Structural Failure of Materials - Failure Flashcards
Derive an expression for the theoretical tensile strength of a material using YM.
Check slide 2
Derive an expression for the theoretical tensile strength of a retrial in terms of surface energy when fracture occurs.
Check slide 3
Why do the experimental tensile strengths of materials not follow the theoretical.
Fracture does not occur by uniform separation of atoms in a plane.
It happens by:
Shear: plastic deformation - ductile failure
Or
Fracture initiates locally at a defect and spreads across the cross section - brittle failure
Which two methods can be used for understanding crack tips?
Griffith energy balance criterion
Linear elastic fracture mechanics (based on stress)
Both are equivalent
Derive the Griffith criterion for fixed grip load.
Check slide 6
Define toughness.
The quality of a material to resist crack propagation
Why is σ(f) less than theoretical strength?
Cracks concentrate stress
Why does σ(f) increase as c decreases?
Less stress concentrated at crack tip
Why does the strength of a material vary from specimens to specimens?
Different c in each material and occurs and fracture occurs at the single largest flaw.
Why doers σ(f) increase as E and γ increase?
Stronger bonding.
Show that Griffith equation applies to fracture stresses under all loading conditions.
Check slide 8
What is the mechanical energy releases rate, G?
Energy released per unit crack area
Derive the mechanical energy release rate, G.
Check slide 8
Why are the surface energy values, γ, deduced from fracture always lower than the true value od surface energy?
Crack surface not flat and crack surrounded by micro cracks that increase the surface area without knowing.
Other mechanisms to absorb energy, eg plastic deformation around the crack tip.
Polymer exhibit crazing which involves drawing molecules from the surface during fracture.
Grain boundary segregation can lower surface energy deduced
Corrosive environments can also lower surface energy deduced.
What is G(c)?
The total energy (new surface + plastic work + work of pullout etc) required to extend a crack through a unit area.
What assumptions are made in defining G(c).
The extra energy of dissipating mechanisms act like a surface energy ie a single value material property not affected by geometry of crack or loading system.
The dissipation at the crack tip does not affect the energy release when the crack propagates eg, the plastic zone must be small compared to the size of the crack.
How is G(c) related to true surface energy?
for ideal brittle fracture:
G(c) = 2γ(s)
What names does G(c) go by?
Critical strain release rate (don’t use)
Critical mechanical energy release rate
Toughness
Crack resistance energy, R
What condition must be satisfied for fracture involving G(c)?
G ≥ G(c)
Mechanical energy driving the crack forward is greater than the critical mechanical energy for fracture.
Are G and G(c) material properties?
G(c) is, G is just the mechanical energy driving a crack forward under certain conditions.
When is LEFM valid?
For near field solutions (close to the crack tip) but not very close to the crack tip as stress would tend ∞
What general assumption is made about the type of crack propagation for LEFM?
Mode ! fracture is most important and dominates because cracks tend to propagate on planes with the maximum principle stress on it.
State the general solution for crack propagation in LEFM.
Check slide 11
What is K in LEFM?
The stress intensity factor