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Physical principles pertaining to ultrasonic and mechanical properties of anisotropic media and their application to nondestructive evaluation of fiber-reinforced composite materials /
Abstract
Thesis (Ph. D.)--Washington University, 1992. Dept. of Physics. Includes bibliographical references.
... The coefficient c 13 is determined from the longitudinal speed of sound measured at some angle relative to the fiber direction between 0°and 90°. Traditionally 45°is used; however, an angle of 77°was chosen for this study because it has been shown to minimize the error when calculating the coefficient c 13 [4]. The compliance matrix was obtained by inverting the stiffness matrix shown in Eq. 14. Equation 15 shows the compliance matrix and how the values of Young's modulus (E), shear modulus (G), and Poisson's ratio (m) were calculated along each axis of the CFR PEEK samples (Fig. 4). ...
... A literature search produced no results for speed of sound values for this grade of CFR PEEK for direct comparison. The longitudinal speed of sound parallel to the fiber orientation is significantly larger than that perpendicular to the fiber orientation as is seen in other anisotropic materials with unidirectional fiber orientation [4]. Also, as expected, the transverse speed of sound values are smaller than the longitudinal speed of sound values. ...
Polyether ether ketone (PEEK) and carbon fiber-reinforced (CFR) PEEK are commonly used in medical implants. This study evaluated
the mechanical moduli of PEEK and CFR PEEK using nondestructive, ultrasonic tests. The Young’s modulus of CFR PEEK was determined
in all the spatial directions. Ultrasonic attenuation has not been studied extensively in PEEK, and not at all in CFR PEEK.
The broadband ultrasound attenuations (BUAs) were determined for PEEK and CFR PEEK. The average Young’s modulus, shear modulus,
bulk modulus, and Poisson’s ratio of PEEK were 4.21, 1.52, 6.25, and 0.388GPa, respectively. The maximum and minimum Young’s
moduli of CFR PEEK were 15.1 and 5.1GPa measured parallel and perpendicular to the fiber axis respectively. The longitudinal
and transverse BUAs of PEEK were 1.33 and 4.37dB/cmMHz, respectively. The longitudinal BUAs of CFR PEEK parallel and perpendicular
to the fiber axis were 2.43 and 1.45dB/cmMHz, respectively. Characterization of Young’s modulus of CFR PEEK in all the spatial
directions is useful for stiffness matching in implant design. The BUA values are useful in modeling the interaction of ultrasound
and the PEEK materials and can also be used for developing non-destructive tests to find structural defects in implants made
from these materials.
... This feature is characteristic of many of the unidirectional graphite fiber reinforced composites our laboratory has investigated in other studies. 15,16 The lower panel of Fig. 1 illustrates our results for formalin fixed normal human myocardium. Similar to fixed bovine tendon, fixed human myocardium exhibits a rapid variation in Young's modulus near 0°and 180°with the maxima occurring parallel to the fiber axis of the tissue. ...
... The physical significance of this feature is unclear, although we have obtained qualitatively similar results using published values 17 for the elastic stiffness coefficients of a number of hexagonal crystals including cadmium sulfide. 16 The elastic properties of hexagonal crystals are described by the same form of the elastic stiffness matrix given in Eq. ͑1͒ for a unidirectional fiber reinforced material. Figure 1 also shows that Young's modulus is larger at all angles for tendon, and that tendon demonstrates a considerably more pronounced anisotropy in Young's modulus. ...
The linear elastic properties of a soft tissue exhibiting a unidirectional arrangement of reinforcing fibers may be described in terms of the five independent elastic stiffness coefficients C11, C13, C33, C44, and C66. In previous studies, ultrasonic measurements of these coefficients for formalin fixed specimens of bovine Achilles tendon and normal human myocardium were reported. In the present study these results are used to analyze the anisotropy of Young's modulus of these tissues. For formalin fixed tendon a value of 1.37 GPa is obtained for Young's modulus along the fiber axis of the tissue, and a value of 0.0706 GPa is obtained perpendicular to the fibers. For formalin fixed myocardium, values of 0.101 and 0.0311 GPa parallel and perpendicular to the fibers, respectively, are obtained. Based on the results for the angular dependence of Young's modulus from unidirectional specimens of myocardium, a model is introduced to estimate these features for the more complicated fiber architecture of the left ventricular wall.
The broad theme of the dissertation is the application of the
generalized Kramers-Krönig dispersion relations to ultrasonic
propagation. We develop the Kramers- Krönig dispersion relations in
the sense of tempered distributions as well as the conventional point
function sense. Non-local and nearly-local forms to the Kramers-
Krönig dispersion relations are derived for the prediction of
dispersion in media with attenuation obeying an arbitrary frequency
power law. Furthermore, a time-domain representation of the generalized
Kramers- Krönig dispersion relations is developed and compared with
a time-causal theory of ultrasonic propagation. The first aspect of
ultrasonic propagation that we investigate is the intimate relation
between the ultrasonic attenuation coefficient and phase velocity.
Recently there have been concerns expressed regarding the validity of
the Kramers-Krönig dispersion relations to media with attenuation
obeying a frequency power law. We demonstrate, however, that ultrasonic
measurements of systems with attenuation obeying a frequency power are
causally consistent. Consequently, valid Kramers- Krönig relations
are available. Theoretical predictions for the frequency dependence of
attenuation and phase velocity compare favorably to experimental
measurements for a series of liquid specimens over a range of
temperatures and acoustic pressures. The second aspect of ultrasonic
measurements we investigate is the phenomenon of phase cancellation at
the face of a phase-sensitive receiver which is present in measurements
of phase-aberrating media. The excess loss due to phase cancellation is
well-known, and has long been of interest. What has not been explicitly
investigated is the possibility that there exists a phase velocity shift
corresponding to this excess loss. In a novel proposal, we relate the
excess loss due to phase cancellation to a phase velocity shift via a
nearly-local form of the Kramers-Krönig dispersion relations.
Furthermore, we provide a measure of the artifact present in a phase
velocity measurement using phase-sensitive and phase-insensitive
detection techniques. We demonstrate the technique on measurements of
textile woven composites using a two-dimensional pseudo-array and a one-
dimensional array.
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