| United States Patent Application |
20100155374
|
| Kind Code
|
A1
|
|
Rabinovich; Joshua E.
|
June 24, 2010
|
process for energy beam solid-state metallurgical bonding of wires having
two or more flat surfaces
Abstract
An energy beam assisted solid-state welding welds a wire material to a
substrate. A wire of coating or repairing material is placed in contact
with a surface or surfaces of a substrate. A beam is directed into an
outer flat surface of the wire, which heats the wire through flat outer
surface of the wire with beam energy. Beam energy produces compression
stress-waves that drive molecules of the material flat wire into a
surface of the substrate, joining the material and the substrate with
strong wave shaped interfaces.
| Inventors: |
Rabinovich; Joshua E.; (Newton, MA)
|
| Correspondence Address:
|
JAMES C. WRAY
1493 CHAIN BRIDGE ROAD, SUITE 300
MCLEAN
VA
22101
US
|
| Family ID:
|
42264540
|
| Appl. No.:
|
12/590249
|
| Filed:
|
November 4, 2009 |
Related U.S. Patent Documents
| | | | |
|
| Application Number | Filing Date | Patent Number | |
|---|
| | 61198203 | Nov 4, 2008 | | |
|
|
| Current U.S. Class: |
219/121.14 ; 219/121.13; 219/121.35; 219/121.6; 219/121.64 |
| Current CPC Class: |
B23K 15/0086 20130101; B33Y 30/00 20141201; B23K 26/324 20130101; B23K 26/32 20130101; B23K 26/342 20151001; B23K 2203/50 20151001; B23K 26/0622 20151001; B23K 35/325 20130101; B23K 35/38 20130101; B23K 35/383 20130101; B23K 35/0227 20130101; B23K 35/0244 20130101; B23K 35/0255 20130101; B23K 35/0261 20130101; B23K 35/0272 20130101; B23K 26/34 20130101 |
| Class at Publication: |
219/121.14 ; 219/121.13; 219/121.35; 219/121.6; 219/121.64 |
| International Class: |
B23K 15/00 20060101 B23K015/00; B23K 26/20 20060101 B23K026/20 |
Claims
1. A process and apparatus for energy beam assisted solid-state
metallurgical bonding of a wire, having two or more flat surfaces, to a
substrate, for the purpose of substrate coating, 3-Dimensional component
buildup, restoration and component surface improvement, and comprising
the steps of: applying of a continuously fed wire to a substrate such
that the bottom of the wire flat surface(s) are tangential to the
substrate such that the contact of the wire with the substrate constitute
substantially a surface(s); an energy beam (for example Laser or Electron
Beam) is simultaneously applied to the wire, with a magnitude controlled
to be sufficient to produce a sudden compressive shock wave and heat at
the surface of the wire to propagate through the wire and the top surface
of the substrate; whilst some material particles of the wire are carried
with the shock wave and are penetrating (forged-in) into the substrate,
producing a strong metallurgical bond without substantial liquefaction of
the substrate (solid-state bonding)
2. The process and apparatus of claim 1 further including a means of
controlling energy beam and its energy and power densities to achieve
various magnitudes of the compressive shock wave at the top surface of
the wire.
3. The process and apparatus of clam 1 further including a means of
controlling energy beam and its energy and power densities and pulse
duration to achieve various temperature gradients through the wire
material and the top layer of the substrate material to produce the
desired amount of penetration of wire material into (forge-in depth) the
substrate material.
4. The process and apparatus of clam 1, further including a means of
controlling energy beam's power and energy densities and pulse time
duration to achieve the required temperature gradient through the wire.
It is controlled such that, while the part of the top surface of the flat
wire is liquefied, the surface of the wire adjacent to the substrate can
be maintained in a solid or semisolid state at the temperatures below the
liquefaction temperature of the substrate material.
5. The process and apparatus of claim 1 further including a wire delivery
means to continuously delivering the wire onto the substrate such that
the contact of the wire with the substrate constitute substantially a
surface(s) to provide a good coupling of wire and substrate for an
effective transportation of thermal-wave and the shock-wave carrying the
wire particles into the substrate.
