A Constitutive Model of Cyclic Plasticity With a Nonhardening Strain Region

1982 ◽  
Vol 49 (4) ◽  
pp. 721-727 ◽  
Author(s):  
N. Ohno
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Cyclic Creep ◽  
Cyclic Hardening ◽  
Present Theory ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Isotropic Hardening ◽  
Hardening Material ◽  
Cyclic Straining

By introducing the concept of a nonhardening region in the plastic strain space, a constitutive model is proposed for cyclic plastic loadings between variable, as well as fixed, strain limits. It is assumed that the isotropic hardening of materials does not occur when the plastic strain point moves inside this region after a load reversal. The region expands and translates as cyclic straining proceeds, and when strain limits are fixed, it eventually occupies the cyclic range of plastic strain so as to describe the saturation of cyclic hardening. The phenomena of cyclic relaxation and cyclic creep are also taken into account in the formulation. In the simple case of a linear hardening material, the present theory is verified by comparing predictions with experimental results on type 304 stainless steel under torsional cyclings between variable, as well as fixed, strain limits at room temperature.

A Constitutive Model of Cyclic Plasticity for Nonlinear Hardening Materials

1986 ◽  
Vol 53 (2) ◽  
pp. 395-403 ◽  
Author(s):  
N. Ohno ◽  
Y. Kachi
Keyword(s):  
Constitutive Model ◽  
Cyclic Hardening ◽  
Cyclic Stress ◽  
Cyclic Plasticity ◽  
Elastoplastic Behavior ◽  
Surface Plasticity ◽  
Proposed Model ◽  
Cyclic Straining ◽  
Nonlinear Hardening ◽  
Mean Strain

A constitutive model is proposed for cyclic plasticity of nonlinear hardening materials. The concept of a cyclic nonhardening range, which enables us to describe the dependence of cyclic hardening on the amplitude of cyclic straining or stressing, is employed together with the idea of a two-surface plasticity model. Results of the proposed model are compared with experiments of 304 and 316 stainless steels in several cases of cyclic loading in which mean strain is zero or nonzero and strain limits are fixed or variable. Thus, it is shown that the model successfully describes both the cyclic hardening phenomenon and the transient elastoplastic behavior after initial and reverse yields of these materials. The capability of the model to provide nonlinear cyclic stress-strain curves is also discussed.

Low-Cycle Fatigue Life of Continuously Cyclic-Hardening Material

2020 ◽  
Author(s):  
Zhong Zhang ◽  
Xijia Wu
Keyword(s):  
Fatigue Life ◽  
Plastic Strain ◽  
Root Mean Square ◽  
Low Cycle Fatigue ◽  
Cyclic Hardening ◽  
Mean Square ◽  
Cycle Fatigue ◽  
Fatigue Crack Nucleation ◽  
Hardening Material ◽  
Plastic Strain Range

Abstract A general fatigue life equation is derived by modifying the Tanaka-Mura-Wu dislocation pile-up model for variable strain-amplitude fatigue processes, where the fatigue crack nucleation life is expressed in terms of the root mean square of plastic strain range. Low-cycle fatigue tests were conducted on an austenitic stainless steel. at 400°C and 600°C, the material exhibits continuously cyclic-hardening behaviour. The root mean square of plastic strain ranges is evaluated from the experimental data for each test condition at strain rates ranging from 0.0002/s to 0.02/s. The variable-amplitude Tanaka-Mura-Wu model is found to be in good agreement with the LCF data, which effectively proves Miner’s rule on the stored plastic strain energy basis.

Low-Cycle Fatigue Life of Continuously Cyclic-Hardening Material

2021 ◽  
Author(s):  
Zhong Zhang ◽  
Xijia Wu
Keyword(s):  
Fatigue Life ◽  
Plastic Strain ◽  
Root Mean Square ◽  
Low Cycle Fatigue ◽  
Cyclic Hardening ◽  
Mean Square ◽  
Cycle Fatigue ◽  
Fatigue Crack Nucleation ◽  
Hardening Material ◽  
Plastic Strain Range

Abstract A general fatigue life equation is derived by modifying the Tanaka-Mura-Wu dislocation pile-up model for variable strain-amplitude fatigue processes, where the fatigue crack nucleation life is expressed in terms of the root mean square of plastic strain range. Low-cycle fatigue tests were conducted on an austenitic stainless steel. At 400 ? and 600 ?, the material exhibits continuously cyclic-hardening behaviour. The root mean square of plastic strain ranges is evaluated from the experimental data for each test condition at strain rates ranging from 0.0002/s to 0.02/s. The variable-amplitude Tanaka-Mura-Wu model is found to be in good agreement with the LCF data, which effectively proves Miner's rule on the stored plastic strain energy basis.

