Yield Surfaces of SUS304 Under Cyclic Loading

1988 ◽  
Vol 110 (4) ◽  
pp. 364-371 ◽  
Author(s):  
H. Ishikawa ◽  
K. Sasaki
Keyword(s):  
Cyclic Loading ◽  
Constitutive Equations ◽  
Isotropic Material ◽  
Quadratic Function ◽  
Cyclic Plasticity ◽  
Induced Anisotropy ◽  
Strain Criterion ◽  
Loading Function ◽  
Anisotropic Coefficient ◽  
Yield Surfaces

To formulate the constitutive equations for cyclic plasticity, the subsequent yield surfaces should be examined carefully. In this paper, the subsequent yield surfaces have been examined from the experiment for the initially isotropic material of SUS304 subject to cyclic loading, using a 50µm/m offset strain criterion for yielding probed at the current center of the yield surface. The experiment shows a translation, distorsion, and rotation of the subsequent yield surfaces because of the deformation-induced-anisotropy due to proportional or nonproportional cyclic loading in tension-torsion space. These yield surfaces could be represented by the quadratic function of stresses with fourth rank anisotropic coefficient tensor components. These anisotropic coefficient tensor components are found to be represented by the strain amplitude of cyclic loading. As a result, the loading function obtained shows availability to derive the constitutive equations of cyclic plasticity.

Constitutive equations for linear elasticity

2020 ◽  
pp. 97-127
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Thermal Expansion ◽  
Elastic Constants ◽  
Linear Elasticity ◽  
Constitutive Equations ◽  
Isotropic Material ◽  
Coefficient Of Thermal Expansion ◽  
Strain Tensor ◽  
Quadratic Function ◽  
Elasticity Tensor ◽  
Thermal Expansion Tensor

In this chapter the constitutive equations for linear elasticity in which the free energy is a quadratic function, and the stress a linear function, of the small strain tensor are introduced. In general, the fourth-order linear elasticity tensor which relates the stress to the strain has twenty-one independent elastic constants. Most solids, however, exhibit some symmetry, the effect of which is to reduce the number of elastic constants. Forms of the linear elasticity tensor for some anisotropic materials, as well as the widely-used forms for an isotropic material, which has only two independent elastic constants, are discussed. The engineering elastic moduli known as the shear modulus and the bulk modulus, as well as the Young’s modulus and the Poisson’s ratio for isotropic linear elastic materials are introduced. Considerations of temperature changes necessitate the introduction of another tensorial material property called the thermal expansion tensor, which for an isotropic material reduces to a scalar coefficient of thermal expansion.

Comparative study of the effective parameters on residual stress relaxation in welded aluminum plates under cyclic loading

2020 ◽  
Vol 21 (5) ◽  
pp. 505
Author(s):  
Yousef Ghaderi Dehkordi ◽  
Ali Pourkamali Anaraki ◽  
Amir Reza Shahani
Keyword(s):  
Residual Stress ◽  
Cyclic Loading ◽  
Stress Relaxation ◽  
Stress Amplitude ◽  
Cyclic Plasticity ◽  
Mean Stress ◽  
Effective Parameters ◽  
Perfect Plasticity ◽  
Residual Stress Relaxation ◽  
Aluminum Plates

The prediction of residual stress relaxation is essential to assess the safety of welded components. This paper aims to study the influence of various effective parameters on residual stress relaxation under cyclic loading. In this regard, a 3D finite element modeling is performed to determine the residual stress in welded aluminum plates. The accuracy of this analysis is verified through experiment. To study the plasticity effect on stress relaxation, two plasticity models are implemented: perfect plasticity and combined isotropic-kinematic hardening. Hence, cyclic plasticity characterization of the material is specified by low cycle fatigue tests. It is found that the perfect plasticity leads to greater stress relaxation. In order to propose an accurate model to compute the residual stress relaxation, the Taguchi L18 array with four 3-level factors and one 6-level is employed. Using statistical analysis, the order of factors based on their effect on stress relaxation is determined as mean stress, stress amplitude, initial residual stress, and number of cycles. In addition, the stress relaxation increases with an increase in mean stress and stress amplitude.

