Cutting elements configured to reduce impact damage and mitigate polycrystalline, superabrasive material failure earth-boring tools including such cutting elements, and related methods

1. A cutting element for an earth-boring tool, comprising:

a substrate;

a polycrystalline, superabrasive material secured to an end of the substrate, the polycrystalline, superabrasive material comprising a curved, stress-reduction feature formed in a cutting face of the polycrystalline, superabrasive material;

a first transition surface extending from an outer peripheral edge of the polycrystalline, superabrasive material and in a first direction oblique to a center longitudinal axis of the substrate, wherein the curved, stress-reduction feature is formed partially on the first transition surface; and

at least one recess defined in the curved, stress-reduction feature of the polycrystalline, superabrasive material and comprising: sidewalls intersecting with a front surface of the curved, stress-reduction feature of the polycrystalline, superabrasive material and extending to a base wall within the polycrystalline, superabrasive material.

2. The cutting element of claim 1 , wherein the curved, stress-reduction feature comprises:

an undulating edge formed proximate a peripheral edge of the polycrystalline, superabrasive material; and

a waveform extending from the undulating edge toward a center longitudinal axis of the cutting element.

3. The cutting element of claim 2 , wherein the at least one recess is concentric with the undulating edge.

4. The cutting element of claim 2 , wherein the at least one recess forms a circle in the waveform of the curved, stress-reduction feature, and wherein the at least one recess is concentric with an outer peripheral edge of the polycrystalline, superabrasive material.

5. The cutting element of claim 2 , wherein the at least one recess comprises a plurality of wide grooves extending outward radially relative to the center longitudinal axis of the cutting element.

6. The cutting element of claim 5 , wherein the plurality of wide grooves at formed in peaks of waves of the waveform of the curved, stress-reduction feature.

7. The cutting element of claim 2 , wherein the at least one recess comprises a plurality of grooves extending outward radially relative to the center longitudinal axis of the cutting element and formed within troughs of waves of the waveform of the curved, stress-reduction feature.

8. The cutting element of claim 1 , wherein an intersection of a sidewall of the at least one recess and the front surface of the curved, stress-reduction feature most proximate an outer peripheral edge of the polycrystalline, superabrasive material is located a distance of 0.5 mm to 4.0 mm from the outer peripheral edge of the polycrystalline, superabrasive material and wherein the at least one recess has a width within a range of 25.0 μm to 650 μm and a depth within a range of 25.0 μm to 600 μm.

9. An earth-boring tool, comprising:

a body; and

a cutting element secured to the body, the cutting element comprising:

a substrate;

a polycrystalline, superabrasive material secured to an end of the substrate, the polycrystalline, superabrasive material comprising a curved, stress-reduction feature formed in a cutting face of the polycrystalline, superabrasive material, the curved, stress-reduction feature comprising:

an undulating edge formed proximate an outer peripheral edge of the polycrystalline, superabrasive material; and

a waveform extending from the undulating edge toward a center longitudinal axis of the cutting element;

a first transition surface extending from an outer peripheral edge of the polycrystalline, superabrasive material and in a first direction oblique to a center longitudinal axis of the substrate, wherein the curved, stress-reduction feature is formed partially on the first transition surface; and

at least one recess defined in the waveform of the curved, stress-reduction feature of the polycrystalline, superabrasive material and comprising: sidewalls intersecting with a front surface of the waveform of the curved, stress-reduction feature of the polycrystalline, superabrasive material and extending to a base wall within the polycrystalline, superabrasive material.

10. The cutting element of claim 9 , wherein an intersection of a sidewall of the at least one recess and the front surface of the waveform of the curved, stress-reduction feature most proximate the outer peripheral edge of the polycrystalline, superabrasive material is located a distance of 0.5 mm to 4.0 mm from the outer peripheral edge of the polycrystalline, superabrasive material and wherein the at least one recess has a width within a range of 25.0 μm to 650 μm and a depth within a range of 25.0 μm to 600 μm.

11. The cutting element of claim 9 , further comprising a second transition surface extending from the first transition surface and in a second direction oblique to the center longitudinal axis, the second direction being different from the first direction.

12. The cutting element of claim 9 , wherein the at least one recess is concentric with the undulating edge.

13. The cutting element of claim 9 , wherein the at least one recess forms a circle in the front surface of the waveform of the curved, stress-reduction feature, and wherein the at least one recess is concentric with the outer peripheral edge of the polycrystalline, superabrasive material.

14. The cutting element of claim 9 , wherein the at least one recess comprises a plurality of grooves extending outward radially relative to the center longitudinal axis of the cutting element and formed within troughs of waves of the waveform of the curved, stress-reduction feature.

15. A method of forming a cutting element for an earth-boring tool, the method comprising:

attaching a polycrystalline, superabrasive material to a substrate;

forming a first transition surface extending from an outer peripheral edge of the polycrystalline, superabrasive material and in a first direction oblique to a center longitudinal axis of the substrate;

forming a curved, stress-reduction feature in a cutting face of the polycrystalline, superabrasive material and partially on the first transition surface, the curved, stress-reduction feature comprising:

an undulating edge formed proximate an outer peripheral edge of the polycrystalline, superabrasive material; and

a waveform extending from the undulating edge toward a center longitudinal axis of the substrate; and

forming at least one recess in the curved, stress-reduction feature of the polycrystalline, superabrasive material, the at least one recess comprising: sidewalls intersecting with a front surface of the curved, stress-reduction feature of the polycrystalline, superabrasive material and extending to a base wall within the polycrystalline, superabrasive material.

16. The method of claim 15 , wherein forming the at least one recess comprises forming the at least one recess to be concentric with the outer peripheral edge of the polycrystalline, superabrasive material.

17. The method of claim 15 , wherein forming the at least one recess comprises forming the at least one recess to be concentric with the undulating edge of the curved, stress-reduction feature.

18. The method of claim 15 , wherein forming the at least one recess comprises forming the at least one recess to include a plurality of recesses grooves extending outward radially relative to the center longitudinal axis of the cutting element and formed within troughs of waves of the waveform of the curved, stress-reduction feature.