A Bounding Surface Theory for Cyclic Thermoplasticity

1992 ◽  
Vol 114 (3) ◽  
pp. 297-303 ◽  
Author(s):  
D. L. McDowell
Keyword(s):  
Yield Surface ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Temperature History ◽  
Isotropic Hardening ◽  
Thermoplastic Material ◽  
History Independence ◽  
Dependent Component ◽  
Hardening Theory ◽  
Temperature Rate

A nonisothermal, rate and time independent generalization of nonlinear kinematic hardening theory for cyclic plasticity is introduced. The model includes decomposition of backstress and of isotropic hardening between the yield surface radius and the backstress amplitude. A purely temperature dependent component of yield surface radius is assumed in addition to an isotropic hardening component. Issues of thermoplastic material stability and temperature history independence are clearly distinguished and addressed via implications of temperature rate terms. Correlations are reported for OFHC copper subjected to thermomechanical cyclic loading.

Cyclic Plasticity for Nonproportional Paths: Part 2—Comparison With Predictions of Three Incremental Plasticity Models

1978 ◽  
Vol 100 (1) ◽  
pp. 104-111 ◽  
Author(s):  
H. S. Lamba ◽  
O. M. Sidebottom
Keyword(s):  
Cyclic Loading ◽  
Material Property ◽  
Yield Surface ◽  
Strain Path ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Limit Surface ◽  
Hardening Rule ◽  
Hardening Models ◽  
Hardening Rules

Experiments that demonstrate the basic quantitative and qualitative aspects of the cyclic plasticity of metals are presented in Part 1. Three incremental plasticity kinematic hardening models of prominence are based on the Prager, Ziegler, and Mroz hardening rules, of which the former two have been more frequently used than the latter. For a specimen previously fully stabilized by out of phase cyclic loading the results of a subsequent cyclic nonproportional strain path experiment are compared to the predictions of the above models. A formulation employing a Tresca yield surface translating inside a Tresca limit surface according to the Mroz hardening rule gives excellent predictions and also demonstrates the erasure of memory material property.

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.

On the Modeling of Nonproportional Cyclic Plasticity of Waspaloy

1994 ◽  
Vol 116 (1) ◽  
pp. 35-44 ◽  
Author(s):  
A. Abdul-Latif ◽  
M. Clavel ◽  
V. Ferney ◽  
K. Saanouni
Keyword(s):  
Cyclic Loading ◽  
Kinematic Hardening ◽  
Experimental Tests ◽  
Point Of View ◽  
Cyclic Plasticity ◽  
Loading Path ◽  
Isotropic Hardening ◽  
Loading Conditions ◽  
Effective Role ◽  
Deformation Modes

The isotropic hardening is known to play an effective role in the overhardening of materials under nonproportional cyclic loading. However, the behavior of the two states of Waspaloy (namely overaged and underaged states) under these loading conditions, shows that the kinematic hardening has also a considerable role in the overhardening. Experimental tests were carried out on these two states under various proportional and nonproportional cyclic loading conditions at room temperature. The effect of loading paths on micro-mechanisms of deformation was studied. From a microstructural point of view, it was shown that the deformation modes (quantitatively and qualitatively) depend on the loading path and the heat treatment. A constitutive model is proposed to describe the effect of overhardening, under the nonproportional loading conditions, on the kinematic hardening. The predicted responses are in good agreement with experimental results.

scholarly journals On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

2021 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Small Strain ◽  
Cyclic Plasticity ◽  
Isotropic Hardening ◽  
Mapping Algorithm ◽  
Hardening Rule ◽  
Return Mapping ◽  
Cyclic Plasticity Model

AbstractIn this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Effect of Yield Surface Curvature on Local Necking in Biaxially Stretched Sheets in Porous Materials

1992 ◽  
Vol 114 (2) ◽  
pp. 196-200 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Porous Materials ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Material Model ◽  
Isotropic Hardening ◽  
Material Models ◽  
Hardening Model ◽  
Local Necking ◽  
Highly Sensitive ◽  
Isotropic Expansion

In this paper, a recently proposed material model (Sun model) that is based on the lower bound approach of plasticity is extended by introducing a family of dilatant plasticity theories. The yield surfaces change by a combination of isotropic expansion and kinematic translation. The sensitivity of the local necking predictions in biaxially stretched sheets to the curvature of the yield surface in porous materials is addressed. The results of the present analysis obtained by using four material models, the isotropic hardening version of Sun, the kinematic hardening version suggested in this paper, the Gurson model, and the Mear and Hutchinson model, indicate that the local necking predictions are highly sensitive to the curvature of the yield surface, and the predictions given by the kinematic hardening model are more reasonable for local necking analysis than those by the isotropic hardening model.

