Note: Descriptions are shown in the official language in which they were submitted.
CA 02669865 2009-06-19
METHOD AND SYSTEM FOR DETERMINING YOUNG'S MODULUS
AND POISSON'S RATIO FOR A CRYSTALLINE MATERIAL
FIELD OF THE INVENTION
The present invention relates to the field of materials science and in
particular to methods and
systems for determining Young's modulus and Poisson's ratio for a crystalline
material.
BACKGROUND
Various methods have been developed to characterize materials in order to
develop a better
understanding of their properties and thereby better predict how such
materials will behave or
interact with other materials in different applications or under different
conditions. For
example, the mechanical properties and/or characteristics of a material, and
the mechanical
constants or parameters qualifying and/or quantifying such properties, can be
quite relevant in
understanding how a material, and a structure or object manufactured from this
material, will
react in different conditions.
One conventional method known in the art for assessing strain-related
characteristics of a
material involves the use of a piezoelectric gauge or the like, as discussed
by J. Marx in the
article entitled "Use of the Piezoelectric Gauge for Internal Friction
Measurements" published
in The Review of Scientific Instruments, Vol. 22, Number 1, pp. 503-509. The
use of such
equipment, however, is generally limited in applicability to certain sample
shapes and sizes,
and for instance, is generally inapplicable to small scale samples. Other
solutions, as described
by Nakasawa, Nihei and Myer in the article entitled "Resonance Inversion for
Elastic Moduli
of Anisotropic Rocks" published in the Berkeley Annual Report, Earth Sciences
Division,
1999-2000, provide methods for the determination of Young's modulus in smaller
scale
samples via acoustic resonance spectroscopy which, however, come at generally
prohibitive
costs.
1
CA 02669865 2009-06-19
Other examples are also known in the art for sampling and characterizing an
object, for
example in assessing the object's elastic properties under stress. For
example, U.S. Patent No.
6,517,679 to Mustonen et al. teaches a method for determining elastic
properties of a paper
web in a papermaking process; U.S. Patent No. 3,881,346 to Scheucher teaches a
method of
continuously measuring the yield point and/or modulus of elasticity of a
continuously moving
wire by subjecting it to a predetermined tensile strain; U.S Patent No.
4,756,195 to Melton et
al. teaches an apparatus for measuring a modulus of elasticity through angular
displacement of
a specimen under an applied torque; whereas U.S. Patent No. 4,719,802 to Adini
and U.S.
Patent No. 6,635,077 to Rauch teach different methods for determining
deformations such as
changes in the linear dimensions of an object using an electrical resistance
strain or
extensometer gauge.
Other methods have also been developed using bulk acoustic wave measurements
to extract
material characteristics. For example, in U.S. Patent No. 3,918,294 to Makino
et al., resonant
ultrasonic waves are used to measure an axial force applied to an object,
whereas U.S. Patent
No. 5,127,268 to Kline teaches the use of acoustic waves to determine a fibre
volume fraction
and resin porosity of a composite material using known parameters such as the
constituent
material's elastic moduli, densities and layup sequence. Also, U.S. Patent No.
4,899,588 to
Titlow et al. teaches a method for determining Young's modulus in tubes by
measuring the
speed at which bulk stress waves (i.e. P or S waves) propagate therein as a
function of known
parameters for the material in question, whereas U.S. Patent No. 5,115,673 to
Kline et al.
teaches a method for determining the elastic moduli of a composite material by
subjecting the
object to x-radiation for determining its density at a sufficient number of
discrete
measurement points to create an image of local material density variation, and
propagating
bulk ultrasonic waves through the material to determine transit times for each
wave at points
corresponding to the measurement points.
The above and other such examples, however, may have various drawbacks, such
as, in some
cases, being limited in applicability to certain types, shapes and/or sizes of
materials, or again,
not allowing for an accounting of various material artefacts such as residual
stresses or
2
CA 02669865 2009-06-19
mechanical deformations generated upon manufacture of the tested material.
