Multiaxial cyclic ratchetting under multiple step loading

Abstract Strain ratchetting responses of 1070 steel are reported for multiple step cyclic loading histories. The stress amplitude and mean stress are varied between loading steps in multiple step loading. Experimental results reveal that the material exhibits a strong memory of the previous loading history, and such memory plays a discerning role on the subsequent ratchetting. The material could ratchet in the opposite direction to the mean stress or could reverse its ratchetting direction with time. The origin of the ratchetting transients has been linked to the variation of the plastic modulus within the loading cycle for proportional loading and the noncoincidence of the plastic strain rate direction and yield surface translation direction for nonproportional loading. Many of the constitutive relations proposed for cyclic loading are not designed to handle the ratchetting evolution. Based on the Armstrong-Frederick hardening algorithm, the model forwarded by Bower can qualitatively predict the ratchetting directions for certain multiple step loading cases, but the predicted ratchetting rates differ from the experimental values. The Ohno-Wang model, which introduces threshold levels of dynamic recovery in nonlinear hardening, can simulate negative ratchetting under positive mean stress, or vice versa, as well as the ratchetting direction reversal during step loadings. This model can provide results that agree with experimental observations for a class of nonproportional cases, where the plastic strain rate direction and yield surface translation direction are noncoincident. Its performance deteriorates for proportional loading.

[1]  Hans-Werner Ziegler.  A Modification of Prager's Hardening Rule , 1959 .

[2]  D. McDowell.  A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 2: Comparison of Theory With Experiments , 1985 .

[3]  R. D. Krieg.  A Practical Two Surface Plasticity Theory , 1975 .

[4]  D. L. McDowell,et al.  Effects of non-linear kinematic hardening on plastic deformation and residual stresses in rolling line contact , 1991 .

[5]  David L. McDowell,et al.  Description of nonproportional cyclic ratchetting behavior , 1994 .

[6]  J. Chaboche,et al.  Modelization of the Strain Memory Effect on the Cyclic Hardening of 316 Stainless Steel , 1979 .

[7]  Egor P. Popov,et al.  A model of nonlinearly hardening materials for complex loading , 1975 .

[8]  Yannis F. Dafalias,et al.  Plastic Internal Variables Formalism of Cyclic Plasticity , 1976 .

[9]  Z. Mroz.  An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model , 1969 .

[10]  William Prager,et al.  The Theory of Plasticity: A Survey of Recent Achievements , 1955 .

[11]  David L. McDowell,et al.  A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 1: Development of Appropriate Equations , 1985 .

[12]  D. McDowell.  An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity , 1985 .

[13]  Allan F. Bower,et al.  Cyclic hardening properties of hard-drawn copper and rail steel , 1989 .

[14]  S. Kyriakides,et al.  Ratcheting in cyclic plasticity, part II: Multiaxial behavior , 1992 .

[15]  N. Ohno,et al.  Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior , 1993 .

[16]  Huseyin Sehitoglu,et al.  Cyclic ratchetting of 1070 steel under multiaxial stress states , 1994 .

[17]  N. T. Tseng,et al.  Simple Plasticity Model of Two-Surface Type , 1983 .

[18]  Ys Garud,et al.  Prediction of Stress-Strain Response under General Multiaxial Loading , 1982 .

[19]  D. C. Drucker,et al.  On Stress-Strain Relations Suitable for Cyclic and Other Loading , 1981 .

[20]  Sumio Murakami,et al.  Inelastic behaviour of 214Cr-1Mo steel under plasticity-creep interaction condition: An interim report of the Bench Mark project by the subcommittee on inelastic analysis and life prediction of high temperature materials, JSMS☆ , 1985 .

[21]  Zenon Mróz,et al.  On the description of anisotropic workhardening , 1967 .

[22]  D. McDowell,et al.  On a Class of Kinematic Hardening Rules for Nonproportional Cyclic Plasticity , 1989 .

[23]  O. M. Sidebottom,et al.  Cyclic Plasticity for Nonproportional Paths: Part 2—Comparison With Predictions of Three Incremental Plasticity Models , 1978 .

[24]  Nobutada Ohno,et al.  Kinematic hardening rules with critical state of dynamic recovery, part II: Application to experiments of ratchetting behavior , 1993 .