6. The process and apparatus of claim 1 further including a means for
adjusting the energy beam size appropriate to the wire width or to the
desired fraction of the wire width.
7. The process and apparatus of claim 1 further including a means for
scanning energy beam across the wire width for the purposes of wire
deposition and cutting.
8. The process and apparatus of claim 1 further including a means of
delivery of inert gas into the area of energy beam impingement with the
wire to prevent the bonding from being effected or contaminated by the
surrounding atmosphere. The process can be also conducted in a vacuum.
9. The process and apparatus of claim 1 further including a means for a
flat or 3-Dimensional component manipulation in 3-Dimensional space
pivoted about the point, which belongs to the normal to the component's
surface at the meeting point of the energy beam and the wire with the
component's surface.
10. The process and apparatus of claim 1 wherein the wire material can be
of any metal material available (or can be made available) in the desired
wire form, and non metal material in the strip or tow form.
11. The process and apparatus of claim 1 wherein the substrate material
can be of any metal material and non metal material.
12. The process and apparatus of claim 1 wherein plurality of
combinations of similar or dissimilar materials of wire and substrate can
be used.
13. A component produced, built-up or coated with a layer or layers of
materials in accordance with the process and apparatus of claim 1.
Description
[0001] This application claims the benefit of U.S. Provisional Application
No. 61/198,203, filed Nov. 4, 2008, which is hereby incorporated by
reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] The present invention generally relates to the field of materials
deposition for a component fabrication, restoration, and surface
improvement and more particularly, is directed to a process and apparatus
for coating or cladding a layer or layers of metal and non-metal
materials onto substrates of dissimilar materials.
[0003] There are variety of methods known in the prior art for coating or
cladding a layer of dissimilar material onto a substrate. Some examples
of the known methods that produce enhanced bonding between the coating
and the substrate as follows: [0004] 1. Thermal Spray processes, [0005]
2. Conventional Arc Welding, [0006] 3. Laser and Electron Beam metal
deposition, [0007] 4. Large Scale Explosion Welding and Micro-explosion
Welding.
[0008] The terms "coating" and "cladding" although sometimes used
interchangeably, usually refer to different application processes.
Cladding refers to a coating layer production process by bonding a plate
or film to a substrate, while coating refers to a coating layer
production process by bonding of materials in the form other than a plate
or a film for example, liquids, powders or wires.
[0009] Thermal Spray Coating processes such as plasma spray or
high-velocity oxy-fuel (HVOF) methods produce a relatively weak
mechanical bond with a substrate and work well in applications where a
component is subjected primarily to compression loads. In more demanding
applications where a component is subjected to torsion, shear, or bending
stresses, the coating needs to have a strong metallurgical bond with a
substrate.
[0010] Metallurgical bond strength welding can be produced with such
welding methods as arc welding, plasma, laser powder deposition, and
Electron Beam wire or powder deposition. However, these welding methods
apply an excessive heat and a melt-pool at the substrate for a time
sufficient to result in melting and intermixing of elements of the alloys
being joined. Such liquid phase intermixing and associated chemical
reactions have been observed to result in the creation of brittle
intermetallic compounds at the joint interface leading to coating
cracking and flaking.
[0011] If the coating and substrate are metallurgically compatible or
"weldable", then conventional welding techniques may be used. This
process is sometimes referred to as fusion welding or hardfacing. Fusion
hardfacing cannot be used in cases where the substrate cannot be heated
to the liquefaction state or the materials are not weldable. For example,
coating of aluminum with high temperature and strength metals, such as
titanium and nickel alloys, can often be bonded by an explosion welding
process. Explosion welding belongs to a solid-state welding methods
allowing for a strong metallurgical bond between materials of dissimilar
physical characteristics and without substantial liquefaction of the
substrate.