Furthermore,
some known methods involve significant data acquisition and computation, and
oftentimes
prohibitive costs.
Therefore, there is a need for a new method and system of determining Young's
modulus and
Poisson's ratio that overcomes some of the drawbacks of known techniques, or
at least
provides a useful alternative.
This background information is provided to reveal information believed by the
applicant to be
of possible relevance to the invention. No admission is necessarily intended,
nor should be
construed, that any of the preceding information constitutes prior art against
the invention.
SUMMARY
An object of the invention is to provide a method and system for determining
Young's
modulus and Poisson's ratio for a crystalline material. In accordance with an
aspect of the
invention, there is provided a method for determining Young's modulus and
Poisson's ratio
comprising the steps of. generating one or more surface acoustic waves in the
material and
recording a velocity thereof; using X-ray diffraction, recording an applied
strain in the
material; and determining from said recorded velocity and applied strain
Young's modulus
and Poisson's ratio of the material.
In accordance with another aspect of the invention, there is provided a system
for determining
Young's modulus and Poisson's ratio for a crystalline material, the system
comprising: a
surface acoustic wave device for generating a surface acoustic wave in the
material and
recording a velocity thereof, a loading mechanism for applying a load to the
material; an X-
ray diffractometer for recording an applied strain in the loaded material; and
a computing
device comprising one or more data storage devices for storing said recorded
velocity and
strain, and one or more processors operatively coupled to said one or more
data storage
devices for calculating from said recorded velocity and strain Young's modulus
and Poisson's
ratio of the material.
3
CA 02669865 2009-06-19
Other aims, objects, advantages and features of the invention will become more
apparent upon
reading of the following non-restrictive description of embodiments thereof,
given by way of
example only with reference to the accompanying drawings.
BRIEF DESCRIPTION OF THE FIGURES
Figure 1 is a diagrammatic representation of an x-ray diffractometer setup
with blown-up
section identifying interactivity between x-rays produced thereby with respect
to the atomic
planes of a crystalline material.
Figure 2 is a schematic diagram of a device for generating one or more surface
acoustic waves
in a material, in accordance with an embodiment of the invention.
Figure 3 is a diagrammatic representation of a surface acoustic wave device
for generating and
detecting propagation of one or more surface acoustic waves in a material, in
accordance with
an embodiment of the invention.
Figure 4 is a schematic diagram of a system for determining Young's modulus
and Poisson's
ratio, in accordance with an embodiment of the invention.
Figure 5 is a schematic diagram of a system for determining Young's modulus
and Poisson's
ratio while accounting for residual stress, in accordance with an embodiment
of the invention.
Figure 6 is a diagrammatic representation of a sample subjected to a two-
dimensional load for
determining Young's modulus and Poisson's ratio with respect to two or more
axes of the
sample, in accordance with an embodiment of the invention.
DETAILED DESCRIPTION OF THE INVENTION
Unless defined otherwise, all technical and scientific terms used herein have
the same
meaning as commonly understood by one of ordinary skill in the art to which
this invention
belongs.
4
CA 02669865 2009-06-19
A method and system for determining Young's modulus and Poisson's ratio for a
crystalline
material will now be described, in accordance with various embodiments of the
invention. In
general, the method and system involve performing a combination of strain and
surface
acoustic wave measurements in the material, and from these measurements,
determining
Young's modulus and Poisson's ratio. For example, while x-ray diffraction has
been used for
some time to assess the properties of crystalline materials, the novel
combination of these
techniques with the use of surface acoustic wave measurements provides an
alternative
approach to studying these characteristics, which, in some embodiments, can
provide for one
or more of greater accuracy and/or precision, increased sampling efficiency
and/or speed,
reduced data processing and/or computation times, reduced exposure to
potentially harmful
radiation, and/or other advantages that will be readily apparent to the person
of ordinary skill
in the art upon reading the following non-limiting description. Furthermore,
the system and
method provides for a determination of both Young's modulus and Poisson's
ratio, which,
using conventional methods, are not readily accessible when neither
characteristic is
previously known.
