An Exponential Stress-Strain Law for Cyclic Plasticity

1976 ◽  
Vol 98 (4) ◽  
pp. 322-329 ◽  
Author(s):  
M. C. M. Liu ◽  
E. Krempl ◽  
D. C. Nairn
Keyword(s):  
Hysteresis Loops ◽  
Cyclic Hardening ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Strain Diagram ◽  
Stress Strain ◽  
Independent Case ◽  
Transcendental Functions ◽  
Product Forms ◽  
Type 304

A previously proposed nonlinear differential constitutive equation for creep-plasticity interaction under a uniaxial state of stress is specialized for the time independent case. The characteristics of the second derivative of the stress-strain diagram are matched by an exponential function. The integration yields higher transcendental functions. For the matching of the stress-strain diagram, four easily obtainable constants are necessary at each cycle which are fed into a newly developed FORTRAN computer program. A plotting routine yields stress-strain diagrams and hysteresis loops. The procedure gives good matches for stress-strain diagrams of Type 304 stainless steel. Specifically, stress-strain diagrams for various product forms and the initial cyclic hardening of this material are reproduced quite accurately without the usual decomposition into elastic and plastic strains.

Modelling of Cyclic Plasticity With Unified Constitutive Equations: Improvements in Simulating Normal and Anomalous Bauschinger Effects

1980 ◽  
Vol 102 (2) ◽  
pp. 215-222 ◽  
Author(s):  
A. K. Miller
Keyword(s):  
Constitutive Equations ◽  
Work Hardening ◽  
Hysteresis Loops ◽  
Experimental Tests ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Cyclic Softening ◽  
Cyclic Plasticity ◽  
Dislocation Loops ◽  
Work Hardening Coefficient

In simulating cyclic plasticity with several existing “unified” constitutive equations, the predicted hysteresis loops are “oversquare” with respect to experimentally-observed behavior. To eliminate this shortcoming in the constitutive equations developed by the present author, the work-hardening coefficient in the equation controlling the back stress (R) has been made a function of the back stress itself and the sign of the effective modulus-compensated stress σ/E – R. This improvement results in simulated hysteresis loops whose curvature closely resembles that in experimental tests. The improvement preserves all of the previously demonstrated capabilities such as cyclic hardening, cyclic hardening, cyclic softening, etc. The same equations can also simulate some unusual experimentally-observed Bauschinger effects involving local reversals in curvature. The curvature reversals in the simulations result from strain softening of the isotropic work-hardening variable in the equations. The physical significance of the behavior of the constitutive equations is discussed in terms of annihilation of previously-generated dislocation loops by reversing dislocations and experimentally-observed decreases in dislocation density and dissolution of cell walls upon stress reversal.

High-Cycle Fatigue Behavior of Solution-Annealed and Thermally-Aged Type 304 Stainless Steel

1980 ◽  
Vol 102 (1) ◽  
pp. 141-146 ◽  
Author(s):  
P. Soo ◽  
J. G. Y. Chow
Keyword(s):  
Stainless Steel ◽  
High Cycle Fatigue ◽  
Fatigue Behavior ◽  
Cyclic Stress ◽  
304 Stainless Steel ◽  
Strain History ◽  
Cycle Fatigue ◽  
Stress Strain ◽  
Type 304 ◽  
Type 304 Stainless Steel

High-cycle, load-controlled fatigue data have been obtained for solution-annealed and thermally-aged Type 304 stainless steel, for temperatures between 22 and 593°C (72-1100°F) at a cycling rate of 40 Hz. Although these data are principally used to assess fatigue failure in components subjected to rapid stress cycling, it has been shown that they may be correlated with available low-cycle data if cyclic stress-strain curves are used for converting the high-cycle stresses to effective strains. Differences in initial stress-strain history and cycling rates for the high- and low-cycle data evaluated are found to be unimportant. For the thermally-aged material there is an initial enhancement of the high-cycle-fatigue strength but, after long aging times, the strength decreases to a value close to that for unaged material. The carbide precipitates formed during aging appear to influence fatigue life through changes they impart in the cyclic work-hardening rates.