[0012] The explosion welding method is based on high velocity oblique
collision of two metal plates. The cladding plate (the "flyer") is
covered with an explosive material and placed at some distance from the
substrate. The explosive material is detonated and it propagates though
the entire surface of the flyer plate. The flyer plate collides with the
substrate at velocities in the range of 400-3000 m/sec. The high
collision pressure and heat created at the collision line allows
hydrodynamic flow to occur creating a strong wavy interface between
dissimilar metals. The shortcoming of this process is in its high cost
and its safety issues due to handling and controlling explosives. Another
limitation of the process is that it is primarily suitable for cladding
of flat surfaces.
[0013] Other methods similar to explosion welding are using laser energy
to evaporate the top layer of a foil or a separate sacrificial layer to
realize the recoil forces, generated by the high velocity of evaporated
gases, to drive the coating foils toward the target substrate.
[0014] Drew et al T988007 (1979) discloses a laser vapor deposition
technique wherein a CW laser beam is directed through a transparent
substrate onto a reservoir of metal on the opposite side of and spaced
from the substrate. The laser beam heats and vaporizes the metal of the
reservoir, which is then redeposited on the opposing surface of the
substrate.
[0015] Mayer et al, " Pulsed Laser Microfabrication" U.S. Pat. No.
4,752,455, proposes a system and method of pulsed-laser microfabrication
wherein a first substrate of transparent material, such as glass, has a
conductive film and then a target material both positioned on a surface
of the transparent substrate. The target material is placed immediately
adjacent to the target substrate surface. Pulsed laser energy is directed
through the transparent substrate onto the conductive film at a
sufficient intensity and for a sufficient duration to rapidly vaporize
the metal film. The target materials are driven by film vaporization
energy and by the reaction thereof against the glass substrate onto the
opposing or object surface of a second substrate.
[0016] This process resembles the large scale explosion welding but on a
micro-level, often referred to as a micro-explosion welding, and is
limited to cladding of very thin films and primarily on flat surfaces.
[0017] Frish et al, " Method for Bonding Using Laser Induced Heat and
Pressure" U.S. Pat. No. 4,684,781, proposes bonding metal foils to
substrates of dissimilar metal by placing the foil in contact with the
substrate and then irradiating the foil surface remote from the substrate
with a laser pulse so as to ablate a portion of the foil surface.
[0018] According to the invention, a foil layer of a material to be
applied as a coating to a substrate is laid over and in contact with the
substrate surface which is to be coated. A laser beam, typically pulsed,
and of a very high instantaneous intensity is applied to the exposed foil
layer.
[0019] The intensity of the radiation as focused onto the foil at a small
spot is extremely high, substantially greater than that used in prior
applications such as laser welding. The extremely high laser intensity
produces an instantaneous vaporization of a small portion of the foil
surface. The reaction to the vapor pressure or "recoil force" generated
by the foil surface vaporization is a pressure or shock wave transmitted
in the opposite direction and through the thin foil layer in the
direction of the interface between the foil and substrate. Laser power
densities, typically usable in the above invention, range from hundreds
of megawatts per square centimeter to hundreds of thousands of megawatts
per square centimeter with pulse durations measured in a few hundredths
of a microsecond up to over twenty microseconds.
[0020] Thermal and pressure waves are generated in the foil and travel
through the foil thickness at differing velocities. If the thermal wave
reaches the foil/substrate interface during irradiation, both materials
will melt and thereafter mix under the influence of the laser-induced
pressure gradients. Thus, the disclosed "laser stamping" technique makes
use of both heat and pressure supplied to the foil by the high intensity
laser pulse.
[0021] The major shortcomings of this method are as follows: [0022] 1.
The foil is pre-placed onto a substrate with sufficiently large gaps
present between the foil and the substrate due to the initial
imperfection in flatness of a foil and the substrate as well as the
additional irregular gaps created during the laser-irradiation of the
foil. These gaps prevent the pressure and thermal waves from reaching the
substrate and thus prevent the production of a reliable uniform bond of
the foil to the substrate. [0023] 2. Because of the above irregular gaps
between the pre-placed foil and the substrate, an extremely high power
densities and very thin foils (2 to 100 micrometers) are required in
order to create sufficient momentum to propel the foil toward the
substrate against the gap resistance. [0024] 3. In addition, these
extremely high power intensities of the laser beam delivered to a very
thin foil, having a plurality of gaps of different distances, would tend
to perforate the foil in many places where there is a gap between a foil
and the substrate, producing unacceptable quality coatings.
