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.

Bridging Length Scales Between Macroscopic Response and Microstructure Through Gradient Anisotropic Damage for MMC

2001 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Robert J. Dorgan ◽  
J. R. Dorroh
Keyword(s):  
Evolution Equations ◽  
Scale Effects ◽  
Internal State ◽  
Multiple Scale ◽  
Mathematical Approach ◽  
State Variables ◽  
Material Inhomogeneity ◽  
Internal State Variables ◽  
Gradient Approach ◽  
Systematic Framework

Abstract This work provides a consistent and systematic framework for the gradient approach in coupled damage-plasticity that enables one to better understand the effects of material inhomogeneity on the macroscopic behavior and the material instabilities. The idea of multiple scale effects is made more general and complete by introducing damage and plasticity internal state variables and the corresponding gradients at both the macro and mesoscale levels. The development of evolution equations for plasticity and damage is treated in a similar mathematical approach and formulation since both address defects such as dislocations for the former and cracks/voids for the later.

Constitutive Model for Sn-Pb Solder Under Fatigue Loading

2002 ◽  
Author(s):  
Y. Wei ◽  
C. L. Chow ◽  
M. K. Nielsen ◽  
H. E. Fang
Keyword(s):  
Constitutive Model ◽  
Mechanical Response ◽  
Internal State ◽  
Hold Time ◽  
Fatigue Loading ◽  
Loading Frequency ◽  
State Variables ◽  
Load Paths ◽  
Internal State Variables ◽  
Failure Predictions

The paper presents a constitutive model for Sn-Pb solder which captures the response of this complex material subject to a variety of load paths including fatigue loading. Internal state variables are established to characterize grain coarsening and material degradation observed experimentally. A damage-coupled viscoplastic constitutive model is formulated to take into account the effects of temperature and loading rates on mechanical response. The influence of fatigue loading frequency or strain rate, hold time and temperature on mechanical behavior and fatigue life for 63Sn-37Pb solder alloy is examined. The fatigue failure predictions are compared with those obtained experimentally and found to be satisfactory.

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.

Anisotropic Constitutive Modeling of a Single Crystal Superalloy at Elevated Temperature

1990 ◽  
Vol 43 (5S) ◽  
pp. S345-S352 ◽  
Author(s):  
D. C. Stouffer ◽  
M. Y. Sheh ◽  
L. T. Dame
Keyword(s):  
Stress State ◽  
Single Crystal ◽  
Back Stress ◽  
Flow Equation ◽  
Single Crystal Superalloy ◽  
Test Results ◽  
State Variables ◽  
State Variable ◽  
Crystallographic Slip ◽  
Nickel Base

An anisotropic constitutive model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables in the inelastic flow equation for slip in each slip system. Experiments were conducted to evaluate the need of back stress in the model. The test results showed the effect of reverse inelastic flow on unloading is orientation dependent, and that a back stress state variable in the inelastic flow equation is necessary for predicting the anelastic behavior. Model correlations and predictions with experimental data are presented for the single crystal superalloy Rene’ N4 at 760C and 982C.

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.

A Crystallographic Model for the Tensile and Fatigue Response for Rene´ N4 at 982°C

1990 ◽  
Vol 57 (1) ◽  
pp. 25-31 ◽  
Author(s):  
M. Y. Sheh ◽  
D. C. Stouffer
Keyword(s):  
Stress State ◽  
Single Crystal ◽  
Back Stress ◽  
Flow Equation ◽  
Stress Effect ◽  
State Variables ◽  
State Variable ◽  
Crystallographic Slip ◽  
Anelastic Behavior ◽  
Nickel Base

An anisotropic constitutive model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the existence of back stress in single crystals. The results showed that the back stress effect of reverse inelastic flow on the unloading stress is orientation dependent, and a back stress state variable in the inelastic flow equation is necessary for predicting anelastic behavior. Model correlations and predictions of experimental data are presented for the single crystal supperalloy Rene´ N4 at 982°C.

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