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Advanced Technology of Plasticity 1990, VoL 4

A Personal Look on My Involvement in the Recent History of Metal Forming Research

A Keynote Presentation By
Betzalel Avitzur

Professor, Institute for Metal Forming
Dept. of Materials Science and Engineering
Lehigh University, 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 contribution.

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 plans.

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:

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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 to learn.

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 curiosity.

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 belonged.

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 semester.

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 solution itself."

With these admirable people, Profs. Robinson, Kurrien, Bunfilioly, and Colwell, shaping my young and impressionable mind, I was fated eventually to study friction 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.

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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 newcomers.

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 the Technion.

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.

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The Broad 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:

  1. Assistance in the development and the introduction of sophisticated mathematical analysis (i.e., limit analysis) for metal forming practice.
  2. Assistance in the introduction of new concepts and technological advances to manufacturing practices.
  3. 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:

  1. A process: Flow Through (Conical) Converging Dies,
  2. A phenomenon: Friction

Both subjects gradually evolved as the analytical techniques for approaching them became more sophisticated.

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Flow Through

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 the process.

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.

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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. [1] 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 picture.

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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.

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The Study of Friction

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]-[3]. 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 commences.

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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 determined.

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. [4]). 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. [4], pp. 300 and 303).

Reference [5] 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 asperities.

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 [6] and then replacing that model by the more suitable three-triangle field [7] 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. [9] and by Avitzur, Choi, and Kim in Ref. [10]. 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 practice.

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Closing Remarks

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. [5]-[8], [10] and [11]. 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 bound approach.

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.

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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.

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  1. Avitzur, B., "Metal Forming: Processes and Analysis", McGraw Hill, 1968.
  2. 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.
  3. 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. 390-395.
  4. Leslie, J., "An Experimental Inquiry Into the Nature and Propagation of Heat", J. Newman, London, 1804.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.

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