Deformation Twinning in Zirconium: Direct Experimental Observations and Polycrystal Plasticity Predictions
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INTRODUCTION
THE deformation behavior of hexagonal closed packed (hcp) metals is more complex than that of cubic metals.[1] Plastic deformation in hcp zirconium alloys is accommodated by the activation of slip systems[2–6] together with deformation twinning systems.[7–11] The set of potentially activated slip and twinning systems is temperature dependent. Deformation twinning can have a significant effect on microstructural development and mechanical behavior.[10,12–17] This has important consequences in the context of zirconium alloy components, whose fabrication and inreactor usage are associated with inelastic deformation.[18,19] Material purity, microstructure, texture, processing temperature, strain mode, and strain-rate are wellestablished parameters that influence deformation twinning in pure zirconium and zirconium alloys. Akhtar and Teghtsoonian[20] showed that alloying elements influence the shape of the hardening curve of single JAIVEER SINGH and GULSHAN KUMAR, Research Scholars, PRITA PANT, Associate Professor, and I. SAMAJDAR, Professor, are with the Department of Metallurgical Engineering & Materials Science, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India. SIVASAMBU MAHESH, Associate Professor, is with the Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600 036, India. Contact e-mail: [email protected] D. SRIVASTAVA, Head of Physical Metallurgy Section, and G.K. DEY, Associate Director of Materials Group, are with Materials Science Division, Bhabha Atomic Research Centre Trombay, Mumbai 400 085, India. N. SAIBABA, Chairman & Chief Executive of Nuclear Fuel Complex, is with Nuclear Fuel Complex, Moula-ali, PO: ECIL, Hyderabad 500 062, India Manuscript submitted March 7, 2015. Article published online August 14, 2015 5058—VOLUME 46A, NOVEMBER 2015
crystals. Reduced grain size has been shown to inhibit deformation twinning,[21–23] and grain boundary character has been shown to be important in determining the ease of twin nucleation.[24] Crystallographic texture influences the resolved shear stresses on slip and twinning systems and thus influences the extent of deformation twinning significantly.[3,5,20,21,23,25–29] The critical resolved shear stress of deformation twinning systems increases less rapidly with decreasing temperature than that of slip systems. Consequently, more deformation twinning occurs at lower temperatures.[5,30] Much research spanning several decades has gone into incorporating deformation twinning into polycrystal plasticity models.[17,31–33] Highlights include the pioneering model due to Chin et al.,[31] proposed for face-centered cubic materials. In this model, each twinning system is associated with a critical resolved shear stress, and twin growth is governed by Schmid’s law.[34] Twinning is thus treated on par with unidirectional slip by assigning critical resolved shear stresses with or without hardening to twinning systems. The methodology to implement the Chin et al. model in rate-independent polycrystals, given by van Houtt
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