This course is an introduction to high-throughput experimental methods that accelerate the discovery and development of new materials. It is well recognized that the discovery of new materials is the key to solving many technological problems faced by industry and society. These problems include energy production and utilization, carbon capture, tissue engineering, and sustainable materials production, among many others. This course will introduce the learner to a remarkable new approach to materials discovery and characterization: high-throughput materials development (HTMD). Engineers and scientists working in industry, academic or government will benefit from this course by developing an understanding of how to apply one element of HTMD, high-throughput experimental methods, to real-world materials discovery and characterization problems. Internationally leading faculty experts will provide a historical perspective on HTMD, describe preparation of ‘library’ samples that cover hundreds or thousands of compositions, explain techniques for characterizing the library to determine the structure and various properties including optical, electronic, mechanical, chemical, thermal, and others. Case studies in energy, transportation, and biotechnology are provided to illustrate methodologies for metals, ceramics, polymers and composites. The Georgia Tech Institute for Materials (IMat) developed this course in order to introduce a broad audience to the essential elements of the Materials Genome Initiative. Other courses will be offered by Georgia Tech through Coursera to concentrate on integrating (i) high-throughput experimentation with (ii) modeling and simulation and (iii) materials data sciences and informatics. After completing this course, learners will be able to • Identify key events in the development of High-Throughput Materials Development (HTMD) • Communicate the benefits of HTMDwithin your organization. • Explain what is meant by high throughput methods (both computational and experimental), and their merits for materials discovery/development. • Summarize the principles and methods of high throughput creation/processing of material libraries (samples that contain 100s to 1000s of smaller samples). • State the principles and methods for high-throughput characterization of structure. • State the principles and methods for high throughput property measurements. • Identify when high-throughput screening (HTS) will be valuable to a materials discovery effort. • Select an appropriate HTS method for a property measurement of interest. • Identify companies and organizations working in this field and use this knowledge to select appropriate partners for design and implementation of HTS efforts. • Apply principles of experimental design, library synthesis and screening to solve a materials design challenge. • Conceive complete high-throughput strategies to obtain processing-structure-property (PSP) relationships for materials design and discovery.
Instrumented Indentation Test
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Из курса от партнера Georgia Institute of Technology
Introduction to High-Throughput Materials Development
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High-Throughput Property Measurements
This module covers techniques to experimentally conduct property measurements suitable for high-throughput screening; optical, electronic, mechanical, chemical, and thermal properties are considered.
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Dr. Richard W. NeuProfessor
The George W. Woodruff School of Mechanical Engineering
Dr. J. Carson MeredithProfessor, Associate Chair for Graduate Studies, and J. Carl Pirkle Sr. Faculty Fellow
School of Chemical & Biomolecular Engineering
[SOUND] Hi,
this is Rick Neu.
In this lesson, we're going to focus on
the instrumented indentation test methodology.
The learning outcome is to explain the principle, methods and
analysis of instrumented indentation tests.
So let's look at a conventional hardness test versus
an instrumented indentation test.
What is so different about instrumented tests versus what you
might think of as just a hardness test that is well-known?
All right, in instrumented indentation tests,
the key difference is we measure many more things.
We measure the complete load, displacement and use all that information.
In addition, we'll see that we actually look at the compliance
of the interface instantaneously as we load and unload, and
we'll see how that's done in a later slide here.
In a conventional hardness test, and I'm going to refer
to something like a Rockwell hardness test, a very standard hardness test.
In that sort of test, what you do is you apply a load, a minimum load,
that's where I put a little dot, let's say you apply that load.
Then you apply a heavy load and that's where this dot is,
where the maximum is and then you unload it back to that minimum load,
and then you look at the displacement that occurred
between the start and end at the minimum load.
And that displacement correlates to the hardness.
And all the other data is thrown away, you don't use it.
So, in other words conventional hardness tests ignore
lots of useful material information
that could tell us something about the stress strain response in material.
And also most conventional hardness tests are designed to go well beyond yield.
So, they're really a measure of the flow strength,
something closer to the tensile strength of the material.
In fact, usually you correlate hardness to tensile strength.
Now one other thing that's important to consider is the shape
of the tip of your indenter.
And so there's two types.
You could have a sharp indenter or a not so sharp indenter and
the most logical one would be a spherical indenter.
And when you indent with a sharp indenter, almost as soon as you touch your material,
you start to plastically deform what you're touching.
That's assuming you're indenter's much harder than what you're indenting.
And so I'd noted is this orange region, plastic deformation.
And then as you indent further, that plastic field grows.
Well if it's a spherical indenter,
you actually get some elastic deformation that occurs first.
And in fact where yielding occurs first, where you meet the von Mises or
Tresca yield criterion is some point below the surface along the center line.
And then as you deform more, then the plastic deformation region grows.
And so when you do a hardness test,
you indent it enough that you reach that third stage shown here.
But the thing about using a spherical indenter is it can tell you something
about the elastic properties too, because we know the relationships
between the geometries of a sphere in contact with another flat body.
And that can tell us something about, it can allow us to get the whole
stress-strain curve, and we'll see how that's done.
So when you do a test like this, you measure the load and
displacement of the indenter.
And you typically will get a curve that might look like this.
You start at 1, at the point 2, when you're just getting yielding in that
spherical indenter, you're still not that far, it's still a rather low load.
And then it becomes non-linear and goes up to 3.
