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

2000 ◽  
Vol 68 (2) ◽  
pp. 304-311 ◽  
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.

scholarly journals The Granular Structure of Snow: An Internal-State Variable Approach

1986 ◽  
Vol 32 (112) ◽  
pp. 434-438 ◽  
Author(s):  
A. C. Hansen ◽  
R. L. Brown
Keyword(s):  
Internal State ◽  
Granular Structure ◽  
High Rate ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables ◽  
Variable Approach ◽  
Quantitative Stereology ◽  
The Mean ◽  
General Relations

AbstractA statistical model characterizing the granular structure of snow is developed using quantitative stereology. The model is based on specific parameters (e.g. bond radius, grain-size, etc.) which take the form of internal-state variables in a constitutive theory for high-rate deformation of snow. In addition to parameters developed by other authors in previous investigations, a new parameter characterizing the mean bond length is developed. More significantly, general relations are derived for the mean number of bonds per grain and mean number of grains per unit volume without making any assumptions regarding the shape or size of the ice grains, or their respective distributions.

A Phenomenologically Based Constitutive Model for Rene´ 95

1992 ◽  
Vol 114 (4) ◽  
pp. 340-347 ◽  
Author(s):  
J. A. Sherwood ◽  
D. C. Stouffer
Keyword(s):  
Constitutive Model ◽  
Damage Accumulation ◽  
Evolution Equations ◽  
Internal State ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Flow Equation ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables

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.

scholarly journals The Granular Structure of Snow: An Internal-State Variable Approach

1986 ◽  
Vol 32 (112) ◽  
pp. 434-438 ◽  
Author(s):  
A. C. Hansen ◽  
R. L. Brown
Keyword(s):  
Internal State ◽  
Granular Structure ◽  
High Rate ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables ◽  
Variable Approach ◽  
Quantitative Stereology ◽  
The Mean ◽  
General Relations

AbstractA statistical model characterizing the granular structure of snow is developed using quantitative stereology. The model is based on specific parameters (e.g. bond radius, grain-size, etc.) which take the form of internal-state variables in a constitutive theory for high-rate deformation of snow. In addition to parameters developed by other authors in previous investigations, a new parameter characterizing the mean bond length is developed. More significantly, general relations are derived for the mean number of bonds per grain and mean number of grains per unit volume without making any assumptions regarding the shape or size of the ice grains, or their respective distributions.

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

2012 ◽  
Vol 134 (4) ◽  
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).

A Micromechanical Basis for Constitutive Equations With Internal State Variables

1984 ◽  
Vol 106 (4) ◽  
pp. 322-325 ◽  
Author(s):  
E. W. Hart
Keyword(s):  
Internal Stress ◽  
Constitutive Equations ◽  
Inelastic Deformation ◽  
Internal State ◽  
Constitutive Relations ◽  
Micromechanical Model ◽  
Friction Stress ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables

A micromechanical model based on the glide and interaction of dislocations is developed to rationalize some of the phenomenological features of inelastic deformation. An origin for an internal stress is explicitly stated. The relation among the applied stress, the internal stress, and the glide friction stress is derived. The internal stress is shown to be linearly proportional to a stored anelastic strain. The micromechanical model is shown to provide a detailed basis for the state variable constitutive relations proposed by Hart.

Elastoviscoplastic Models with Relaxed Configurations and Internal State Variables

1990 ◽  
Vol 43 (7) ◽  
pp. 131-151 ◽  
Author(s):  
Sanda Cleja T¸igoiu ◽  
Eugen Soo´s
Keyword(s):  
Experimental Data ◽  
Structural Analysis ◽  
Internal State ◽  
State Variables ◽  
Internal State Variables ◽  
Local Current

We present the microstructural basis, the initial macroscopical formulations, and a possible axiomatic reconstruction of the elastoviscoplastic model for metals based on the use of the local, current, relaxed configurations. Structural analysis and experimental data show that using these configurations offers advantages for the formulation of the material laws when the deformations are small or moderately large. Our review aims to be a concise, historical, and critical exposition of the main stages, contributions and results, which led, during the late sixties and the beginning of seventies, to the formulation of the fundamental ideas lying at the basis of the model. We delineate the role played by Lee, Liu, Teodosiu, Sidoroff, Mandel, and Kratochvil in the first formulation of the theory between 1966 and 1972, as well as the contributions of Dafalias and Loret to the development of the model between 1983 and 1985. Finally, we discuss some results obtained between 1985 and 1988 with models based on local current relaxed configurations.

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