Cyclic Plasticity and Cyclic Creep in Austenitic-Ferritic Duplex Steel

2011 ◽  
Vol 465 ◽  
pp. 431-434
Author(s):  
Jaroslav Polák ◽  
Martin Petrenec ◽  
Jiří Man ◽  
Tomáš Kruml
Keyword(s):  
Creep Rate ◽  
Plastic Strain ◽  
Strain Amplitude ◽  
Cyclic Creep ◽  
Cyclic Stress ◽  
Plastic Strain Amplitude ◽  
Cyclic Plasticity ◽  
Stress Strain ◽  
Duplex Steel ◽  
Mean Stresses

Smooth specimens made from austenitic-ferritic duplex steel were subjected to constant stress amplitude loading with positive mean stresses. Hysteresis loops were recorded during the fatigue life and plastic strain amplitude and cyclic creep rate were determined. Fatigue hardening/softening curves, cyclic creep curves and cyclic stress-strain curves for different positive mean stresses were evaluated. Typical dislocation structures developed in both phases of the duplex steel were identified using TEM, compared with the saturated plastic strain amplitude and correlated with the decrease of the cyclic creep rate during cycling and the slope of the cyclic stress-strain curve.

Modeling the Hydrogen Effect on the Constitutive Response of a Low Carbon Steel in Cyclic Loading

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Zahra S. Hosseini ◽  
Mohsen Dadfarnia ◽  
Akihide Nagao ◽  
Masanobu Kubota ◽  
Brian P. Somerday ◽  
...  
Keyword(s):  
Carbon Steel ◽  
Cyclic Loading ◽  
Constitutive Model ◽  
Kinematic Hardening ◽  
Low Carbon Steel ◽  
Cyclic Hardening ◽  
Hydrogen Effect ◽  
Low Carbon ◽  
Japanese Industrial Standard ◽  
Cyclic Straining

Abstract Hydrogen-accelerated fatigue crack growth is a most severe manifestation of hydrogen embrittlement. A mechanistic and predictive model is still lacking partly due to the lack of a descriptive constitutive model of the hydrogen/material interaction at the macroscale under cyclic loading. Such a model could be used to assess the nature of the stress and strain fields in the neighborhood of a crack, a development that could potentially lead to the association of these fields with proper macroscopic parameters. Toward this goal, a constitutive model for cyclic response should be capable of capturing hardening or softening under cyclic straining or ratcheting under stress-controlled testing. In this work, we attempt a constitutive description by using data from uniaxial strain-controlled cyclic loading and stress-controlled ratcheting tests with a low carbon steel, Japanese Industrial Standard (JIS) SM490YB, conducted in air and 1 MPa H2 gas environment at room temperature. We explore the Chaboche constitutive model which is a nonlinear kinematic hardening model that was developed as an extension to the Frederick and Armstrong model, and propose an approach to calibrate the parameters involved. From the combined experimental data and the calibrated Chaboche model, we may conclude that hydrogen decreases the yield stress and the amount of cyclic hardening. On the other hand, hydrogen increases ratcheting, the rate of cyclic hardening, and promotes stronger recovery.

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.

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.

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.

Uniaxial Ratchetting of 316FR Steel at Room Temperature— Part I: Experiments

1999 ◽  
Vol 122 (1) ◽  
pp. 29-34 ◽  
Author(s):  
M. Mizuno ◽  
Y. Mima ◽  
M. Abdel-Karim ◽  
N. Ohno
Keyword(s):  
Plastic Strain ◽  
Room Temperature ◽  
Kinematic Hardening ◽  
Hysteresis Loops ◽  
Strain Range ◽  
Cyclic Hardening ◽  
Isotropic Hardening ◽  
Cyclic Tension ◽  
Tension Tests ◽  
Almost All

Uniaxial ratchetting characteristics of 316FR steel at room temperature are studied experimentally. Cyclic tension tests, in which maximum strain increases every cycle by prescribed amounts, are conducted systematically in addition to conventional monotonic, cyclic, and ratchetting tests. Thus hysteresis loop closure, cyclic hardening and viscoplasticity are discussed in the context of constitutive modeling for ratchetting. The cyclic tension tests reveal that very slight opening of hysteresis loops occurs, and that neither accumulated plastic strain nor maximum plastic strain induces significant isotropic hardening if strain range is relatively small. These findings are used to discuss the ratchetting tests. It is thus shown that uniaxial ratchetting of the material at room temperature is brought about by slight opening of hysteresis loops as well as by viscoplasticity, and that kinematic hardening governs almost all strain hardening in uniaxial ratchetting if stress range is not large. [S0094-4289(00)00401-1]

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