Fracture mechanics 3 theory

Question 1

When including the effect of the plastic zone, how is the stress intensity factor approximated?

Answer 1

By adding half the plastic zone length to the real crack.

K=σ(pi(a+rp))^0.5

Noting that the stress normal to the crack plane is given by:

σy = K/(2pirp)^0.5

Then rearrange to get rp.

Question 2

What is Dugdale’s Model for the estimate of plastic zone size using elastic-plastic analysis?

Answer 2

ry = (pi/8)*(K/σy)

Question 3

What is the formula for the crack tip opening displacement (CTOD), δ?

Answer 3

δ = (K^2)/Eσy

Question 4

What is Rice’s J-Integral?

Answer 4

A parameter which characterises fracture under elastic-plastic and fully plastic conditions.

Question 5

What is the formula for the J-Integral?

Answer 5

J = ∫r(Wn - T(du/dx))ds

where:
W - elastic strain energy density
T - surface traction vector
u - displacement vector
r - counter clockwise contour beginning on the lower crack surface and ending on any point on the upper crack surface.

Question 6

How is J and CTOD related for a linear elastic material?

Answer 6

δ = J/σy

Question 7

For linear elastic materials, what is the J integral the same as, and how are they related to K?

Answer 7

J is equal to the strain energy release rate, G.

J = G =Plane stress, (K^2)/E, Plane strain, ((K^2)/E)*(1-v^2)

Question 8

What is the formula for the Griffith’s approach to fracture

Answer 8

K^2 = EG