Furthermore, in some embodiments where residual stress in the material may
affect surface
acoustic wave measurements, additional x-ray diffraction measurements may be
implemented
to determine or at least approximate an amount of residual stress in the
material, which can
then be taken into account when processing surface acoustic wave measurements
to thereby
improve an accuracy and/or precision of such measurements in determining
Young's modulus
and Poisson's ratio. For example, in one embodiment, two or more strain
measurements may
be processed to assess residual stress in the material. In another embodiment,
x-ray diffraction
may be used at the extremity of the sample material, for example after
electric discharge
machining, to ascertain the amount of residual stress present in the surface
of the material in
which surface acoustic wave measurements are conducted, relative to the core
of the material,
for example, where residual stress may be of lesser significance or even
negligible.
In addition, or alternatively, two or more loads can be applied simultaneously
with respect to
distinct sample axes (i.e. two dimensional load) to generate a biaxial stress
state in the
5
CA 02669865 2009-06-19
material, thereby enabling determination of Young's modulus and Poisson's
ratio with respect
to different axes of the material, for example, in sampling an anisotropic
material.
As will be described in greater detail below, the system and method may be
applicable to a
variety of materials in a variety of applications. For example, in some
embodiments, the
method and system can provide a non-destructive approach to sample
characterization, which,
in certain applications, may be necessary to preserve the integrity of the
tested samples. In
other examples, the system may be transportable for field use on location,
thereby facilitating
the material characterization procedure. Also, the system and method may be
applicable to
different material types, for example by selecting appropriate surface
acoustic wave devices
for generating such waves in the material in question. For instance, in
electrically conductive
materials, an electromagnetic device such as an electromagnetic acoustic
transducer (EMAT)
can be used to generate these waves, whereas for a non-conductive material,
alternate means
for imparting material vibrations in the surface of the material can be used.
In the former
application, it will be appreciated that the use of an EMAT can enable
generation of surface
acoustic waves in materials of different sizes and shapes, for example, thin
wires or other such
materials having rounded or irregular surfaces otherwise difficult to process
via standard
means. These and other such approaches will be readily appreciated by the
person of ordinary
skill in the art upon reference to the following description of exemplary
embodiments.
With reference to Figure 1, general principles relating to x-ray diffraction
and applicable in
some embodiments of the invention will now be presented. In this figure, a
sample plate 100
is provided for which are defined arbitrary sample axes Si and S2 within a
plane of this plate,
and axis S3 perpendicular to this plane. Given this reference frame, a stress
a~ generated by a
load applied to the plate in a selected direction forming an angle 0 relative
to the S 1 axis can
be broken into respective components al and a2. An x-ray beam incident on the
plate 100 at
an angle W from the normal of the material's surface (i.e. relative to the
cross product of Si
and S2) and projecting in the S3-4 plane, can be used to assess a strain c
induced by the
load, which is provided generally by a relative deformation of the crystalline
structure of the
material denoted by a relative change in the atomic spacing d,,o between the
crystalline planes
6
CA 02669865 2009-06-19
of the material in the v-direction. As will be known to the person of skill in
the art, the atomic
spacing d,,~ can generally be measured from the Bragg equation:
nX = 2d, sin8 (1)
wherein n is an integer, k is the wavelength of the x-ray beam and 8 is the
angle of incidence
of the x-ray beam relative to the atomic planes in question.
Given this generic setup, Young's modulus E and Poisson's ratio v of the
material can be
expressed relative to load axis 0 as a function of the strain measured via x-
ray diffraction by
the following equation:
doa-d = I +v 60 sine t,u - V
(61 +a'2) (2)
0
wherein,
dov -do =E (3)
d 4w
0
and wherein -Ow denotes the directional strain measured in the horizontal 0 -
direction along
the stress direction a and at the angle W from the normal 61 x a2 to the
material surface
formed by the principal directions 61 and 62, dow denotes the spacing between
atomic planes
in this direction, and do denotes the original crystalline spacing in the
absence of the applied
load.
