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Deformation and Recrystallization of Single Crystal Nickel-Based Journal of Materials Processing Technology 217 (2015) 1–12 Contents lists available at ScienceDirect Journal of Materials Processing Technology jo urnal homepage: www.elsevier.com/locate/jmatprotec Deformation and recrystallization of single crystal nickel-based superalloys during investment casting a b a,∗ b a Li Zhonglin , Xiong Jichun , Xu Qingyan , Li Jiarong , Liu Baicheng a School of Materials Science and Engineering, Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Tsinghua University, Beijing 100084, China b National Key Laboratory of Advanced High Temperature Structural Materials, Beijing Institute of Aeronautical Materials, Beijing 100095, China a r t i c l e i n f o a b s t r a c t Article history: A semi-quantitative, macroscopic, phenomenon-based, thermo-elastic–plastic model was developed to Received 28 August 2014 predict the final plastic strains of single crystal nickel-based superalloys by considering their orthotropic Received in revised form 21 October 2014 mechanical properties. Various cases were considered and simulated to investigate the basic factors Accepted 23 October 2014 that influence the final plasticity. Thermo-mechanical numerical analysis was conducted to predict the Available online 4 November 2014 recrystallization sites of simplified cored rods, with the results in good agreement with the experimental results. These hollowed rods with thin walls showed an increased propensity for recrystallization. The Keywords: geometric features, especially stress concentration sites, are more significant to the induced plasticity Single crystal Superalloys than the material’s orientation or shell/core materials. This paper also attempts to provide useful sug- gestions, such as introducing filets, to avoid causing plastic strains during the casting process that induce Investment casting Plastic deformation recrystallization. Recrystallization © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). 1. Introduction Meng et al. (2010) and Moverare et al. (2009), RX is potentially detrimental to creep and fatigue properties, respectively. Turbine blades for gas turbine applications are fabricated by Work has been done to study the phenomenon of RX in single investment casting, often in single crystal form, which can allow crystal nickel-based superalloys. Some research has focused on the higher inlet gas temperatures to be used and increase efficiency. influence of microstructural features on RX, such as ␥ -precipitates, However, the external and internal geometries of single crystal carbides, and ␥/␥ eutectics. For example, Dahlen and Winberg blades are becoming increasingly complicated, making them more (1980) have discussed the influence of ␥ -precipitation on the RX of difficult to cast as greater care is required to prevent defects, such as nickel-based superalloys. Wang et al. (2013) and Xiong et al. (2010) stray grains and freckles, being introduced during the manufactur- have investigated the effect of carbon content on the RX of sin- ing process. Recrystallization (RX) is one of the major difficulties gle crystal (SX) nickel-based superalloys. In addition, Wang et al. and can be ascribed to plastic deformation, as demonstrated by (2009) studied the influence of eutectics on plastic deformation Burgel et al. (2000). During the manufacture of new parts, plastic and the subsequent RX of the SX nickel-based superalloy CMSX-4. deformation can be caused by several possible sources: thermal Meanwhile, some research has concentrated on the effect of differ- contraction during solidification and subsequent cooling, remov- ent annealing conditions and crystallographic orientations on RX ing the ceramic mold and core material mechanically, stamping behavior. Wu et al. (2012) conducted surface RX of a Ni3Al-based identification marks, grinding the airfoil, etc. In practice, plastic SX superalloy at different annealing temperatures and blasting deformation will induce RX during subsequent heat treatments or pressures. Xie et al. (2012) studied the crystallographic orienta- long-term service. For example, RX can introduce high-angle grain tion dependence of RX in a Ni-based SX superalloy. However, little boundaries, which are obviously undesirable. As demonstrated by attention has been paid to the effect of geometric features, ceramic shell and core material, and processing details. Certain critical ques- tions need to be answered, such as at what temperature will RX occur? What is the critical plastic deformation required to induce ∗ RX?, and what is the influence of the geometric features, including Corresponding author. Tel.: +86 10 62795482; fax: +86 10 62773637. holes and platforms? Answers to these questions will allow more E-mail addresses: [email protected] (Z. Li), [email protected] efficient foundry processes, even process-friendly blade designs, to (J. Xiong), [email protected] (Q. Xu), [email protected] (J. Li), [email protected] (B. Liu). be developed. Modeling has been used to analyze the directional http://dx.doi.org/10.1016/j.jmatprotec.2014.10.019 0924-0136/© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). 