Technology of Plasticity 1990, VoL 4
A Personal Look on My Involvement in the
Recent History of Metal Forming Research
A Keynote Presentation By
Professor, Institute for Metal Forming
of Materials Science and Engineering
Bethlehem, PA 18015
It is a great honor to be asked to present a
keynote lecture at this prestigious Third International
Conference on Technology of Plasticity (ICTP). At the same
time, the impact of this first invitation to summarize my
lifetime of work is devastating. First I paused to think:
"Am I at the end of the road?" But then I overcame the
shock. I accepted the challenge and the opportunity to
acknowledge great teachers, colleagues, and students that
shaped my thoughts: they paved the way for my contributions
to metal forming technology. In this era when metal forming
changed from art to science my participation was their
I will make my acknowledgments through the presentation
of two major projects that span over a long period. They are
a tribute to many people with whom I interacted. These
projects are not yet finished and still need plenty of team
work to forge ahead. And so, let me start.
I often find an ancient Jewish saying (Hillel, Ethics of
the fathers 1:14, about 2000 years ago) very appropriate. it
states: "If I am not for myself, no body is, and by myself I
am nobody." Following the guidelines of the organizing
committee, I will describe the route of my career. The route
was not smooth. And initially failed (and it still fails) to
meet the approval of the Official experts. But, "I did it my
way," not at the feet of any famous mentor. That takes care
of the first part of Hillells quote.
"If I am not for myself, no body is"
As for the second part, I was lucky throughout my entire
professional life to be supported by the people to whom this
note is a tribute. Regretfully only a few of those deserving
it are mentioned by name. To avoid a chronological listing,
I will stick to select areas and mention those who played an
essential role. Not every activity is covered and not
everybody who deserves my gratitude is included. Only those
who fit the story. And they are not necessarily from the
world of metal forming.
I met fascinating people through my work and developed
personal relations with many of the leading contributors to
the metal forming industry. Their impact on me rather than
on the field is acknowledged here. of those omitted I ask
forgiveness; the book is not yet closed. While the bulk of
the presentation will nostalgically dwell on the glorious
good old days, I also address my present work and future
In the request for this keynote presentation, the
guidelines suggested I include mention of: "What brought me
to my particular field of study-" Well, here I start, from
the beginning, or:
My School Days
My interest in metal working can be traced
back to my childhood, when I acted as my father's
apprentice, handing him tools or activating our hand
operated drill press. At an early age learned much from my
own mistakes. For example when trying to build a lamp stand
made of marble, I had my
first serious failure.
Thus I learned that marble is brittle, and should not be
hammered. This was before Prof. P. W. Bridgman taught us how
to form marble and other brittle materials under pressure.
The primary and secondary school teachers in my
birthplace, Israel, were all overqualified, highly motivated
educators. Since nobody wanted them elsewhere, they returned
home to Israel to build their place under the sun. Later in
life I realized that we kids had the unique fortune of being
exposed to and excited by true intellect and devotion. I
recognize now their role in shaping my curiosity and desire
From those years, I mention a few people. First there was
my vocational high school physics teacher, Dr. Robinson. He,
with his contagious enthusiasm and unique teaching methods,
introduced us all to the mysterious world of friction. I
remember that we were assigned to write an essay on our
conception of this phenomenon. And we did it. We high school
students. I had greater confidence in my explanation then,
than I now have in my present work. He did indeed kindle my
Later, in the engineering college, the same Prof.
Robinson again taught me physics. You see, by this time he
finally found a position at the Technion in Haifa, where he
One person in specific who
shaped my conception of the engineering profession was Prof.
Dr. Dipl. Engineer, Max Kurrien. Singlehandedly this
internationally prominent authority built and headed the
Dept. of Mechanical Engineering at the Technion. He taught
most of the engineering courses in that department. I had
his class 4 hours a day, six days a week. He also taught
other classes. And today we complain about professional
burnout when we teach more than one three credit course per
The other early, lasting influence on my work was Prof.
Louise Bunfilioly, whose teaching methods in Descriptive
Geometry were so alive, descriptive, and exciting that you
could easily conceptualize the three-dimensional
intersection line of two cylinders of different diameters,
at a 30 degree inclination. At the time, I thought that that
was what engineering was all about. In fact I still think so
today, mainly because this conviction was reinforced in
graduate school at the University of Michigan in Ann Arbor.