It will be appreciated by the person of ordinary skill in the art that applied
stresses are additive
and therefore, when dealing with a material wherein residual stress has been
induced, for
example, during manufacture of the material or sample at hand, such residual
stress may be
expressed in the above examples in a relatively straightforward manner. For
example, and in
accordance with one embodiment wherein the disclosed method and system are
applied to a
filamentary material, such as a metallic wire in the surface of which residual
stress is
7
CA 02669865 2009-06-19
relatively common, equation (2) can be expressed as follows (assuming an axial
load and
applied strain in the ao = 6, direction):
d d-d =lEv(a +6R)sin 2y/-EV (a +o ) (4)
0
wherein al and 6R represent the applied and residual stresses respectively.
Accordingly, upon
repeating two or more strain measurements, a reasonably accurate determination
of the
residual stress may be achieved. This can then be used, as will be described
further below, to
improve an accuracy of the calculations relying on surface acoustic wave
measurements. As
will be appreciated by the person of ordinary skill in the art, other
techniques to ascertain or at
least approximate the residual stress in a material can also be considered
herein without
departing from the general scope and nature of the present disclosure. For
example, following
from the above scenario wherein the sampled material is comprised of a
filamentary material,
further x-ray measurements may be implemented at an extremity of the material
to compare
the atomic spacing of the crystalline material toward the surface and core of
the material
respectively.
As introduced above, measuring the propagation characteristics of surface
acoustic waves in a
material can provide a suitable approach for determining Young's modulus and
Poisson's
ratio. For instance, the propagation characteristics of such waves in a
material can generally be
expressed as a function of this material's elastic properties, such that a
determination of these
properties can be extracted provided sufficient data can be accumulated. For
instance, in a
simplified application where Poisson's ratio, for example, is well known or
sufficiently well
known, a determination of Young's modulus can be extracted directly from
surface acoustic
wave measurements alone. For example, provided the relationship between the
propagation
characteristics of surface acoustic waves and the material properties is
known, and that one or
more of the materials characteristics can be relatively well approximated, a
relatively accurate
determination of these properties can be extracted from surface acoustic wave
measurements
either from direct calculation, or through various iterative and/or data
fitting algorithms and
processes, which should be apparent to the person of skill in the art.
However, when neither
8
CA 02669865 2009-06-19
material characteristics are known, which is often the case when seeking to
determine
Young's modulus and Poisson's ration for a given sample, the embodiments of
the invention
herein described provide for a combined approach wherein x-ray diffraction
strain
measurements, as described above, can provide suitable results that, in
combination with
surface acoustic wave measurements described below, can lead to a relatively
accurate
determination of both Young's modulus and Poisson's ratio.
For example, in one such embodiment, Rayleigh waves are used, which are also
at times
referred to as Rayleigh-Lamb waves, Lamb waves or generalized Rayleigh waves
when
guided in layers, and which generally comprise surface waves that travel on a
solid. As will be
appreciated by the person of skill in the art, Rayleigh waves are distinct
from other types of
acoustic waves such as longitudinal (P) and shear (S) waves that generally
travel in the bulk of
the material and are generally referred to herein as bulk waves.
As known in the art, surface acoustic waves, such as Rayleigh waves, can be
generated by an
acoustic transducer or the like. For example, in one embodiment, these waves
are generated in
an electrically conductive material using an electromagnetic acoustic
transducer (EMAT).
These and other such surface acoustic wave devices will be known to the person
of ordinary
skill in the art, and are therefore not meant to depart from the general scope
and nature of the
present disclosure.
