US20110113950A1

US20110113950A1 - Composite material having a layer including entrained particles and method of making same

Info

Publication number: US20110113950A1
Application number: US11/328,631
Authority: US
Inventors: Charles K. Reed; David L. Hunn; Michael L. Fortner
Original assignee: Lockheed Martin Corp
Current assignee: Lockheed Martin Corp
Priority date: 2006-01-10
Filing date: 2006-01-10
Publication date: 2011-05-19

Abstract

A composite material suitable for use as an armor includes a first layer of a metallic material and a second layer, metallurgically bonded with the first layer. The second layer includes a matrix of the material of the first layer and a plurality of brittle particles dispersed in the matrix. A method for making a composite structure suitable for use as an armor from a workpiece of a metallic material includes the steps of plasticizing a fractional thickness of the workpiece using a friction stir process, introducing a plurality of brittle particles into the plasticized, fractional thickness of the workpiece, and dispersing the plurality of brittle particles into the plasticized, fractional thickness of the workpiece using the friction stir process.

Description

BACKGROUND

1. Field of the Invention
The present invention relates to a composite material. In particular, the present invention relates to a composite material suitable for use as an armor.
2. Description of Related Art
In combat situations, such as in military, police, and/or armored transport operations, it is desirable to protect vehicles, such as tanks, personnel carriers, trucks, and the like, as well as the vehicle's contents from damage by enemy fire. Accordingly, such vehicles are known to have armor to reduce the likelihood that ballistic rounds or other such projectiles will penetrate the vehicle. If the rounds penetrate the vehicle, the occupants of the vehicle may be injured or the vehicle's ability to operate may be impaired. It may also be desirable for the armor to be able to survive multiple rounds striking the armor in close proximity to one another, so that the integrity of the vehicle is not compromised or is only minimally compromised. Moreover, it is generally desirable for armor to include a relatively hard outer layer that the round encounters first. The hard outer layer starts the projectile or round defeat sequence by increasing the projectile dwell time on the armor, thus slowing the projectile down, or by blunting or fracturing the projectile early in the penetration event.
While protecting the vehicle and its occupants is generally of primary importance, other factors may play a role in the design of armor for the vehicle. It is desirable for the vehicle to be as lightweight as possible. Generally, a vehicle's fuel consumption increases as the vehicle's weight increases. A heavier vehicle usually requires a heavier drive train than a lighter vehicle, which further increases weight. Increased weight may also reduce the mobility of the vehicle and, thus, reduce the utility of the vehicle in combat. As the weight of the vehicle's armor contributes to the overall weight of the vehicle, it is desirable for the vehicle's armor to be as lightweight as possible. Many known armor systems, while protecting the vehicle from ballistic damage, add significant weight to the vehicle and provide little or no additional structural strength to the vehicle.
It is also not desirable for the vehicle's armor to greatly increase the overall size of the vehicle (e.g., the vehicle's height, width, length, volume, and the like), so that existing transportation equipment (e.g., trucks, trailers, aircraft, and the like) are capable of transporting the vehicle. If the size of the vehicle is increased over previous vehicles, the existing transportation equipment may not be capable of transporting the vehicle, or the existing transportation equipment may be limited to carrying fewer vehicles per load. Additionally, it is desirable to maximize the internal volume of the vehicle to allow adequate space to house the crew and crew gear. Accordingly, armor having lower volumes generally result in vehicle designs having larger internal volumes. The overall size of the vehicle is also a factor in combat situations. Generally, smaller targets (i.e., smaller vehicles) are more difficult to hit with artillery, such as rockets, mortars, missiles, and the like. Thus, it is desirable for the vehicle's overall size to be smaller, rather than larger, to reduce the likelihood of an artillery hit.
It is also desirable that the vehicle's armor be durable. During combat and during travel between combat locations, the vehicle may encounter flying rocks, debris, shrapnel, and the like. If the armor is overly thin or brittle, it may not be capable of surviving impacts from such sources.
Cost is also a consideration in vehicle armor. Armor that uses exotic materials (e.g., laminated ceramics of boron carbide, silicon carbide, and alumina; fiberglass/epoxy laminates; fiberglass/phenolic laminates; and the like), or armor that has many components in difficult-to-produce configurations, may be quite effective in combat but may be unaffordable.
Other applications exist for materials that are suitable for use as armor. Specifically, such materials may also be suitable as wear-resistant materials in high-wear applications. For example, armor materials may be suitable for use in equipment used in oilfield and/or gasfield operations, such as in drill pipe fixtures.
There are many designs of materials that are useful as armors and that are well known in the art; however, considerable shortcomings remain.