A Dislocation Density Based Constitutive Model for Cyclic Deformation

1996 ◽  
Vol 118 (4) ◽  
pp. 441-447 ◽  
Author(s):  
Y. Estrin ◽  
H. Braasch ◽  
Y. Brechet
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Cyclic Deformation ◽  
Internal Variables ◽  
Density Evolution ◽  
Alloy 800H ◽  
Material Response ◽  
Dislocation Densities

A new constitutive model describing material response to cyclic loading is presented. The model includes dislocation densities as internal variables characterizing the microstructural state of the material. In the formulation of the constitutive equations, the dislocation density evolution resulting from interactions between dislocations in channel-like dislocation patterns is considered. The capabilities of the model are demonstrated for INCONEL 738 LC and Alloy 800H.

scholarly journals Simulation of Cyclic Loading on Pipe Elbows Using Advanced Plane-Stress Elastoplasticity Models1

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Konstantinos Chatziioannou ◽  
Yuner Huang ◽  
Spyros A. Karamanos
Keyword(s):  
Cyclic Loading ◽  
Large Scale ◽  
Mechanical Response ◽  
Low Cycle Fatigue ◽  
Constitutive Relations ◽  
Cyclic Plasticity ◽  
Integration Scheme ◽  
Repeated Loading ◽  
Finite Element Software ◽  
Hardening Models

Abstract This work investigates the response of industrial steel pipe elbows subjected to severe cyclic loading (e.g., seismic or shutdown/startup conditions), associated with the development of significant inelastic strain amplitudes of alternate sign, which may lead to low-cycle fatigue. To model this response, three cyclic-plasticity hardening models are employed for the numerical analysis of large-scale experiments on elbows reported elsewhere. The constitutive relations of the material model follow the context of von Mises cyclic elasto-plasticity, and the hardening models are implemented in a user subroutine, developed by the authors, which employs a robust numerical integration scheme, and is inserted in a general-purpose finite element software. The three hardening models are evaluated in terms of their ability to predict the strain range at critical locations, and in particular, strain accumulation over the load cycles, a phenomenon called “ratcheting.” The overall good comparison between numerical and experimental results demonstrates that the proposed numerical methodology can be used for simulating accurately the mechanical response of pipe elbows under severe inelastic repeated loading. Finally, this paper highlights some limitations of conventional hardening rules in simulating multi-axial material ratcheting.

The Use of Anisotropic Yield Surfaces in Cyclic Plasticity

2008 ◽  
pp. 49-49-15 ◽  
Author(s):  
SJ Harvey ◽  
AP Toor ◽  
P Adkin
Keyword(s):  
Cyclic Plasticity ◽  
Yield Surfaces

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.

Prediction of Fatigue Crack Initiation Life Based on the Extended Cyclic Plasticity Model

2012 ◽  
Author(s):  
Seiichiro Tsutsumi
Keyword(s):  
Cyclic Loading ◽  
Kinematic Hardening ◽  
Fatigue Crack Initiation ◽  
Fatigue Cracking ◽  
Carbon Steels ◽  
Cyclic Plasticity ◽  
Plasticity Model ◽  
Hardening Law ◽  
Crack Initiation Life ◽  
Cyclic Plasticity Model

In order to simulate mechanical fatigue phenomena under macroscopically elastic condition, the plastic stretching within a yield surface has to be described, whilst the plastic strain is induced remarkably as the stress approaches the dominant yielding state. In this study, a phenomenological plasticity model, proposed for the description of the cyclic loading behavior observed for typical carbon steels during the high-cycle fatigue subjected to stresses lower than the yield stress, is applied for the prediction of fatigue initiation life. The model is formulated based on the unconventional plasticity model and is applied for materials obeying isotropic and kinematic hardening law. The mechanical responses under cyclic loading conditions are examined briefly. Finally, the initiation life of fatigue cracking is discussed based on the proposed model with the damage counting parameter.

A Fast Method for Ratchetting Strain Prediction

2006 ◽  
Author(s):  
Mohammad Noban ◽  
Hamid Jahed
Keyword(s):  
Cyclic Loading ◽  
Single Step ◽  
Frame Of Reference ◽  
Cyclic Plasticity ◽  
Moving Frame ◽  
Fast Method ◽  
Proportional Loading ◽  
Proposed Model ◽  
Cyclic Plasticity Model ◽  
Deviatoric Stresses

A time efficient method for predicting ratchetting strain is proposed. By finding the ratchetting rate, at only a few cycles, the ratchetting strain of any cycle can be determined. It is shown that a trajectory of the origin of stress may be defined in the deviatoric stress space as the ratchetting progresses. The method for obtaining this trajectory from a standard uniaxial asymmetric cyclic loading is presented. At the beginning, this trajectory coincides with the initial stress origin and approaches the mean stress, displaying a power law relationship with the number of loading cycles. This path defines a moving frame of reference for stress tensor calculations. Ratchetting rates for different cyclic loading are calculated with the knowledge of this frame of reference and through utilizing a constitutive cyclic plasticity model which incorporates deviatoric stresses and back stresses that are measured with respect to this moving frame. The proposed model is used to predict ratchetting strain of 1070 steel under single step constant amplitude and multi-step loading. The method is also applied to non-proportional loading. Results obtained agree with the available experimental measurements.

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