Multilayer Kinematic Hardening Model for Carbon Steel and its Application to Inelastic Analyses of an Elbow Subjected to Cyclic In-Plane Bending

2015 ◽  
Author(s):  
Koji Iwata ◽  
Yasuhisa Karakida ◽  
Chuanrong Jin ◽  
Hitoshi Nakamura ◽  
Naoto Kasahara
Keyword(s):  
Carbon Steel ◽  
Kinematic Hardening ◽  
Isothermal Condition ◽  
Cyclic Hardening ◽  
Bending Test ◽  
Cyclic Plasticity ◽  
Repeated Loading ◽  
Stress Strain ◽  
Hardening Model ◽  
Plane Bending

Carbon steel STS410 (JIS Standard), which is widely used for high pressure piping components, exhibits cyclic hardening under repeated loading. Extreme seismic loading can cause repetitive large strains, eventually leading to the failure of components. For failure assessment of such components, inelastic analyses using cyclic plasticity constitutive models are needed. In this paper, a multilayer kinematic hardening model for cyclic plasticity, equipped with a set of standard stress-strain characteristics, is developed for STS410 under isothermal condition of various temperatures. This model can express not only the nonlinearity of stress-strain relations, but cyclic hardening of a material by introducing a generic stress-strain relation composed of a combination of monotonic and steady state cyclic stress-strain curves. Finite element large deformation elastic-plastic analyses with this model are conducted for a cyclic in-plane bending test of an elbow. The proposed constitutive model predicted well characteristic features of global deformation and local strain behaviors of the elbow.

Nonproportional Low Cycle Fatigue Criterion for Type 304 Stainless Steel

1995 ◽  
Vol 117 (3) ◽  
pp. 285-292 ◽  
Author(s):  
Takamoto Itoh ◽  
Masao Sakane ◽  
Masateru Ohnami ◽  
Darrell F. Socie
Keyword(s):  
Stainless Steel ◽  
Low Cycle Fatigue ◽  
Cyclic Hardening ◽  
304 Stainless Steel ◽  
Cycle Fatigue ◽  
Nonproportional Loading ◽  
Loading Tests ◽  
Strain Paths ◽  
Type 304 ◽  
Type 304 Stainless Steel

This paper describes a multiaxial low cycle fatigue parameter for correlating Hues under nonproportional loadings. Constant amplitude low cycle fatigue tests were carried out under 14 proportional and complex nonproportional cyclic strain paths using type 304 stainless steel hollow cylinder specimens at room temperature. In nonproportional loading tests, fatigue lives are decreased by as much as a factor of 10 in comparison with those in proportional loading tests with the same strain range. Reduction in fatigue life due to nonproportional loading is closely related to additional nonproportional cyclic hardening. The product of the maximum principal stress and strain ranges correlated the nonproportional fatigue data. A nonproportional cyclic hardening parameter computed from the strain path is also proposed that allows life estimates to be obtained directly from the strain history without the need for a cyclic plasticity model.

On a Class of Kinematic Hardening Rules for Nonproportional Cyclic Plasticity

1989 ◽  
Vol 111 (1) ◽  
pp. 87-98 ◽  
Author(s):  
J. C. Moosbrugger ◽  
D. L. McDowell
Keyword(s):  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Image Point ◽  
Isotropic Hardening ◽  
Proportional Loading ◽  
Modeling Material ◽  
Hardening Rules ◽  
Type 304 ◽  
Type 304 Stainless Steel

Two surface theories for rate-independent plasticity have previously been shown to offer superior correlative capability in modeling material response under non-proportional loading. In this study, a class of kinematic hardening rules characterized by a decomposition of the total kinematic hardening variable is discussed. The concept of generalized image point hardening in conjunction with mulitple loading surface interpretations is presented. The ability of this class of rules to correlate experimental data from stable nonproportional cycling of Type 304 stainless steel at room temperature is examined. In addition, the proper framework for inclusion of isotropic hardening for this class of models is discussed.