[0025] Rabinovich "Rapid Prototyping System" U.S. Pat. No. 5,578,227,
which is fully incorporated herein by reference, describes a part making
method and apparatus with laser assisted fusion of a rectangular wire to
a substrate. In this method the feedstock fusion is performed with a
laser beam of the size and power density sufficient for reliable spot or
continuous fusion welding of the feedstock to the previous layer while
keeping the feedstock cross-section in substantially original shape and
producing fusion with a limited local heat input into the part. This
limited heat input is achieved through the wire surface-to-surface
contact with the substrate, which provides good thermal conductivity to
heat flow. This effective heat conduction eliminates the need in the
creation of a molten-pool in the substrate prior to metal deposition, as
it is the case in other energy beam metal deposition processes, which
utilize metal powders or round wires. Although the advantages of this
melt-pool free, ultra-low heat input process have been instrumental for
repairs of many complex and thin wall structures and many dissimilar
materials, the true solid-state welding capabilities required for strong
metallurgical bonding of many dissimilar materials was not anticipated at
that time.
[0026] While practicing the method of U.S. Pat. No. 5,578,227, under a
trademark of Precision Metal Deposition (PMD.TM.), the author discovered
new and unexpected qualities of this method, which with a number of
improvements, allow bonding of extremely dissimilar metals to be
performed in a solid-state mode of welding.
SUMMARY OF THE INVENTION
[0027] In accordance with the teaching of the present invention, a process
is disclosed for energy beam assisted solid-state metallurgical bonding
of a wire with two or more flat surfaces, to a substrate, for the purpose
of substrate coating, 3-Dimensional component buildup, restoration, and
component surface improvement. It is thus possible, by controlling energy
beam produced temperature gradient through the wire and a suddenly
applied energy induced compression stress-wave effects, to join, in a
solid-state welding mode, metals with extremely dissimilar physical
characteristics, which could not be joined by conventional welding
methods.
[0028] The disclosed process allows for a solid-state welding on flat and
curved surfaces with extremely strong wave-shape interface morphology,
reminiscent to the explosion welding but without its high cost, component
shape limitations, and safety disadvantages. The process allows for
strong, metallurgical bond coating of components made out of inexpensive,
light weight metals, such as aluminum alloy, with high strength alloys
thus transforming these components into stronger metal-composite
components without loosing their light weight value.
[0029] Yet another revolutionary capability of the disclosed process is in
restoration of high value aircraft jet engine components, such as turbine
blades, made out of single crystal alloys. Single crystal alloys cannot
tolerate repairs with temperatures reaching liquefaction levels; they
re-crystallize and loose their single crystal structure and fatigue
strength qualities. The disclosed process can restore these extremely
expensive components by keeping the temperatures of the parent material
below the material's liquefaction point, thus maintaining the single
crystal advantages.
[0030] In practicing this invention, a continuously fed flat wire is
delivered to a substrate such that the bottom of the wire flat surface(s)
is tangential to the substrate such that the contact of the wire with the
substrate constitutes substantially a surface(s), allowing efficient
conduction of the energy beam produced stress and thermal waves from the
wire to the substrate. The flat wire surface conforms to the surface of
the substrate and provides repeatable and reliable contact during coating
process.
[0031] An energy beam, (for example Laser or Electron Beam), preferably
pulsed, is simultaneously applied to the wire, with a magnitude
controlled to be sufficient to produce a sudden compressive stress shock
wave at the surface of the wire and a thermal wave from the energy beam.
The thermal wave establishes a temperature gradient through the wire
thickness and, together with the compressive stress shock wave,
propagates through the wire and the top surface of the substrate.
