TECHNICAL PAPERS
Jan 1, 1991

Verification of Endochronic Theory for Nonproportional Loading Paths

Publication: Journal of Engineering Mechanics
Volume 117, Issue 1

Abstract

A procedure for the numerical integration of the constitutive equations of the endochronic theory of plasticity is presented. Methods are established for the determination of endochronic material functions from the results of cyclic uniaxial tests. The endochronic theory is examined for its ability in modeling random nonproportional tests on oxygen‐free, high‐conductivity copper. Qualitative response of the theory is studied under cyclic‐hardening, cyclic‐relaxation, and cyclic‐creep tests. Finally, an attempt is made to discover some typical plasticity properties of the endochronic theory by constructing equiplastic‐strain surfaces in the tension‐torsion stress space. In conclusion, the endochronic theory is a versatile tool for the constitutive characterization of isothermal, rate‐independent behavior of initially isotropic engineering materials.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Bažant, Z. P., Ansal, Z. M., and Krizek, R. J. (1979). “Viscoplasticity of transversely isotropic clays.” J. Geotech. Engrg. Div., ASCE, 105(4), 549–565.
2.
Bažant, Z. P., and Bhat, P. D. (1976). “Endochronic theory of inelasticity and failure of concrete.” J. Engrg. Mech. Div., ASCE, 102(4), 701–722.
3.
Bažant, Z. P., and Krizek, R. J. (1976). “Endochronic constitutive law for liquefaction of sand.” J. Engrg. Mech., ASCE, 102(2), 225–238.
4.
Hsu, S. Y., Jain, S. K., and Griffin, O. H. (1989). “A procedure for determining endochronic material functions and verification of endochronic theory for nonproportional loading paths.” Tech. Report VPI‐E‐89‐25, College of Engineering, Virginia Polytechnic Inst. and State Univ., Blacksburg, Va.
5.
Khan, A. S., and Wang, X. (1988). “On non‐proportional infinitesimal plastic deformation after finite plastic prestraining and partial unloading.” J. Mech. Phys. Solids, 36(5), 519–535.
6.
Lamba, H. S. (1977). “Nonportional cyclic plasticity,” thesis presented to the University of Illinois, at Urbana, Ill. in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
7.
Lamba, H. S., and Sidebottom, O. M. (1978a). “Cyclic plasticity for nonproportional paths: Part 1—Cyclic hardening, erasure of memory, and subsequent strain hardening experiments.” J. Engrg. Mater. Tech., 100(1), 96–103.
8.
Lamba, H. S., and Sidebottom, O. M. (1978b). “Proportional biaxial cyclic hardening of annealed oxygen‐free high‐conductivity copper.” J. Test. Eval., 6(4), 260–267.
9.
McDowell, D. L., Socie, D. F., and Lamba, H. S. (1982). “Multiaxial nonproportional cyclic deformation.” Low‐cycle fatigue and life prediction, ASTM, STP770, 500–518.
10.
Murakami, H., and Read, H. E. (1989). “A second‐order numerical scheme for integrating the endochronic plasticity equations.” Comput. Struct., 31(5), 663–672.
11.
Sandler, I. S. (1978). “On the uniqueness and stability of endochronic theories of material behavior.” J. Appl. Mech., 45(2), 263–266.
12.
Sugiura, K., Lee, G. C., and Chang, K. C. (1987). “Endochronic theory for structural steel under nonproportional loading.” J. Engrg. Mech., ASCE, 113(12), 1901–1917.
13.
Tanaka, E., Murakami, S., and Ooka, M. (1985). “Effects of plastic strain amplitudes on non‐proportional cyclic plasticity.” Acta Mechanica, 57(3–4), 167–182.
14.
Valanis, K. C. (1971a). “A theory of viscoplasticity without a yield surface, Part I. General theory.” Arch. Mech., 23(4), 517–533.
15.
Valanis, K. C. (1971b). “A theory of viscoplasticity without a yield surface, Part II. Application to mechanical behavior of metals.” Arch. Mech., 23(4), 535–551.
16.
Valanis, K. C. (1980). “Fundamental consequences of a new intrinsic time measure: Plasticity as a limit of the endochronic theory.” Arch. Mech., 32(2), 171–191.
17.
Valanis, K. C. (1984). “Continuum foundations of endochronic plasticity.” J. Engrg. Mater. Tech., 106(4), 367–375.
18.
Valanis, K. C., and Fan, J. (1983). “Endochronic analysis of cyclic elastoplastic strain fields in a notched plate.” J. Appl. Mech., 50(4), 789–794.
19.
Valanis, K. C., and Fan, J. (1984). “A numerical algorithm for endochronic plasticity and comparison with experiment.” Comput. Struct., 19(5–6), 717–724.
20.
Valanis, K. C., and Lee, C. F. (1984). “Endochronic theory of cyclic plasticity with applications.” J. Appl. Mech., 51(2), 367–374.
21.
Valanis, K. C., and Wu, H. C. (1975). “Endochronic representation of cyclic creep and relaxation of metals.” J. Appl. Mech., 42(1), 67–73.
22.
Watanbe, O., and Atluri, S. N. (1985). “A new endochronic approach to computational elastoplasticity: Example of a cyclically loaded cracked plate.” J. Appl. Mech., ASME, 52(4), 857–864.
23.
Watanbe, O., and Atluri, S. N. (1986). “Internal time, general internal variable, and multi‐yield‐surface theories of plasticity and creep: A unification of concepts.” Int. J. Plasticity, 2(1), 37–57.
24.
Wu, H. C., and Yang, R. J. (1983). “Application of the improved endochronic theory of plasticity to loading with multi‐axial strain‐path.” Int. J. Non‐Lin. Mech., 18(5), 395–408.
25.
Wu, H. C., Yao, J. C., and Chu, S. C. (1986). “Investigation of endochronic constitutive equation subject to plastic strain‐controlled axial‐torsional deformation.” J. Engrg. Mater. Tech., 108(3), 262–269.
26.
Wu, H. C., and Yip, M. C. (1980). “Strain rate and strain rate history effects on the dynamic behavior of metallic materials.” Int. J. Solids Struct., 16(6), 515–536.
27.
Wu, H. C., and Yip, M. C. (1981). “Endochronic description of cyclic hardening behavior for metallic materials.” J. Engrg. Mater. Tech., 103(3), 212–217.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 117Issue 1January 1991
Pages: 110 - 131

History

Published online: Jan 1, 1991
Published in print: Jan 1991

Permissions

Request permissions for this article.

Authors

Affiliations

S. Y. Hsu
Grad. Student, Dept. of Engrg. Sci. and Mech., Virginia Polytech. Inst. and State Univ., Blacksburg, VA 24061
S. K. Jain
Asst. Prof., Dept. of Engrg. Sci. and Mech., Virginia Polytech. Inst. and State Univ., Blacksburg, VA
O. Hayden Griffin, Jr.
Assoc. Prof., Dept. of Engrg. Sci. and Mech., Virginia Polytech. Inst. and State Univ., Blacksburg, VA

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share