SUMMARY OF THE INVENTION

There is a need for a composite structure that is useful as an armor.
Therefore, it is an object of the present invention to provide a composite structure that is useful as an armor.
These and other objects are achieved by providing, in one aspect, a composite material suitable for use as an armor, including a first layer of a metallic material, metallurgically bonded with the first layer. The second layer includes a matrix of the material of the first layer and a plurality of brittle particles dispersed in the matrix.
In another aspect, the present invention provides an armor, including a first layer made of a material selected from the group consisting of titanium and titanium alloys and a second layer metallurgically bonded to the first layer. The second layer includes a matrix made of the material of the first layer and a plurality of particles dispersed in the matrix.
In yet another aspect of the present invention, a method for making a composite structure suitable for use as an armor from a workpiece of a metallic material is provided. The method includes the steps of plasticizing a fractional thickness of the workpiece using a friction stir process, introducing a plurality of brittle particles into the plasticized, fractional thickness of the workpiece, and dispersing the plurality of brittle particles into the plasticized, fractional thickness of the workpiece using the friction stir process.
The present invention provides significant advantages, including: (1) providing a material, useful as an armor, that is lighter in weight than conventional armor; (2) providing a material, useful as an armor, that occupies less volume than conventional armor; (3) providing a material, useful as an armor, that is less expensive to produce than conventional, light-weight armors; and (4) providing a lower-cost means for forming an integral, hard, outer layer on a metallic structure.
Additional objectives, features and advantages will be apparent in the written description which follows.

DESCRIPTION OF THE DRAWINGS

The novel features believed characteristic of the invention are set forth in the appended claims. However, the invention itself, as well as, a preferred mode of use, and further objectives and advantages thereof, will best be understood by reference to the following detailed description when read in conjunction with the accompanying drawings, in which the leftmost significant digit(s) in the reference numerals denote(s) the first figure in which the respective reference numerals appear, wherein:

FIG. 1 is a stylized, perspective view of an illustrative embodiment of a composite structure according to the present invention;

FIG. 2 is a stylized, perspective view of an illustrative embodiment of a body panel for a vehicle according to the present invention;

FIG. 3 is a photomicrograph of a cross-sectional portion of the composite structure of FIG. 1;

FIG. 4 is a stylized, perspective view depicting a first illustrative embodiment of a method for forming a composite structure, all according to the present invention;

FIG. 5 is a stylized, perspective view depicting a second illustrative embodiment of a method for forming a composite structure, all according to the present invention; and

