Elastic properties of rocks: Why shouldn’t they be constant?

2020 ◽  
Author(s):  
Federica Sandrone ◽  
Lucas Pimienta ◽  
Laurent Gastaldo ◽  
Marie Violay
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Rock Physics ◽  
Strain Range ◽  
Ultrasonic Waves ◽  
Static Stress ◽  
Seismic Wave Velocities ◽  
Potential Factors ◽  
Non Destructive

<pre><span lang="EN-US">         Over past decades, different approaches have been suggested for assessing the elastic constants of materials. In mechanics, the elastic properties are evaluated according to Hooke’s law from the static stress-strain curves, in the strain range before the material failure. In rock mechanics, this approach is used as well for characterizing elastic constants of rocks. Moreover, thanks to development of seismology and applied geophysics, seismic wave velocities were found to allow evaluating rock elastic properties. This approach has been largely developed by the rock physics/petrophysics community as a simple and non-destructive  mean of characterization of rock elastic constants.</span></pre> <pre><span lang="EN-US">         Ideally, being expected to probe the same material constants, the two approaches should yield the same results. However, in practice, the results seldom compare for a number of potential reasons, such as strains rate and amplitude. </span></pre> <pre><span lang="EN-US">This work aims to investigate, discuss and – possibly – reconcile these two approaches. Different igneous and sedimentary rocks are tested in the laboratory to investigate the influence of different potential factors. Three measuring methods are used: i) static stress-strains, ii) ultrasonic waves velocities, iii) stress-strains oscillations of varying amplitude. The experimental results are then discussed on the basis of existing theories.  </span></pre>

The Elastic Characterization of Composite Based on Ultrasonic Waves

2021 ◽  
Author(s):  
Y. H. Park ◽  
J. Dana
Keyword(s):  
Composite Materials ◽  
Fatigue Failure ◽  
Elastic Constants ◽  
Material Properties ◽  
Weight Ratio ◽  
Transversely Isotropic ◽  
Ultrasonic Waves ◽  
Material Strength ◽  
Isotropic Composite

Abstract Anisotropic composite materials have been extensively utilized in mechanical, automotive, aerospace and other engineering areas due to high strength-to-weight ratio, superb corrosion resistance, and exceptional thermal performance. As the use of composite materials increases, determination of material properties, mechanical analysis and failure of the structure become important for the design of composite structure. In particular, the fatigue failure is important to ensure that structures can survive in harsh environmental conditions. Despite technical advances, fatigue failure and the monitoring and prediction of component life remain major problems. In general, cyclic loadings cause the accumulation of micro-damage in the structure and material properties degrade as the number of loading cycles increases. Repeated subfailure loading cycles cause eventual fatigue failure as the material strength and stiffness fall below the applied stress level. Hence, the stiffness degradation measurement can be a good indication for damage evaluation. The elastic characterization of composite material using mechanical testing, however, is complex, destructive, and not all the elastic constants can be determined. In this work, an in-situ method to non-destructively determine the elastic constants will be studied based on the time of flight measurement of ultrasonic waves. This method will be validated on an isotropic metal sheet and a transversely isotropic composite plate.

scholarly journals A rock physics model for the characterization of organic-rich shale from elastic properties

2015 ◽  
Vol 12 (2) ◽  
pp. 264-272 ◽  
Author(s):  
Ying Li ◽  
Zhi-Qi Guo ◽  
Cai Liu ◽  
Xiang-Yang Li ◽  
Gang Wang
Keyword(s):  
Elastic Properties ◽  
Rock Physics ◽  
Physics Model ◽  
Rock Physics Model

Bulk Ultrasonic Techniques for Evaluation of Elastic Properties

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Fatigue Testing ◽  
Pulse Length ◽  
Ultrasonic Pulse ◽  
Ultrasonic Waves ◽  
Ultrasonic Velocities ◽  
Space Length ◽  
Ultrasonic Methods ◽  
Wave Methods

Currently, the design of most composite components is based on stiffness, and therefore methods for static measurement of stiffness are in wide use. The disadvantages of these methods lie in their destructive nature (the samples must be cut from parts of different orientations), in the difficulty of measuring shear properties, and in the need for extra care when measuring Young’s modulus in off-axis directions. Ultrasonic methods are more accurate and have higher spatial resolution than static measurements. As we showed in Chapter 2, by measuring ultrasonic velocities in several predefined directions, all elastic constants can be determined. The generic method described there is also destructive, however, requiring cutting numerous samples with appropriate fiber orientation. Specialized nondestructive methods for determining the elastic moduli of composite materials are more powerful and they can be applied to composite coupons before, during, and after strength or fatigue testing. It is important to have a fast and inexpensive technique to estimate input parameters for composite design. It is even more important to have a technique to evaluate composites during service to verify that the manufactured elastic stiffnesses match those assumed in the design. Several methods that utilize bulk ultrasonic waves for measurement of composite elastic constants are considered in this chapter. By bulk wave methods, we mean quasilongitudinal and quasitransverse ultrasonic wave velocity measurement methods that are applicable when the sample thickness h is larger than both the ultrasonic pulse space length τV and the wavelength λ (τ is the ultrasonic pulse length in time, and V is the wave speed). Other methods, which are applicable in the range h < τV and which account for wave interference with the boundaries of the specimen, will be considered in the following chapters. The most promising way to evaluate composite elastic properties nondestructively is to measure ultrasonic velocities in different directions in the composite material and reconstruct the elastic constants from these values using some kind of an inversion technique. One possible method has been suggested by Markham in the 1970s, who used ultrasonic waves obliquely incident from water onto a composite plate to measure ultrasonic velocities in various directions and evaluated the results to determine elastic constants.