There, Prof. Colwell, teaching the concepts of the design of
Jigs and Fixtures, convinced us of his axiom that. "Any
engineering problem can and should first be reduced to its
geometrical parameters. Then, once you have defined the
problem through its geometry, you are half way towards the
With these admirable people, Profs. Robinson, Kurrien,
Bunfilioly, and Colwell, shaping my young and impressionable
mind, I was fated eventually to study
in terms of the geometry of surface irregularities. And what
method should I use, but the upper bound approach, which by
its very nature deals with the concepts of shape and motion.
The Early Years
Attending graduate school, and graduating,
was a struggle whose outcome was never a sure thing. Not
that the academic challenge was too much, but the route was
full of traps. However each block in the obstacle course was
always more than compensated for by men of good will to whom
I owe my gratitude and my diploma.
Mr. Lucian Chaney hired me for my first job during my
studies, and introduced me to the sponsors of my soon to be
funded research thesis. He and his wife adopted our family
and we became very good friends. For my thesis at Michigan I
studied the spinning process. After stress analysis led me
nowhere, I employed the upper bound approach.
Profs. Hucke and Ragone of the Department of Metallurgy
provided funds to support my research thesis. Without their
funding there would have been no further studies for me!
Later, my close relationship with Prof. Kudo, the father of
the modern upper bound approach, as well as the inherent
strength of the upper bound approach itself, resulted in my
dedication to this approach.
Through Prof. Eric Thomsen (the mentor of my thesis
advisor Prof. Yang) I was introduced to Prof. S. Kalpakjian,
then of Cincinatti Milling Machines.
These three salvaged my thesis. Through Professor's
Kalpakjian generous permission to access his experimental
data I gained approval of my thesis. I did not believe then
that sound analysis needed experimental verification. But I
was not in a position to argue. Years later a good friend of
mine, the late Prof. Bobrowsky, argued this case for me as
follows: "Some investigators collect many data points to
plot a line, but Avitzur is known to plot a family of
characteristic lines around a single experimental point." I
cherish his observation.
Upon earning my Ph.D. in Mechanical Engineering from the
University of Michigan, I joined the Scientific Labs. of
Ford Motor Co. This was my first "Real Job" in research.
There, the parental supervision of Dr. Phillips built my
confidence in my choice of a career. He was a strong role
model for me.
I received full support from Ford Motor Co. to proceed.
My initial steps were inspired by the extensive work of
Prof. H. Kudo with whom I started to communicate frequently.
Prof. Kudo was always there for me, getting deeply involved
in my work, as he also did for a generation of other
On my enthusiastic return home to Israel, I continued
developing some of my earlier solutions and upper bound
techniques. Discussions with Profs. Z. Rotem, D. Pnueli, and
M. Bentwitch shaped my understanding of the fundamentals of
Limit Analysis. These discussions were priceless!
Unfortunately they were cut short when I was forced out of
I was welcomed back to the United States. Here, my
professional and personal relations with prominent people
like Prof. Al Bobrowsky, Mr. Derek Green, and Mr. Alex
Zeitlin, all in the field of hydrostatic extrusion, were an
inspiration. My colleague, Prof. Walter Hahn, of the Dept.
of Mat. SC. at Lehigh University, was a pillar of support,
integrity and stability for my teaching the mechanics of
metal forming in a materials oriented environment. My
parallel path with that of Prof. Shiro Kobayashi of Berkeley
Cal. brought us together constantly. His quite posture and
sharp analytical mind were a comfort confirmation for our
similar (upper bound) yet different routes.
One special colleague, Dr. Samy Talbert, started working
with me 28 years ago. He was then an undergraduate student
at the Technion. We are still working and growing together.
Dr. Talbert is responsible for the more sophisticated
mathematical analyses. Our cooperation is evident by the
large number of research papers we coauthored. But this is
only the tip of the iceberg. The real depth of our cross
fertilization is in exchanging ideas, complementing each
other, and building a common language. We are presently
completing a text book entitled: "Elementary Mechanics of
Metal Forming". I hope for many more years of collaboration
with Dr. Talbert.
Picture, Major Contributions
A list of my main contributions in the field
of metal forming was compiled when I was recommended for
promotion to the honored rank of an ASME Fellow Member. Here
is my condensed version of that list into three categories:
- Assistance in the development and the introduction of
sophisticated mathematical analysis (i.e., limit
analysis) for metal forming practice.
