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Research Papers

Reduced-Order Constitutive Modeling of Directionally Solidified Ni-Base Superalloys

[+] Author and Article Information
S. D. Neal

The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

R. W. Neu

The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Materials Science and Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: rick.neu@gatech.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 12, 2013; final manuscript received December 11, 2013; published online January 17, 2014. Assoc. Editor: Tetsuya Ohashi.

J. Eng. Mater. Technol 136(2), 021003 (Jan 17, 2014) (11 pages) Paper No: MATS-13-1111; doi: 10.1115/1.4026271 History: Received June 12, 2013; Revised December 11, 2013

Temperature-dependent crystal viscoplasticity models are ideal for modeling large-grained, directionally solidified Ni-base superalloys but are computationally expensive. This work explores the use of reduced-order models that are potentially more efficient with similar predictive capability of capturing temperature and orientation dependence. First, a transversely isotropic viscoplasticity model is calibrated to a directionally solidified Ni-base superalloy using the response predicted by a crystal viscoplasticity model. The unified macroscale model is capable of capturing isothermal and thermomechanical responses in addition to secondary creep behavior over the temperature range of 20–1050 °C. A second approach is an extreme reduced-order microstructure-sensitive constitutive model that uses an artificial neural network to provide a set of parameters that depend on orientation, temperature, and strain rate to give a first-order approximation of the material response using a simple constitutive model. This simple relationship is then used in a Neuber-type fatigue notch analysis to predict the local response.

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Figures

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Fig. 1

Calibration curve comparing TIVP and CVP models at 20 °C, 1.0 × 10−4 s−1, 0 deg off-axis

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Fig. 2

Calibration curve comparing TIVP and CVP models at 650 °C, 1.0 × 10−4 s−1, 0 deg off-axis

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Fig. 3

Calibration curve comparing TIVP and CVP models at 950 °C, 1.0 × 10−4 s−1, 0 deg off-axis

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Fig. 4

Elastic modulus at 850 °C as a function of orientation showing how the response from the TIVP simulation is compared to literature [24]

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Fig. 5

Elastic modulus as a function of orientation for various temperatures from the TIVP simulation

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Fig. 6

0.2% offset yield strength as a function of orientation for various temperatures predicted from the TIVP simulation

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Fig. 7

A typical multilayer feedforward artificial neural network layout [25]

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Fig. 8

Training methodology for extreme reduced-order model

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Fig. 9

Schematic of ANN used for extreme reduced-order model

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Fig. 10

Comparisons of the multigrain CVP and extreme reduced-order model (ANN) predictions at (a) 623 °C, 2.0 × 10−5 s−1, 78 deg off-axis, (b) 886 °C, 5.0 × 10−6 s−1, 27 deg off-axis, and (c) 1031 °C, 5.0 × 10−4 s−1, 53 deg off-axis

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Fig. 11

Procedure for component analysis using extreme reduced-order modeling method

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Fig. 12

Finite element mesh of cylindrically notched specimen

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Fig. 13

Comparison of predicted and actual responses of critical element at third reversal using Neuber relation, 950 °C, Rσ = −1, σa = 250 MPa

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Fig. 14

Finite element mesh of square plate with circular hole at center (one-fourth symmetry model)

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Fig. 15

Comparison of notch root (element A) responses and extreme-reduced order model predictions, 950 °C

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Fig. 16

Comparison of notch root (element A) responses and extreme-reduced order model predictions, 750 °C

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Fig. 17

Nomenclature for notch surface elements

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Fig. 18

Comparisons of various element responses along notch surface, 950 °C

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Fig. 19

Comparisons of various element responses along notch surface, 750 °C

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