[0032] The desired temperature gradient is established through the wire
and the top surface of the substrate by controlling the energy beam-spot
energy, power density and pulse period. The temperature gradient through
the wire is controlled such that while the part of the top surface of the
flat wire is liquefied, the surface adjacent to the substrate can be
maintained in a solid or semisolid state at the temperatures below of the
temperature of liquefaction of the substrate material.
[0033] With the simultaneous action of the compression wave generated by
the laser beam at the top surface of the wire, some particles of the wire
are moving with the compression wave, and penetrating through their
common surface of contact into the substrate cause hydrodynamic wavy
interface of the materials of wire and the substrate. The wire contact
surface and the substrate top layer are maintained at the temperatures
below the substrate's liquefaction temperature, thus producing a strong
metallurgical bond between the coating and substrate in a solid-state
mode.
[0034] These and further and other objects and features of the invention
are apparent in the disclosure, which includes the above and ongoing
written specification, with the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0035] FIG. 1 is a system block diagram of functional modules, software
and controls of the apparatus and a detail of the interface of the flat
wire with a substrate in a solid-state mode coating.
[0036] FIG. 2 is an Electron Scan Microscope image of a coating of
aluminum with titanium and nickel alloys produced with the present
invention in a solid-state welding mode and the typical wave-shape
interface.
[0037] FIG. 3 is a photomicrograph of Inconel alloy coating of high carbon
steel alloy produced with the present invention in a solid-state welding
mode and the typical wave-shape interface.
[0038] FIG. 4 is a diagram showing a coating in a solid-state welding mode
of a surface with a rectangular wire
[0039] FIG. 5 is a diagram showing a solid-state bonding of two adjacent
components, or repairing a crack in the same component, with a wire
having a wedge form with multiple flat surfaces.
[0040] FIG. 6 is a photograph of aluminum Al-6061 tube, coated with
titanium Ti-64 alloy produced with the present invention in a solid-state
welding mode.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENT
[0041] The present invention disclosed a process for energy beam assisted
solid-state metallurgical bonding of a wire with two or more flat
surfaces, to a substrate, for the purpose of substrate coating,
3-Dimensional component buildup, restoration, and component surface
improvement. An energy beam, (for example Laser or Electron Beam),
preferably pulsed, is used. For the purpose of this description, a laser
1 is used and its focused beam 2 as shown in the block diagram of FIG. 1.
The laser beam focused spot 3 of an adjustable small diameter is directed
to the top surface 7 of the wire 4.
[0042] A continuously fed flat wire 4 is dispensed from a wire nozzle 5
and delivered to a substrate 6 such that the bottom of the wire flat
surface(s) is tangential to the substrate 6 top surface 9. The contact of
the wire with the substrate constitutes substantially a surface(s), thus
allowing efficient conduction of the laser beam produced stress and
thermal waves from the wire to the substrate. The flat wire surface
conforms to the surface of the substrate and provides repeatable and
reliable contact during coating process.
[0043] The laser beam 2 is simultaneously applied to the wire, with a
magnitude controlled by the GUI Module 12, to be sufficient to produce a
sudden compressive stress shock wave at the surface of the wire and a
thermal wave from the applied laser energy. The thermal wave establishes
a temperature gradient through the wire thickness and, together with the
compressive stress shock wave, propagates through the wire 4 and the top
surface 9 of the substrate 6.
[0044] The desired temperature gradient is established through the wire 4
and the top surface of the substrate 6 by controlling the laser beam-spot
3 energy and power densities as well as the pulse period. The temperature
gradient is controlled such that while the part of the top surface 7 of
the flat wire 4 is liquefied, the wire surface 8, adjacent to the
substrate 6, can be maintained in a solid or semisolid state at the
temperatures below of the temperature of liquefaction of the substrate
material. The laser power, energy and the pulse duration are controlled
by the system's computer 11, and a controller and its Graphic User
Interface module 12. The system's controller has a two-way communication
with all the modules of the system including the laser system 1 to obtain
the desired laser parameters.
