National Aeronautics and

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George C. Marshall Space Flight Center

Marshall Space Flight Center, Alabama

35812
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i

NASA/TM—2010–216449

Welding As Science: Applying Basic

Engineering Principles to the Discipline

A.C. Nunes, Jr.

Marshall Space Flight Center, Marshall Space Flight Center, Alabama

October 2010

National Aeronautics and

Space Administration

Marshall Space Flight Center • MSFC, Alabama 35812
ii

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076 –1320

443–757–5802

This report is also available in electronic form at

<https://www2.sti.nasa.gov>

Acknowledgments

This Technical Memorandum (TM) discusses technical issues that the author encountered as a member of the welding 

group at Marshall Space Flight Center. His usual role was that of analyst, interpreting phenomena in terms 

of physical models and attempting to ‘put things together.’ Over the years, skilled technicians solved most 

of the technical problems that emerged, without need of the author’s help. In cases where the author was involved, 

the Processes Development team of engineers and technicians (and sometimes the Materials Diagnostic team 

of the Metals Engineering Branch) planned and carried out empirical studies. A Summer Faculty program 

provided a pool of colleagues who carried out various research projects and contributed their considerable 

expertise. Occasional contractors also contributed, such as Susan Hessler of Jacobs Engineering, Science, 

and Technical Services Group/Snyder Technical Services, who performed an initial edit of this TM. 

Lately, the Intergovernmental Personnel Act has supplied the benefit of colleague Dr. Judy Schneider 

of Mississippi State University. In short, the author is indebted to a great many people 

and grateful to them all.
iii

TABLE OF CONTENTS

1. INTRODUCTION .............................................................................................................. 1

1.1 Philosophical Preface..................................................................................................... 1

1.2 Conceptual Models........................................................................................................ 1

1.3 Mathematical Models.................................................................................................... 1

1.4 Statistical Models .......................................................................................................... 2

1.5 Symbolic Logic .............................................................................................................. 2

2. PENETRATION AND LACK OF PENETRATION ........................................................ 3

2.1 Variability of Penetration ............................................................................................. 3

2.2 Monopole Heat Sources ............................................................................................... 3

2.3 Dipole Heat Sources and Phase Change ....................................................................... 4

2.4 Quadrupole Heat Sources and Weld Pool Currents ...................................................... 4

2.5 Marangoni Circulations and Penetration Variability .................................................... 5

2.6 Penetration by Plasmas and High-Power Density Beams .............................................. 5

3. A MECHANISM FOR MICROFISSURES....................................................................... 7

3.1 Transient Thermal Stresses ........................................................................................... 7

3.2 Liquid Film Embrittlement ........................................................................................... 9

4. DEFECTS OR ENIGMAS?................................................................................................ 11

4.1 What is an Enigma? ...................................................................................................... 11

4.2 Segregation Enigmas ..................................................................................................... 11

4.3 Diffraction Enigmas ...................................................................................................... 12

5. THE PLASMA TORCH THAT WOULD NOT SHIELD ................................................. 15

5.1 Porosity in Aluminum Alloy Welds ............................................................................... 15

5.2 Variable Polarity Plasma Arc Welding .......................................................................... 15

5.3 The Strength of Variable Polarity Plasma Arc Welds .................................................... 16

5.4 Shield Gas Turbulence .................................................................................................. 16

6. SPARKING AND SPATTER IN SPACE .......................................................................... 18

6.1 The Soviet Universal Hand Tool ................................................................................... 18

6.2 Arcs and Paschen Curves .............................................................................................. 19

6.3 Weld Spatter ................................................................................................................. 20
iv

TABLE OF CONTENTS (Continued)

7. WELDING WITHOUT MELTING .................................................................................. 22

7.1 The British Friction Stir Welding Process ..................................................................... 22

7.2 How Does Friction Stir Welding Work? ........................................................................ 23

7.3 A Kinematic Model of Friction Stir Welding Metal Flow ............................................ 24

7.4 Particle Interactions ...................................................................................................... 26

7.5 Torque and Drag Forces ............................................................................................... 26

7.6 Weld Defects ................................................................................................................. 27

8. CONCLUSION .................................................................................................................. 29

REFERENCES........................................................................................................................ 30
v

LIST OF FIGURES

1. A broadening temperature profile can cause central regions of a weld 

to contract while peripheral regions expand. Stresses at the juncture 

of these regions can cause microfissures in electron beam welds ................................ 8

2. Simplified model of cracking at liquated grain boundary. It occurs within 

a temperature range where tension below that causing plastic metal flow 

is sufficient to overcome surface tension forces holding the liquid layer in place. 

An embrittled liquid layer does not actually rupture until a certain amount 

of strain is imposed upon it ....................................................................................... 9

3. Filaments of segregation can be produced by a combination of solidification 

effects and pressure-induced flows of liquids in partially solidified alloys. These 

filaments are hard to observe using metallographic techniques, but can be seen 

as segregation ‘enigmas’ using radiography ................................................................ 12

4. Diffraction effects from large grains can shift a noticeable portion of the power 

of a radiographic beam by a small angle. At one edge of the diffracted image 

of the grain, the shifted power adds to the background radiation, producing 

a dark image. At the other edge, the diffracted image subtracts, producing 

a light line. These boundaries are diffraction ‘enigmas,’ sharply enough defined 

to be visible when the edge of a large grain lines up parallel to the beam direction .... 14

5. The external shape of a plasma jet nozzle makes a difference in torch 

performance. A spherical shape allows the wake separation point to move close 

enough to the shield gas surface at high flow rates for the wake turbulence 

to entrain atmospheric contamination (and lose shielding). A conical shape 

confines the turbulent wake deep within the shield gas flow, avoiding 

atmospheric entrainment even at high shield gas flows .............................................. 17

6. The Paschen curve V=V(Pd) bounds the values of voltage (V), pressure (P), 

and gap width (d) for which arcing occurs in a specific gas. To the right, electron 

collisions occur so frequently with the gas that they do not build up enough 

kinetic energy to knock out other electrons. To the left, there are too few gas 

atoms in the gap for significant multiplication of electrons ........................................ 20

7. In friction stir welding, a rotating pin stirs the sides of a weld seam together. 

A shoulder prevents the upwelling of metal around the pin, which would result 

in plowing, not welding. In conventional FSW, a large plunge force maintains 

proper shoulder contact; it is balanced by a heavy fixed anvil underneath the workpiece. In self-reacting FSW, a pinch force maintains proper shoulder contact, 

making a heavy supporting anvil unnecessary ............................................................ 23
vi

LIST OF FIGURES (Continued)

8. Plan view of trace of seam around pin during FSW in simplified two-dimensional 

flow model. An eccentricity d of the shear surface accommodates the backflow 

of metal around the pin. Metal inflow volume en route at weld speed V for a shear 

surface of unit height and radius R is 2RV. Backflow at the outer edge of a plug 

of metal rotating with the tool at angular velocity is dRΩ ......................................... 24
vii

LIST OF ACRONYMS AND SYMBOLS

ASEE American Society for Engineering Education

Cu copper

ESTS engineering, science, and technical services

FSW friction stir welding

GTA gas tungsten arc (welding)

ISWE International Space Welding Experiment

Li lithium

Mn manganese

MSU Mississippi State University

NDE nondestructive evaluation

Si silicon

SMAW shielded metal arc welding

TM Technical Memorandum

UHT Universal Hand Tool

VPPA variable polarity plasma arc (welding)
viii

NOMENCLATURE

d	 distance; gap width

Fd drag force 

k thermal conductivity

L length

M torque

P power; pressure

R radius, fixed

r radius, varying

T temperature

Tm melting temperature

To ambient temperature

V	 voltage; weld speed; velocity

v radial velocity component in friction stir welding

w thickness of plate

x	 coordinate along direction of motion

y lateral coordinate perpendicular to x-coordinate in plane of weld

Z axial penetration distance

z axial coordinate perpendicullar to x-y plane of weld

DδC	 thickness increase causing rupture in intergranular liquid film

Dt time increment

δ thickness of intergranular liquid film; additional radial thickness of friction stir welding 

rotating plug on retreating side of tool which accommodates weld metal backflow

eC critical strain causing rupture in intergranular liquid film

θ angle from direction of motion positive

μ surface tension

μd dipole heat source

μq quadrupole heat source

sF normal flow stress of weld metal

τ shear flow stress of weld metal

Ω angular velocity of friction stir welding tool

w angular velocity of friction stir welding rotating plug
1

TECHNICAL MEMORANDUM

WELDING AS SCIENCE: APPLYING BASIC ENGINEERING PRINCIPLES 

TO THE DISCIPLINE

1. INTRODUCTION

For those who know, the discipline of welding is a rich source of technically interesting

problems. For those who do not know, this Technical Memorandum (TM) describes sample problems illustrating ways in which basic engineering science has been applied to the discipline of 

welding. Perhaps inferences may be drawn regarding optimal approaches to particular welding 

problems, as well as for the optimal education of welding engineers. Perhaps also some readers may 

be attracted to the science(s) of welding and may make worthwhile contributions to the discipline.

