PSI - Issue 14

Ritam Chatterjee et al. / Procedia Structural Integrity 14 (2019) 251–258 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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grains and the cycle continues. In other words, recrystallization could be described as alternate stressing and relaxation of the material. The word dynamic when added as a prefix to recrystallization refers to work input being continuously provided to the material in order to facilitate plastic deformation. Recrystallization plays a pivotal role in imparting strength and desirable mechanical properties to the material via microstructural changes. Dynamic recrystallization was first observed nearly 80 years back by Greenwood and Worner (1939) while carrying out creep studies on an alloy of lead (Pb). Titanium is one of the most important metals known to mankind. Commercially pure titanium has widespread applications across a spectrum of industries such as aerospace, medical, nuclear, food processing etc. Due to required heat transfer characteristics, it is ideal for gas turbine blades and aircraft components. Pure titanium has excellent corrosion resistance due to which it is increasingly being used in architectural artifacts to protect them from acid rain. Due to its non-toxicity and compatibility with the human body, commercial purity Ti is used in dental and bone implants, artificial heart valves and pacemaker housings. The present work focuses on simulating the phenomenological behaviour of pure titanium under physical conditions that lead to occurrence of dynamic recrystallization. Pure titanium has been chosen as the material since the present work will later be used to compare the effect of alloying additions on the flow stress response to DRX of the strategically important aerospace alloy alpha Ti-5Al-2.5Sn. This will aid in design of optimal thermo-mechanical treatment to impart the best possible physical and mechanical properties to Ti-5Al-2.5Sn by taking advantage of beneficial facets of microstructural and texture evolution during DRX. Section 2 of the present work consists of a mathematical description of the nucleation and growth model which is based on the work of Ding and Guo (2001) and Zhou et. al (2017). The dislocation density hardening model is based on the work of Beyerlein and Tome (2008) implemented in viscoplastic self-consistent (VPSC) framework as developed by Lebensohn & Tome (1993). To update slip resistance of a slip system, the sum of contributions due to initial slip resistance, forest dislocations and debris is considered for each slip system. The dislocation density in each grain is thereafter updated based on the equation formulated by Essmann and Mughrabi (1979) that was further developed by Kocks and Mecking (1981, 2003). The occurrence of DRX in each grain is subject to achieving critical dislocation density. A flow chart is shown that depicts the complete modelling process. Nucleation is modelled based on a probabilistic scheme that allows nucleation to occur in a grain subject to its nucleation probability exceeding a critical value. Section 3 consists of a detailed discussion of results obtained from simulation of plastic deformation using VPSC which demonstrates proof concept for modeling of DRX in Ti. The flow stress behaviour of CP Ti under DRX has been captured at temperature 1173K and strain rate 0.001s -1 . The updating of number of grains at each deformation step due to formation of new nuclei has been shown. Initial dislocation density has been assigned to new grains and the average dislocation density variation over all grains has been shown. Random crystallographic texture is assigned to the old grains initially as well as to the new grains.

2. Model Implementation

2.1. Nucleation and Growth Model The Ding and Guo approach (2001) for predicting the microstructural evolution due to the onset of DRX is based on achieving critical dislocation density in the grain. The approach is an attempt at improving the earlier models proposed