Fracture Mechanics Lecture 1Recap

By visiting student from SkTech (Moscow), Dmitrii (Dima) Vasilev

18.10.2012

We started with the problem to be solved in fracture mechanics

• What is the magnitude of the load that will cause the body (material) to fracture?

Let us assume we are creating a new material

Then,

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

F

Stress concentration

Stress concentration

Due to linearity…• τ(max)=c*τ(app)

F

F

Stress concentration

Stress concentration

C=3 C=1+2a/b

Strength of material

• Theory cannot accurately predict strengthBut

• 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

a*=2γE/πσ^2

Why the discussed material is tremendously important?

My previous work

300 tons of liquid

steelNew 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