Figure 2 provides, in accordance with one embodiment of the invention, a
general
representation of a device 200 for generating a surface acoustic wave, such as
a Rayleigh
wave or the like, in an electrically conductive solid material, in this
example, a curved solid
material 202 having a cylindrical or tubular structure. For instance, in
Figure 2, the device 200
is generally comprised of an electromagnetic acoustic transducer (EMAT)
comprising a
magnet 204, which induces a magnetic field B, disposed such that its north (N)
and south (S)
poles rest on either side of a wire 206 disposed substantially perpendicular
to the magnet's N-
S axis. In operation, the wire 206 is generally configured to conduct an
alternative current I
(e.g. provided by an AC power source, not shown), which induces a current J
(not shown) in
the surface of the material flowing in an opposite direction to current I. The
action force
9
CA 02669865 2009-06-19
F=JxB, identified by the double arrow F in this figure, can thus generally
induce a vertical
oscillation of the material's surface, which ultimately results in a surface
acoustic wave
propagating in that surface in both directions of the magnet, i.e. along the N-
S axis thereof.
Figure 3 provides a diagrammatic representation of a surface acoustic wave
device 300 for
transmitting and receiving one or more surface acoustic waves, such as
Rayleigh waves, in
accordance with one embodiment of the invention. In this embodiment, the
device 300 is
comprised of an electromagnetic acoustic transducer transmitter-receiver pair
comprising a
transmitter (T) 302 and receiver (R) 304. In general, the transmitter 302,
such as described
above in relation to Figure 2, is configured to generate one or more surface
acoustic waves in
the material, depicted herein as a Rayleigh wave pulse 306, whereas the
receiver 304 is
configured to detect at least some of these waves, and in one embodiment,
determine a transit
time thereof within the material. From this transit time, a propagation
velocity of the Rayleigh
waves 306 in the medium can be determined. As will be appreciated by the
person of ordinary
skill in the art, velocity calculations may be based not only on direct
transit times based on a
known distance between the transmitter 302 and receiver 304, but also via
indirect transit
times calculated from waves reflected from one or more extremities, edges
and/or other
known interfering/reflecting elements (e.g. material defects, structures,
etc.) of the sample or
test subject provided distances are known between these elements and the
transmitter/receiver.
It will be further appreciated by the person of skill in the art that the
surface acoustic wave
device may comprise different levels and/or complexities of integrated
circuitry and/or
computation capacity, and therefore be configured to interface with one or
more additional
computing devices to enable calculation of the detected wave velocities. For
example, in one
embodiment, the surface acoustic wave device comprises a fully integrated
device wherein
velocity determinations are implemented automatically by the device for output
to a display or
to a downstream computing device for further processing. Alternatively, and in
accordance
with another embodiment, the surface acoustic wave device may comprise simple
data
acquisition functionalities wherein most or all computations and calculations
are performed by
one or more downstream computing devices configured to control activation of
the transmitter
and/or receiver. Other configurations and levels of automation will be readily
apparent to the
CA 02669865 2009-06-19
person of skill in the art and are therefore not intended to depart from the
general scope and
nature of the present disclosure.
As will be demonstrated below, by orienting the acoustic system 300 so to
measure a velocity
of a surface acoustic wave propagating in a selected direction of the
material, the measured
velocity, in combination with one or more strain measurements derived via x-
ray diffraction
with respect to this direction, Young's modulus and Poisson's ratio of the
material can be
determined relative to this direction.
For instance, in one embodiment, the following equation can be used, in
combination with
equation (2) above, to determine Young's modulus E and Poisson's ratio v of an
electrically
conductive crystalline material. Namely, the physical relationship between E
and v relative to
a given direction, and the propagation characteristics (i.e. propagation
speed) of a Rayleigh
wave propagating in a material in this direction can be provided by:
(5)
4[4_84+C_.J_lo[1_J]=o 2
CT CT CT CT 2 2 2
CL CL
wherein CR denotes the measurable speed of the Rayleigh wave in the medium,
and CT and cL
respectively denote the speed of transverse and longitudinal waves in the same
material,
which depend on E and v through the following relations:
2 E I- v
(6)
CL =_ p (1 +vXl - 2v)
CT - E I- v
(7)
T p 2(1+v)
Accordingly, given that two equations can ultimately be provided for the same
two unknowns
E and v, these unknown characteristics can be extracted, and 0 denotes
material's density.
