PSI - Issue 14

Amit Singh et al. / Procedia Structural Integrity 14 (2019) 78–88

79

Amit Singh et al./ Structural Integrity Procedia 00 (2018) 000 – 000

2

alloy is used in the form of rotors and stators in aeroengines, Noda et al. (1995), Honnorant (1988), Balasundar (2010). It has many advantages such as high specific strength, corrosion /erosion resistance and high temperature workability when compared to other high temperature Ti alloys. The β transus tempera ture for this alloy is 1333 K, Neal (1984). This alloy shows wide variety of microstructure depending up on the solution treatment temperature, holding time and cooling rate. It favors the formation of Ti 3 Al (α 2, aluminide phase) and (Ti, Zr) 6 Si 3 (S 2, silicide phase) after aging at 973 K for 2 hours followed by air cooing, Lutjering and Williams (2007). The α 2 and S 2 phases are coherent and incoherent with the matrix, respectively. The crystal structure of both the precipitate phases is hexagonal with different c/a ratio, Madsen and Ghonem (1995), Popov et al. (2015). It is well reported that, S 2 precipitates at interface of α/β phase, while α 2 precipitates in the matrix of α phase . Hence, by changing the fraction of α/β phase , the morphology and topology of microstructure can be changed and this can be achieved by changing the solution treatment temperature and cooling rate, Lutjering and Williams (2007), Kumar et al. (2003). In literatures it is reported that bimodal microstructure has good combination of creep and fatigue properties, Omprakash et al. (2010), Rao et al. (2009). Few researchers, Kumar et al. (2003), Omprakash et al. (2010) and Balasundar et al. (2014) have also studied tensile behavior of the bimodal microstructures however, studies on the role of α p phase fraction on tensile and strain hardening behavior of IMI 834 alloy at room temperature is rather limited. For the detailed understanding of the effect of primary α (α p ) phase fraction on tensile and strain hardening behavior, the constitutive flow behavior must be investigated. There are several empirical constitutive equations to model the flow behavior of polycrystalline materials. Hollomon, Ludwik, Voce, Swift and Ludwigson equations are few of them. These empirical flow stress models and their parameters have been used extensively to investigate the underlying mechanism and changes in microstructure which occur during deformation. Further, the strain hardening parameters were also found to be useful in characterizing the formability behavior, Mondal (2013). In this work, an attempt has been made to study the role of α p phase fraction on the tensile and strain hardening behavior of IMI 834 alloy at room temperature. The flow stress behavior of the polycrystalline materials is generally described by several empirical relationships between stress and strain. The widely used relationships are, Hollomon (Hollomon 1945), Ludwik (Ludwik 1909), Voce (Voce 1948), Swift (Swift 1952) and Ludwigson (Ludwigson 1971). These relationship help to understand the deformation mechanisms and formability of the material. The simplest and earliest model for strain hardening is known as power law hardening proposed by Hollomon = (1) where is true stress, p is true plastic strain, is strength coefficient and n is strain hardening exponent. Materials can show varied yield strength with similar strain hardening behavior or similar yield strength with varied strain hardening behavior, therefore yield strength and strain hardening cannot be uniquely described by equation 1. This leads to introduction of prior mechanical history as an additional term to the equation 1. Ludwik and Swift individually modified Equation (1) by adding o which could account for the positive deviation from equation 1 at the early stages of deformation and o which could account for pre-strain in the material, respectively. Hence, the power law hardening Ludwik and Swift equations are = 0 + 1 1 (2) = 2 ( 0 + ) 2 (3) where ͳ ǡ ʹ are strength coefficients,  ͳ ǡ  ʹ are strain hardening exponents, o and o are yield strength and strain due to prior condition of the material, respectively. However, it can be seen from literature of Bergstrom and 2. Theoretical background 2.1. Flow stress behavior