Research Papers

Temperature-Dependent Modulus of Metals Based on Lattice Vibration Theory

[+] Author and Article Information
Honghong Su

College of Resource and Environment Science,
Chongqing University,
Chongqing 400044, China;
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Xue Feng

e-mail: fengxue@tsinghua.edu.cn
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Bo Yan

College of Resource and Environment Science,
Chongqing University,
Chongqing 400044, China

1Corresponding author.

Manuscript received August 14, 2013; final manuscript received September 8, 2013; accepted manuscript posted September 12, 2013; published online October 29, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(4), 041017 (Oct 29, 2013) (4 pages) Paper No: JAM-13-1343; doi: 10.1115/1.4025417 History: Received August 14, 2013; Revised September 08, 2013; Accepted September 12, 2013

Fundamentally understanding the temperature-dependent modulus is the key issue for materials serving in high temperature environments. This paper proposes a model based on lattice vibration theory to predict the temperature-dependent modulus with respect to isothermal and isentropic assumption. The thermal vibration free energy is expressed as a function of the two independent scalars from the strain tensor and temperature. By using the Einstein theory, we present the analytical expression for the temperature-dependent Young's modulus, bulk modulus, shear modulus, and Poisson's ratio. The theoretical prediction agrees well with the experimental data. The proposed model is further degenerated to Wachtman's empirical equation and provides the physical meaning to the parameters in Wachtman's equation.

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Grahic Jump Location
Fig. 1

Temperature-dependent modulus of molybdenum. Experimental data from literature [13,14].

Grahic Jump Location
Fig. 2

Temperature-dependent Poisson's ratio of molybdenum



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