Viscoplastic Flow in Solids Produced by Shear Banding. Ryszard B. Pecherski

where τ₀ is yield stress in shear and denotes the shear strain rate. Neglecting τ₀ = 0, one arrives at the linear model of ‘Newtonian fluid’. An analogy with magnetorheological materials appears here. From the papers of Frąś (2015), Frąś and Pęcherski (2018), it seems that the linear Bingham model does not conform to experimental data contrary to the original nonlinear viscoplasticity model of Perzyna (1963). The similar conclusion leads the above discussion on a viscous flow resulting from the massive production of point defects activated in KOBO processes. In my view, a more comprehensive theory of the viscoplastic flow produced by shear banding is in order. The observation about the importance of viscous effects accompanying rate‐dependent plastic flow during KOBO processes is accounted for in the book.

1.4 Summary of the Work Content

      The preface introduces novel concepts and the framework of the book. Chapter 1 presents the motivation and leading thread of the work related to a detailed discussion of the physical basis developed in Chapter 2. This chapter contains the synthetic approach to observations that appear helpful in formulating the viscoplastic flow description in metallic solids produced by shear banding. These views are underlined in the text as the set of statements denoted Observations 2.1, 2.2, … 6.1, including the results of own inquiries. The heuristic foundations of the theoretical description of large inelastic deformations create the rational formulation of a multiscale system of shear bands formation. Chapter 3, on the other hand, accounts for shear banding in the continuum model of inelastic deformations. This chapter contains the results of the earlier author's investigations related to micromechanical foundations of finite plastic deformations theory accounting for the shear‐banding mechanism summarised in Observation 3.1 and Hypothesis 3.1, extending the generally accepted concept of representative volume element (RVE). The extension provides the possibility of the existence in RVE of the singular discontinuity surface of order one of the microscopic velocity field on which the tangential component of velocity experiences a jump travelling at the speed V_s. Further, Chapter 4 presents the basics of rational mechanics of materials. A small historical account of rational mechanics is given here. The continuum mechanics description of shear banding is the subject of Chapter 5. The theoretical foundations of the deformation of a body due to shear banding are presented in Chapter 6. In Chapter 7, the yield limit versus shear banding is considered, and, in particular, state of the art regarding the yield condition for modern materials is the subject of thorough study. Viscoplasticity models accounting for shear banding with related examples are under investigation in Chapter 8. The conclusions and remarks concerning further possible studies are provided in Chapter 9.

Acknowledgements

      Many friends and coworkers supported and helped the author pursue this complex never‐ending story on multiscale deformation mechanisms of different hard deformable metallic solids that I would like to recount, at least partly. As mentioned above, Andrzej Korbel, a Polish Academy of Arts and Sciences member, and Włodzimierz Bochniak became ‘spiritus movens’ of my long‐time activity in this field. It happened due to the help of Mrs Romana Ewa Śliwa, a professor at the Rzeszów University of Technology. She was the first to see my preliminary presentations on localisation phenomena long ago, wisely suggesting contacts with already‐knowledgeable and experienced material science researcher Andrzej Korbel. Then, during many years of my works on shear banding phenomena, it was Zdzisław Nowak, PhD, DSc, who showed me the possibilities of numerical analysis of plastic deformation processes accounting for the shear bands effects and identifying the shear banding contribution function. Also, Katarzyna Kowalczyk – Gajewska, PhD, DSc, gave me a helping hand in the numerical simulations of experimentally realised channel‐die compression and shearing processes. The studies showed a valuable perspective with the significant experience and knowledge of professor Zenon Mróz, a Member of the Polish Academy of Sciences, and Katarzyna Kowalczyk – Gajewska on cyclically loaded tubes on the KOBO processes. I also received a big help from Mrs Aleksandra Manecka – Padaż, MSc, in elaborating the book's graphics. Together with discussions in statu nascendi of the work, her contribution became invaluable. The late professor Piotr Perzyna, my PhD advisor and scientific tutor, contributed to my studies with many valuable discussions about the shear banding model and its applications in the studies of viscoplastic processes.

References