Modeling of High Homologous Temperature Deformation Behavior Using the Viscoplasticity Theory Based on Overstress (VBO): Part I— Creep and Tensile Behavior

1995 ◽  
Vol 117 (4) ◽  
pp. 456-461 ◽  
Author(s):  
Yukio Tachibana ◽  
Erhard Krempl
Keyword(s):  
Cyclic Hardening ◽  
Back Stress ◽  
Tensile Tests ◽  
Tensile Behavior ◽  
Temperature Deformation ◽  
State Variables ◽  
Homologous Temperature ◽  
Variable Theory ◽  
Alloy 800 ◽  
High Homologous Temperature

The viscoplasticity theory based on overstress (VBO) is a state variable theory without a yield surface and without loading/unloading conditions. It contains two tensor valued state variables, the equilibrium (back) stress and the kinematic stress that is a repository for work hardening (softening). The scalar valued isotropic or time (rate)-independent stress models cyclic hardening (softening). For application to high homologous temperature, the effects of diffusion which counteracts the hardening of inelastic deformation has to be accounted for. Recovery of state terms are introduced in the growth laws for the state variables. A high homologous temperature VBO model is introduced and applied to the creep and tensile tests of Alloy 800 H between 750°C and 1050°C. Primary, secondary and tertiary creep as well as tensile behavior were well reproduced. It is shown that the transition to fluid state can be modeled with VBO.

Modeling of High Homologous Temperature Deformation Behavior Using the Viscoplasticity Theory Based on Overstress (VBO): Part II—Characteristics of the VBO Model

1997 ◽  
Vol 119 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Yukio Tachibana ◽  
Erhard Krempl
Keyword(s):  
Hold Time ◽  
Cyclic Strain ◽  
Tensile Tests ◽  
Temperature Deformation ◽  
Extreme Conditions ◽  
Alloy 800H ◽  
Homologous Temperature ◽  
High Homologous Temperature ◽  
Term Creep

Characteristics of the high homologous temperature VBO model under extreme conditions such as very fast and very slow tensile tests, long-term-creep and relaxation tests are investigated via numerical experiments and analysis. To this end, material constants of Alloy 800H determined from other tests in Part I were utilized for the prediction. Although no experiments are available for the extreme conditions, the predictions are plausible. For cyclic, strain controlled hold-time tests the predictions compare well with sparse experimental data. The results give confidence that VBO can be used to predict the long-term behavior at high homologous temperature once the constants have been determined from regular, short-term tests.

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.

Modeling of High Homologous Temperature Deformation Behaviour Using the Viscoplasticity Theory Based on Overstress (VBO): Part III—A Simplified Model

1998 ◽  
Vol 120 (3) ◽  
pp. 193-196 ◽  
Author(s):  
Yukio Tachibana ◽  
Erhard Krempl
Keyword(s):  
Deformation Behaviour ◽  
Three Dimensional ◽  
Simplified Model ◽  
Temperature Deformation ◽  
Alloy 800H ◽  
Homologous Temperature ◽  
Static Recovery ◽  
Long Time Behaviour ◽  
Long Time ◽  
High Homologous Temperature

A simplified version of the Viscoplasticity Theory Based on Overstress (VBO) is applied to modeling of Alloy 800H at homologous temperatures between 0.6 and 0.8 The present formulation is simplified to the extent that omission of any constant would deprive the model to represent phenomena. Examples of such a phenomenon are tertiary creep and static recovery. The three-dimensional formulation of the simplified model for Alloy 8OOH at high homologous temperature needs a total of 10 constants. The parent theory from which the simplified model is derived has 18 constants that must be determined from experiments. The simplified theory has essentially the same modeling capability as the parent theory. There are differences in the predictions of the two versions for very long-time behaviour for which no test data are available. When material data are available for comparison the modeling of the regular and the simplified versions are very good and show roughly the same amount of deviation. The results suggest that the simplified version should be tried first when a given material has to be modeled.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

High Temperature Deformation Mechanism Maps of NiAl

2004 ◽  
Vol 449-452 ◽  
pp. 57-60
Author(s):  
I.G. Lee ◽  
A.K. Ghosh
Keyword(s):  
High Temperature ◽  
Strain Rate ◽  
Deformation Mechanism ◽  
Calculation Method ◽  
Deformation Behavior ◽  
Tensile Tests ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Grain Sizes ◽  
Temperature Strain

In order to analyze high temperature deformation behavior of NiAl alloys, deformation maps were constructed for stoichiometric NiAl materials with grain sizes of 4 and 200 µm. Relevant constitute equations and calculation method will be described in this paper. These maps are particularly useful in identifying the location of testing domains, such as creep and tensile tests, in relation to the stress-temperature-strain rate domains experienced by NiAl.

Estimation of Back Stress Produced by Dislocation Interaction in Icosahedral Al-Pd-Mn

2000 ◽  
Vol 643 ◽  
Author(s):  
Hisatoshi Hirai ◽  
Akira Kitahara ◽  
Fuyuki Yoshida ◽  
Hideharu Nakashima
Keyword(s):  
Shear Stress ◽  
High Temperature ◽  
Main Part ◽  
Unit Length ◽  
Back Stress ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Dislocation Interaction ◽  
Burgers Vector ◽  
Phonon Component

AbstractWe attempted to calculate the breakaway stress σb of dislocation from attractive junction made by reaction of dislocations. Assuming that the force f acting on the unit length of dislocation with the Burgers vector B under a shear stress τa is f τ∣b˝∣ where b˝ is the phonon component of B, and that the elastic energy per unit length of dislocation W is approximated by W = G(∣b˝∣2 + c2 ∣b˔∣2) where G is the shear modulus, b˔ the phason component of B and c2 a coefficient of about 3.1 × 10−3. Using the values G = 48.4 GPa at 1070 K, the Taylor factor M = 3 and the measured dislocation density of 1.8 × 1013 m−2, we calculated σb for 21 possible dislocation reactions. Picking up the most possible dislocation reactions, σb distributed between 50 and 80 MPa, and the average of them was 64 MPa. This result strongly suggested the possibility that the main part of the internal stress of the high-temperature deformation of icosahedral Al-Pd-Mn is explained by σb.

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