Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T04:05:56.190Z Has data issue: false hasContentIssue false

A Material Function of Endochronic Theory and its Application to Test Under Axisymmetrically Cyclic Loading Conditions

Published online by Cambridge University Press:  05 May 2011

H.-Y. Lin*
Affiliation:
Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan 32001, R.O.C.
W.-C. Yeh*
Affiliation:
Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan 32001, R.O.C.
W.-J. Lee*
Affiliation:
Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan 32001, R.O.C.
*
*Graduate Assistant
**Professor, corresponding author
*Graduate Assistant
Get access

Abstract

A material function of endochronic theory is proposed for investigating the plastic behaviors of material. Depending on the material parameters properly chosen, the present model can be classified into four categories, and is appropriate for describing various materials behaving cyclic strain hardening inherently with respect to the deformation history. Experimental verification of the theory was demonstrated using the experimental results of Shiao [1] and Lamba and Sidebottom [2]. The theory is in good agreement with experimental results obtained by Shiao [1] through comparing the stress-strain hysteresis loops of SAE 4340 steel under axisymmetrically cyclic loading condition with various amplitudes. In addition, the present model is shown to be capable of describing the behavior of erasure of memory of materials, as experimentally observed by Lamba and Sidebottom [2].

Type
Articles
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Shiao, Y. P., “A Study on Multiaxial Cyclic Loading and Anisotropic Plasticity of Structural Metals,” Ph.D. Thesis, National Taiwan University, Dept. of C.E (2000).Google Scholar
2.Lamba, H. S. and Siderbottom, O. M., “Cyclic Plasticity for Nonproportional Path: Part1 : Cyclic Hardening, Erasure of Memory, and Subsequent Strain Hardening Experiments,” J. ofEng.Mat. and Tech., 100, pp. 96103 (1978).CrossRefGoogle Scholar
3.Valanis, K. C., “A Theory of Viscoplasticity Without a Yield Surface, Part I : General Theory,” Arch. of Mech. 23, pp. 517551(1971).Google Scholar
4.Sandler, I. S., “On the Uniqueness and Stability of Endochronic Theories of Material Behavior,” J. of Applied Mechanics, 45, pp. 263266 (1978).CrossRefGoogle Scholar
5.Rivlin, R. S., “Some Comments on the Endochronic Theory of Plasticity,” Int. J. of Solids and Structures, 17, pp. 231248(1981).CrossRefGoogle Scholar
6.Valanis, K. C.,”Fundamental Consequence of a New Intrinsic Time Measure-Plasticity as a Limit of the Endochronic Theory,” Arch. of Mech., 32, pp. 171191 (1980).Google Scholar
7.Valanis, K. C., “Continuum Foundations of Endochronic Plasticity,” J. of Eng. Mat. and Tech., 106, pp. 367375 (1984).CrossRefGoogle Scholar
8.Wu, H. C. and Yip, M. C., “Endochronic Description of Cyclic Hardening Behavior of Metallic Material,” J. of Eng. Mat. and Tech., 103, pp. 212217 (1981).CrossRefGoogle Scholar
9.Watanabe, O. and Atluri, S. N., “Constitutive Modeling of Cyclic Plasticity and Creep, Using an Internal Time Concept,” Int. J. of Plasticity, 2, pp. 107134 (1986).CrossRefGoogle Scholar
10.Yeh, W. C., Cheng, J. Y. and Her, R. S., “Analysis of Plastic Behavior to Cyclically Uniaxial Tests Using an Endochronic Approach,” J. of Eng. Mat. and Tech. ASME, 116, pp. 6267(1994).CrossRefGoogle Scholar
11.Lee, C. F., “Endochronic Theory of Cyclic Plasticity with Applications,” J. of Applied Mechanics, 51, pp. 367374 (1984).Google Scholar
12.Lee, C. F., “Recent Finite Element Applications of the Incremental Edochronic Plasticity,” Int. J. of Plasticity, 11, pp. 843865(1995).CrossRefGoogle Scholar
13.Pan, W. F. and Chern, C. H., “Endochronic Description for Viscoplastic Behavior of Materials Under Multiaxial Loading,” Int. J. of Solids and Structures, 34, pp. 21312160(1997).CrossRefGoogle Scholar
14.Pan, W. F., Chiang, W. J. and Wang, C. K., “Endochronic Analysis for Rate-Dependent Elasto-Plastic Deformation,” Int. J. of Solids and Structures, 36, pp. 32153237 (1999).CrossRefGoogle Scholar