FIG. 6 is a stylized, top, plan view depicting an exemplary path over which a friction stir processing tool is traversed to produce a composite structure of the present invention.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Illustrative embodiments of the invention are described below. In the interest of clarity, not all features of an actual implementation are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developer's specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure.
It should be appreciated that the following terms and phrases are intended to have a particular meaning throughout the following detailed description: The term “composite structure” refers to a structure made from two or more constituent materials that remain separate and distinct on a macroscopic level while forming a single component. The term “brittle particles” is intended to refer to particles comprising a material that, when stressed, tend to fracture before any substantial plastic deformation takes place. The term “metallurgically bonded” refers to the bonding within metals, which involves the delocalized sharing of free electrons within a lattice of metal atoms. The term “mixture” is intended to refer to a chemical substance comprising two or more materials, in a homogeneous or heterogeneous association, without chemical bonding of elements and/or compounds, such that the materials retain their own individual properties and makeup.
The present invention represents to a composite material or structure suitable for use as a ballistic armor comprising a first layer of a metallic material and a second layer, such that the second layer is metallurgically bonded to the first layer along an interface. The second layer comprises a plurality of brittle particles dispersed in a matrix. The particles act to increase the outer layer hardness of the composite structure. Specifically, the matrix, which comprises the same material as the first layer, is metallurgically bonded to the first layer along the interface. In one embodiment, which is particularly useful as an armor, the first layer and the matrix comprise a metallic material having a specific gravity of at least about four grams per cubic centimeter. Preferably, the second layer is a mixture of the metallic material of the first layer and the plurality of particles. Moreover, it is preferable for the plurality of brittle particles to comprise chemical elements that do not readily chemically combine with the material of the matrix. While the structure of the present invention has many applications, the structure is particularly useful as an armor to inhibit the penetration of ballistic projectiles. In such armor applications, materials having a specific gravity of at least about four grams per cubic centimeter are particularly useful as the first layer and the matrix of the second layer.
Preferably, the structure of the present invention is produced using friction stir processing, in which a fractional thickness of a precursor, comprising a metallic material having a specific gravity of at least about four grams per cubic centimeter, is frictionally heated to a plastic but non-molten state by a rotating, non-consumable tool. The non-consumable tool disperses the plurality of brittle particles into the frictionally-heated, plastic portion of the precursor. Thus, the plurality of brittle particles is dispersed in a matrix of the frictionally-heated portion of the precursor. Upon cooling, the plurality of brittle particles dispersed in the matrix comprising the frictionally-heated portion of the precursor becomes the second layer. The fractional thickness of the precursor that was not heated to a plastic state by the rotating tool is the first layer, which is metallurgically bonded to the second layer.
FIG. 1 depicts one particular, illustrative embodiment of a structure 101 according to the present invention. Structure 101 comprises a first layer 103 metallurgically bonded to a second layer 105 along an interface 107. First layer 103 comprises a metallic material. Preferably, for example, in armor applications, first layer 103 comprises a material having a specific gravity of at least about four grams per cubic centimeter, such as titanium or a titanium alloy. In one particular embodiment, first layer 103 comprises an alpha-beta titanium alloy, such as, for example, Ti-6Al-4V or Ti-4Al-2.5V—Fe—O. No matter the particular material, second layer 105 comprises the same metallic material as first layer 103. Additionally, second layer 105 comprises a plurality of dispersed, brittle particles, as will be discussed in greater detail below.
In one particular embodiment wherein structure 101 is used as an armor, a thickness t of second layer 105 is within a range of about two percent of a total thickness T of structure 101 to about 20 percent of total thickness T of structure 101. The scope of the present invention, however, is not so limited. Rather, thickness t of second layer 105 may be only a miniscule portion of thickness T of structure 101, may approach thickness T, or may be any suitable portion of thickness T depending upon the implementation of structure 101. It should be noted, however, that thickness t of second layer 105 may vary across structure 101.
