Multi‐scale fracture characterization using fractal frequency‐power‐law attenuation models

2003 ◽  
Author(s):  
Vladimir Rok ◽  
Alexander Druzhinin ◽  
Russ Evans ◽  
Xiang‐Yang Li
Keyword(s):  
Power Law ◽  
Fracture Characterization ◽  
Multi Scale ◽  
Attenuation Models ◽  
Frequency Power

scholarly journals Extended power-law scaling of air permeabilities measured on a block of tuff

2012 ◽  
Vol 16 (1) ◽  
pp. 29-42 ◽  
Author(s):  
M. Siena ◽  
A. Guadagnini ◽  
M. Riva ◽  
S. P. Neuman
Keyword(s):  
Power Law ◽  
Structure Functions ◽  
Self Similarity ◽  
Scaling Exponents ◽  
Multi Scale ◽  
Sample Structure ◽  
Heavy Tailed ◽  
Non Gaussian ◽  
Nonlinear Fashion ◽  
Extended Power

Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

scholarly journals Temperature Resistance of Mo3Si: Phase Stability, Microhardness, and Creep Properties

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 564 ◽  
Author(s):  
Olha Kauss ◽  
Susanne Obert ◽  
Iurii Bogomol ◽  
Thomas Wablat ◽  
Nils Siemensmeyer ◽  
...  
Keyword(s):  
Power Law ◽  
Phase Stability ◽  
Gas Turbines ◽  
Constitutive Models ◽  
Creep Properties ◽  
Multi Scale ◽  
Scale Modeling ◽  
Significant Difference ◽  
Before And After ◽  
Multi Phase

Mo-Si-B alloys are one of the most promising candidates to substitute Ni based superalloys in gas turbines. The optimization of their composition can be achieved more effectively using multi-scale modeling of materials behavior and structural analysis of components for understanding, predicting, and screening properties of new alloys. Nevertheless, this approach is dependent on data on the properties of the single phases in these alloys. The focus of this investigation is Mo3Si, one of the phases in typical Mo-Si-B alloys. The effect of 100 h annealing at 1600 °C on phase stability and microhardness of its three near-stoichiometric compositions—Mo-23Si, Mo-24Si and Mo-25Si (at %)—is reported. While Mo-23Si specimen consist only of Mo3Si before and after annealing, Mo-24Si and Mo-25Si comprise Mo5Si3 and Mo3Si before annealing. The latter is then increased by the annealing. No significant difference in microhardness was detected between the different compositions as well as after annealing. The creep properties of Mo3Si are described at 1093 °C and 1300 °C at varying stress levels as well as at 300 MPa and temperatures between 1050 °C and 1350 °C. Three constitutive models were used for regression of experimental results—(i) power law with a constant creep exponent, (ii) stress range dependent law, and (iii) power law with a temperature-dependent creep exponent. It is confirmed that Mo3Si has a higher creep resistance than Moss and multi-phase Mo-Si-B alloys, but a lower creep strength as compared to Mo5SiB2.

Improved description of shock wave evolution in media with frequency power law dependent attenuation

2001 ◽  
Vol 109 (5) ◽  
pp. 2263-2265 ◽  
Author(s):  
Kirk D. Wallace ◽  
Mark R. Holland ◽  
James G. Miller
Keyword(s):  
Shock Wave ◽  
Power Law ◽  
Wave Evolution ◽  
Frequency Power

On an attenuation obeying a frequency power law

2018 ◽  
Vol 144 (3) ◽  
pp. 1981-1981
Author(s):  
Michael J. Buckingham
Keyword(s):  
Power Law ◽  
Frequency Power

Frequency-Power-Law Attenuation – Scattering by Fractal Inclusions

2003 ◽  
Author(s):  
A. Druzhinin ◽  
V. Rok ◽  
J.R. Evans ◽  
X-Y. Li
Keyword(s):  
Power Law ◽  
Frequency Power

On Variants of the Frequency Power Law for the Electromagnetic Characterization of Hydraulic Concrete

2011 ◽  
Vol 60 (11) ◽  
pp. 3658-3668 ◽  
Author(s):  
Amine Ihamouten ◽  
Khaled Chahine ◽  
Vincent Baltazart ◽  
Géraldine Villain ◽  
Xavier Derobert
Keyword(s):  
Power Law ◽  
Hydraulic Concrete ◽  
Frequency Power
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