ISovector fields and self-similar solutions for power law creep

1983 ◽  
Vol 21 (9) ◽  
pp. 1061-1067 ◽  
Author(s):  
T.J. Delph
Keyword(s):  
Power Law ◽  
Self Similar ◽  
Power Law Creep ◽  
Similar Solutions

Computational and Experimental Characterization of Indentation Creep

2003 ◽  
Vol 795 ◽  
Author(s):  
Ming Dao ◽  
Hidenari Takagi ◽  
Masami Fujiwara ◽  
Masahisa Otsuka
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Constant Load ◽  
Dislocation Creep ◽  
Solid Solution Alloy ◽  
Indentation Creep ◽  
Creep Tests ◽  
Uniaxial Creep ◽  
Self Similar ◽  
Power Law Creep

ABSTRACT:Detailed finite-element computations and carefully designed indentation creep experiments were carried out in order to establish a robust and systematic method to accurately extract creep properties during indentation creep tests. Finite-element simulations confirmed that, for a power law creep material, the indentation creep strain field is indeed self-similar in a constant-load indentation creep test, except during short transient periods at the initial loading stage and when there is a deformation mechanism change. Self-similar indentation creep leads to a constitutive equation from which the power-law creep exponent, n, the activation energy for creep, Qc and so on can be evaluated robustly. Samples made from an Al-5.3mol%Mg solid solution alloy were tested at temperatures ranging from 573 K to 773 K. The results are in good agreement with those obtained from conventional uniaxial creep tests in the dislocation creep regime.

Converging gravity currents over a permeable substrate

2015 ◽  
Vol 778 ◽  
pp. 669-690 ◽  
Author(s):  
Zhong Zheng ◽  
Sangwoo Shin ◽  
Howard A. Stone
Keyword(s):  
Power Law ◽  
Gravity Current ◽  
Gravity Currents ◽  
Numerical Predictions ◽  
Front Position ◽  
Dependent Position ◽  
Self Similar ◽  
Vertical Leakage ◽  
Similar Solutions ◽  
Lock Gate

We study the propagation of viscous gravity currents along a thin permeable substrate where slow vertical drainage is allowed from the boundary. In particular, we report the effect of this vertical fluid drainage on the second-kind self-similar solutions for the shape of the fluid–fluid interface in three contexts: (i) viscous axisymmetric gravity currents converging towards the centre of a cylindrical container; (ii) viscous gravity currents moving towards the origin in a horizontal Hele-Shaw channel with a power-law varying gap thickness in the horizontal direction; and (iii) viscous gravity currents propagating towards the origin of a porous medium with horizontal permeability and porosity gradients in power-law forms. For each of these cases with vertical leakage, we identify a regime diagram that characterizes whether the front reaches the origin or not; in particular, when the front does not reach the origin, we calculate the final location of the front. We have also conducted laboratory experiments with a cylindrical lock gate to generate a converging viscous gravity current where vertical fluid drainage is allowed from various perforated horizontal substrates. The time-dependent position of the propagating front is captured from the experiments, and the front position is found to agree well with the theoretical and numerical predictions when surface tension effects can be neglected.

scholarly journals Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents

2014 ◽  
Vol 747 ◽  
pp. 218-246 ◽  
Author(s):  
Zhong Zheng ◽  
Ivan C. Christov ◽  
Howard A. Stone
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Gravity Currents ◽  
Similar Solution ◽  
Phase Plane Analysis ◽  
Plane Analysis ◽  
Self Similar Solution ◽  
Theoretical Predictions ◽  
Self Similar ◽  
Similar Solutions

AbstractWe report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.

scholarly journals Indentation of power law creep solids by self-similar indenters

2010 ◽  
Vol 527 (21-22) ◽  
pp. 5613-5618 ◽  
Author(s):  
Wei-Min Chen ◽  
Yang-Tse Cheng ◽  
Min Li
Keyword(s):  
Power Law ◽  
Self Similar ◽  
Power Law Creep

On annular self-similar solutions in resistive magnetogasdynamics

2008 ◽  
Vol 464 (2098) ◽  
pp. 2535-2547 ◽  
Author(s):  
R.M Lock ◽  
A.J Mestel
Keyword(s):  
Electrical Resistivity ◽  
Power Law ◽  
Finite Time ◽  
Sound Speed ◽  
Plasma Temperature ◽  
Ideal Gas ◽  
Singular Limit ◽  
Constant Diffusivity ◽  
Self Similar ◽  
Similar Solutions

We consider the implosion of a hollow cylinder of ideal gas with non-zero electrical resistivity. It is shown that there exist self-similar solutions that collapse in a finite time for a range of power-law dependences of the resistivity on the plasma temperature, η ∼ T δ . In contrast to the earlier work with zero resistivity, all field variables are finite up to the instant of collapse and the compression is homogeneous. A solution in closed form is found for constant diffusivity, δ =0. It is shown that δ →0 is a singular limit with the density and sound speed adjusting over a layer of thickness | δ | 1/2 at the inner boundary.

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