Lecture 7

Question 1

Fatigue analysis

Answer 1

• failure of a stent due to fatigue can result in loss of radial support, thrombus formation or focal restenosis, or perforation of the vessel by the struts
• fatigue analysis can help provide indication of device durability (combined with stress/strain and accelerated durability)

Question 2

Material failure

Answer 2

• associated with static loading
• under long-term dynamic loading, many materials fail at stresses below their ultimate tensile strength
• called fatigue!!
• fatigue failure is caused by crack formation and propagation over a number of cycles

Question 3

Stress Concentrations

Answer 3

• any discontinuity in a part will alter distribution of stress (stress raisers), and their regions are called stress concentrations
• ex: holes, tool marks, fillets
• theoretical stress concentration factor Kt:
  Kt = sigma max / sigma 0
• depends only on geometry of the part

Question 4

Stress Concentrations elliptical

Answer 4

• Kt = 1 + 2 (a / b)
• if flaw becomes sharp, maximum stress tends to infinity, which is physically impossible
• led to fracture mechanics

Question 5

Griffith Theory of Fracture

Answer 5

• failure stress (sigmaF) decreases with crack length a, but also depends on modulus E and critical energy release rate Gc)
• Gc is associated with bond separation and formation of a new surface
  sigmaF = sqrt(Gc * E / (pi * a))

Question 6

Where does Griffith Theory come from?

Answer 6

• strain energy density
• when atoms are pulled apart, the attraction/resistance to this movement generates a force and strain energy
• energy must be input to break atomic bonds and create a new surface:
  U(bond) = 2 * (gamma S) * a * B
  gamma S = energy required to break bonds per surface area, a = crack length, B = part thickness

Question 7

System Energy

Answer 7

• stored strain energy reduces as crack grows
• total system energy is the stored energy summed with the energy from growth of a new surface
• there is a point where crack will grow spontaneously… comes from thermodynamics and minimization of free energy
  Gc = 2 * gamma S

Question 8

Crack Modes

Answer 8

• Mode I: tensile stress gives rise to opening crack propagation (MOST COMMON)
• Mode II: in-plane shear causes sliding
• Mode III: out-of-plane shear drives a tearing mode

Question 9

Stress Intensity Factor

Answer 9

• K(I) = beta * sigma * sqrt(pi * a)
• beta is a stress intensity modification factor that depends on the geometry of the part and crack
• when K(I) reaches critical K(IC), crack propagation occurs… a material’s fracture toughness
  stress f (applied before material experiences uncontrollable crack growth) = K(IC) / (beta * sqrt(pi * a))
• beta goes to 1 when crack is very small
  K(IC) = sqrt(Gc * E)