1.1 Philosophical Preface

Arguably, the normal mode of welding evolution is by cut-and-try methods at the level 

of the welding technician. ‘All men by nature desire to know,’ but the world is not likely to provide funding unless the potential exists for a commercial payoff. However, technicians sometimes 

encounter problems that they are unable to solve. Sometimes, too, a broader perspective is wanted 

to help give direction to the developmental process; then, scientific methodology may be called 

upon for assistance. ‘Science’ entails a clear idea of the way in which the process works with implications as to how to achieve the desired results; i.e., understanding the situation. An appropriate 

approach is required to achieve understanding, and it is not always obvious either.

1.2 Conceptual Models

Conceptual models—essentially visualizations—may be considered intrinsic to an understanding of any process. Conceptual modeling is an old faculty that is shared in greater or lesser 

degree with other sentient animals, primed through education in a variety of technical specializations, and facilitated through general education in language, which includes visual, auditory, and 

tactile perceptions. But understanding cannot be forced. Problems are ingested and then what will 

emerge emerges. Given an adequate level of mental composure and a healthy physical constitution, 

advance preparation is the crux of the ability to solve problems and is critical. Technical breadth 

is important; overspecialization may prematurely fix on an unfruitful approach.

1.3 Mathematical Models

Mathematical models may be useful per se or merely as a means to select among alternate 

conceptual models. Models may be classified by how much mathematical apparatus or abstraction 
2

exists between the model implementation and a simple visualization. The geometrical mechanics of Newton’s Principia (1687)1 is a more visually direct approach to mechanics than Lagrange’s 

Méchanique analytique (1788)2 in which the potential (a new mathematical apparatus invented by 

Lagrange) plays a major role in mechanical modeling. Since then, potentials have become so popular that they have become fundamental constituents of our models of the world (as energy, entropy, 

temperature, etc.) and their construct nature tends to be forgotten.

The popular finite element models incorporate so much mathematical apparatus between 

starting assumptions and predicted system behavior that one is likely to have to remodel the finite 

element model in terms of a less elaborate model in order to understand it. Finite element models 

may present extremely detailed information, but modeling errors may produce deceptive artifacts. 

In the author’s opinion, finite element analyses are best used for detailed representations of well 

understood systems while, for exploratory studies, it is best to begin with an assemblage of the 

simplest possible modeling elements that might represent the target system.

1.4 Statistical Models

Statistical models are perhaps best used as clues for constructing conceptual models. Statistical models per se do not provide understanding as do conceptual models. Statistical models 

depend upon often unconscious—and never guaranteed—global assumptions about the systems 

being analyzed; conclusions are in terms of odds for particular outcomes dependent upon the 

global assumptions. Statistics can deceive if one is not very clear on what has been assumed and 

what the statistical conclusion really means.

In the course of a study of microfissuring in electron beam welds, the author encountered 

a statistical study that asserted suppression of microfissuring by manganese (Mn) in excess of 

0.2% and silicon (Si) in excess of 0.25%.3 A second study asserted promotion of microfissuring by 

Mn and Si in excess of 0.15%.4 These apparently contradictory yet statistically based conclusions 

impressed the author with a skeptical attitude regarding statistics.

1.5 Symbolic Logic

Symbolic logic can be useful on occasion. The author can recall an instance where a truth 

table helped sort out the implications of a complex set of observations. A predilection for philosophy and its tools for thinking is an asset for weld analysis. The business of philosophers is to make 

things clear.

It may be added that an overly reverential attitude toward prior ideas may be an obstacle 

to a correct understanding of a phenomenon of interest. The analyst needs the confidence engendered by fluency in his/her disciplines, fluency such as a teacher acquires. A background in the historical development of science and technology in general (and the subject technology in particular) 

also imparts confidence, as well as the occasional good idea. However, confidence is not incompatible with humility, and falling in love with one’s theoretical constructions can lead to theoretical 

catastrophe.
3

2. PENETRATION AND LACK OF PENETRATION

The usual image evoked by the word ‘welding’ is probably a little pool of molten metal 

beneath a dazzling electric arc, being coaxed along a metal seam by a helmeted welder peering out 

through a very dark glass. The molten metal solidifies behind the weld pool to the depth penetrated 

by the pool, leaving solid metal in place of an open seam. The seam—or part of it—is now welded.

If the weld does not penetrate the seam completely but instead leaves a bit of seam 

unwelded, a weld defect known as ‘lack of penetration’ has been made. Lack of penetration can 

cause a large reduction in the strength of a weld. In critical welded structures, where a failed weld 

could mean loss of life, it is likely that welds will be checked by a nondestructive evaluation (NDE) 

procedure, such as x-ray radiography. In radiography, the weld is placed between a source of 

x rays and a detector (say, x-ray film) and an image of the weld is examined on the detector. Lack 

of penetration reveals itself as a dark line down the center of the weld. If present, lack of penetration may be ground out and the location rewelded.

2.1 Variability of Penetration

But why should all this be necessary? How hard should it be to precisely control penetration? Suppose the arc is produced by a torch that is mounted on a mechanical drive and all the 

welding parameters are fixed; e.g., electrode standoff distance from the workpiece, electric current, 

torch speed, shield-gas flow rate, electrode tip shape, etc. for, say, the gas-shielded, nonconsumable 

tungsten electrode process known as gas tungsten arc (GTA) welding. Even so, weld penetration 

is so sensitive to slight within-specification variations in alloy composition that a compositiondependent range of depths from 100% to 70% penetration have been observed in mechanized, 

constant parameter welds in type 304 stainless steel.5 Heat sinks in the vicinity of the weld can 

also have a noticeable effect. The author has observed a 69% partial penetration GTA weld in an 

aluminum alloy reduced to approximately 65% upon being clamped in a fixture and, upon passing 

close to a hold-down clamp, to approximately 47%.6 Even a precision mechanized GTA welding 

apparatus needs to be manned by an experienced welder who can adjust the welding parameters to 

produce the desired level of penetration.

2.2 Monopole Heat Sources

What determines penetration? Why should it be sensitive to weld metal composition? Imagine a heat source of power 2P in an infinite metal continuum of thermal conductivity (k); the 

source raises the temperature (T) in its vicinity until the thermal gradient is able to conduct the heat 

away, after which the local temperature becomes fixed. There being no preferred radial direction in 

an infinite continuum, the isotherms are spheres surrounding the point heat source. For conduction 

of heat through the spherical surface at radius (r),
4

2P = −k dT

dr

⎛

⎝

⎜ ⎞

⎠

⎟ 4πr

2 . (1)

The spherical symmetry ensures that no heat is transferred circumferentially, so the same 

differential applies to a half continuum with a heat source of power (P) on its surface dissipated 

through area 2πr2. Integration of equation (1) from very large radii, where the temperature is the 

ambient temperature To to the edge of the molten pool at radius (R) and melting temperature (Tm) 

yields a rudimentary estimate of penetration for a slow-moving weld on a large block of metal:

R = P

2πk Tm −T ( o ) . (2)

A corresponding solution exists for a faster moving weld, but the weld pool is distorted 

along the direction of movement and is no longer spherical.7 An infinite array of heat sources 

placed 2w apart have planes of symmetry across which there is no transfer of heat, one kind of 

plane containing a heat source, the other not containing a heat source. The temperature distribution in the space between two dissimilar planes represents that in a plate of thickness (w). A threedimensional array of point sources can be used to represent the temperature distribution in a block 

of metal bounded on all six sides.