By the time you're at 3,
you have a fairly large area of plastic deformation and then you unload.
And the slope of that unload, as we'll see, can be related to
the effective modulus of the indenter and that substrate material.
And it turns out we can take that information, and
create what's known as an indentation stress-strain curve.
So it's not exactly the same as an uniaxial stress-strain curve but
it has the same elements, and as we'll see,
can be correlated to a uniaxial stress-strain curve.
So we have to call it something different, either effective stress, effective strain,
or perhaps better just to say indentation stress,
indentation strain, and we'll use those terms later on.
By using a spherical indenter we can capture the elastic plastic transition
during the initial loading so we can obtain that elastic response.
With a sharp indenter, you really can't obtain that elastic
response because it plastically deforms from almost
the instant you touch your sample you're probing.
And so we normalize the load and displacement into some effective stress
and strain, and we'll look at the mechanics that allows us to do that.
And spherical tips are the logical choice here.
So we're going to focus on spherical tips here.
Now one other thing I said, with instrumented indentation testing,
we also measure the stiffness continuously as we load up.
And this is done by super imposing a sinusoidal waveform
on the loading part of your load displacement curve.
And the slope of that tells us something about the stiffness of the contact and so
we have a continuous stiffness measurement by using this sort of methodology.
This can also be done manually by periodically unloading during
a loading of a curve, if your equipment doesn't have this capability, and
get the same sort of data.
Now this gets to the meat of things,
in the indentation stress-strain analysis using spherical indenters.
So everything's based on Hertz theory.
Hertz theory describes the elastic,
frictionless contact between two isotropic materials with quadratic surfaces.
Basically a special case is a sphere on a flat contact.
Now when you deform the bodies, what happens is you deform
the body you're indenting.
And the maximum deformation is shown as the solid circular curve on this plot.
And then you remove the load and it springs back and
that's the elastic spring back.
And the dashed curve shows the position after you've remove the load, so
the two bodies are just in contact right along one point at that point,
and that distance is this h sub e.
So it's essentially the displacement between the two bodies.
And we'll see that come up in the equations.
And so first of all, there's two things you need to know.
The geometries of the bodies, so
the geometries of the bodies are related to the effective radii.
And the thing is, as you deform it, you change the radius
of the sample you're deforming too, so you have to take that into account.
And so that can be taken into account in your two radii.
The other thing we have to take into account is the effective modulus.
The modulus, because it's a multi-axial state of stress, depends on both Poisson's
ratio and Young's modulus of both the indenter and the material being indented.
Presumably we know the properties of the indenter, it's usually tungsten,
carbide or diamond in most cases.
And we make some assumptions about the Poisson's ratio.
And if you do that, you can get the modulus.
Now, the key relations to get that indention stress-strain curve.
From Hertz theory, there's two key relationships, the size of the contact.
So the size of the contacts a here is related to the load that's applied,
that's p, this effective radii of the two bodies and
the effective modulus by this equation.
The other thing you get from Hertz theory is that displacement is related
to the size of the contact squared divided by the effective radii.
And this just comes from the mechanics of the analysis of theory of elasticity.
Now if you take that first equation of Hertz and
rearrange it, you can put it in the form as shown here.
And this form we're putting it into a stress-strain like relationship,
looks kind of like Hooke's law, stress equals Young's modulus times strain.
Now we're going to do one other thing, we're going to take that displacement
relation and replace the a over R effective with h,
the displacement, over a, and there's a good reason for doing that.
If you look at the schematic on the left side, you see
that the displacement is basically the h, and the reference length,
the gauge length Is essentially 3 pi a over 4.
And that's shown in that hash region.
So it's basically a measure of strain.
So it's a clever way of measuring strain, a change in length over some gauge length.
And so this allows us to come up with some effective indentation strain measure.
And then indentation stress is just load over the projected area,
standard way to measure stress.
And then they're related by effective modulus, so
then we come up with our indentation stress-strain relation.
And what we do is compute this stress, this strain and plot it for
every indent and we can get an effective stress-strain.
Now there's one other thing that we have to consider is
how do you determine the size of the contact?
What's obviously related to the profiles of the bodies.
So you can get that from Hertz theory too.
Actually just taking those equations I had in the previous slide and
rearranging them again and then taking the derivative of it where load and
displacement are changing and you get this equation at the bottom that
says the size of the contact is related to 1 over 2 times the effective radii,
times the slope, or stiffness of the contact.
Now, in a traditional indentation test,
you might measure that stiffness just upon unloading after you reach the peak load.
But if you're using continuous stiffness measurement,
you actually know that stiffness at all points during the loading.
So here's just an example of an analysis and
data you might generate from doing this.
So the initial loading segment where it's elastic is actually just,
it's just the beginning of that load displacement curve.
But since we know it follows Hertz theory,
we can do a regression analysis knowing what functional form that
should follow and use that to establish the elastic response.
Once you've done that, then you can compute the indentation stress and
strain once you go into the plastic regime and
plot on the bottom right which is our indentation stress-strain curve.
And see, from this curve we can get a modulus value.
We can get the yield strength when it becomes non-linear.
And you can even get some elements of the hardening behavior.
So quite a bit of information from just a simple indentation test.
So in this lesson we've explained the principles, methods,
and analysis for instrumented indentation testing.
So what's next?
We're going to look at measurements using high-throughput indentation methods.
Thank you.
[SOUND]
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