Constitutive modeling of creep behavior in single crystal superalloys: Effects of rafting at high temperatures

A tensorial thermodynamic framework to account for theγ' rafting in nickel-based single crystal superalloys

“…In case a) the consideration of two tensorial variables among the three ℓ ℓ ℓ, w, λ λ λ, seems an adequate choice (but the question of the tensors coaxiality arises then). In case b) different choices are pertinent, including scalars variables -for instance index of rafting ξ (Fan et al , 2015, Fedelich et al , 2006, isotropic periodicity λ or precipitates volume fraction f γ ′ Cormier and Cailletaud (2010a), Ghighi et al (2013), Giraud et al (2013), le Graverend et al (2014a). One has simply to be careful to the independency of the variables retained.…”

“…Pineau (1976) by using a micro-mechanics approach and more recently by using unit cell Finite Element computations have shown that the strain energy during a creep test decreases as yielding and rafting proceed (see also (Fan et al , 2015)). As there is a lack of experimental evidences on the rafting-elasticity coupling, one can simply assume that elasticity remains cubic and sets…”

“…No effect is considered when coarsening (ω eq = 3 2 ω ′ is the norm of deviatoric part ω ′ = ω − 1 3 tr ω 1 1 1), if needed replace ω eq by ω . The thermodynamics framework derived next will consider such a coupling (in order to recover the energetic contribution to rafting driving force derived in Fan et al (2015)) but the final model proposed in section 6 will neglect it (κ E ω eq << 1, Eq. (74)).…”

“…γ ′ coarsening or rafting) cannot be avoided at temperatures above 850 • C, several studies have been conducted to determine the rafting kinetics of the γ ′ -phase (Zhou et al , 2007, Svobda and Lukas , 1996, Svoboda and Lukas , 1997, considering uniaxial loadings leading to an homogeneous stress field or under different applied stresses to be able to model the γ ′ rafting process has a function of time, temperature and applied stress (Epishin et al , 2008, 2012a. Based on such experimental characterizations, various models have been proposed to be able to account for the consequences of the γ/γ ′ microstructure degradation on the isothermal creep, tensile and LCF properties (Fan et al , 2015, Fedelich et al , 2012a,b, le Graverend et al , 2014a, Leidermark et al , 2010, Svoboda and Lukas , 1998, Svoboda and Lukas , 2000. However, most of these approaches were devoted to account for the mechanical behavior evolution along the < 001 > crystallographic orientation with little attention on the γ ′ rafting kinetics along other crystallographic orientations whose process is quite different than along the < 001 > direction (Gaubert et al , 2015, Tian et al , 2012, Tien and Copley , 1971, leading to different consequences on the mechanical behavior.…”

The Compositional Dependence of the Microstructure and Properties of CMSX-4 Superalloys

“…Fan et al [22] follow the approach of Fedelich et al's work [20] in describing the channel width and rafting degree but attempt to bring in a more physical approach. They describe the isotropic coarsening of the microstructural periodicity, as follows:…”