While structure 101 is illustrated in FIG. 1 as being generally planar, the scope of the present invention is not so limited. Rather, the structure of the present invention may exhibit a planar shape, a simple contoured shape (such as illustrated in FIG. 2), or a complex contoured shape. Moreover, while structure 101 is illustrated in FIG. 1 as being a separate, distinct article, the scope of the present invention includes embodiments wherein the structure of the present invention is incorporated into another element or part. For example, as illustrated in FIG. 2, the scope of the present invention encompasses a body panel 201 for a vehicle. As in the embodiment of FIG. 1, body panel 201 comprises a first layer 203 comprising a metallic material having a specific gravity of at least about four grams per cubic centimeter. Body panel further comprises a second layer 205, metallurgically bonded to first layer 203 along an interface 207, comprising the same material as first layer 203 and additionally comprising a plurality of dispersed, brittle particles. In the embodiment of FIG. 2, body panel 201 serves as a structural member for the vehicle as well as inhibiting the penetration of ballistic projectiles.
FIG. 3 is a photomicrograph of a portion of structure 101 of FIG. 1, taken along the line 3-3 in FIG. 1. It should be noted that, while the following description particularly relates to structure 101, body panel 201 (shown in FIG. 2) also comprises such a configuration. As illustrated in FIG. 3, second layer 105 comprises a plurality of brittle particles 301 dispersed in a matrix 303 of the same material as first layer 103. Preferably, second layer 105 comprises a mixture of the material of first layer 103 (i.e., matrix 303) and the plurality of brittle particles 301. Preferably, brittle particles 301 comprise one or more carbides, such as tungsten carbide, titanium carbide, or the like; however, other brittle particles 301 may comprise other brittle materials, such as a ceramic material. Generally, it is preferable for brittle particles 301 to comprise one or more materials that do not readily chemically combine with the material of matrix 303 to form, for example, intermetallics. Moreover, in armor applications, it is preferable for brittle particles 301 to have an average sieve size within a range of about 0.5 microns to about 80 microns, although the present invention is not so limited. It should be noted that the average sieve size of brittle particles 301 may vary within second layer 105, depending upon the implementation of structure 101.
Furthermore, it is preferable, in armor applications, for brittle particles 301 to comprise a volume fraction of second layer 105 within a range of about one percent to about 30 percent, although embodiments of structure 101 having other volume fractions of brittle particles may be very effective in armor applications. Accordingly, the scope of the present invention includes any suitable volume fraction of brittle particles 301 in second layer 105, depending upon the implementation. Moreover, the volume fraction of brittle particles entrained in second layer 105 may vary across structure 101, depending upon the implementation of structure 101. Preferably, matrix 303 has an average grain size that is smaller than an average grain size of first layer 103. It should also be noted that second layer 105, and, thus, matrix 303, may or may not extend continuously across a part or first layer 103, depending upon the implementation of structure 101.
Preferably, structure 101 is formed using a friction stir process. Generally, friction stir processes engage a rotating, non-consumable tool with a stationary workpiece to plasticize, but not melt, a fractional thickness of the workpiece. Typically, friction stir processes are used to weld adjacent portions of a workpiece. According to the present invention, however, a friction stir process is utilized to plasticize a fractional thickness of a workpiece and to disperse a plurality of brittle particles into the plasticized volume of the workpiece. It should be noted, however, that, while the friction stir tool is not designed to transfer material from the friction stir tool into the plasticized, fractional thickness of the workpiece, in some situations minute portions of the friction stir tool may indeed be transferred into the plasticized, fractional thickness of the workpiece. Thus, a friction stir tool of the present invention is considered “non-consumable”, even though minute portions of the tool are transferred into the plasticized, fractional thickness of the workpiece.
Specifically, as shown in FIG. 4, a tool 401 having a shoulder 403 and a pin 405 extending from shoulder 403 is rotated (as indicated by an arrow 407) and plunged (as indicated by an arrow 409) into a workpiece 411. Workpiece 411, prior to friction stir processing according to the present invention, is a precursor to a structure (e.g., structure 101), also of the present invention. Workpiece 411 comprises the material of the first layer 103, as shown in FIG. 1 and described above. As pin 405 contacts workpiece 411, friction between pin 405 and workpiece 411 generates heat, thus plasticizing a fractional thickness of workpiece 411 proximate pin 405. As pin 405 continues to plunge into workpiece 411, more material is plasticized, thus allowing pin 405 to plunge further into workpiece 411. Plunging stops when shoulder 403 abuts workpiece 411.
