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             8.  Itoh T., Sakane M., Ohnami M. and Socie D. F. (1999), Nonproportional Low Cycle Fatigue
               of 6061 Aluminum Alloy under 14 Strain Paths, In: Multiaxial Fatigue & Fracture, pp.41-54,
               E. Macha, W. Bqdkowsky and T. Lagda (Eds). ESIS-25.
             9.  McDowell D. L. (1983), On the Path Dependence of Transient Hardening and Softening to
                Stable States under Complex Biaxial Cyclic Loading, Proc. Znt. Con$  on Constitutive Laws
               for Engng. Mater., Desai and Gallagher, (Eds), 125.
             10. Doong  S. H.,  Socie D.  F.  and  Robertson, I.  M.  (1990), Dislocation Substructures and
                Nonproportional Hardening,  ASME J. of  Engng. Mater. Tech., 112,456.
             11. Kida S., Itoh T., Sakane M.,  Ohnami M. and Socie D. F. (1997), Dislocation Structure and
                Nonproportional Hardening of  Type 304 Stainless Steel, Fatigue  Fract.  Engng  Mater.
                Struct., 20, 1375.
             12. Smith R. N., Watson P. and Topper T. H. (1970), A Stress-Strain Function for the Fatigue of
                Materials, J. Materials JMLSA, 5,767.
             13. Fatemi A. and Socie D. F. (1988). A Critical Plane Approach to Multiaxial Fatigue Damage
                Including Out-of-Phase Loading, Fatigue and Fracture  of Engng. Mater, and Struct., 11,
                149.
             14. Krempl E. and Lu H.  (1983), Comparison of the Stress Responses of an Aluminum Alloy
                Tube to Proportional and Alternate Axial  and  Shear Strain Paths at  Room Temperature,
                Mechanics of Materials, 2, 183.
             15. Benallal  A.  and  Marquis D.  (1987), Constitutive Equations for Nonproportional Cyclic
                Elasto-Viscoplasticity,  ASME J. of Engng. Mater. Tech., 109,326.
             16. Doong S. H. and Socie D. F. (1991), Constitutive Modeling  of Metals under Nonproportional
                Loading, ASME J. of  Engng. Mater. Tech., 113,23.
             17. Wang C. H. and Brown M. W. (1996), Life Prediction Techniques for Variable Amplitude
                Multiaxial Fatigue-Part 1: Theories,  ASME J. of  Engng. Mater. Tech., 118,367.
             18. Bannantine J. A.  and Socie, D. F. (1991), A Variable Amplitude Multiaxial Fatigue Life
                Prediction Method,  In:  Fatigue  under  Biaxial  and  Multiaxial  Loading,  pp.35-51,  K.F.
                Kussmaul, D. L. McDiarmid and D. F Socie (Eds). ESIS-IO.
             19. Kim K. S. and Park J. C. (1999), Shear Strain Based Multiaxial Fatigue Parameters Applied
                to Variable Amplitude Loading, International J. of  Fatigue, 21,475.
             20. Itoh T, Sakane M. and Ohnami M. (1994), High Temperature Multiaxial Low Cycle Fatigue
                of Cruciform Specimen,  ASME J. of Engng. Mater. Tech., 116,90.
             21. Sakane M.  Ohnami M.  and  Sawada M.  (1987), Fracture Modes and  Low Cycle Biaxial
                Fatigue Life at Elevated Temperature,  ASME J. of  Engng. Mater. Tech., 109,236.




             Appendix : NOMENCLATURE


                   a        Parameter  for  degree  of  additional  hardening  due  to  nonproportional
                            straining
                   fNP      Nonproportional intensity factor for nonproportional straining
                   Edt)     Maximum amplitude of principal strain at time t
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