[0045] With the simultaneous action of the compression wave generated by
the laser beam at the top surface 7 of the wire, some particles of the
wire are moving with the compression wave, and penetrating through their
common surface of contact into the substrate causing hydrodynamically
produced wavy interface 20 of the materials of wire and the substrate.
See FIGS. 1, 2, 3,4 and 5. The wire contact surface 8 and the substrate
top layer 9 are maintained at the temperatures below the substrate's
liquefaction temperature, thus producing a strong metallurgical bond
between the coating and substrate in a solid-state welding mode. The
calculations estimating the amount of material penetration waves 20 into
the substrate are presented in the Appendix of this application.
[0046] FIG. 5 demonstrates the applicability of this invention for
connecting two components, or repairing a crack in a single component by
means of a wire with multiple flat surfaces. The sides 21 of the
components or crack are pre-machined such that the sides 21 or connecting
surfaces have the same angles as the sides 22 of the wedged wire 4. The
momentum of particles moving with the stress-wave propagation is
distributed along the sides 22 of the wedge-shape wire 4 cross-section,
thus producing a similar wave shape protrusions 20 of wire material into
the substrate material in a solid-state mode of welding with the same
mechanism as described above.
[0047] Energy beam power and energy densities used in the present
invention, are commensurate with the wire and substrate materials, wire
thickness, and the desired amount of wave-shape morphology at the
wire-substrate interface, for example, for a titanium Ti-64 alloy wire
with thickness of .about.0.020 (0.5 mm) deposition onto an aluminum
AL-6061 alloy substrate in a solid-state welding mode, the laser beam
power density used was only 0.0785 megawatts per square centimeter with a
pulse time duration of approximately 10 milliseconds.
[0048] The bonding of the flat wire coating to the substrate is conducted
in an inert gas atmosphere, such as Argon gas, delivered with a gas flow
nozzle 10.
[0049] A wire delivery means, with the wire dispensing nozzle 5, is
continuously delivering the wire onto the substrate 6 such that the
contact of the wire with the substrate constitute substantially a
surface(s) to provide a good coupling of wire and substrate for an
effective transportation of thermal-wave and the shock-wave carrying the
wire particles into the substrate. With the present YAG laser of
300-Watts average power, the wires of 100 microns (0.004'') to 500
microns (0.020'') thick have been successfully bonded at the linear
velocities of 12 in/min (300 mm/min). Scaling up the sizes and the
deposition speeds can be achieved by utilizing higher average power
energy-source.
[0050] An opto-mechanical module 15, FIG. 1, is provided for adjusting the
laser beam spot suitable to the wire 4 width or to the desired fraction
of the wire width. In addition, a means for scanning a laser beam across
the wire width is provided in module 15 for the purposes of wire
deposition and cutting FIG. 4.
[0051] Thus, for example, a bonding of the flat titanium wire to an
aluminum substrate was achieved in a solid-state mode, i.e. with the
aluminum substrate being in a solid-state. FIG. 2 is an Electron Scanning
Microscope (ESM) image 30 of thus produced coatings 34, 36 of aluminum
6061 substrate 32 with titanium Ti-64 alloy 34 and with a subsequent
coating 36 of titanium layer 34 with nickel-based superalloy Inconel-718.
[0052] Other modules used in the present invention include but not limited
to a surface scanning and reverse engineering module 14, Graphic User
Interface (GUI) and Numerical Control Code Generating Module 12, Milling
and Grinding Finish Machining Module 16, Part Manipulation Module13 are
employed to facilitate part scanning and reverse engineering, automated
linear and rotary motion control of the component as well as the wire
delivery and optical modules, in 3-Dimensional space. The component
motion and the wire delivery modules are manipulated in X, Y, Z linear
axis and A, B, and C rotation axis about these linear axis, respectively.
The Part Manipulation Module 13 allows for a flat or 3-Dimensional
component manipulation in 3-Dimensional space pivoted about the point,
which belongs to the normal to the component's surface at the meeting
point of the laser beam spot 3 and the wire 4 with the component's
surface 9.