11
CA 02669865 2009-06-19
As described above, and in accordance with one embodiment, residual stress
that may be
present in a tested material may affect surface acoustic wave measurements,
and, if not
properly accounted for, may adversely affect a determination of the material's
elastic
properties. Namely, it is known in the art that the velocity of a surface
acoustic wave may be
expressed by the following equation:
CR(a)=CR(0)+K6 (8)
wherein 6 is the total stress in the material's propagation surface, which may
include both
applied and residual stresses, K is an experimental constant and cR(0) is the
velocity in the
absence of stress in the propagation surface. As will be appreciated by the
person of ordinary
skill in the art, upon conducting different velocity measurements for
different applied stresses,
a value for the constant K can be experimentally determined. However, without
knowing how
much residual stress is present in the material, a determination of cR(0) may
be difficult to
achieve, which can then affect a determination of Young's modulus and
Poisson's ratio which
depend from this value as expressed by equations (5) to (7). However, as
described above, if
residual stress is suspected for a given material, or again, to verify to
which extent residual
stress may be present in a given material even when suspected to be
negligible, x-ray
diffraction measurements may first be used to assess this value, which can
then be used to at
least adjust surface acoustic wave measurements to improve an accuracy
thereof.
In one exemplary embodiment, the above considerations are applied to a
filamentary material,
such as a metallic wire or the like, wherein the velocity and x-ray
measurement are
implemented along a longitudinal axis of this filamentary material such that
Young's modulus
and Poisson's ratio can be calculated with respect to this axis. In this
embodiment, it will be
appreciated that equation (2) can be simplified by expressing the stress
generated by a load P
applied in the longitudinal axis of the filamentary material by a2 = 0 and 6~
= 61 = 6 = P/A,
wherein A is the cross-section of the material in question.
Figure 4 provides an example of a system and apparatus 400 for implementing
the above
procedure on a filamentary material such as metallic wire 402. For example,
the apparatus 400
12
CA 02669865 2009-06-19
comprises a frame 404 to which an end of the wire 402 is solidly anchored
(e.g. removably
anchored via one or more fastening means or devices that will be readily known
to the person
of ordinary skill in the art). A pulley 406 is also operatively mounted to the
frame 404 so to
enable application of a known gravitational load P on the opposite end of the
wire 402 (e.g.
via a weight or the like mounted or otherwise attached to this opposite end)
when this end of
the wire 402 is extended from its anchor and suspended over the pulley 406. A
surface
acoustic wave device comprising for example an EMAT transmitter (T) 408 and
receiver (R)
410 operatively disposed about the wire 402, and an x-ray diffraction device
(partially shown),
configured to focus an incident beam (IB) on a point of the wire 402 and
further comprising,
in this embodiment, left (LD) and right (RD) x-ray detectors 412, are also
provided.
Accordingly, both acoustic and x-ray measurements can be executed in a same
setup
configuration which provides for the application of one or more loads to the
sampled material
without requiring that the installation be disturbed or altered. In one
exemplary embodiment,
the compact setup of the illustrated embodiment can allow for greater
transportability and/or
operability of the system, thereby, in some embodiments, facilitating
implementation of this
system in remote/field testing applications.
