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Research Papers

Constitutive Relations for Modeling Single Crystal GaN at Elevated Temperatures

[+] Author and Article Information
Antoinette Maniatty

Professor
Fellow ASME
Department of Mechanical, Aerospace, and
Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180-3590
e-mail: maniaa@rpi.edu

Payman Karvani

Mem. ASME
Department of Mechanical, Aerospace, and
Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180-3590
e-mail: paymaan@gmail.com

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received April 28, 2014; final manuscript received August 8, 2014; published online September 24, 2014. Assoc. Editor: Irene Beyerlein.

J. Eng. Mater. Technol 137(1), 011002 (Sep 24, 2014) (7 pages) Paper No: MATS-14-1094; doi: 10.1115/1.4028441 History: Received April 28, 2014; Revised August 08, 2014

Thermal–mechanical constitutive relations for bulk, single-crystal, wurtzite gallium nitride (GaN) at elevated temperatures, suitable for modeling crystal growth processes, are presented. A crystal plasticity model that considers slip and the evolution of mobile and immobile dislocation densities on the prismatic and basal slip systems is developed. The experimental stress–strain data from Yonenaga and Motoki (2001, “Yield Strength and Dislocation Mobility in Plastically Deformed Bulk Single-Crystal GaN,” J. Appl. Phys., 90(12), pp. 6539–6541) for GaN is analyzed in detail and used to define model parameters for prismatic slip. The sensitivity to the model parameters is discussed and ranges for parameters are given. Estimates for basal slip are also provided.

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Figures

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Fig. 1

Orientation of the GaN hexagonal lattice relative to the compression experiment, where the x1, x2 are coordinates of the global reference frame with x2 aligned with the compressive axis, and x¯1,x¯2 are the lattice reference frame coordinates

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Fig. 2

Stress–strain curves of GaN bulk single crystals, based on data from Yonenaga and Motoki [9]

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Fig. 3

Stress–strain curves of GaN bulk single crystals at temperatures of 900, 950, and 1000 °C, based on data from Yonenaga and Motoki [9], corrected for machine compliance

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Fig. 4

Computed plastic strain rate for Yonenaga and Motoki [9] experiment at temperatures of 900, 950, and 1000 °C

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Fig. 5

Stress–strain curves from proposed model for GaN versus experiment data [9], at temperatures of 900, 950, and 1000 °C. Model A assumes Eq. (20) and model B assumes Eq. (21).

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Fig. 6

Computed dislocation density for the experiment [9], at temperatures of 900, 950, and 1000 °C

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