ORIGINAL PAPER
Determination of Constant Parameters of Copper as Power-Law Hardening Material at Different Test Conditions
More details
Hide details
1
Department of Mechanical Engineering Dhaka University of Engineering and Technology (DUET) Gazipur, Bangladesh
Online publication date: 2014-12-30
Publication date: 2014-11-01
International Journal of Applied Mechanics and Engineering 2014;19(4):687-698
KEYWORDS
ABSTRACT
In this paper a technique has been developed to determine constant parameters of copper as a power-law hardening material by tensile test approach. A work-hardening process is used to describe the increase of the stress level necessary to continue plastic deformation. A computer program is used to show the variation of the stress-strain relation for different values of stress hardening exponent, n and power-law hardening constant, α . Due to its close tolerances, excellent corrosion resistance and high material strength, in this analysis copper (Cu) has been selected as the material. As a power-law hardening material, Cu has been used to compute stress hardening exponent, n and power-law hardening constant, α from tensile test experiment without heat treatment and after heat treatment. A wealth of information about mechanical behavior of a material can be determined by conducting a simple tensile test in which a cylindrical specimen of a uniform cross-section is pulled until it ruptures or fractures into separate pieces. The original cross sectional area and gauge length are measured prior to conducting the test and the applied load and gauge deformation are continuously measured throughout the test. Based on the initial geometry of the sample, the engineering stress-strain behavior (stress-strain curve) can be easily generated from which numerous mechanical properties, such as the yield strength and elastic modulus, can be determined. A universal testing machine is utilized to apply the load in a continuously increasing (ramp) manner according to ASTM specifications. Finally, theoretical results are compared with these obtained from experiments where the nature of curves is found similar to each other. It is observed that there is a significant change of the value of n obtained with and without heat treatment it means the value of n should be determined for the heat treated condition of copper material for their applications in engineering fields.
REFERENCES (25)
2.
Batdorf S.B. and Budiansky B. (1949): A mathematical theory of plasticity based on the concept of slip. - NACA TN 1871.
3.
Denke P.H. (1956): The matrix solution of certain nonlinear problems in structural analysis. - Journal of Aerospace and Sciences, vol.23, No.3, pp.231-236.
4.
Hodge P.G. (1959): Plastic Analysis of Structures. - New York: McGraw Hill.
5.
Hosford F. William (2005): Mechanical Behavior of Materials. - USA: University of Michigan.
6.
Hue L.W. and Bratt J.F. (1958): Effect of tensile plastic deformation on the yield condition. - Journal of Applied Mechanics, vol.25, pp.111.
7.
Hutchinson J.W. (1967): Singular behavior at the end of a tensile crack in a hardening material. - Journal of the Mechanical and Physics of Solids, vol.16, pp.13-31.
8.
Isakson G., Armen H. Jr. and Pifko A. (1967): Discrete-element methods for the plastic analysis of structures. - National Aeronautics and Space Administration, Washington D.C..
9.
Kowser M.A. and Mahiuddin M. (2012): Technique for determining the constant parameters of power-law hardening material by tensile test. - Proceedings of 6 IMEC & 14 APM, Dhaka, Bangladesh.
10.
Kowser M.A. and Mahiuddin M. (2013): Technique for determining the constant parameters of Cu as a power-law hardening material at different conditions. - Proceedings of ICERIE, SUST, Sylhet, Bangladesh, Jan. 11 ̶ 13.
11.
Kucharski S. and Mróz Z. (2007): Identification of yield stress and plastic hardening parameters from a spherical indentation test. - International Journal of Mechanical Sciences, vol.49, pp.1238-1250.
12.
Lin X. and Tzuchiang W. (1992): The interfacial crack between two dissimilar elastic-plastic materials. - Acta Mechanica Sinica, vol.8, No.2.
13.
Lin Xia and Wang T. (1993): Singular behavior near the tip of a sharp V-notch in a power law hardening material. - International Journal of Fracture, 59:83-93.
14.
Marin J. and Hue L.W. (1953): On the validity of assumptions made in theories of plastic flow for metals. - Transaction ASME, vol.75, No.6, pp.1181.
15.
Naghdi P.M. (1960): Stress-strain relations in plasticity and thermo-plasticity. - Proceedings of 2nd Symposium on Naval Structural Mechanics, pp.121.
16.
Neal B.G. (1950): Plastic collapse and shakedown theorems for structures of strain-hardening material. - Journal of Aerospace and Sciences, vol.17, No.5, pp.297.
17.
Parker J. and Basset M.B. (1964): Plastic stress-strain relationships-some experiments to derive a subsequent yield surface. - Journal of Applied Mechanics, vol.31, pp.676.
18.
Perrone N. and Hodge P.R. Jr. (1957): Applications of a consistent theory for strain-hardening plastic solids. - PIBAL Report 403.
19.
Prager W. (1956): A new method of analyzing stress and strain in work hardening plastic solids. - Journal of Applied Mechanics, vol.23, P.493.
20.
Prager W. (1955): The theory of plasticity: a survey of recent achievements. - Proceedings of Institution of Mechanical Engineers, vol.169, pp.41.
21.
Ramberg W. and Osgood W.R. (1960): Description of stress-strain curves by three parameters. - NACA TN 902.
22.
Rivello R.M. (1960): Ramberg-Osgood and hill parameters of aircraft structural materials at elevated temperatures. - University of Maryland, Aerospace Engineering Department, Rep. 60-1.
23.
Sanders Jr. J.L. (1954): Plastic stress-strain relations based on linear loading functions. - Proceedings of 2nd U.S. National Congress Appl., pp.455.
24.
Symonds P.S. and Prager W. (1950): Elastic-plastic analysis of structures subjected to loads varying arbitrarily between prescribed limits. - Journal of Applied Mechanics, vol.17, No.3, pp.315.
25.
Xia L. and Tzuchiang W. (1994): Higher-order analysis of near-tip fields around an interfacial crack between two dissimilar power law hardening materials. - Acta Mechanica Sinica, vol.10, No.1.