Still referring to FIG. 4, frictional heat is generated between shoulder 403 and workpiece 411 and between pin 405 and workpiece 411. This heat causes the fractional thickness of workpiece 411 proximate shoulder 403 and pin 405 to soften or plasticize without reaching the melting point of workpiece 411, thus allowing tool 401 to traverse along workpiece 411, as indicated by an arrow 413. Preferably, a temperature of the plasticized portion of workpiece 411 is less than about 80 percent of a melting temperature of workpiece 411. A plurality of brittle particles is introduced into the plasticized portion of workpiece 411, as indicated by an arrow 419 and described in greater detail below. As downward pressure is maintained (as indicated by arrow 409) and tool 401 moves along workpiece 411 (as indicated by arrow 413), plasticized material of workpiece 411 and the plurality of particles is transferred from a leading edge 415 of tool 401 toward a trailing edge 417 of tool 401, such that the plurality of particles is dispersed and entrained into the plasticized portion of workpiece 411. The plasticized portion of workpiece 411 with the plurality of particles entrained therein is forged by intimate contact with shoulder 403 and pin 405 against adjacent, solid portions of workpiece 411. Upon cooling, the plasticized portion of workpiece 411, with the plurality of particles entrained therein, forms a solid-state portion 421.
As disclosed above, the plurality of brittle particles is introduced into the plasticized portion of workpiece 411. In one particular embodiment, depicted in FIG. 5, workpiece 411 defines a groove 501 in which a plurality of brittle particles 503 are disposed. In various embodiments, groove 501 may be, for example, generally rectangular, generally U-shaped, generally triangular, or the like in cross-section. Upon encountering plurality of brittle particles 503, tool 401 disperses plurality of brittle particles 503 in the plasticized portion of workpiece 411, as discussed above, to form solid-state portion 421.
Irrespective of the means for introducing the plurality of brittle particles into the plasticized portion of workpiece 411, according to the present invention, tool 401 is traversed across a desired area of workpiece 411 in which second layer 105 (shown in FIG. 1) is desired. The desired area may encompass the entire workpiece 411 or only a portion of workpiece 411. For example, in one illustrative embodiment depicted in FIG. 6, tool 401 is traversed across workpiece 411 in a pattern 601 to produce second layer 105 in workpiece 411 over an area 603 (shown in phantom). Note that pattern 601 represents a center point of tool 401. In some embodiments, a path or pattern may be used such that an entire surface of workpiece 411 is subjected to the present friction stir process. In other embodiments, a path or pattern may be utilized such that only one or more portions of workpiece 411 are subjected to the present friction stir process. Patterns and areas other than that illustrated in FIG. 6, however, are within the scope of the present invention.
It should be noted that, in some embodiments, friction stir processing refines the grain size of the metallic grains comprising the plasticized portion of workpiece 411. Accordingly, the resulting solid state portion 421 (and thus matrix 303) exhibits an average grain size that is less than an average grain size of first layer 103, since first layer 103 was not subjected to friction stir processing.
It should also be noted that the scope of the present invention is not limited to the particular configuration of tool 401. For example, in some embodiments, pin 405 may define circumferential threads or other such features to promote mixing of the plurality of particles into the plasticized portion of workpiece 411, to enhance the transfer of plasticized material of the workpiece from leading edge 415 of tool 401 toward trailing edge 417 of tool 401, and/or to generally enhance the friction stir process. Moreover, the particular shape of tool 401, shoulder 403, and/or pin 405 is implementation specific and, thus, shapes other than those shown in FIGS. 4 and 5 of tool 401, shoulder 403, and/or pin 405 are within the scope of the present invention.
Other means for introducing the plurality of brittle particles into the plasticized portion of a workpiece are contemplated by the present invention. For example, the plurality of brittle particles may be introduced into the plasticized portion of a workpiece via a passageway defined by a friction stir tool, such as friction stir welding tools 302, 402, 502, 602, 1102, or 1202 of commonly-assigned U.S. Pat. No. 6,543,671 to Hatten et al., entitled “Apparatus and Method for Friction Stir Welding Using Filler Material”, which is incorporated by reference herein for all purposes. Moreover, a workpiece or precursor, such as workpiece 411, may define or comprise other features for retaining the plurality of particles, such that the plurality of particles are incorporated into the plasticized portion of the workpiece or precursor by a friction stir processing tool, such as tool 401.
The particular embodiments disclosed above are illustrative only, as the invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope and spirit of the invention. Accordingly, the protection sought herein is as set forth in the claims below. It is apparent that an invention with significant advantages has been described and illustrated. Although the present invention is shown in a limited number of forms, it is not limited to just these forms, but is amenable to various changes and modifications without departing from the spirit thereof.