2.3 Dipole Heat Sources and Phase Change

But there is more. As the weld moves forward, energy is absorbed in melting metal at the 

front of the pool and recovered at the rear of the pool as metal solidifies and gives off its latent 

heat of melting. This phase change effect on temperature may be very simply approximated by 

adding a dipole heat source (μd):

T −T ( o )dipole = −limΔx→0

ΔxΔP→μd

∂

∂x

ΔP

2πkr

⎛

⎝

⎜ ⎞

⎠

⎟ Δx = μd

2πkr

2

x

r . (3)

x is the coordinate along the direction of motion while r = x

2 + y2 + z2 is the radial coordinate. 

The dipole comprises a pair of equal and opposite heat sources of power (DP) separated by distance (Dx). As Dx approaches zero, the strength of the dipole DxDP approaches μd.

2.4 Quadrupole Heat Sources and Weld Pool Currents

Of greater interest for present purposes is a surface tension effect on the temperature field 

that can be most simply approximated by a quadrupole field constructed of pairs of equal and 

opposite dipoles:

T −To ( )quadrupole = −limΔx→0

ΔxΔμd →μq

∂

∂x

Δμd

2πkr

2

x

r

⎛

⎝

⎜ ⎞

⎠

⎟ Δx − limΔy→0

ΔyΔμd →μq

∂

∂y

Δμd

2πkr

2

y

r

⎛

⎝

⎜ ⎞

⎠

⎟ Δy

= μq

2πkr

3 1− 3 z

2

r

2

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟ . (4)
5

Ignoring dipole effects and taking the maximum penetration to occur along the z-axis by 

symmetry, penetration Z comprises the solution to

Z3 − P

2πk Tm −T ( o)

Z2+

μq

πk Tm −T ( o)

= 0 . (5)

By differentiation,

dZ

dμq

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

μq =0

≈ − 2

PZ . (6)

2.5 Marangoni Circulations and Penetration Variability

Increased surface temperature tends to reduce surface tension. The center of the weld 

pool—where the arc impinges and the heat source is strongest—tends to have a lower surface tension. The resultant surface tension imbalance on the pool surface induces a flow of molten metal 

from the pool center out to the pool edge. Heat is transferred to the outer edge of the pool by 

convection (positive μq), penetration is reduced, and the pool takes on a wide shallow shape.

Pool surface contamination also tends to reduce surface tension, but contamination is often 

driven off by heat. If the contamination effect dominates, close to the center of the pool surface, 

the surface tension is raised. Molten metal is induced to flow toward the pool center and down into 

the depths of the pool. Heat is transferred to the depths of the pool and the pool takes on a narrow 

deep shape.

Large variations in penetration due to small variations in alloy composition were explained 

in 1982 by Heiple and Roper,8 researchers at Rockwell International, as caused by surface tension 

gradient-driven currents in the weld pool called Marangoni9 circulations. Pool circulations can also 

be driven by other factors, such as electromagnetic induction or gravitational circulation, but the 

Marangoni circulations generally dominate. Hence, obviously different penetration levels in fusion 

welding experiments may not be an occasion for drawing conclusions, unless one accounts for the 

Marangoni circulation effect, and not just in GTA welding. 

2.6 Penetration by Plasmas and High-Power Density Beams

High-power density electron and laser beams ride up on the forward surface of a vapor 

cavity. The higher the angle of the forward surface, the greater the area exposed to the beam. The 

angle increases until the area is sufficient to dissipate the beam power through phase changes (e.g., 

melting, evaporation) and conduction into the metal; this determines the penetration of the beam. 

Marangoni forces induce the flow of molten metal to the cooler surfaces behind the beam, where 

it solidifies and welds the seam together. Faster extraction of molten metal from under the beam 

removes heat faster and may be expected to reduce penetration and vice versa.
6

This brief discussion suggests a penetration mechanism that may be sensitive to the power 

distribution over the cross sections of high-power density beams, which is indeed the case. A slight 

change in focus of an electron beam may cause a large change in penetration. Laser beams sometimes have irregular cross-sectional power distributions (modal patterns) at higher power levels. 

These irregularities cause welding problems.
7

3. A MECHANISM FOR MICROFISSURES

Electron beams can concentrate power so densely that when they strike a metal surface, the 

strike area is not adequate to dissipate the beam energy at temperatures where the metal can remain 

solid or even liquid. Under a welding electron beam, a metal surface evaporates to form a cavity. 

The cavity wall makes a steep angle with the beam, and the area under the beam enlarges to a point 

where the power in the beam can be dissipated at endurable temperatures. A beam moving forward 

along a metal seam rides up on the forward surface of the vapor cavity, where it melts the metal. 

The molten metal flows back around the beam, pulled by increased surface tension to the cooler 

region beside and behind the arc, where it solidifies, leaving a welded seam. Electron beam welds 

are very narrow and minimize heat damage to the environment. They are made in a vacuum chamber because, outside of very unusual circumstances, the beam will not penetrate air. The vacuum 

also minimizes risk of contamination from atmospheric constituents. Thus, electron beam welding 

tends to produce very high-quality welds.

However, electron beam welds have their share of defects also. For example, they can exhibit 

tiny cracks called microfissures at the edges of the weld, particularly in the region where the nailhead (a broad melted region at the top of the weld) joins the spike (a narrow melted region closely 

following the vapor cavity of the beam). How might they be eliminated? 

Metallurgists, observing that microfissures followed grain boundaries, hypothesized a culprit 

trace constituent that would promote grain boundary melting. Perhaps the presence of potential 

scavengers, Mn and Si, would exhibit a beneficial effect on microfissuring? But as noted above,3,4

this approach was unsuccessful. 

3.1 Transient Thermal Stresses

Technicians thought that microfissuring tended to occur at higher weld speeds. Indeed, 

microfissuring was not observed in the slower arc welds, which suggested that thermal gradients 

and gradient-related stresses might be a culprit. Further, the crack surfaces were roughly parallel 

to the weld metal surface, as if opened up by stresses perpendicular to the surface. These data and 

conjectures suggested a thermal stress model of microfissuring. See figure 1.

It was supposed that the temperature field broadens just behind the beam. The weld begins 

to cool down at the centerline and heat up away from the centerline. Perpendicular to the plate, the 

outer metal expands and tends to pull apart the inner metal, which is contracting. (In the plane of 

the plate, the expanding environment compensates for the contracting inner metal and may even 

compress it.) If the inner metal is still hot and not completely solidified, grain boundary liquefaction may embrittle the metal, so that it cracks instead of deforming plastically under the deformation forced by differential thermal expansion.
8

Initial

Temperature

Profile

Subsequent

Temperature

Profile

Microfissures

Electron Beam

Weld

Thermal Contraction With

Falling Temperature

Thermal Expansion With

Rising Temperature

Figure 1. A broadening temperature profile can cause central regions of a weld 

to contract while peripheral regions expand. Stresses at the juncture 

of these regions can cause microfissures in electron beam welds.

This model was implemented mathematically. The weld temperature field was approximated 

by a moving line heat source for the spike and a moving point source for the nailhead.7 The weld 

temperature field first subjects a thin column of metal adjacent to the weld to a thermal expansion as it heats up and then to a thermal contraction as it begins to cool. Beyond the column the 

environment continues to heat up and expand for a bit as the column cools, and, during this time 

interval, since the column is attached to the environment, the column is forcibly expanded in a succession of plastic strain increments. These plastic strain increments were calculated approximately. 

The critical strain necessary to cause cracking at a given temperature was determined by observing 

the strain required to crack the surface of hot tensile specimens at various temperatures. By comparing the computed strains with the critical cracking strains through a ‘damage’ computation it 

was possible to estimate not only whether a given set of weld parameters would cause microfissuring, but at what weld depth the microfissures would be located.

This crude model worked surprisingly well. Weld parameters such as speed, power, type of 

process (i.e., electron beam or arc or plasma) were introduced into the model through the temperature profile, and predictions emerged as a computed damage curve through the thickness of the 

plate. The model showed that microfissures would form in high-speed electron beam welds (but not 

low-speed arc welds, with reduced transient thermal stresses) at the junction between the spike and 

the nailhead. Its predictions corresponded well with observed phenomena.