- Assistance in the introduction of new concepts and
technological advances to manufacturing practices.
- Assistance in the education of a generation of
engineers, researchers, and educators in the field.
The above categories cover many activities. Here I choose
to discuss only two pet subjects:
- A process: Flow Through (Conical) Converging Dies,
- A phenomenon: Friction
Both subjects gradually evolved as the analytical
techniques for approaching them became more sophisticated.
In the flow through processes the workpiece
is forced through a die of a specific orifice. While passing
through the die the workpiece transforms into a longitudinal
rod, acquiring a cross section of the shape of the opening
in the die. Typical processes are wire drawing, conventional
and hydrostatic extrusion, Conforming, and Extrolling (my
invention). Here we will observe the analysis of the flow of
a cylindrical rod through conical converging dies. Because
this is not a technical paper I will only briefly describe
In Fig. <1> the characteristics of the drawing or
extrusion pressure are plotted on the ordinate against the
changing die angle on the abscissa. As the die angle
changes, so does the flow pattern, as indicated by the
inserts. Different descriptions of the flow patterns are
approximated by different velocity fields. While the outline
of the deformation region changes with the die angle and the
flow, the elements from which the velocity field is
constructed are also changed.
FIGURE 1 [
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The basic elements are the spherical, triangular, and
trapezoidal fields. Analytical solutions were obtained for
each, and a comparison in Fig. <2> reveals the degree
of agreement among them, and how they compare to a lower
bound solution. The agreement is reasonable, but not nearly
as good as in the treatment of ring forming. (see Ref. 
Fig. 7.28). Next to each insert in Fig. <1>, reference
is made to a co-worker from the Institute for Metal Forming
with whom the work was done, and the year it was published.
I would like to emphasize that each study, piece by piece,
spreading over a length of time, fit into the evolving
FIGURE 2 [
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For example, central burst is a failure mode whereby
ductile fracture develops internally at the axis of symmetry
of the wire. The treatment of failure by the upper bound
approach is still considered a breakthrough. While dealing
with the phenomenon of central burst, the first steps were
taken in applying the upper bound approach to flow with
fracture. The concepts adopted there, were soon extended to
the study of bimetallic and composite rod, and the
development of criteria for the prevention of sleeve and
core fracture. Then, central burst in plane strain drawing,
as well as central burst and split ends fracture in rolling
followed. Much more still has to be done.
The Study of
Friction is the last frontier in the study of
metal forming. For example in the process of wire drawing,
the independent parameters: reduction, die angle and the
like are parameters that can be measured directly. Not so
for friction. There is no instrument called "Frictionmeter"
to measure friction. Friction is not directly measurable,
nor is it really an independent parameter. But, in many
metal forming process the effect of friction is as strong as
that of reduction, die geometry, etc. Hence the importance
of that factor and its elusive characteristics.
My interest in friction started in high school with my
physics teacher Dr. Robinson. My use of the friction factor
m as a variable, and my treatment of hydrodynamic
lubrication, for example are evident in Refs. [l]-. But
our present effort in modeling friction started in the
summer of 1980, during a stay as a visiting scholar with
Prof. T. Wanheim at the University of Copenhagen. There I
was introduced to the analytical treatment of the behavior
of the surface asperities as Means for the modeling of
friction. Later on, during a summer in New Zealand, I made
sure to visit Prof. Oxley in Australia, to discuss this
approach. In those days only a small number of investigators
supported the 'wave model'. Profs. Wanheim and Oxley studied
the model by the slip line technique. It was my conviction
that the upper bound approach is better suited to handle the
mobility of the asperities, especially the contribution of
the trapped lubricant.
Models of the typical characteristics of two solids in
contact under pressure and sliding with respect to each
other are described in Models 1 and 2 (see Fig. <3>
and the insert to Fig. <3>) . In Model 1 wedges of the
harder surface indent into the softer surface due to the
applied pressure, thus producing opposing ridges on the
surface of the softer component. The gap between the
opposing asperities is filled with liquid, establishing
boundary lubrication. As sliding is maintained, the ridges
are mobilized and an eddy flow is established in the trapped
lubricant. The power required to mobilize the ridges and to
establish flow in the lubricant is calculated and thus the
friction resistance to sliding is determined.