Claims

1. A composite material suitable for use as an armor, comprising:

a first layer comprising:

a metallic material; and

a second layer, metallurgically bonded with the first layer, the second layer comprising:

a matrix of the material of the first layer; and

a plurality of brittle particles dispersed in the matrix.

2. The composite material, according to claim 1, wherein the metallic material has a specific gravity of at least about four grams per cubic centimeter.

3. The composite material, according to claim 1, wherein the metallic material of the first layer comprises:

a material selected from the group consisting of titanium and titanium alloys.

4. The composite material, according to claim 1, wherein at least some of the plurality of brittle particles comprises:

a material selected from the group consisting of ceramic, carbide, tungsten carbide, and titanium carbide.

5. The composite material, according to claim 1, wherein the plurality of brittle particles has an average sieve size within a range of about 0.5 micron to about 80 microns.

6. The composite material, according to claim 1, wherein the plurality of brittle particles comprises:

a volume fraction of the second layer within a range of about one percent to about 30 percent.

7. The composite material, according to claim 1, wherein the second layer exhibits an average grain size that is less than an average grain size exhibited by the first layer.

8. The composite material, according to claim 1, wherein the second layer is a mixture of the plurality of particles and the matrix.

9. The composite material, according to claim 1, wherein the composite material forms an armor.

10. The composite material, according to claim 1, wherein the armor comprises:

a portion of a vehicle.

11. The composite material, according to claim 1, wherein the second layer is formed by a friction stir processing method.

12. The composite material, according to claim 1, wherein the structure is formed by a method comprising the steps of:

engaging a rotating, non-consumable tool with a precursor comprising the metallic material of the first layer to plasticize a fractional thickness of the precursor, leaving a remaining fractional thickness of the precursor unplasticized;

introducing the plurality of brittle particles into the plasticized, fractional thickness of the precursor;

dispersing the plurality of brittle particles into the plasticized, fractional thickness of the precursor; and

traversing the rotating, non-consumable tool across the precursor, such that the plasticized, fractional thickness of the precursor with the plurality of brittle particles dispersed therein forms the second layer and the remaining unplasticized thickness of the precursor forms the first layer.

13. A composite material, according to claim 1, wherein a thickness of the second layer is within a range of about two percent of a total thickness of the composite structure to about 20 percent of the total thickness of the composite structure.

14. An armor, comprising:

a first layer made of a material selected from the group consisting of titanium and titanium alloys; and

a second layer metallurgically bonded to the first layer, the second layer comprising:

a matrix made of the material of the first layer; and

a plurality of particles dispersed in the matrix.

15. The armor, according to claim 14, wherein at least some of the plurality of particles comprises:

16. The armor, according to claim 14, wherein the armor forms a portion of a vehicle.

17. The armor, according to claim 14, wherein the armor is operably associated with a vehicle.

18. The armor, according to claim 14, wherein the second layer is formed by a friction stir processing method.

19. The armor, according to claim 14, wherein the armor is formed by a method comprising the steps of:

engaging a rotating, non-consumable tool with a precursor comprising the material of the first layer to plasticize a fractional thickness of the precursor, leaving a remaining fractional thickness of the precursor unplasticized;

20. A method for making a composite structure suitable for use as an armor from a workpiece of a metallic material, the method comprising the steps of:

plasticizing a fractional thickness of the workpiece using a friction stir process;

introducing a plurality of brittle particles into the plasticized, fractional thickness of the workpiece; and

dispersing the plurality of brittle particles into the plasticized, fractional thickness of the workpiece using the friction stir process.

21. The method, according to claim 19, further comprising the step of:

refining the grain structure of the plasticized, fractional thickness of the workpiece using the friction stir process.

22. The method, according to claim 19, wherein the friction stir process comprises the steps of:

engaging a rotating, non-consumable tool with the workpiece; and

traversing the tool across the workpiece.

23. The method, according to claim 19, wherein the step of introducing the plurality of brittle particles is accomplished by introducing the plurality of brittle particles at a specified rate to produce a volume fraction of brittle particles dispersed in the plasticized, fractional thickness of the workpiece within a range of about one percent to about 30 percent.

24. The method, according to claim 19, wherein the step of dispersing the plurality of brittle particles further comprises the step of:

mixing the plurality of brittle particles and the plasticized, fractional thickness of the workpiece.

25. The method, according to claim 18, wherein the fractional thickness is within a range of about two percent of a total thickness of the workpiece to about 20 percent of the total thickness of the workpiece.