Constitutive Modeling of Anisothermal Cyclic Plasticity of 304 Stainless Steel

1989 ◽  
Vol 111 (1) ◽  
pp. 106-114 ◽  
Author(s):  
N. Ohno ◽  
Y. Takahashi ◽  
K. Kuwabara
Keyword(s):  
Stainless Steel ◽  
Constitutive Modeling ◽  
Phase Changes ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Temperature History ◽  
Isotropic Hardening ◽  
Plastic Behavior ◽  
Extended Model ◽  
Thermomechanical Cycling

Temperature-history dependence in anisothermal cyclic plasticity of 304 stainless steel is studied for the constitutive modeling within the temperature range from room temperature to 600°C. Cyclic plastic behavior under in-phase and out-of-phase changes of temperature and athermal strain is analyzed first by use of an elaborate constitutive model with its material constants determined from isothermal experiments; good agreement is obtained between the predictions and experiments, if we assume that the internal change proper to higher temperature prevails under such thermomechanical cycling. This finding leads us to extend the evolution equation of isotropic hardening so that it can be valid for more complex variations of temperature. The extended model simulates well the recent experiments of Niitsu and Ikegami under multi-step changes of temperature.

An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity

1987 ◽  
Vol 54 (2) ◽  
pp. 323-334 ◽  
Author(s):  
D. L. McDowell
Keyword(s):  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Modulus Function ◽  
Isotropic Hardening ◽  
Hardening Rule ◽  
Hardening Modulus ◽  
Recent Developments ◽  
Distance Vector ◽  
Plastic Hardening ◽  
Hardening Rules

The Mroz kinematic hardening rule has previously demonstrated superior capability to correlate cyclically stable nonproportional stress-strain response. In this paper, recently proposed kinematic hardening rules for single and multiple surface cyclic plasticity models are evaluated. Significant improvement over the Mroz rule, without loss of generality, is achieved with a deviatoric stress rate-dominated rule proposed by Tseng and Lee for two surface theory. Recent approaches for correlation of the modulus function and isotropic hardening are discussed. The norm of the Mroz distance vector is found to uniquely correlate the variation of plastic hardening modulus through a cycle; it is necessary to include a measure of instantaneous nonproportionality, however, to properly normalize the modulus function. A new evolution equation is offered to correlate the additional isotropic hardening observed during nonproportional loading, and several contemporary approaches are also considered.

A combined hardening model of anisotropically consolidated cohesive soils

1991 ◽  
Vol 28 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Hiroyoshi Hirai ◽  
Takeshi Kamei
Keyword(s):  
Yield Surface ◽  
Kinematic Hardening ◽  
Strain Curve ◽  
Cohesive Soil ◽  
Stress Path ◽  
Yield Function ◽  
Triaxial Tests ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Cohesive Soils

A model introduced in the present paper is capable of describing the mechanical behaviour of anisotropically consolidated cohesive soils reasonably well. The salient features of the proposed model are summarized as follows: (i) generalized forms of the Cambridge models are given to both yield function and plastic potential; (ii) a combination of isotropic and kinematic hardening is used; (iii) a nonassociated-flow rule is proposed; (iv) the isotropic hardening involves plastic work not only related to volumetric change but also to deviatoric deformation; (v) the translation of the yield surface is specified by extending Ziegler's rule of kinematic hardening; (vi) the constitutive model has versatility and flexibility to describe expansion, translation, and rotation of a yield surface in stress space. Several undrained triaxial tests of anisotropically consolidated cohesive soils are simulated, and good agreement is observed between simulation and experimental data. Key words: anisotropy, dilatancy, cohesive soil, consolidated undrained shear, constitutive equation, stress-strain curve, pore pressure - strain curve, effective-stress path.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

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