This understanding suggests two methods other than weld parameter adjustment that 

might be used to eliminate microfissuring: (1) a roller to compress the metal behind the beam and 

(2) rastering of the beam to reduce transient thermal stresses. However, both would require further 
9

development and, as far as the author is aware, neither has yet been successfully introduced into 

welding practice.

3.2 Liquid Film Embrittlement

Although the original software predicting microfissuring is no longer readable by contemporary computers, equivalent (and doubtless better) software can be constructed based upon the 

information given here. One thing that the author would do differently today is to try to interpret 

observations of critical cracking strain in terms of a mechanical model. Suppose that microfissures 

are a result of the rupture of a thin melted film at a grain boundary. See figure 2. A liquid film of 

thickness (d) and surface tension (μ) becomes unstable and begins to ‘unzip’ when subjected to 

tensile stress:

σ = 2μ

δ . (7)

This can only happen if the plastic flow stress σF of the weld metal is greater than the stress to 

rupture a grain boundary. Hence, the temperature range in which microfissuring can occur would 

be determined by

2μ(T )

δ (T ) < σ F (T ) . (8)

The temperature (T) dependencies indicated in inequality (8) are not well known and 

depend upon the state of microsegregation of the alloy. Interpretations are feasible, but probably 

not computations from first principles. Within the embrittled range, the liquid in an originally 

liquid-filled boundary of length (L) and width (d) ruptures when extended to width δ +∆δC where

ΔδC ≈ Lδ

1− π

4

⎛

⎝

⎜ ⎞

⎠

⎟

− L . (9)

If the grain size and the separation between cracks is ~2L, then an upper bound for the 

critical strain for forming microfissures εC is

εC  ΔδC

2L  1

2

1

1− π

4

⎛

⎝

⎜ ⎞

⎠

⎟

δ

L − 1

⎡

⎣

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

. (10)

Appropriate values of εC may be appreciably smaller if the liquid layer does not completely 

rupture, but solidifies while only partially separated.

Liquation cracking is very common, so detailed studies of the underlying mechanism could 

be useful. Unfortunately the author is unaware of any such studies.
10

2L

σ

σ

δ

μ

μ

L

Initial

Fluid

Fluid at 

Rupture

δ δ +∆

Figure 2. Simplified model of cracking at liquated grain boundary. It occurs within 

a temperature range where tension below that causing plastic metal flow 

is sufficient to overcome surface tension forces holding the liquid layer in place. 

An embrittled liquid layer does not actually rupture until a certain amount 

of strain is imposed upon it.
11

4. DEFECTS OR ENIGMAS?

Critical welds that cannot be allowed to fail are inspected using NDE methods such as 

radiography, in which a weld is placed between a source of x rays and x-ray sensitive film. X rays 

darken film. Hollow spaces in the weld (e.g., porosity or cracks) let through more x rays and produce darker areas on the film. Such radiographs can provide a trained radiographer with a good 

idea of the soundness of a weld and the kind of defects present, if any.

4.1 What is an Enigma?

But what is to be made of a line—usually dark, but sometimes light or mixed light and 

dark—appearing along the edge of a weld without any apparent cause to be seen when the weld 

is cut open? Such apparently uncaused radiographic indications are well known to welders as 

‘enigmas.’

Space vehicles, in large part, consist of light metal tanks typically fabricated from aluminum 

alloys. These tanks contain critical welds that are radiographed and, upon the introduction of 

a new plasma welding process, many ‘straightline enigmas’ began to appear in the welds. A proposal was made to intentionally create a number of these enigmas for testing, in order to determine 

whether the defective welds would have to be ground out and rewelded—an expensive undertaking 

at best. But nobody knew how to make the enigmas.

4.2 Segregation Enigmas

An embarrassingly long and fruitless series of trial-and-error attempts to find out what 

might cause ‘straightline enigmas’ ensued. Then a revelation occurred. It came in the form of 

a radiograph of a slice of the first-pass weld bead not yet covered by a second-pass cover bead. 

In figure 3, the key features of the radiograph are sketched. Sometimes structural features reduce 

to the imperceptible on the two dimensions presented by a polished and etched surface, but add 

up to a visible presence over the third-dimensional length increment of a radiograph.

The crown of the weld pass had a hump in the center and troughs running along the edges 

of the weld. It is common knowledge among welding engineers that the expanding temperature 

profile in the wake of a weld causes thermal expansion of the metal outside the weld, which can 

give a squeeze to the weld even though the weld itself is cooling and shrinking. The radiograph 

showed a thin light line on the bottom of the troughs, with a complementary dark area below the 

troughs. Clearly, the thin light line was extruded copper- (Cu-) rich metal, the Cu-rich still-molten 

constituent of not-quite solidified aluminum-Cu alloy being squeezed by the plate edges. The dark 

area was the Cu-poor volume, which had supplied the Cu-rich extrusion metal.

When the welders ran a tapered cover pass over the initial pass, they found that the deep end 

of the pass (higher power) entirely dispersed the segregate and no enigma resulted. The shallow end 
12

of the pass uncovered the bottom of the troughs and produced a genuine defect. But in the middle 

between the deep and the shallow ends, the thin residual undispersed filament of segregate (usually 

Cu-poor) produced the observed (usually dark) enigma. 

Their nature discovered, production began that day on a batch of enigmas for testing. In the 

end, ultrasonic testing was required to distinguish them from exposed troughs, but it was no longer 

considered necessary to grind out and replace the weld metal that produced these enigmas.

Enriched Area

Cover Pass

Initial Pass Depleted Area

Segregation Enigma

Figure 3. Filaments of segregation can be produced by a combination of solidification 

effects and pressure-induced flows of liquids in partially solidified alloys. These 

filaments are hard to observe using metallographic techniques, but can be seen 

as segregation ‘enigmas’ using radiography.

4.3 Diffraction Enigmas

A second kind of enigma is caused not by segregation but by diffraction effects. In one 

instance, dark lines seen on radiographs of an Inconel 718 duct weld were alleged to be harmless 

enigmas, not requiring action, by a welding contractor. In response, a study was undertaken to 

produce and observe enigmas and to determine characteristic features by which diffraction enigmas 

could be clearly identified.10
13

When a collimated polychromatic x-ray beam impinges upon a single crystal, x rays 

scattered in certain directions are in phase and add up to produce strong reflected beams. On 

a detecting surface, the strong reflections produce patterns of spots called Laue patterns, which 

are typically used to determine the orientation of single crystals. The reflection angles depend 

upon both crystal structure and orientation. The Laue spots are images of the diffracted beam, 

the cross section of which is made small for precise spot location.

Slower weld speeds with rounded (not teardrop-shaped) weld puddles tend to promote 

the formation of large grains running down the center of the weld. The very broad polychromatic 

radiographic beam encompasses the entire working area including the grains and, in addition to 

the transmitted beam image, may produce other shifted images of the grain equivalent to Laue 

spots. If the grain edges are aligned to give sharp boundary images and if the intensity is sufficient, 

the boundary becomes visible as shown in figure 4. The shifted image reduces the x-ray intensity 

where it vacates boundary and increases the intensity over the boundary where it is superimposed. 

Thus, the grain is outlined in dark on one side and in light on the other. These lines are ‘diffraction enigmas.’ Only one side need be sharp enough to be visible. Dark lines—suggesting a possible 

lack of penetration or a crack—are more ominous than light lines and are the chief concern of an 

inspector.
14

Large Single Crystal

Orientation

Diffraction Enigma

Diffraction Image

Figure 4. Diffraction effects from large grains can shift a noticeable portion of the power 

of a radiographic beam by a small angle. At one edge of the diffracted image 

of the grain, the shifted power adds to the background radiation, producing 

a dark image. At the other edge, the diffracted image subtracts, producing 

a light line. These boundaries are diffraction ‘enigmas,’ sharply enough defined 

to be visible when the edge of a large grain lines up parallel to the beam direction.
15

5. THE PLASMA TORCH THAT WOULD NOT SHIELD

5.1 Porosity in Aluminum Alloy Welds

Hydrogen can easily dissolve in the molten aluminum alloy of a weld pool after being 

liberated from small amounts of moisture or grease decomposed by an electric arc. The molten 

metal can dissolve more hydrogen than can the solidified metal. The excess hydrogen dissolved in 

the liquid tends to precipitate out as porosity upon solidification of aluminum alloy welds. The 

GTA process used to fabricate space vehicle tanks— despite stringent cleaning procedures, solvent 

wipedown, scraping, and white gloves—generates enough porosity that must be ground out and 

rewelded to be of economic concern.

