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.

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 squeezing property and its applications to a description of long-time behaviour in the three-dimensional viscous primitive equations

2014 ◽  
Vol 144 (4) ◽  
pp. 711-729 ◽  
Author(s):  
Igor Chueshov
Keyword(s):  
Three Dimensional ◽  
Ocean Dynamics ◽  
Primitive Equations ◽  
Time Behaviour ◽  
Time Dynamics ◽  
Squeezing Property ◽  
Long Time Behaviour ◽  
New Information ◽  
Determining Modes ◽  
Long Time

We consider the three-dimensional viscous primitive equations with periodic boundary conditions. These equations arise in the study of ocean dynamics and generate a dynamical system in a Sobolev H1-type space. Our main result establishes the so-called squeezing property in the Ladyzhenskaya form for this system. As a consequence of this property we prove the finiteness of the fractal dimension of the corresponding global attractor, the existence of a finite number of determining modes and the ergodicity of a related random kick model. All these results provide new information concerning the long-time dynamics of oceanic motion.

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.

scholarly journals Global averaging and parametric resonances in damped semilinear wave equations

2006 ◽  
Vol 136 (5) ◽  
pp. 1053-1097 ◽  
Author(s):  
S. Zelik
Keyword(s):  
Wave Equations ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
Initial Energy ◽  
Uniform Attractor ◽  
Long Time Behaviour ◽  
Parametric Resonances ◽  
Long Time ◽  
Uniform Attractors ◽  
Resonant Part

The long-time behaviour of solutions to a semilinear damped wave equation in a three-dimensional bounded domain with the nonlinearity rapidly oscillating in time (f = f(ε, u, t/ε)) is studied. It is proved that (under natural assumptions) the behaviour of solutions whose initial energy is not very large can be described in terms of global (uniform) attractors Aε of the corresponding dynamical processes and that, as ε → 0, these attractors tend to the global attractor A0 of the corresponding averaged system. We also give the detailed description of these attractors in the case where the limit attractor A0 is regular.Moreover, we give explicit examples of semilinear hyperbolic equations where the uniform attractor Âε (for the initial data belonging to the whole energy phase space) contains the irregular resonant part, which tends to infinity as ε → 0, and formulate the additional restrictions on the nonlinearity f which guarantee that this part is absent.

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