An internal state variable approach to constitutive theories for granular materials with snow as an example

1988 ◽  
Vol 7 (2) ◽  
pp. 109-119 ◽  
Author(s):  
A.C. Hansen ◽  
R.L. Brown
Keyword(s):  
Granular Materials ◽  
Internal State ◽  
Internal State Variable ◽  
Constitutive Theories ◽  
State Variable ◽  
Variable Approach

Constitutive Modeling of Beta Titanium Alloy Ti-10V-4.5Fe-1.5Al during Hot Deformation Process

2012 ◽  
Vol 510 ◽  
pp. 729-733
Author(s):  
Feng Bo Han ◽  
Jin Shan Li ◽  
Hong Chao Kou ◽  
Bin Tang ◽  
Min Jie Lai ◽  
...  
Keyword(s):  
Titanium Alloy ◽  
High Temperature ◽  
Dislocation Density ◽  
Internal State ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Model Parameters ◽  
Internal State Variable ◽  
Dislocation Interaction ◽  
State Variable

A constitutive model using dislocation density rate as an internal state variable has been proposed for hot working of β titanium alloy in this paper. The β phase was only taken into consideration during high temperature deformation. The solution strengthening and dislocation interaction were included in the constitutive equations. The strength coefficient was determined by equivalent vanadium content, Veq, which was calculated according to the alloy constituent. A Kocks-Mecking model was adopted to describe the variation of dislocation density. The constitutive relationship of a β titanium alloy Ti-10V-4.5Fe-1.5Al for high temperature deformation was established using the internal-state-variable based model. Model parameters were determined by the genetic algorithm based objective optimization method. The predicted results agree fairly well with the experimental value.

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