On the Definition of State Variables for an Internal State Variable Constitutive Model Describing Metal Deformation

A unified constitutive model incorporating internal state variables based upon the deformation phenomena that are observed to occur at the microstructural level has been developed and applied to Rene´ 95. Material hardening is modeled using dragstress and back-stress state variables, while the reduction in the material’s load-carrying capability is described by using a damage-accumulation state variable. Application of the model to the tensile, cyclic, and creep loadings of Rene´ 95 at 650°C demonstrated that the model is capable of capturing cyclic hardening, damage accumulation, and tertiary creep by using one inelastic flow equation in concert with the state-variable-evolution equations.

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A Strain-Based Formulation for the Coupled Viscoelastic/Damage Behavior

Journal of Applied Mechanics ◽

10.1115/1.1348013 ◽

2000 ◽

Vol 68 (2) ◽

pp. 304-311 ◽

Cited By ~ 11

Author(s):

K. Abdel-Tawab ◽

Y. J. Weitsman

Keyword(s):

Internal State ◽

Internal State Variable ◽

State Variables ◽

Viscoelastic Creep ◽

Damage Behavior ◽

State Variable ◽

Internal State Variables ◽

Interfacial Cracks ◽

Induced Changes ◽

The Continuum

A strain-based thermodynamics framework is proposed for modeling the continuum damage behavior of viscoelastic materials. Damage is represented by an internal state variable in the form of a symmetric second rank tensor. The effect of damage on the constitutive behavior is introduced through direct coupling between the damage variable and the viscoelastic internal state variables. This approach accounts for time-dependent damage as well as damage-induced changes in material symmetry. Also, damage evolution is modeled by employing the concept of damage surfaces. This work is motivated by experimental observations of the response of swirl-mat and random chopped fiber mat polymeric composites where viscoelastic creep was accompanied by a multitude of fiber/matrix interfacial cracks.

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An Internal State Variable Constitutive Model for Deformation of Austenitic Stainless Steels

Journal of Engineering Materials and Technology ◽

10.1115/1.4006822 ◽

2012 ◽

Vol 134 (4) ◽

Cited By ~ 10

Author(s):

Paul S. Follansbee

Keyword(s):

Dislocation Density ◽

Nitrogen Content ◽

Yield Stress ◽

Stainless Steels ◽

Activation Volume ◽

Internal State ◽

Austenitic Stainless Steels ◽

Internal State Variable ◽

State Variables ◽

State Variable

Austenitic stainless steels—particularly the 304 and 316 families of alloys—exhibit similar trends in the dependence of yield stress on temperature. Analysis of temperature and strain-rate dependent yield stress literature data in alloys with varying nitrogen content and grain size has enabled the definition of two internal state variables characterizing defect populations. The analysis is based on an internal state variable constitutive law termed the mechanical threshold stress model. One of the state variables varies solely with nitrogen content and is characterized with a larger activation volume. The other state variable is characterized by a much smaller activation volume and may represent interaction of dislocations with solute and interstitial atoms. Analysis of the entire stress–strain curve requires addition of a third internal state variable characterizing the evolving stored dislocation density. Predictions of the model are compared to measurements in 304, 304L, 316, and 316L stainless steels deformed over a wide range of temperatures (up to one-half the melting temperature) and strain rates. Model predictions and experimental measurements deviate at temperatures above ∼600 K where dynamic strain aging has been observed. Application of the model is demonstrated in irradiated 316LN where the defect population induced by irradiation damage is analyzed. This defect population has similarities with the stored dislocation density. The proposed model offers a framework for modeling deformation in stable austenitic stainless steels (i.e., those not prone to a martensitic phase transformation).

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Finite deformation constitutive model for macro-yield behavior of amorphous glassy polymers with a molecular entanglement-based internal-state variable

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2019.105064 ◽

2019 ◽

Vol 161-162 ◽

pp. 105064 ◽

Cited By ~ 4

Author(s):

Han Jiang ◽

Chengkai Jiang

Keyword(s):

Constitutive Model ◽

Finite Deformation ◽

Internal State ◽

Glassy Polymers ◽

Internal State Variable ◽

Yield Behavior ◽

State Variable

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A Unified Constitutive Model for Creep and Cyclic Viscoplasticity Behavior Simulation of Steels Based on the Absolute Reaction Rate Theory

Advances in Materials Science and Engineering ◽

10.1155/2017/2129478 ◽

2017 ◽

Vol 2017 ◽

pp. 1-13

Author(s):

Huayan Chen ◽

Xiangguo Zeng ◽

Yang Guo ◽

Fang Wang

Keyword(s):

Constitutive Model ◽

Reaction Rate ◽

Internal State ◽

Rate Theory ◽

State Variables ◽

Absolute Reaction Rate Theory ◽

Reaction Rate Theory ◽

Absolute Reaction Rate ◽

The Absolute ◽

Absolute Reaction

In this work, the viscoplasticity and creep behavior for modified 9Cr-1Mo and 316 stainless steels were investigated. Based on the absolute reaction rate theory, a unified constitutive model incorporating internal state variables was proposed to characterize the evolution of the back stress. Also, the model was implemented by the ABAQUS system with the semi-implicit stress integration. Compared to the experimental data, the results demonstrated that the proposed approach could effectively simulate the cyclic softening and hardening behavior for such structural steels.

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