The apparatus 400 further generally comprises, or is configured for operative
coupling to, one
or more computing devices configured to operate the apparatus in order to
acquire data
representative of the measured acoustic wave characteristics (e.g. transit
times) and x-ray
diffractions (e.g. diffraction angle, etc.). In one embodiment, for example,
the computing
device(s) comprises one or more data storage devices or media and one or more
processors
operatively coupled thereto, wherein the data storage device(s) comprise
stored therein
statements and instructions for operating the apparatus 400, or components
thereof, in
accordance with one or more preset data sampling, acquisition and/or storing
routines
consistent with a given sample type, or again, applied generically. The
storage device(s) may
further comprise statements and instructions for automatically calculating,
from the measured
sample characteristics, Young's modulus and Poisson's ratio for the sample in
question. It will
be appreciated by the person of ordinary skill in the art that the apparatus
400, and cooperative
computing device(s), may be adequately configured to perform sufficient tests
and
13
CA 02669865 2009-06-19
measurements to promote or ensure statistically significant and/or consistent
results, be it via
appropriate testing and/or calibration sequences, sampling sequences (e.g.
multiple discrete
and/or continuous x-ray diffraction angles, multiple wave transit measurements
that may
include direct and/or reflected wave transit times, etc.). For example, in one
embodiment, the
apparatus 400 is configured to oscillate about a localized angle of incidence
for a number of
data samples in order to improve the precision of the measured diffraction
angle. For example,
in one embodiment, the x-ray unit oscillates through 15 different angles
within a range of
+/-3 degrees. High resolution detectors, which may for example include high
density pixel
counts, can also be used to improve/maximise precise and accurate readings.
In one embodiment, the apparatus 400 is configured to provide measurements for
wires 402
having a diameter greater than about 1 millimetre. In another embodiment, the
apparatus 400
can further be operated with wires 402 having a diameter greater than 0.7
millimetres. In yet
another embodiment, the apparatus 400 is configured to operate with wires 402
having a
diameter as low as 0.5 millimetres. In yet another embodiment, the apparatus
400 is
configured for operation with wires 402 having a diameter less than 0.5
millimetres.
In order to achieve such measurements, in accordance with some embodiments of
the
invention, the x-ray diffractometer comprises an aperture through which the
incident x-ray
beam is provided to the sample. In one such embodiment, an aperture of about
10 thousandths
of an inch is provided. In another embodiment, an aperture of about 7
thousandths of an inch
is provided. It will be appreciated by the person of ordinary skill in the art
that while smaller
apertures may lead to more localized results, as appropriate and/or necessary
for smaller
samples, longer data acquisition times will generally be required to ensure
sufficient data (i.e.
statistically significant data) is acquired for a selected level of accuracy
and precision in the
ensuing results.
One exemplary application for which the above embodiments may be considered
advantageous over known systems is in the determination of Young's modulus and
Poisson's
ratio for thin metallic wires. For example, a precise and accurate
determination of Young's
modulus and Poisson's ratio for a thin wire, for instance as used in string
instruments or the
14
CA 02669865 2009-06-19
like, can enable one to study the principles associated with this string's
behaviour when
driven, for example as played when mounted on a particular instrument or the
like. In
addition, given that the disclosed method and system does not generally
require that the
material be sized or prepared for testing, sensitive materials, for example
antique strings or the
like to follow from the above example, can be tested without perturbing or
significantly
altering the integrity of the sample.
Another exemplary application for which the above and similar embodiments may
be
particularly interesting is in field testing, wherein a material for testing
cannot be extracted
from its operative environment to be tested. One such example includes
materials found on
large scale transportation equipment, such as an airplane or submarine,
wherein removal and
transportation of the part to be tested is not readily applicable. Other
examples may also
include pipelines, bridges or other such large scale structural bodies where
testing on the
ground may be beneficial, if not necessary. As the equipment required to
implement the
disclosed method can readily be made transportable, and is generally
unaffected by the sample
materials shape and/or size, testing of the above and other such exemplary
materials can, in
accordance with some embodiments, be achieved more easily than with
conventional
methods.
Furthermore, it will be appreciated by the person of ordinary skill in the art
that, as the
disclosed method provides a substantially non-invasive and generally non-
destructive
approach, various materials for which a destructive approach would not be
suitable or
appropriate can be otherwise tested in accordance with the various embodiments
of the
invention herein described.