5.2 Variable Polarity Plasma Arc Welding

Plasma arc welding can improve the situation. In this process, a ‘plasma gas’ is heated by 

an internal arc and then emerges through a water-cooled nozzle as a plasma jet, like the output of 

a little rocket engine. The stagnation pressure of the plasma jet is high enough so that it can penetrate to the bottom of the molten weld metal and melt more metal until it emerges out of the root 

of the weld in a little tongue of flame in what is called the ‘keyhole’ mode of welding. In the keyhole mode of welding, porosity-causing gaseous impurities tended to be entrained in the plasma. 

The welders claimed it was hard to make porosity in the keyhole mode.

However, the powerful affinity for oxygen of aluminum alloys presents a problem for plasma 

arc welding. The metal flowing back behind the plasma jet in its keyhole can easily be covered in 

a thin oxide layer with a quality like plastic film wrap, producing a trail of barely attached metal 

lumps in place of the desired weld. The remedy is to clean the surface of oxide using ‘reverse polarity,’ which is electrode positive and workpiece negative. A high-speed movie of the workpiece surface during reverse polarity operation GTA welding exhibits a field of sparkling mini-explosions. 

Apparently the mechanism by which cleaning takes place is by the explosive dielectric breakdown 

of oxide charged by the positive ions flowing from the plasma onto the oxide surface with an 

induced negative countercharge on the metal side, and not by sputtering, as has sometimes been 

asserted.11

A problem still exists with reverse polarity. The current is carried by slower moving heavy 

positive ions, which transfer less heat to the workpiece, while the lighter, faster electrons transfer 

a larger amount of heat to the electrode of the plasma torch. This reduces the usable welding 

power. Apparently, circuitry to vary the polarity was originally introduced by B.P. VanCleave, 

Boeing Co., starting in the late 1960s, creating the variable polarity plasma arc (VPPA) process, 

with its characteristic buzzing noise as the polarity is reversed. Investigations began at Marshall 

Space Flight Center (MSFC) with a commercial Hobart VPPA welding machine in 1979.12
16

5.3 The Strength of Variable Polarity Plasma Arc Welds

Welds made by the new VPPA process had a slightly lower tensile strength than GTA welds, 

although nowhere near enough to overcome its advantage over the GTA process. This was thought 

to be due to a more perpendicular orientation of the VPPA weld boundary to the tensile testing 

force axis, but there was a competing theory of ‘multiple pass strengthening’ that seized on a second difference between VPPA and GTA welds; VPPA welds were made with substantially fewer 

passes than GTA welds. As the strengths of both VPPA and GTA welds were very well documented empirically, it was not considered necessary to incur the expense of pursuing the cause 

of this difference.

Any attempt to understand the strength of welds must, of course, treat welds holistically. 

It will not do to merely consider the parts. The reader will recall that the strength of a brazed joint 

is in no way dictated by the strength of the braze metal. Brazed joints are generally much stronger 

than braze metal, a feature of the joint structure. The Soviets were long active in weld studies, 

and a simple ‘soft-interlayer’ model13 applicable to aluminum alloy welds was developed by 

O.A. Bakshi et al. at Chelyabinsk Polytechnic Institute in the early 1960s.

5.4 Shield Gas Turbulence

It is consonant with our portrayal of welding as a highly multidisciplinary endeavor to 

conclude the treatment of VPPA welding by using this approach to solve a mystery. Welding engineers at MSFC redesigned the VPPA welding torch so as to eliminate water coolant joints and, 

in so doing, to eliminate chances for leakage problems. The redesigned torch worked very well up 

to a point, but the inert gas shielding failed (and the weld metal began to oxidize) at higher shield 

gas flow rates. Technicians adjusted the torch but could not make it work. What could be wrong? 

Of course, it was obvious to someone with a background in fluid mechanics. The designers had 

changed the exterior shape of the plasma nozzle (from which the shield gas flows in the interior of 

the shield gas cup) from conical to spherical. As shown in figure 5, the new exterior of the plasma 

nozzle allowed the shield gas separation point and the associated turbulent wake to move far 

enough out into the shield gas at high shield gas flow rates to reach the gas/atmoshere interface, 

where the turbulence began to entrain air and mix it into the shield gas. After obervation of torch 

gas flow by spark photography to confirm the hypothesis, the nozzle exterior was put back the way 

it was and the problem disappeared.
17

Shield Gas

Shield Gas

Wake Separation Point Plasma Jet

Wake Turbulence Confined Within Shield Gas Surface

Wake Turbulence Reaches Shield Gas Surface and Entrains Air

Figure 5. The external shape of a plasma jet nozzle makes a difference in torch performance. 

A spherical shape allows the wake separation point to move close enough to the 

shield gas surface at high flow rates for the wake turbulence to entrain atmospheric 

contamination (and lose shielding). A conical shape confines the turbulent wake 

deep within the shield gas flow, avoiding atmospheric entrainment even at high 

shield gas flows.
18

6. SPARKING AND SPATTER IN SPACE

Welded joints are inherently lightweight and gas tight. A safe and easy-to-use welding 

process could be very handy for making repairs in space or fabricating large structures from parts 

small enough to be carried up in practical-sized space vehicles.

6.1 The Soviet Universal Hand Tool

Although some electron beam welding experiments were carried out on Skylab (launched 

in 1973), the development of space welding was pioneered by the Paton Electric Welding Institute 

at Kiev, initially under the Soviets and later the Ukrainians. In October 1969, the Soviets made 

the first space welds with their ‘Vulkan’ automatic welding unit in a depressurized bay on the spacecraft Soyuz-6. It could operate in three modes—electron beam, low-pressure confined plasma, and 

consumable electrode. In July 1984, Svetlana Savitskaya and Vladimir Dzhanibekov carried out 

extravehicular trials of a hand-held electron beam Уинверсальный Ручной Инструмент on space 

station Salyut-7. NASA now refers to this instrument as the Universal Hand Tool (UHT).

The UHT emits an 8-kV beam that is defocused to avoid the deep penetration of a vapor 

cavity, which would make the welding process too sensitive to control by hand. The process takes 

advantage of the vacuum of space, necessary for the passage of an electron beam. The UHT is 

designed to cut and spray metal as well as to weld, this versatility being the occasion of the name 

‘universal.’ A current advanced version, the product of a series of improving modifications, is available from the Paton Electric Welding Institute.

A workshop on space welding was held in 1989.14 The International Space Welding Experiment (ISWE) was planned as a joint venture between NASA and the Paton Welding Institute, in 

which the UHT was scheduled to be tested aboard the space shuttle in 1997. Due to a scheduling 

problem caused by time lost when a hatch failed to open on a previous flight, ISWE was never 

flown, but a large part of the 1990s was spent preparing for it. The emphasis was on safety issues, 

and the welding group had to defend the safety of ISWE before a Safety Board. 

“Would the 8-kilovolt beam puncture a space suit?” asked the Board. Swatches of a ceramic 

cloth intended as part of a protective garment for space welding were exposed to the 8-kV beam at 

various distances.15 The expectation was that the electrons would rapidly coat the insulating fabric 

until the voltage would be sufficient to repel further incursions of electrons and that nothing further would happen. Instead, the beam sometimes did shoot holes in the fabric, with an accompanying flash, but only sometimes and after a substantial delay. Delay time depended upon standoff 

distance from the fabric. Minimum delay time of 6 to 8 s resulted from standoff distances of 0.5 to 

2 ft. Longer and shorter standoff distances both yielded longer and longer delays. At 2 in, delays 

around 30 s were observed; at 4 ft, no burn-throughs were observed.
19

6.2 Arcs and Paschen Curves

After some thought and computation, the interpretation was that a fraction of the beam 

power was transmitted to the negative-charged fabric by positive ions generated by collisions 

between electrons in the beam and gas contaminant atoms in the less-than-perfect vacuum in which 

the experiment was performed. The flash was an indication of arcing in an atmosphere emitted 

from the fabric heated by the positive ion beam. In space, arcing is a very real hazard, not just in 

welding, but anywhere electric power is transmitted or where static electricity may accumulate.