Elastic Properties of Structural Phases in Shape Memory Alloys Investigated by Resonant Ultrasound Spectroscopy

2005 ◽  
Vol 482 ◽  
pp. 351-354 ◽  
Author(s):  
Michal Landa ◽  
Václav Novák ◽  
Petr Sedlák ◽  
Lluís Mañosa ◽  
Petr Šittner
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Ultrasonic Waves ◽  
Resonant Ultrasound Spectroscopy ◽  
Ultrasonic Methods ◽  
Resonance Frequencies ◽  
Resonant Ultrasound

Elastic constants of solids were, until recently, evaluated predominantly by pulse-echo ultrasonic methods which are based on measuring the speed of ultrasonic waves propagation in solids. Resonant ultrasound spectroscopy (RUS) is a relatively novel method in which all components of elastic tensor are determined from measured resonance frequencies of a freely vibrating specimen. The RUS technique has been employed in this work to investigate temperature dependence of the elastic properties of the parent austenite phase in CuAlNi shape memory alloy single crystals. This phase exhibits very high elastic anisotropy (anisotropy factor A 12) and softening the shear coefficient C0 upon cooling when approaching the Ms transformation temperature. The complications (need for large number of resonant frequencies) emerging when one tries to determine all elastic constants of highly elastically anisotropic materials by the RUS technique are discussed. It is concluded that the shear coefficients C0 and C44, which are the most important for shape memory alloys, are, nevertheless, determined reliably.

Mechanical behavior and ultrasonic non-destructive characterization of elastic properties of cordierite-based ceramics

2013 ◽  
Vol 39 (1) ◽  
pp. 21-27 ◽  
Author(s):  
A. Benhammou ◽  
Y. El Hafiane ◽  
L. Nibou ◽  
A. Yaacoubi ◽  
J. Soro ◽  
...  
Keyword(s):  
Mechanical Behavior ◽  
Elastic Properties ◽  
Non Destructive ◽  
Non Destructive Characterization

Failure Analysis of Flip-Chip Interconnections Through Acoustic Microscopy

1996 ◽  
Author(s):  
O. Diaz de Leon ◽  
M. Nassirian ◽  
C. Todd ◽  
R. Chowdhury
Keyword(s):  
Failure Analysis ◽  
Large Scale ◽  
Flip Chip ◽  
Ultrasonic Waves ◽  
Acoustic Microscopy ◽  
Acoustic Microscope ◽  
Chip Technology ◽  
Ball Joints ◽  
Non Destructive ◽  
Scanning Acoustic Microscope

Abstract Integration of circuits on semiconductor devices with resulting increase in pin counts is driving the need for improvements in packaging for functionality and reliability. One solution to this demand is the Flip- Chip concept in Ultra Large Scale Integration (ULSI) applications [1]. The flip-chip technology is based on the direct attach principle of die to substrate interconnection.. The absence of bondwires clearly enables packages to become more slim and compact, and also provides higher pin counts and higher-speeds [2]. However, due to its construction, with inherent hidden structures the Flip-Chip technology presents a challenge for non-destructive Failure Analysis (F/A). The scanning acoustic microscope (SAM) has recently emerged as a valuable evaluation tool for this purpose [3]. C-mode scanning acoustic microscope (C-SAM), has the ability to demonstrate non-destructive package analysis while imaging the internal features of this package. Ultrasonic waves are very sensitive, particularly when they encounter density variations at surfaces, e.g. variations such as voids or delaminations similar to air gaps. These two anomalies are common to flip-chips. The primary issue with this package technology is the non-uniformity of the die attach through solder ball joints and epoxy underfill. The ball joints also present defects as open contacts, voids or cracks. In our acoustic microscopy study packages with known defects are considered. It includes C-SCAN analysis giving top views at a particular package interface and a B-SCAN analysis that provides cross-sectional views at a desired point of interest. The cross-section analysis capability gives confidence to the failure analyst in obtaining information from a failing area without physically sectioning the sample and destroying its electrical integrity. Our results presented here prove that appropriate selection of acoustic scanning modes and frequency parameters leads to good reliable correlation between the physical defects in the devices and the information given by the acoustic microscope.

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