Fracture Mechanics Lecture 1
Recap
18.10.2012
By visiting student from SkTech (Moscow),
Dmitrii (Dima) Vasilev
We started with the problem to be
solved in fracture mechanics
Let us assume we are creating a new material
Then,
• What is the magnitude of the load that will
cause the body (material) to fracture?
The procedure to answer the question
is the following
• What is the maximum stress in the body?
• What is the strength of material?
• When τ(max) = X(Material Strength) – material fractures
To proceed we need to use Theory of
Linear Elasticity
Let’s assume we found each stress component for each particle
Then we find maximum stresses from eigenvalues
Stress concentration
• It turns out that in some specific areas of the
body the stresses may be higher than the
applied load
F
Stress
concentration
F
Stress
concentration
Due to linearity…
• τ(max)=c*τ(app)
C=3
C=1+2a/b
F
Stress
concentration
F
Stress
concentration
Strength of material
• Theory cannot accurately predict strength
But
• We can conduct experiments
However…
• The maximum stress in a body is sensitive to
the shape of the flaw
• The shape of the flaw inside the body is
seldom known
• We assume linear elasticity
• Strength depends on the sample shape
Griffith attempts
Some experiments were conducted on the glass
sample. Conclusions:
1) In a body of glass cracks pre-exist.
2) The tip of such crack concentrate stresses.
3) The intense stress breaks atomic bonds one
by one, like opening a zipper.
4) As the crack advances,
The main conclusion is that there is a
competition between 2 factors while the crack
advances: releasing elastic energy forces the
crack to grow, while surface crack energy (which
grows) is trying to stop the crack expansion (to
heal the crack).
U
a*=2γE/πσ^2
a
Why the discussed material is
tremendously important?
My previous work
300 tons
of liquid
steel
New material for
ladle lining –
Carbonized
Periclase,
which has a
thermal expansion
coefficient
significantly higher
than previous
materials
What I found
Video of numerical methods that I used to solve that problem