15.Krempl, E. and Lu, H., “The Hardening and Rate Dependent Behavior of Fully Annealed Aisi Type 304 Stainless Steel Under Biaxial In-Phase and out-of –Phase Strain Cycling at Room Temperature,” J. Eng. Mater. Tech., 106, pp. 376384 (1984).CrossRefGoogle Scholar
16.Tanaka, E., Murakami, S. and Ooka, M., “Effects of Strain Path Shapes on Non-Proportional Cyclic Plasticity,” J. Mech. Phys. Solids, 33(6), pp. 559575 (1985).CrossRefGoogle Scholar
17.Tanaka, E., Murakami, S. and Ooka, M., “Effects of Plastic Strain Amplitudes on Non-Proportional Cyclic Plasticity,” ActaMech., 57, pp. 167192 (1985).Google Scholar
18.Hopperstad, O. S., Langseth, M. and Remseth, S., “Cyclic Stress-Strain Behaviour of Alloy AA6060 T4, Part I: Biaxial Experiments and Modeling,” Int. J. of Plasticity, 11, pp. 725739(1995).CrossRefGoogle Scholar
19.Hopperstad, O. S., Langseth, M. and Remseth, S., “Cyclic Stress-Strain Behaviour of Alloy AA6060 T4, Part II: Biaxial Experiments and Modeling,” Int. J. of Plasticity, 11, pp. 741762(1995).CrossRefGoogle Scholar
20.Wu, H. C., Yao, J. C. and Chu, S. C., “Investigation of Endochronic Constitutive Equation Subject to Plastic Strain-Controlled Axial-Torsional Deformation,” J. of Eng. Mat. and Tech., 108, pp. 262269 (1986).CrossRefGoogle Scholar
21.Cailletaud, G., “Some Elements on Multiaxial Behavior Of 316L Stainless Steel at Room Temperature,” Mech. Of Mat, 3, pp. 333345(1984).CrossRefGoogle Scholar
22.Ellyin, F. and Wolodko, J.D., “Testing Facilities for Multiaxial Loading of Tubular Specimens, Multiaxial Fatigue and Deformation Testing Techniques,” ASTM STP 1280, Kalluri, S. and Bonacuse, P. J., Eds, ASTM, pp. 724 (1997).CrossRefGoogle Scholar
23.Basuroychowdhury, I. N. and Voyiadjis, G. Z., “A Multiaxial Cyclic Plasticity Model for Nonproportional Loading Cases,” Int. J. of Plasticity, 14, pp. 855870 (1998).CrossRefGoogle Scholar
24.Yeh, W. C., “Verification of the Endochronic Theory of Plasticity Under Biaxial Load,” J. of the Chinese Institute of Engineers, 18(1), pp. 2534 (1995).CrossRefGoogle Scholar
25.Yeh, W. C., Ho, C. D. and Pan, W. F., “An Endochronic Theory Accounting for Deformation Induced Anisotropy,” Int. J. of Plasticity, 12, pp. 9871004 (1996).CrossRefGoogle Scholar
26.Yeh, W. C. and Lin, H. Y., “An Endochronic Model of Yield Surface Accounting for Deformation Induced Anisotropy,” Int. J. of Plasticity, 22, pp. 1638 (2006).CrossRefGoogle Scholar
27.Liu, C. S., “Reconcile the Perfectly Elastoplastic Model to Simulate the Cyclic Behavior and Ratcheting,” Int. J. of Solids and Structures, 43, pp. 222253 (2006).CrossRefGoogle Scholar
28.Lee, C. F., “Numerical Method of the Incremental Endochronic Plasticity,” The Chinese J. of Mechanics, 8, pp. 377396 (1992).Google Scholar
29.Pan, W. F., “A Future Verification of Endochronic Theory or Metals Under Multiaxial Loading Paths,” The Chinese J. of Mechanics, 10, pp. 255262 (1994).Google Scholar
30.Wu, H. C. and Yeh, W. C., “Some Considerations in the Endochronic Description of Anisotropic Hardening,” ActaMechanica, 69, pp. 5967 (1987).Google Scholar
31.Lee, C. F., “Intrinsic Time Measure of Endochronic Plasticity with Plastic Strain Induced Anisotropy,” The Chinese J. of Mechanics, 13, pp. 161174 (1997).Google Scholar
32.Lee, C. F and Shieh, T. J., “Theory of Endochronic Cyclic Viscoplasticity of Eutectic TIN/LEAD Solder Alloy,” Journal of Mechanics, 22, pp. 181192 (2006).CrossRefGoogle Scholar
33.Valanis, K. C. and Fan, J. H., “ANumerical Algorithm for Endochronic Plasticity and Comparison with Experiment,” Computer & Structures, 19, pp. 717724 (1984).CrossRefGoogle Scholar
34.Kucher, N. K. and Borodii, M. V., “A Version of Endochronic Theory of Plasticity for Describing Non- Proportional Cyclic Deformation,” Int. J. Non-Linear Mechanics, 28(2), pp. 267278 (1993).CrossRefGoogle Scholar
35.Hsu, S. Y., Hayden Griffin, O. and Jr., “Algorithmic Tangent Matrix Approach for Mixed Hardening Model of Endochronic Plasticity,” Comput. Methods Appl. Mech. Engrg, 133, pp. 114 (1996).CrossRefGoogle Scholar
36.Bakhshiani, A., Mofid, M., Khoei, A. R. and McCabe, S. L., “Finite Strain Simulation of Thin-Walled Tube Under Torsion Using Endochronic Theory of Plasticity,” Thin-Walled Structures, 41, pp. 435459 (2003).CrossRefGoogle Scholar