Theoretical Relationship between Modulus of Elasticity and Temperature for Engineering Materials

*, **
* Department of Mechanical Engineering, Kettering University.
** Professor and Doctor of Technical Science with expertise in Material Science and Nondestructive Testing.
*** Chair and Professor, Department of Mechanical and Manufacturing Engineering, School of Engineering and Applied Science, Miami University.
Periodicity:May - July'2012
DOI : https://doi.org/10.26634/jme.2.3.1866

Abstract

The modulus of elasticity is one of the most important mechanical properties of a material. It needs to be determined accurately in order to facilitate mechanical design, ensure reliability and promote compliance with legislative restrictions. The modulus-temperature relationship is traditionally determined experimentally, and the procedure is time consuming, expensive, and often impossible. The main goal of this work is to obtain a comprehensive analytical relationship between modulus of elasticity and temperature, based on the kinetic nature of the strength of solids and a nonlinear equation of state for materials. The analytical modulus-temperature relationship is compared with existing experimental data. Results demonstrate the potential of the nonlinear approach to predict the static and dynamic elastic modulus of different engineering materials (metals, plastics, and concrete) as a function of temperature.

Keywords

Modulus of Elasticity, Temperature, Stress, Strain, Activation Energy.

How to Cite this Article?

Yaomin Dong, Iosif E. Shkolnik and Timothy M. Cameron (2012). Theoretical Relationship Between Modulus Of Elasticity And Temperature For Engineering Materials. i-manager’s Journal on Mechanical Engineering, 2(3), 15-25. https://doi.org/10.26634/jme.2.3.1866

References

[1]. Bell, J.F. (1983). Mechanics of Solids: The experimental foundations of solid mechanics, Springler-Verlag, New York.
[2]. Regel, V.R., Slutzker A.I., and Tomashevsky, E.E. (1974). Kinetic Nature of Solids Strength, Nauka: Moscow (in Russian).
[3]. Frenkel, J. (1946). Kinetic Theory of Liquids, Dover Publications, Inc.
[4]. Layus L.A., Slutzker, A.I., Gofman I.V., and Gilarov, V.L. (2004). “Correlation of the characteristics of reversible thermal, and force deformations in solid bodies of different structures.” Phys. Solid States, 46(6), 1115-1122 (in Russian).
[5]. Shkolnik, I.E. (2006). “Nonlinear NDE of concrete mechanical properties.” Innovations in Nonlinear Acoustics, AIP Conference Proceedings, 43-50.
[6]. Betekhtin, V.I., Kuksenko, V.S., Slutzker, A.I., and Shkolnik, I.E. (1994). “Fracture kinetics and the dynamic strength of concrete.” Physics of the Solid State, American Institute of Physics; 1416-1421.
[7]. Shkolnik I.E. (2005). “Effect of nonlinear response of concrete on its elastic modulus and strength.” Cement and Concrete Composites, 27, 747-757.
[8]. Shkolnik, I.E. (2008). “Influence of high strain rates on stress-strain relationship, strength and elastic modulus of concrete,” Cement and Concrete Composites, 30, 1000-1012.
[9]. Shkolnik, I.E. (1996). “Evaluation of dynamic strength of concrete from results of static tests.” ASCE J. Engineering Mechanics, 122(12), 1133-1138.
[10]. Shkolnik, I.E., and Cameron, T.M. (1996). “Nonlinear acoustic methods for strength testing of materials.” Nonlinear Acoustics in Perspective, 14th International Symposium on Nonlinear Acoustics, Nanjing University Press, Nanjing, 316-320.
[11]. Shkolnik, I.E., Cameron, T.M., and Dong, Y. (2008). “Non-destructive evaluation of the relationship between modulus of elasticity and temperature based on the nonlinear equation of state for industrial materials.” Nonlinear Acoustics - Fundamentals and Applications, edited by B. O. Enflo, C. M. Hedberg and L. Kari, © American Institute of Physics, 565-568.
[12]. Fabco Plastics (2007). http://www.fabcoplastics. com/ file_library/documents/1_FabcoEngineeringData.pdf,The Engineering Toolbox, http://www.engineeringtoolbox.com, accessed November 19, 2009.
[13]. ASTM Standard E8 (2009). "Standard test methods for tension testing of metallic materials." ASTM International, West Conshohocken, PA, DOI: 10.1520/E0008_E0008M-09, www.astm.org.
[14]. ASTM Standard E111 (2004). "Standard test method for young's modulus, tangent modulus, and chord modulus." ASTM International, West Conshohocken, PA, DOI: 10.1520 /E0111-04, www.astm.org.
[15]. NIST. Database for Solder Properties with Emphasis on New Lead-free Solders, Release 4.0.
[16]. Cheng, Y.W., and Siewert, T.A. (2003). “Predicting of tensile properties of the bulk 96Sb-3.5Ag lead-free solder.” J. Electronic Materials, 32 (6), 535-540.
[17]. Shkolnik, I., Palmer, M., Dong, Y., and Cameron, T. (2007). “The relationship between elastic modulus of lead-free solders and temperature.” Proceedings of ASNT Fall Conference and Quality Testing Show, Las Vegas, NV, November 12-16, 244-246.
[18]. Syed, A. (2004). “Accumulated creep strain and energy density based thermal fatigue life prediction models for snagcu solder joints.” 54th ECTC Conference Proc., 737-746.
[19]. ASTM Standard D638 (2008). "Standard test method for tensile properties of plastics." ASTM International, West Conshohocken, PA, DOI: 10.1520/D0638-08, www.astm. org.
[20]. Phan, L.T., and Carino, N.J. (2002). “Effects of test conditions and mixture proportions on behavior of high-strength concrete exposed to high temperatures.” ACI Materials Journal, 54-66.
[21]. ASTM Standard C469-02e1 (2002). "Standard test method for static modulus of elasticity and poisson's ratio of concrete in compression." ASTM International, West Conshohocken, PA, DOI: 10.1520/C0469-02E01, www. astm.org.
[22]. ASTM Standard C215 (2008). "Standard test method for fundamental transverse, longitudinal, and torsional frequencies of concrete specimens." ASTM International, West Conshohocken, PA, DOI: 10.1520/C0215-08, www.astm.org.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Online 15 15

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.