat and comprises a third radius of curvature, wherein the second section is flatter than the first and third sections and wherein the third radius of curvature is greater than the first radius of curvature, wherein the surface portion in cross-section comprises at least 35 sections, each section having a different radius of curvature than its adjacent section.

20. The cutting element as recited in claim 19 , wherein the second section is flat.