An arc comprises an avalanche of electrons. When electrons are accelerated by an electric 

field to energies high enough to knock still more electrons out of ambient gas atoms, an avalanche 

of electrons is produced. An arc can absorb a great deal of energy from an electric field and impart 

it to an anode. Arcing will not occur if the gas is so dense that, between collisions, the electric field 

is inadequate to impart enough energy to an electron to knock further electrons out of an ambient gas atom. Arcing will not occur if the gas is so rarified that an electron emitted at a cathode 

(perhaps knocked out by a passing photon) reaches an anode before colliding with any ambient gas 

atom. Arcing will not occur, regardless of pressure, if the voltage is insufficient to impart enough 

energy to produce ionization over the entire gap between cathode and anode. Given a voltage difference (V) between two metal surfaces separated by distance (d), the electric field in the gap is

V

d . (11)

At a given electric field, arcing can occur over a range of pressures bounded by a curve: 

V

d = f(P) (12)

or, more commonly,

V = f (Pd ) . (13)

Equation (13) is called a Paschen curve, named after the German physicist L.K.H.F. Paschen 

(1865–1947). See figure 6. It applies for a specific gas and a flat Cu electrode configuration.

Under normal atmospheric conditions, points (V, P, d) are far to the right. To ‘strike an 

arc’ in the most commonly used welding process, shielded metal arc welding (SMAW), where the 

electrode is consumed to become part of the weld and the coating of the electrode decomposes to 

shield the hot weld metal from the atmosphere, the electrode is touched to the surface of the workpiece and d is reduced enough to induce arcing conditions. If a vacuum is pulled on an operating 

plasma torch, the arc jet retreats inside the torch and incinerates the torch. Under the high vacuum 

conditions of space, points (V, P, d) are to the left. A bit of gas leakage can induce arcing. Longer 

arc paths may be favored over shorter ones.
20

Gap

d

V

Paschen Curve

V=V(Pd)

Conditions Permitting Arcing

Figure 6. The Paschen curve V=V(Pd) bounds the values of voltage (V), pressure (P), 

and gap width (d) for which arcing occurs in a specific gas. To the right, electron 

collisions occur so frequently with the gas that they do not build up enough 

kinetic energy to knock out other electrons. To the left, there are too few gas 

atoms in the gap for significant multiplication of electrons.

First efforts at producing a ‘hollow cathode’ low-voltage alternative to a high-voltage electron beam welder turned out to be rather prone to arcing. A hollow cathode welder uses a trickle of 

low-pressure inert gas over the cathode to enable a powerful low-voltage discharge. Whoever recalls 

vacuum tube electronic technology will recall that to get a substantial current discharge in a vacuum tube requires a high voltage due to an inhibiting space-charge buildup at the cathode surface. 

On the other hand, gas-filled power tubes can pass large currents at low voltage by neutralizing the 

space charge. Hollow cathode arcing presumably occurred at local pressure concentrations due to 

minute gas leaks. When due care is taken to control leaks, hollow cathode welders are quite feasible.

So how dangerous is the electron beam itself? First, it is difficult to see how the beam could 

be held steady for a dwell time sufficient to provoke arcing by accident, even under the low vacuum 

chamber conditions. Merely sweeping the beam across fabric would hardly be sufficient. Second, 

the vacuum in the test chamber being appreciably lower than that anticipated in space, the arcing 

tendency in space should be much less.

6.3 Weld Spatter

“Could weld spatter damage a spacesuit?” the Board wanted to know. Teflon-coated spacesuit outer covering fabric exposed to liquid metal droplets of various size were seen to produce 

a vapor that repelled the liquid metal. Unless the metal was trapped against the fabric, gradual 

deterioration would be anticipated rather than catastrophic damage. Nevertheless, could weld 

spatter be eliminated?
21

Weld spatter comprises tiny pieces of molten metal hurled away from the molten weld puddle when gas bubbles emerge at the metal surface. When a bubble breaks the surface, the surface 

tension of the depression left in the molten metal surface acts like the stretched bands of a slingshot, accelerating surrounding molten metal and causing it to rise above the molten surface. Spatter 

is the expelled metal droplets that detach and shoot away from the surface. It is limited by the size 

of the bubbles. Because vigorous evaporation cooling sets in at superheats substantially above melting, temperatures for the weld pool and the point at which spatter droplets are emitted are close to 

the melting temperature of the weld metal.

If, by careful control of cleanliness and diligent prior outgassing of weld materials, gas 

porosity with its attendant spatter is eliminated, a second possible source of weld spatter exists—

a sudden exposure of already hot metal to the full force of a high-energy density heat source like 

an electron beam. This is reminiscent of the sudden, violent evaporation of superheated liquid, 

which sometimes occurs in liquids heated in a microwave oven, and, as in the case of coffee in a 

microwave oven, it is avoided by careful user technique. The author recalls how a sudden retraction 

of focal point of an electron beam left a crater in the crown of a weld bead. But the electron beam 

of the UHT is defocused. It is anticipated that education in the avoidance of this kind of spatter 

would normally be included in preflight astronaut training.

All these potential hazards derive from arcs and molten metals. Recently, a type of solidstate welding has become popular that eliminates arcs and molten metals—the friction stir weld 

(FSW) process. Currently, large forces are needed to wield this tool, but research is under way to 

determine whether this process can be adapted for space welding.
22

7. WELDING WITHOUT MELTING

Unanticipated welding problems emerged when new lighter, stiffer, stronger alloys (made 

by adding lithium (Li) to aluminum) came into use for space vehicle tanks. Speaking very broadly, 

‘more highly alloyed’ metals tend to be harder due to more obstacles to dislocation motion, but 

have a tendency to grain boundary melting at temperatures close to melting due to segregation 

of alloying elements to grain boundaries. This can mean a tendency to grain boundary liquation 

cracking at high temperature, which can cause welding problems. In addition, Li compounds are 

known for capability to store and release hydrogen, and the alloy exhibited a tendency to secondary 

porosity; i.e., porosity absent in newly solidified metal, but emergent upon reheating.

7.1 The British Friction Stir Welding Process

In 1994, an investigation was initiated to explore the possibility of circumventing fusion 

welding problems by switching to a FSW solid state welding process patented in 199116 by The 

Welding Institute in Cambridge, England. In the FSW process, a rotating pin, usually threaded, 

is translated along the weld seam and stirs the seam together as it goes. See figure 7. So that the pin 

welds (and does not merely plow up the weld metal), a shoulder attached to the pin presses down 

on the weld metal adjacent to the pin. The weld metal is supported during welding by a platform, 

the ‘anvil,’ which has to be heavy due to the high ‘plunge’ force (typically a few tons) pushing the 

pin and shoulder down onto the workpiece.

In 1999, MTS Systems Corporation devised the self-reacting FSW tool now in common 

use.17 The self-reacting FSW tool has two shoulders that sandwich the weld, one bearing on the 

weld crown and the other on the weld root. The shoulder at the weld root is fastened to the FSW 

pin, which passes through the workpiece and through the crown shoulder, which can be moved 

along the pin to squeeze the workpiece in a pinch force that takes the place of the plunge force in 

conventional FSW. The crown and root forces essentially balance one another, leaving little net 

plunge force to be absorbed by a fixture.

Initially, the weld metal flow was something of a mystery, and one still hears the term ‘chaotic flow’ for some FSW structures. Now, a clear understanding of basic flow patterns and the weld 

structures generated has been attained and work is under way to determine the mechanisms of 

formation of subtler structural features, particularly weld defects.

The breakthrough in understanding FSW flow was the realization that the main deformation was taking place over a very narrow ‘adiabatic’ shear band, the ‘shear surface,’ enclosing the 

tool and separating a plug of metal sticking to the tool from the stationary weld metal surrounding 

it. (Similar shear surfaces are observed in metal cutting.) An abrupt change takes place across the 

shear surface, going from relatively coarse parent metal grains to very fine grains. Flow streamlines 

pass through the shear surface, arc around the tool in the rotating plug, pass out through the shear 

surface, and are abandoned to the wake of the tool.
23

Plunge Force

Pinch Force

Conventional Friction

Stir Welding

Self-Reacting Friction

Stir Welding

Shoulder

Shoulder Shoulder

Anvil

Pin Pin

Vortex Workpiece Vortices

Figure 7. In friction stir welding, a rotating pin stirs the sides of a weld seam together. 