Simultaneously, the pressure generated in the liquid due to
shear is also evaluated. It becomes clear that the higher
the sliding speed, the higher the liquid pressure that is
countering the loading pressure and the smaller the
indentation. At a high enough Sommerfeld Number the entire
load is supported by the pressure generated in the liquid,
indentation is eliminated, and hydrodynamic lubrication
FIGURE 3 [
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The classic model for hydrodynamic lubrication where two
inclined surfaces glide atop each other is described in the
insert of Fig. <3>. Here the gap between the two
surfaces (emin) at their closest point is a
monotonically increasing function of the Sommerfeld Number
(S). The resistance to sliding, as established through the
shear in the liquid, determines the friction value. This
model leads directly to the characteristic of Coulomb or
Emonton, where, for diminishing values of the Sommerfeld
Number the resistance to sliding is proportional to the
pressure. The proportionality factor is equal to the tangent
of the angle of inclination. The increase in friction with
increasing values of the Sommerfeld Number is also
Combining the two models one notices that, at low speeds
and low values of the Sommerfeld Number, the liquid pressure
is not sufficient to float the two surfaces and indentation
prevails together with boundary lubrication. With increasing
speed (Sommerfeld Number) the height of the ridge (by Model
1) decreases, and when the height diminishes to values lower
than those predicted for the gap between the surfaces in the
second model for the same speed, the boundary lubrication
ceases and hydrodynamic lubrication commences.
Ridge mobility (see Figure <3>) as one of the
mechanisms responsible for the resistance to sliding motion
between solids is gaining acceptance. The need for such an
explanatory mechanism and its nature is indicated by J.
Leslie (Ref. ). He observed that the asperities on the
harder surface (called "wedges" here) push on the opposing
ridges of the softer surface. Opposing the popular thought
of those days that climbing motion occurred, (which ignores
the inevitable downhill companion motion), Leslie suggested
that the softer ridge was pushed into and under the surface,
producing a perpetual uprising ahead of the wedge of the
harder surface and resulting in an endless climb (Ref. ,
pp. 300 and 303).
Reference  by Dr. W. Pachla does not deal with the
friction model directly, but this work was undertaken while
we were extensively pursuing friction and strip rolling. It
became obvious to all of us at the Institute for Metal
Forming that the treatment of plane strain problems can be
based on the handling of the deformation region by
subdivision into triangular rigid motion regions. I then
consulted with my life long coworker, Dr. Talbert in Canada.
We observed that the most general rigid body motion is the
rotational motion. From there the rules of the interfacing
of two arbitrary rigid body motions can easily be cataloged.
As a matter of fact these rules were originally scribbled
on paper plates at Tony's Pizza Place where our group lunch
meetings became free-for-all discussions on any topic, in a
relaxed atmosphere undisturbed by telephones. Tony's place
became an extension of Lehigh's seminar and conference
rooms. Some of our best work began there. Incidentally,
these rules were determined from kinematic considerations
before we derived any mathematical expression. It took the
better part of the rest of the year to get the derivations,
and much longer to struggle with the manuscripts.
The development of the friction wave model, that now
looks so tame, was tedious, and full of obstacles that
provided great joy in tackling. First we selected the wrong
arbitrary parameters for describing the geometry of the
When the rigid body triangles were defined through their
angles, the arithmetic became unbearable. When the
coordinates of the apex of each triangle replaced the
angular parameters, the derivation turned out well. Then we
played for a while with different configurations of the
asperities, starting with a two triangle field  and then
replacing that model by the more suitable three-triangle
field  and (8].
The pivotal obstacle, or so it seemed for a while, was
our inability to determine the height of the asperity by the
upper bound approach. Salvation came when we observed that
the upper bound solution can be obtained either by the power
or by the force balance expression, as treated by D.
Westwood and J. F. Wallace in Refs.  and by Avitzur,
Choi, and Kim in Ref. . The solution became possible
when we applied the force balance constraint to the
optimization of the object power function.
From this model and from the derivation of the explicit
mathematical expressions, we quantitatively presented the
characteristics of friction in graphs that show friction as
a function of pressure, Fig. <4>, and as a function of
Sommerfeld Number, Fig. <5>.
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In the opening I stated that in our era we witnessed the
transition from art to science in the metalforming field. In
the area of friction and lubrication the application of
soaked burlap sacks to the hot rolling of steel plate is
replaced by scientific formulation of the bland of
lubricants, and design of roll surface irregularities. The
effect of a well determined and controlled friction value on
roll pressure and torque is predictable. Friction values are
no longer used as a fudge factor to reconcile formulae with
In the request for this keynote presentation,
the second guideline suggested that I mention obstacles
encountered and overcome. This request I handle by quoting
loosely the acknowledgment to a recent publication.