A Simple Model for Stable Cyclic Stress-Strain Relationship of Type 304 Stainless Steel Under Nonproportional Loading

1999 ◽  
Vol 122 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Takamoto Itoh ◽  
Xu Chen ◽  
Toshimitsu Nakagawa ◽  
Masao Sakane
Keyword(s):  
Stainless Steel ◽  
Cyclic Stress ◽  
304 Stainless Steel ◽  
Surface Model ◽  
Stress Strain ◽  
Nonproportional Loading ◽  
Strain Relationship ◽  
Strain Paths ◽  
Type 304 ◽  
Type 304 Stainless Steel

This paper proposes a simple two-surface model for cyclic incremental plasticity based on combined Mroz and Ziegler kinematic hardening rules under nonproportional loading. The model has only seven material constants and a nonproportional factor which describes the degree of additional hardening. Cyclic loading experiments with fourteen strain paths were conducted using Type 304 stainless steel. The simulation has shown that the model was precise enough to calculate the stable cyclic stress-strain relationship under nonproportional loadings. [S0094-4289(00)00101-8]

An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity

1985 ◽  
Vol 107 (4) ◽  
pp. 307-315 ◽  
Author(s):  
D. L. McDowell
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Yield Surface ◽  
Hysteresis Loops ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Plastic Strain Rate ◽  
Hardening Modulus ◽  
Rate Vector ◽  
Strain Rate Vector

Three type 304 stainless steel specimens of the same geometry were subjected to complex, cyclic axial-torsional histories characterized by varying degrees of non-proportionality of straining. All tests were at room-temperature. The data from cyclically stable hysteresis loops were reduced and the direction of the plastic strain rate vector, variation of plastic hardening modulus, and direction of translation of a rate and time-independent yield surface were studied. It is shown that the independent variables in a Mroz-type formulation map the experimental results with a higher degree of uniqueness than other popular formulations studied for both the hardening modulus and direction of yield surface translation. Also, the plastic strain rate is not, in general, in the direction of the deviatoric stress or stress rate.

Creep, Stress Relaxation and Biaxial Ratchetting of Type 304 Stainless Steel After Cyclic Preloading

1994 ◽  
Vol 116 (2) ◽  
pp. 133-141 ◽  
Author(s):  
Hiromasa Ishikawa ◽  
Katsuhiko Sasaki
Keyword(s):  
Stainless Steel ◽  
Stress Relaxation ◽  
Back Stress ◽  
Material Behavior ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Cyclic Shear ◽  
Creep Stress ◽  
Type 304 ◽  
Type 304 Stainless Steel

A series of tests for creep, stress relaxation, and biaxial ratchetting of type 304 stainless steel after cyclic preloading were carried out to investigate their interaction. The interesting fact was pointed out that back stress in cyclic plasticity played an important role to describe creep, relaxation, and biaxial ratchetting following cyclic preloading. Then, the test results showed that the material behavior due to creep after cyclic preloading could be represented by the modified Bailey-Norton law with stress levels evaluated from the current center of the yield surface, i.e., back stress which was determined by the hybrid constitutive model for cyclic plasticity proposed by the authors. In addition, biaxial ratchetting of axial strain induced by cyclic shear straining after cyclic preloading was expressed by the shear stress amplitude, the number of cycle and the axial stress level from the current center.

Anisotropic Nonlinear Kinematic Hardening Rule Parameters From Reversed Proportional Axial-Torsional Cycling

1999 ◽  
Vol 122 (1) ◽  
pp. 18-28 ◽  
Author(s):  
J. C. Moosbrugger
Keyword(s):  
Kinematic Hardening ◽  
Transverse Isotropy ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Hardening Rule ◽  
Thin Walled ◽  
Hardening Rules ◽  
Type 304 ◽  
Type 304 Stainless Steel ◽  
Tubular Specimens

A procedure for determining parameters for anisotropic forms of nonlinear kinematic hardening rules for cyclic plasticity or viscoplasticity models is described. An earlier reported methodology for determining parameters for isotropic forms of uncoupled, superposed Armstrong-Frederick type kinematic hardening rules is extended. For this exercise, the anisotropy of the kinematic hardening rules is restricted to transverse isotropy or orthotropy. A limited number of parameters for such kinematic hardening rules can be determined using reversed proportional tension-torsion cycling of thin-walled tubular specimens. This is demonstrated using tests on type 304 stainless-steel specimens and results are compared to results based on the assumption of isotropic forms of the kinematic hardening rules. [S0094-4289(00)00301-7]

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