A shoulder prevents the upwelling of metal around the pin, which would result 

in plowing, not welding. In conventional FSW, a large plunge force maintains 

proper shoulder contact; it is balanced by a heavy fixed anvil underneath the workpiece. In self-reacting FSW, a pinch force maintains proper shoulder contact, 

making a heavy supporting anvil unnecessary.

7.2 How Does Friction Stir Welding Work?

How does the tool weld? Solid state welding processes work by bringing metal surfaces into 

contact at the atomic level. These surfaces must be clean and unobstructed, and they must be subjected to pressure adequate to compress any surface asperities and bring the surfaces into full contact. As a length of weld seam VDt, where V is the weld speed and Dt is a time increment, crosses 

the shear surface, it is accelerated to the rotational speed RΩ of the rotating plug of metal attached 

to the tool, where R is the radius of the shear surface and Ω is the angular velocity of the tool. See 

figure 8. If the acceleration is uniform, the seam increment VDt is stretched out to approximately

1

2

RΩΔt (14)

at the shear surface, increasing the area by a factor of approximately
24

1

2

RΩ

V . (15)

A typical order of magnitude of

RΩ

V  50 (16)

amounts to a surface that is at least 96% bondable (24 clean areas to 1 contaminated area). Given 

a pressure on the surface approximately three times the tensile flow stress of the metal at the shear 

surface temperature or greater to ensure good surface contact, one may expect a sound weld from 

the friction stir process.

Seam Trace

Seam

Shear Band Width

at Shear Surface

Shear Surface

Lateral

Displacement

of Seam

Vcosθ ∆t∼V∆t

∼R Ω∆t/2

Ω

V Pin

Figure 8. Plan view of trace of seam around pin during FSW in simplified two-dimensional 

flow model. An eccentricity d of the shear surface accommodates the backflow 

of metal around the pin. Metal inflow volume en route at weld speed V for a shear 

surface of unit height and radius R is 2RV. Backflow at the outer edge of a plug 

of metal rotating with the tool at angular velocity is dRΩ.

7.3 A Kinematic Model of Friction Stir Welding Metal Flow

If the volume rate at which metal encounters the tool, approximately 2 RV, is equated to 

the volume rate of backflow, approximately dRΩ, around the tool, the eccentricity d of the shear 

surface can be estimated:
25

δ  2V

Ω . (17)

The lateral displacement of the seam trace shown in figure 8 may be attributed to a ring 

vortex flow encircling the tool. The rotations in radial sections of the vortex ring are shown in figure 7. The ring vortex flow is driven by pin threads, shoulder scrolls, and, it appears pending 

further study, by any axial flow component up or down a smooth pin with axis tilted away from 

the vertical.

The lateral displacement of the seam trace can be estimated from a kinematic model combining displacements of an element of seam within the rotating plug. There is a displacement due 

to tool velocity (V), tool rotation (w), and ring vortex circulation, represented in plane section by 

a radial velocity component (v). With radius r and angle θ from tool motion direction representing 

the position of an element of weld seam in polar coordinates, the radial and circumferential velocities inside the rotating plug can be computed:

dr

dt ≈ −V cosθ + v (18)

rdθ

dt ≈ rω +V sinθ . (19)

Equation of the time increment in equations (18) and (19) yields the differential equation for the 

streamline of the seam trace within the rotating plug. A further approximation can be made if, as 

in equation (16), the translational weld speed is much smaller than the surface rotation speed of the 

tool:

dr ≈

−cosθ +

v

V

1+

V

rω

sinθ

⎛

⎝

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

V

ω

dθ ~ −d sinθ +

v

V

dθ ⎛

⎝

⎜ ⎞

⎠

⎟

V

ω . (20)

The seam enters the rotating plug at radius R and angle θo, is initially buried beneath successive 

deposits of weld metal on the plug (dr negative), is eventually uncovered (dr positive), and is finally 

abandoned when the radius is again R (dr=0) and the angle is θ, which can be found from equation 

(20). The maximum change in r is small compared to R (see eqn. (17)), and converting from polar 

coordinates, the lateral displacement y–yo, positive toward the retreating side of the tool, 

can be estimated:

y − yo ≈ R v

V

θ − θ ( o ) . (21)

In typical welds radial velocity v is negative (inward) near the shoulder and positive (outward) at the pin end (conventional) or center (self-reacting). The seam trace then is displaced to 
26

the advancing side of the tool near the shoulder and to the retreating side at the bottom of the pin 

(conventional) or the pin center (self-reacting).

Note that if the shear surface radius R or the weld speed V varies in equation (20), the displacement will also vary. These variations will be periodic and may produce lateral waves as well as 

interruptions in weld streamlines. Variations in R could be produced by changes in shoulder contact from sticking to slipping; this would produce a lateral dispersion of tracers mainly close to the 

shoulder.

All this is seen in the steel shot tracer patterns produced at Boeing Co. and published in 

1999 by K. Colligan.18 Periodic emissions of weld metal from under the shoulder produce the ‘tool 

marks’ in the wake of the weld, as well as internal banding seen as the oval ‘onion ring’ pattern 

on a transverse section of the weld. Variations on the theme are presented by other tracers, such 

as a lead wire that melts and disperses in ‘wisps’ along the ‘tool marks’19 and a tungsten wire that 

breaks into segments.

7.4 Particle Interactions

In order to push an indenter into a metal surface, a pressure on the order of three times 

the flow stress of a tensile specimen is needed, due to the constraint of the metal surrounding the 

indentation. (This is an approximate result obtained from plastic slip-line theory.20) The same pressure is needed to push a surface asperity in and hence is needed on the seam trace at the tool if the 

seam is to close and form a sound weld. Plastic flow past an inclusion may be anticipated to exert 

about double the pressure, six times the tensile flow stress, on the inclusion, if the flow is visualized 

as a positive indentation forward and a negative indentation behind, each requiring three times the 

tensile flow stress. Particles passing through the shear interface may be treated as beams loaded by 

opposing pressures to determine whether or not they will be fractured by the flow. It is not a matter of ‘random’ chewing up of particles. What happens to embedded particles is the result of an 

orderly process subject to analysis, as is tool wear caused by these particles. Particle trajectories as 

estimated above and metal supporting forces determine whether they will gouge out abrasive wear 

trenches and how deep, etc.

7.5 Torque and Drag Forces

If the shear surface shape is given in cylindrical coordinates, radius (r), and depth (z), by 

relation r(z), and if the shear stress at the shear surface is roughly constant, then the torque (M) 

required to operate the tool is

M ≈ 2πτr

2 dr2 + dz2

Shear

Surface

∫ . (22)

The mechanical power input to the weld is essentially MΩ, where Ω is the tool angular 

velocity; the power input to move the tool against the drag force is not generally significant in 

comparison. The power requirement for making an FSW is not very different from that needed 
27

to make the equivalent fusion weld. Why should this be? The power input for both fusion and friction stir welds is principally determined by the requirement that it make up for heat losses to workpiece, tool, and fixture, which losses generally overshadow the contribution to weld metal structural 

changes. Given the same penetration depth, the surface of the molten metal pool of a fusion weld 

is very roughly the same as the shear surface of a friction stir weld. The temperature of these surfaces is very roughly the same, say Tm, the melting temperature of the weld metal, for the fusion 

weld and perhaps 0.8 Tm for the shear surface. Hence the heat loss to the workpiece and fixture, the 

major heat loss, from similar embedded surfaces at similar temperatures ought to be very roughly 

the same.

Further, the power remains roughly constant even when the rpm is changed, so that the 

power is inversely proportional to the rpm. This is because the shape and temperature of the shear 

surface changes little with rpm and hence the heat losses, which have to be made up to maintain 

welding conditions, remain about the same. Of course, if power is constant, the torque must drop 

as the rpm rises. The rise in rpm must be accompanied by the small temperature rise needed to 

reduce the temperature sensitive shear stress and the torque to appropriate levels. So the power is 

not quite constant, but increases somewhat with rpm. But the power increase is small compared to 

the overall power because of the sensitivity of the shear stress to small changes in temperature.

