Hello.
Welcome to Fracture Synopsis Two.
We'll have a basic introduction to fracture mechanics.
All right, so the first thing to address
is, of course, what fracture mechanics is all about.
And we'll remember from Synopsis One
that fracture involves a crack of some length,
the length of which increases upon loading.
And fracture mechanics then is about when--
is about understanding when that crack becomes critical.
So when the crack gets to a sufficiently long length
that the crack propagation goes from being
stable to being unstable.
And it turns out that we can describe fracture mechanics
in its basic sense using this equation here.
And this is something known as the stress intensity factor,
stress intensity factor.
And that relates the stress and the crack length
through this geometric factor here.
Geometric factor is just a function of the sample size
and the size of the crack.
So this is a very useful equation for us.
And it's, as I said, the basis for fracture mechanics.
So then to help understand the stress intensity factor,
there's a great little statement in Hertzberg.
And this is an excellent book that he's written
on fracture and deformation.
Anyway, the statement is at the top of the slide there.
Stress is to strength as stress intensity factor
is to fracture toughness.
So let's just explore that.
And of course, we've seen earlier
in the course, a stress strain curve.
And on that stress strain curve, we
identified a number of points, say the yield strength,
the ultimate tensile strength, and the fracture strength.
And you remember that we called them strength values,
and strength being a specific value of stress,
a specific value of stress.
So now we have the stress intensity factor K.
And a specific value of that is the critical stress intensity
factor, that is the stress intensity factor when
the crack becomes critical.
The crack has grown to a sufficient length
that it is critical, that is the propagation
is now going to become unstable.
And more specifically, actually, we're
going to look at the most common form of the stress intensity
factor-- sorry, of the critical stress intensity factor,
the plane strain fracture toughness, K IC.
And the one, the Roman numeral one there
actually refers to mode one crack displacement.
That's crack opening.
Just out of interest sake, crack two, mode is sliding.
And mode three is referred to as tearing.
But mode one is what we're going to be interested in.
That's the most common form of crack displacement
that we'll encounter.
And so the K IC is the fracture toughness.
And remember that the fracture toughness is a specific value
of stress intensity factor.
So the last thing I'd like to just address
is this clarification.
And we've covered a number of things here.
Stress concentration factor, which
was covered in the Synopsis number one, you'll remember,
was K sub t.
That's the stress concentration factor at the crack tip.
And that was just the ratio of the maximum stress
at the tip of a elliptical crack, in our case,
to the applied stress.
So stress concentration factor, how much is the stress
concentrated.
And now we also earlier in the year
seen this property of the toughness.
And we define the toughness as the area under the stress
strain curve up to fracture.
OK, so that's the toughness.
That's essentially how much energy
is involved in breaking and fracturing a sample.
So it's somewhat related.
But it is a different term to this new term
that we've just introduced, which was the critical stress
intensity factor.
Just remember, the stress intensity
factor K, when it becomes critical the crack grows.
And we have a specific value of the stress intensity factor
under the right conditions, which we call the K IC.
And that's the fracture toughness.
So it's important to realise that the fracture toughness is
different from toughness, which is the area under the curve.
And K IC is as well different from the stress concentration
factor.
So stress intensity factor, stress concentration factor,
and toughness are related.
But they are each unique.
And it's important to appreciate that difference.
So quickly, fracture mechanics is
about understanding when a crack becomes critical.
We have this relationship here for fracture mechanics.
In fact, we saw that the stress intensity factor,
under specific conditions and when it becomes critical,
is known as the fracture toughness.
And that is a material property.
So that's a function of the material
that you've chosen for the application.
Stress is, of course, a function of the design,
or the application.
And this is the crack size.
And that could be something that you
determine through non-destructive testing.
Or it could be a function of an element of the design
or your processing conditions.