"The steady progress in the application of the Upper
Bound Approach to the 'Wave Model' and to the behavior of
the trapped lubricant for the description of the
characteristics of friction by this model was made possible
by the many students, visiting scholars, and colleagues, who
joined enthusiastically in the ongoing research. This team
deserves full credit, because in the absence of funding for
this work, their recognition of the potential of this
approach made the results possible.."
A list of those acknowledged is provided by the list of
authors of Refs. -,  and . I suppose the above
quote says it all. First, it identifies the kind of
financing obstacles you can expect when you have
non-conventional ideas, the only ones worth pursuing. And
second, it identifies where you can find comfort: from
sympathetic colleagues who get excited by the same ideas you
subscribe to. With that kind of support you can overcome the
technological obstacles, from the brittle fracture of the
marble lamp post, to the 'Inadmissibility' of the upper
Prof. Ed Kay of
Lehigh University and I are presently proceeding with the
study of friction. we are upgrading the wave model to
include treatment by rotational, rather than linear, rigid
body motions. For me the time left is short, and there is
much more inspiring work to be done. My advice to the young
scholar is to pursue a career in the study of the wonderful
world of friction. Getting another chance, I would.
For a crucial period of over 15 years, during
which I published three books and over 120 papers, Dean J.
D. Lieth of Lehigh University edited every manuscript I
submitted, taught me how to write, and was a most
enthusiastic student of my work. Because of his dedication
and professional perfection, I will always have a spot for
him in my heart.
- Avitzur, B., "Metal Forming: Processes and Analysis",
McGraw Hill, 1968.
- Avitzur, B. and Grossman, G., "Hydrodynamic
Lubrication in Rolling of Thin Strip," Trans. ASME,
Series B, Vol. 94, No. 1, Feb. 1972, PP. 317-328.
- Avitzur, B., "The Application of Hydrodynamic
Lubrication to Rolling of Thin Strip," Proc. of the Int.
Conf. on Prod. Eng., Part I, Tokyo, Japan, 1974, pp.
- Leslie, J., "An Experimental Inquiry Into the Nature
and Propagation of Heat", J. Newman, London, 1804.
- Avitzur, B. and Pachla, W., "The Upper Bound Approach
to Plane Strain Problems Using Linear and Rotational
Velocity Fields, Part I: Basic Concepts, and Part II:
Applications, 11 Trans. ASME, J. Engineering for Ind.,
Nov. 1986, Vol. 108, No. 4, pp. 29 5-3 16.
- Avitzur, B. , Huang, C. K. and Zhu, Y.D., "A Friction
Model Based on the Upper-Bound Approach to the Ridge and
Sublayer Deformations," WEAR, Vol. 95, No. 1. Published
by Elsevier oxford, UK, 1984, pp. 59-77.
- Avitzur, B. and Zhu, Y.D., "A Friction Model Based on
the Upper-Bound Approach to the Ridge and Sublayer
Deformations - Update," Presented at NAMRC XIII, May
19-22, 1985 in Berkeley, CA and published in the
proceedings, SME, pp. 103-109.
- Avitzur, B. and Nakamura, Y., "Analytical
Determination of Friction Resistance as a Function of
Normal Load and Geometry of Surface Irregularities,"
published in WEAR, Vol. 107, No. 4, pp. 367-383, 1986.
- Westwood, D., and Wallace, J.F., "Upper Bound Values
for the Loads on a RigidPlastic Body in Plane Strain", J.
Mech. Engrg. Sc., 2 (3) (1960) 178-187.
- Avitzur, B., Choi, J. C., & Kim, J. M.,
"Application of Force Balance Method to Several Metal
Forming Problems," Proceedings of NAMRC 15, Lehigh Un.
Bethlehem, PA., May 27-29, 1987. PP. 269-277.
- Avitzur, B., Van Tyne, C.J., Luo, Z.J. and Tang,
C.R., "A Model for Simulation of Friction Phenomenon
Between Dies and Workpiece," Proc., lst. Int. Conf. on
Technology of Plasticity (ICTP), Tokyo, Japan, Sept. 3-7,
1984, pp. 200-207.
FIGURE 6 [
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