The drag force (Fd) on the tool may be estimated from an integral of pressure and shear 

forces over the surface of the shear surface:

Fd ≈ Pr cosθ ∫∫ dθdz − τr sinθ ∫∫ dθ dr2 + dz2 . (23)

Note that the weld metal is swept back with the tool rotation where the metal is hot and the flow 

stress is low and does not flow back according to the indentation model. The drag force behaves 

in a complicated way; sometimes it declines with rpm, sometimes it rises. The drag equation (23) 

yields no drag at all unless pressure (P) and/or flow stress (τ) varies with θ along the circumference 

of the shear surface. Tentatively, it appears as if there may be a pressure drag that is reduced by 

rpm and a shear drag that rises with rpm, but not enough data has been analyzed yet to be confident.

7.6 Weld Defects

Insufficient space is available to present more physics as they pertain to FSW, but it should 

be clear that the basics of the process are pretty well understood. Currently, the main research 

effort is devoted to understanding specific weld defects and problems.

For example, hollow tube-like defects called ‘wormholes’ are sometimes encountered inside 

welds. The ring vortex flow component brings tracer surface metal from the metal surface into 

the interior of the weld and is currently a suspect in the formation of wormholes. Could it be that 

wormholes are formed when seam gaps at the crown of the weld pass under the tool shoulder too 

far out to be subjected to adequate pressure to bring their surfaces into full contact? Might such 

gaps become entrained with the ring vortex flow into the weld interior, where they may become 

wormholes?
28
29

8. CONCLUSION

A few welding problems and processes have been presented here, including penetration, 

microfissures, enigmas, shielding mechanics, space welding, and FSW. Each situation has been 

understood and made tractable by applying an appropriate physical discipline.

Other approaches to tractability could have been taken. Cut-and-try plus statistical analysis 

is popular, a potential universal approach, but it depends more than one might think upon physical 

understanding, without which it is often unsuccessful, particularly in complex situations. Consultation with external experts may be effective, but, depending upon the discipline of the expert picked, 

one is likely to receive rather different understandings of the problem. Extradisciplinary factors 

may be dismissed as unexplained fluctuations.

The importance of breadth in the welding engineering education needed to treat uncategorized welding problems and processes (as they are encountered in nature) is striking. The applications cited above call up heat transfer, thermal stresses, solidification theory, segregation theory, 

optics/diffraction, fluid mechanics, electromagnetic theory, and plasticity theory. This seems a tall 

order for a baccalaureate welding engineering curriculum, particularly when a bit of mathematics 

is generally needed to verify initial physical insights.

But if the welding engineer who takes the first cut at it should pigeonhole a problem in the 

wrong discipline, a great deal of money may be spent without ever obtaining a useful solution. 

Specialists cannot be relied upon at the outset; the initial task is to select the right specialist. Nor 

can all-purpose statistical methods be relied upon. Asking the right questions of statistics requires 

physical expertise and understanding. If any substitute exists, the author is unaware of it.
30

REFERENCES

 1. Newton, I.: Philosophiae Naturalis Principia Mathematica, London: Joseph Streater for the 

Royal Society, 1687.

 2. Lagrange, J.-L.: Méchanique analitique (sic), Paris: Chez la Veuve Desaint, 1788.

 3. Morrison, T.J.; Shira, C.S.; and Weissenberg, L.A.: “The Influence of Minor Elements on 

Alloy 718 Weld Microfissuring. Effects of Minor Elements on the Weldability of High-Nickel 

Alloys,” Proceedings of a Welding Research Council Symposium, Houston, TX, October 3, 

1967.

 4. Lucas, M.J., Jr.; and Jackson, C.E.: “The Welded Heat-Affected Zone in Nickel Base Alloy 

718,” Welding Journal, Vol. 49, No. 2, p. 46-s, 1970.

 5. Lambert, J.A.: “Cast-to-Cast Variability in Stainless Steel Mechanized GTA Welds,” Welding

Journal, Vol. 70, No. 55, pp. 41–52, 1991.

 6. Nunes, A.C., Jr.: “Weld Puddle Physics,” Unpublished Report: ASEE-NASA Summer Faculty 

Fellowship Program, 1975.

 7. Nunes, A.C., Jr.: “An Extended Rosenthal Weld Model,” Welding Journal, Vol. 62, No. 6, 

pp. 165-s–170-s, 1983.

 8. Heiple, C.R.; and Roper, J.R.: “Mechanism for Minor Element Effect on GTA Fusion Zone 

Geometry,” Welding Journal, Vol. 61, No. 4, pp. 97-s–102-s, 1982.

 9. Marangoni, C.: “Ueber die Ausbreitung der Tropfen einer Flüssigkeit auf der Oberfläche einer 

anderen,” Annalen der Physik und Chemie. CXLIII(7), pp. 337–354, 1871.

10. Walley, J.L.; Nunes, A.C.; Clounch, J.L.; and Russell, C.K.: “Study of Radiographic Linear 

Indications and Subsequent Microstructural Features in Gas Tungsten Arc Welds of Inconel 

718,” NASA/TM—2007–215075, Marshall Space Flight Center, AL, September 2007.

11. Pang, Q.; Pang, T.; McClure, J.C.; and Nunes, A.C.: “Workpiece Cleaning During Variable 

Polarity Plasma Arc Welding of Aluminum,” Journal of Engineering for Industry, Vol. 116, 

pp. 463–466, 1994.

12. Nunes, A.C., Jr.; Bayless, E.O., Jr.; Jones III, C.S.; et al.: “Variable Polarity Plasma Arc 

Welding on the Space Shuttle External Tank,” Welding Journal, Vol. 63, No. 9, pp. 27–35, 1984.
31

13. Bakshi, O.A.; and Shron, R.Z.: “The Static Tensile Strength of Welded Joints with a Soft 

Interlayer,” Welding Production, Vol. 9, No. 5, pp. 915, 1962.

14. Kuvin, B.F.: “Welding in Space: Questions Remain,”Welding Design and Fabrication, 

pp. 22–24, May 1990.

15. Nunes, A.C., Jr.; Russell, C.K.; Zimmerman, F.R.; and Fragomeni, J.M.: “Low-Pressure Gas 

Effects on the Potency of an Electron Beam Against Ceramic Cloth,” NASA/TM—1999–

209762, Marshall Space Flight Center, AL, November 1999.

16. Thomas, W.M.; et al.: “Friction Stir Butt Welding,” International Patent Application No. PCT/

GB92/02203 and GB Patent Application No. 9125978.8, December 1991.

17. Campbell, C.L.; Fullen, M.L.; Skinner, M.J.: “Welding Head,” U.S. Patent No. 6,199,745, 

March 2001.

18. Colligan, K.: “Material Flow Behavior During Friction Stir Welding of Aluminum,” Welding

Journal, Vol. 78, No. 7, pp. 229-s–237-s, 1999.

19. Schneider, J.; Beshears, R.; and Nunes, A.C., Jr.: “Interfacial Sticking and Slipping in the 

Friction Stir Welding Process,” Materials Science & Engineering A, Vol. 435–436, pp. 297–304, 

2006.

20. Johnson, W.; and Mellor, P.B.: Plasticity for Mechanical Engineers, D. Van Nostrand Company 

Ltd., pp. 330–334, 1962.
32

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Welding As Science: Applying Basic Engineering Principles 

to the Discipline

A.C. Nunes, Jr.

George C. Marshall Space Flight Center

Marshall Space Flight Center, AL 35812

National Aeronautics and Space Administration

Washington, DC 20546–0001

Unclassified-Unlimited

Subject Category 26

Availability: NASA CASI (443–757–5802)

Prepared by the Materials and Processes Laboratory, Engineering Directorate

M–1298

Technical Memorandum

NASA/TM—2010–216449

welding, weld defects, friction stir welding, conceptual models, mathematical models, finite 

element models

01–10–2010

UU 40

NASA

U U U

This Technical Memorandum provides sample problems illustrating ways in which basic engineering 

science has been applied to the discipline of welding. Perhaps inferences may be drawn regarding optimal 

approaches to particular welding problems, as well as for the optimal education for welding engineers.

Perhaps also some readers may be attracted to the science(s) of welding and may make worthwhile 

contributions to the discipline.

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