[0053] While the invention has been described with reference to specific
embodiments, modifications and variations of the invention may be
constructions without departing from the scope of the invention.
Appendix
[0054] The disclosed process exploits a compression stress-wave generated
in the top "skin-deep" surface of the wire due to a very fast material
expansion in a limited volume and in the initial near zero time of the
energy pulse. The maximum value of this stress can be determined from the
equation:
So=.alpha.*.DELTA.T*E; [1]
[0055] Where: [0056] .alpha.--coefficient of thermal expansion for the
wire material [0057] .DELTA.T--Temperature change during this initial
time (from room temperature to the temperature of liquefaction) [0058]
E--Modulus of Elasticity of the material
[0059] It can be seen, for example, that for a metal such as nickel alloy
with E=30.times.10.sup.6 psi, with its liquefaction temperature around
2460.degree. F. and the coefficient of thermal expansion of
7.1.times.10.sup.-6 in/in x .degree. F., the stress generated in the top
thin layer of the wire at the initial near zero time of the energy pulse
is: So=511,200 psi.
[0060] This stress, suddenly applied to the surface of the wire initially
compresses the layer adjacent to it and then transferred to the next
layer, and so on. Thus, the energy beam of area A applied to the top
surface of the wire produces a compression zone and a compression
stress-wave propagating through the wire thickness and into the substrate
with velocity C. After time t, the compressed thickness of wire is equal
to L=Ct.
[0061] The deformation .delta. of the compressed zone is:
.delta.=So.times.C.times.t/E [2]
[0062] The velocity V of the particles in the compressed zone is:
V=.delta./t=So.times.C/E or C=V.times.E/So [3]
[0063] The mass of particles moving in the wave is equal to
.rho..times.A.times.C.times.t, where A is the cross-section of the area
under the energy beam. The force on the surface of the wire is
So.times.A. Momentum and impulse equation states that the mass times
velocity is equal to force times time. Hence
.rho.33 A.times.C.times.t.times.V=So.times.A.times.t or
So=C.times..rho..times.V and So=V.times.SQRT (E.times..rho.) [4]
[0064] The force required to compress the unit length is K=AE/L, where L
is the wire thickness;
[0065] The impact force delivered by the particles moving with the
pressure stress-wave at the particles velocity V is:
F=So.times.A=V SQRT (K.times.W/g) [5]
[0066] Where W is the weight of compressed zone with moving particles and
g is a gravitational constant;
[0067] Combining equations [3] and [4] gives the compression stress-wave
front propagation velocity C=SQRT (E/.rho.)
[0068] Substitution of parameters for nickel alloy wire, gives C=200,280
in/sec or 3.2 miles/sec; and the particle front wave velocity V is
calculated to be 3,447 in/sec and the impact force imparted by the
particles moving with the stress-wave is F=1004 lbf;
[0069] The stress-wave propagation through the wire thickness and the top
layer of the substrate, both being under high temperature gradients and
changing Young's Modulus, is a complex, transient process. Nevertheless,
the above mathematical model of the process gives sufficiently good
approximation and prediction of the acting thermal and mechanical forces
involved.
[0070] For example, the deformation of the pre-selected stress-wave travel
length of 0.026 inches, the deformation of .delta.=0.0028 inches is
predicted. This is considering the material of substrate is carbon steel
and it reaches the temperature of 2100.degree. F. at the wire/substrate
interface, (below its liquefaction temperature) and having its Modulus of
Elasticity at that temperature of about 4.times.10.sup.6 psi. Thus
predicted deformation of .delta.=0.0028 inches is an approximate amount
of penetration (forged-in wave-shape interface) of the wire material
particles into the substrate material. The values thus determined
correlate closely with the test data derived from the micrographs 30 and
40. See FIG. 3, where an Inconel layer 44 is welded on a Cr42 steel
substrate 42.
[0071] FIG. 6 shows a structure 50 formed by a titanium layer 54 welded to
an aluminum tube substrate 52.
* * * * *