9R30. Superplastic Flow: Phenomenology and Mechanics. Engineering Materials Series. - KA Padmanabhan (Indian Inst of Tech, Kanpur, 208016, India), RA Vasin (Moscow State Univ, Moscow, 119899, Russia), FU Enikeev (Inst of Metals Superplasticity Prob, Ufa, 450081, Russia). Springer-Verlag, Berlin. 2001. 363 pp. ISBN 3-540-67842-5. $99.00.

Reviewed by MJ Zyczkowski (Inst of Mech and Machine Des, Politechnika Krakowska, Cracow Univ of Tech, ul Warszawska 24, 31-155 Krakow, Poland).

Superplasticity is defined as the ability to exhibit very large tensile elongation prior to failure. From the viewpoint of solid mechanics, it corresponds to finite-strain plasticity and viscoplasticity including metal forming processes. On the other hand, from the viewpoint of materials science, the most important is the microstructure that determines necessary properties, finding the composition of alloys, the ranges of temperature and strain rate making it possible to obtain large elongations. The classical example of a superplastic material is that of the eutectoid system of approximately 80% aluminum and 20% zinc.

The book under review aims at a presentation of superplasticity both from the mechanical and from the metallurgical point of view. It is divided into six chapters and four appendices. The first introductory chapter gives historical background, basic concepts, and typical mathematical descriptions of uniaxial state of stress. Particular attention is paid to Norton’s power creep law and its direct generalization to viscoplasticity—they are the most frequently used in superplasticity. The second chapter, Mechanics of solids, presents fundamental concepts of continuum mechanics, in particular of plasticity and creep, and discusses various aspects of experimental investigations in solid mechanics. Chapter 3, the longest, Constitutive equations for superplastics (80 pp) is in its majority devoted to uniaxial states and just the last 15 pages deal with the general multiaxial states and use tensorial notation. The uniaxial constitutive equations are divided into phenomenological and physical equations. The first group discusses many generalizations of Maxwell’s and Bingham’s bodies and the relevant mechanical models including nonlinear viscous elements. Examples of the materials conforming to particular models are supplied in most cases. Physical equations include microstructural parameters like the grain size, but the authors state that the problem of validity and meaning of physical parameters is beyond the scope of their book. Multiaxial states are restricted to the strain-hardening creep and Ilyushin’s theory of elastic-plastic processes. Chapters 4 and 5 consider applications to the problems of metalworking: bulging, sheet forming, bulk forming, extrusion, drawing, and deformation processing. Numerical methods are discussed in detail, but several analytical solutions are given as well. Short Chapter 6 is devoted to theoretical and experimental perspectives of superplasticity. Two appendices deal with finite-strain kinematics of solids and its applications. The remaining two discuss dimensional analysis and group properties of thermoviscoplasticity.

The book is written clearly, from the viewpoint of mechanics, physics, and materials science, with mathematics kept at an intermediate level. One can agree with the authors that it is intended for a broad variety of readers: researchers working in superplasticity and related topics, engineers in industry, and students. It contains many original results of the authors shown at the background of the present state-of-the-art. The list of references quotes 621 entries plus 15 ascribed separately to Chapter 2; they undoubtedly cover the majority of related books and papers. The subject index is well prepared, whereas the author index is lacking. The theoreticians may be disappointed by a scarce treatment of constitutive equations for multiaxial states, in particular valid for finite strains (though such equations may be found in many papers on plasticity or viscoplasticity). On the other hand, the students will be happy not to see very complicated formulas based on difficult concepts introduced in such cases.

The book contains some inconsistencies. For example, on page 35, the authors state that the analysis in superplasticity should follow the theory of finite strain, but on the same page they note that all the problems in their book are discussed for small deformation. On page 37, the authors write: “Only logarithmic strain tensor is popular and clear among specialists in superplasticity,” but the general definition of such a tensor is not given (like, for example, by J Betten, Kontinuumsmechanik, Springer 1993, p 44).

Nevertheless, in conclusion Superplastic Flow: Phenomenology and Mechanics may be recommended to the researchers, engineers, and students, in view of its originality, comprehensive treatment, valuable references, and formulation of many directions of future research.