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

type is a gradual, cumulative shear banding that collects micro‐shear bands' particular contributions and clusters. Finally, they accumulate in the localisation zone spreading across the macroscopic volume of considered material. Such a deformation mechanism appears in amorphous solids as glassy metals or polymers. It seems that there are the local shear transformation zones (s) behind the cumulative kind of shear banding, cf. Argon (1979, 1999), Scudino et al. (2011), and Greer et al. (2013). The volumetric contribution function of shear banding appears in such a case.

      Often both types of the above‐mentioned shearing phenomena appear with variable contribution during the deformation processes. During shaping operations, this situation can arise in polycrystalline metallic solids, typically accompanied by a distinct change of deformation or loading paths or a loading scheme. Also, materials revealing the composed, hybrid structure characterizing with amorphous, ultra‐fine grained (), and nanostructural phases are prone to the mixed type of shear banding responsible for inelastic deformation, cf. the recent results of Orava et al. (2021) and Ziabicki et al. (2016).

      The commonly used averaging procedures over the RVE need deeper analysis to account for the multilevel shear‐banding phenomena. The RVE of crystalline material is the configuration of a body element idealized as a particle. The particle becomes a carrier of the inter‐scale shearing effect producing the viscoplastic flow. It leads to an original and novel concept of the particle endowed with the transfer of information on a multilevel hierarchy of micro‐shear bands developing in the body element of crystalline material. The discussion about the difficulties and shortcomings of applying a traditional direct multiscale integration scheme appears in Chapter 4. The remarks mentioned above motivate the core subject of the work and underline the new way of thinking.

      Ryszard B. Pęcherski

      2022

      Kraków and Warszawa, Poland

Acknowledgements

I want to express my gratitude for the helpful and friendly guidance offered during my writing efforts shown by Wiley’s competent and patient staff led by Ms Juliet Booker, Managing Editor. Thank you very much for accompanying me on my long journey to navigate the bumpy roads of British syntax and phraseology. In such a case, the role of my cicerone – Ms Nandhini Tamilvanan, Content Refinement Specialist – appeared invaluable. Last but not least, acknowledgement belongs to the Creative Services Team coordinated by Ms Becky Cowan, Editorial Assistant, in preparing the book’s cover. Their professionalism led me to choose the motif that sheds new light in Chapter 1 on the relevant issues related to industrial applications.

References

      1 Anand, L. and Kothari, M. (1996). A computational procedure for rate‐independent crystal plasticity. J. Mech. Phys. Solids. 44: 525–558.

      2 Argon, A.S. (1979). Plastic deformation in metallic glasses. Acta Metall. 27: 47–58.

      3 Argon, A.S. (1999). Rate processes in plastic deformation of crystalline and noncrystalline solids. In: Mechanics and Materials: Fundamentals and (ed. M.A. Linkages, R.W.A. Meyers and H. Kirchner), 175–230. New York: Wiley.

      4 Bai, Y. and Wierzbicki, T. (2008). A new model of metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24: 1071–1096.

      5 Dequiedt, J.L. (2018). The incidence of slip system interactions on the deformation of FCC single crystals: system selection and segregation for local and non‐local constitutive behavior. Int. J. Solids Struct. 141–142: 1–14.

      6 Dunand, M. and Mohr, D. (2010). Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals. Int. J. Solids Struct. 47: 1130–1143.

      7 Dunand, M. and Mohr, D. (2011). On the predictive capabilities of the shear modified Gurson and the modified Mohr–Coulomb fracture models over a wide range of stress triaxialities and Lode angles. J. Mech. Phys. Solids. 59: 1374–1394.

      8 Gorij, M.B. and Mohr, D. (2017). Micro‐tension and micro‐shear experiments to characterize stress‐state dependent ductile fracture. Acta Mater. 131: 65–76.

      9 Greer, A.L., Cheng, Y.Q., and Ma, E. (2013). Shear bands in metallic glasses. Mater. Sci. Eng., R.74: 71–132.

      10 Gurson, A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth. I. Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99: 2–15.

      11 Havner, K.S. (1992). Finite Plastic Deformation of Crystalline Solids. Cambridge University Press.

      12 Nielsen, K.L. and Tvergaard, V. (2010). Ductile shear failure of plug failure of spot welds modeled by modified Gurson model. Eng. Fract. Mech. 77: 1031–1047.

      13 Orava, J., Balachandran, S., Han, X. et al. (2021). In situ correlation between metastable phase‐transformation mechanism and kinetics in a metallic glass. Nat. Commun. 12: 2839. https://doi.org/10.1038/s41467=021‐23028‐9.

      14 Pardoen, T. (2006). Numerical simulation of low stress triaxiality of ductile fracture. Comput. Struct. 84: 1641–1650.

      15 Pęcherski, R.B. (1997). Macroscopic measure of the rate of deformation produced by micro‐shear banding. Arch. Mech. 49: 385–401.

      16 Pęcherski, R.B. (1998). Macroscopic effects of micro‐shear banding in plasticity of metals. Acta Mech. 131: 203–224.

      17 Petryk, H. and Kursa, M. (2013). The energy criterion for deformation banding in ductile single crystals. J. Mech. Phys. Solids. 61: 1854–1875.

      18 Scudino, S., Jerliu, B., Pauly, S. et al. (2011). Ductile bulk metallic glasses produced through designed heterogeneities. Scr. Mater. 65: 815–818.

      19 Shima, S. and Oyane, M. (1976). Plasticity for porous solids. Int. J. Mech. Sci. 18: 285–291.

      20 Shima, S., Oyane, M., and Kono, Y. (1973). Theory of plasticity for porous metals. Bull. JSME. 16: 1254–1262.

      21 Tvergaard, V. and Needleman, A. (1984). Analysis of the cup‐cone fracture in a round tensile bar. Acta Metall. 32: 157–169.

      22 Ziabicki, A., Misztal‐Faraj, B., and Jarecki, L. (2016). Kinetic model of non‐isothermal crystal nucleation with transient and athermal effects. J. Mater. Sci. 51 : 8935–8952.

1 Introduction

      1.1 The Objective of the Work

The subject of the book evolved since the 1990s from the many years' studies, in several joint research projects conducted together with the investigation group of Andrzej Korbel and Włodzimierz Bochniak, professors at the Faculty of Non‐Ferrous Metals of the AGH University of Science and Technology in Kraków, Poland (formerly Akademia Górniczo – Hutnicza, in English: Academy of Mining and Metallurgy), cf. Figure 1.1. It concerned physics and theoretical description of deformation processes in metals, particularly in hard deformable alloys. The long‐time joint efforts to understand the physical mechanisms responsible for observed phenomena coined the subject of this work. Many years of investigations of metal‐forming processes based on multilevel observations – on a macroscopic scale with the naked eye, microscopic ones using optical microscopy, high‐resolution transmission electron microscopy, and scanning electron microscopy – led to the critical conclusion. The traditional approach of classical plasticity theory based solely on crystallographic slip and twinning in separate grains is inadequate for predicting and modelling observed deformation processes. Such an observation played a pivotal role in developing an innovative metal‐forming method called KOBO, the acronym of inventors names ‘Korbel’ and ‘Bochniak’. This book attempts to provide theoretical foundations and empirical evidence of viscoplastic flow produced by shear banding. In the future, the presented results should