2 Z. Li et al. / Journal of Materials Processing Technology 217 (2015) 1–12 T solidification of SX superalloys from thermal and microstructural {ε} = [ε11ε22ε33122331] perspectives. Pan et al. (2010) conducted multiscale modeling and T {} = [ ] (4) simulations of the directional solidification process of turbine blade 11 22 33 12 23 31 casting, which resulted in good predictions of temperature pro- − [S] = [C] 1 files and grain number. Dai et al. (2011) investigated grain selection ⎛ ⎞ in spiral selectors during investment casting of SX turbine blades 1/E −/E −/E 0 0 0 through both experimental and numerical modeling techniques. ⎜ ⎟ ⎜ −/E 1/E −/E 0 0 0 ⎟ One advantage simulation provides over experiments is that it can ⎜ ⎟ −/E −/E 1/E 0 0 0 S = ⎜ ⎟ predict the plastic strains that cause RX. [ ] ⎜ ⎟ (5) ⎜ 0 0 0 1/G 0 0 ⎟ The overarching goal of this study was to build a physics-based ⎝ ⎠ 0 0 0 0 1/G 0 tool for predicting casting-induced plasticity and subsequent RX /G during the heat treatment of SX superalloys by considering the 0 0 0 0 0 1 material’s anisotropic mechanical properties. Panwisawas et al. where {} and {ε} are the stress and strain vectors, respectively. (2013a,b) developed a mathematical model to predict plasticity and Sij and Cij denote the elastic compliance and stiffness constants, RX in investment-cast SX superalloys. However, this model consid- respectively, which measure the strain (or stress) necessary to ered SX superalloys as isotropic materials, which does not conform maintain a given stress (or strain). E, , and G are the Young’s mod- to the reality. Many mechanical models have been proposed to ulus, Poisson’s ratio, and shear modulus, respectively, in the three describe the mechanical properties of anisotropic materials. Ding principal orientations: 0 0 1, 0 1 0, and 1 0 0. The stiffness and et al. (2004) proposed a macroscopic phenomenon-based model compliance constants have the following relations: built on a modified Hill plasticity model. Zambaldi et al. (2007) C + C employed a microscopic crystal plasticity model, which was built 11 12 S11 = (6) C − C C + C on the physical deformation mechanisms of materials, to predict ( 11 12) ( 11 2 12) the distribution of crystallographic slip in SX nickel-based super- C S = 12 (7) alloys. The former gained great popularity for its concise equations, 12 C C − C + C ( 11 12) ( 11 2 12) as well as its convenience and speed of calculations, though the 1 latter model can give more accurate predictions of slips and grain S = (8) 44 C size. 44 This paper proposed a mathematical thermo-mechanical model The matrix phase, ␥, and precipitate phase, ␥ , both exhibit using the Hill’s plasticity model as a basis, which considers the FCC structures and have coherent interfaces. Therefore, the nickel- orthotropic mechanical properties of SX superalloys, and took into based SX superalloys can be considered approximately orthotropic account both the scale effect and convenience. Numerical analy- materials with three identical principal orientations. There are only sis using this model was performed to identify the major factors 3 independent constants in [S]. that cause the plasticity during investment casting and RX during By applying spatial geometry transformations, the Young’s the subsequent heat treatment. A series of simplified thermo- modulus, E , and shear modulus, G , in a given crystallographic ori- mechanical numerical analyses with the DD6 superalloy were entation can be obtained as follows: conducted and compared with experimental results to test the S 1 11 − S12 − S44 = S = S − JS validity of the model. This model could be employed to optimize 2 (9) E 11 11 2 processing conditions to reduce the likelihood of RX. with the orientation parameters J and S given by: 2. Mathematical model of SX superalloys J 2 2 2 2 2 2 = l m + l n + m n (10) S = 2S − 2S − S (11) Plastic deformation during investment casting mainly occurs 11 12 44 because of the different thermal expansion coefficients of the where l, m, and n represent the directional cosines relative metals, and the ceramic shell and core. Assuming the plasticity is to the axes 1, 2, and 3, respectively. Thus, the degree of ε ε rate-independent, the thermal strain ( th), elastic strain ( el), and anisotropy depends on the orientation parameter, which has ε plastic strain ( pl) follow the relation below: a minimum value of zero along 0 0 1, a maximum value of 1/3 along 1 1 1, and a value of 1/4 along 0 1 1. For a pure εth + εel + εpl = 0 (1) nickel SX at room temperature, typical values for the compliance The thermal strain can be calculated as −5 –1 −5 –1 constants are S11 = 0.799 × 10 MPa , S12 = −0.312 × 10 MPa , −5 –1 ε = and S = 0.844 × 10 MPa .
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