It will be appreciated by the person of ordinary skill in the art that the
above and other similar
examples are not meant to be limiting, and that numerous other applications,
which may not
be limited by their sample size, shape or mobility, can also be considered
herein without
departing from the general scope and nature of the present disclosure.
CA 02669865 2009-06-19
In one embodiment, and with reference to Figure 5, a system and apparatus 500
is provided
and used in a manner so as to account for residual stress in the sampled
material. For instance,
to follow from the above example, thin wires of diameter greater than about
0.75mm generally
exhibit some residual stress in a thin layer below their surface, which
residual stress, as
discussed above, can affect surface acoustic wave measurement. The apparatus
500 in this
example, while similar to apparatus 400 described above with reference to
Figure 4, is
operated so to enable an accounting for residual stress in the sampled
material. For example,
in the manufacture of a metallic wire or string, for example during swaging
and/or drawing of
such a wire, the material is disproportionately stretched or deformed on the
surface relative to
the core, thereby leading to distinct material characteristics in the
material's surface. Similar
residual stresses can also be detected in other manufactured materials
depending on the
process by which they are manufactured, material characteristics and
resiliencies, and other
such parameters readily known to the person of skill in the art.
In order to account for such residual effects, for instance in surface
acoustic wave
measurements that may be skewed by the presence of residual stress, and in
accordance with
one embodiment of the invention, the x-ray diffractometer of apparatus 500 can
be operated
for successive loads P, thereby allowing one to remove or at least
substantially reduce the
effect of residual stress, diagrammatically depicted herein as a region of
stress 6R, from a
determination of Young's modulus and Poisson's ratio. Namely, as discussed
above, the
application of successive loads may allow for the effect of residual stress on
calculated
measurements to be substantially eliminated.
As will be appreciated by a person of ordinary skill in the art, the above
examples provide
methods for assessing Young's modulus and Poisson's ratio with respect to a
single material
axis. It will however be appreciated that for a substantially isotropic
material, the above
determinations can be applied, in most cases, for all material directions as a
determination of
Young's modulus and Poisson's ratio in respect of an arbitrary axis for an
isotropic material
generally applies substantially equally for all material axes.
16
CA 02669865 2009-06-19
It will be appreciated, however, that the embodiments of the invention are not
limited to
isotropic materials as the systems and apparatuses described above can readily
be adjusted to
enable a determination of Young's modulus and Poisson's ratio with respect to
different
material axes when such respective parameters are not the same for all
directions. For
instance, it is generally known that for anisotropic materials, Young's
modulus and Poisson's
ratio with respect to two distinct material directions (which may but need not
be orthogonal)
are directionally dependent. For example, as depicted in Figure 6 and in
accordance with
another embodiment of the invention, an anisotropic sheet material 600 is
provided for
testing, wherein distinct loads P1 and P2 can be applied in different
directions along the
material surface to produce a biaxial stress state expressed by the principal
stress components
al and 62, wherein the directional stress component ao varies along the stress
ellipse
determined by these principal stress components. By implementing the above
surface acoustic
wave and x-ray diffraction measurements and calculations, but in this
scenario, with respect to
different axes, a determination of Young's modulus and Poisson's ratio with
respect to two
distinct directions (i.e. E1, E2, vl and v2) can be achieved.
Once again, residual stress in the material can also be accounted for via
sufficient x-ray
diffraction measurements. Accordingly, to determine Young's modulus and
Poisson's ratio in
two distinct directions for an anisotropic material (i.e. E1, E2, v1 and v2)
while accounting for
residual stress in these directions, a sequence of surface acoustic wave and x-
ray diffraction
measurements are needed, which will be readily appreciated by the person of
ordinary skill in
the art.
It is apparent that the foregoing embodiments of the invention are exemplary
and can be
varied in many ways. Such present or future variations are not to be regarded
as a departure
from the spirit and scope of the invention, and all such modifications as
would be obvious to
one skilled in the art are intended to be included within the scope of the
following claims.
17
