Fractures- Linear Elastic Fracture Mechanics

Question 1

What are assumptions in Linear Elastic Fracture Mechanics?

Answer 1

LEFM.
Materials can be treated as continua
Hooke’s law is obeyed until failure

Question 2

Formula for theoretical tensile strength of materials

Answer 2

σth=rt(Eγs/a0)
E is YM
γs is surface energy
a0 is interatomic distance

Question 3

Why do materials not normally reach their theoretical strength?

Answer 3

Stress concentrating effect of sharp corners, defects and cracks.
Results in crack growth from these features

Question 4

Inglis equation and when it applies

Answer 4

For large plate with elliptical hole whose width is much length than width of plate subject to uniform uniaxial stress viewed vertically.
σc=σapp(1+2a/b)
σc is stress at hole
σapp is force over CSA it acts on from top
2a is hole width and 2b hole height
Doesn’t take hole size into account so is insufficient

Question 5

Griffith equation 1 and when it’s used

Answer 5

Same large plate with crack but b«a></a>

Question 6

Griffith equation 2

Answer 6

Condition for fast fracture to occur
σ>=σc=rt(2E’γs/πa)
Where E’ is modified YM for either plane stress or plain strain

Question 7

What is the modified YM, E’ for Griffith equation 2?

Answer 7

Plane stress: E’=E (thin plates)
Plane strain: E’=E/1-ν (thick plates
ν is poissons ratio

Question 8

Why is Griffith equation 2 not practically very useful?

Answer 8

Surface energy is hard to measure.

Assumes ideal plastic behaviour when really some plastic deformation also occurs at crack tips.

Question 9

Modified Griffith equation

Answer 9

σ>=σc=rt(2E’(γs+γp)/πa)
Where γp is energy associated with plastic work
p subscript

Question 10

Irwin equivalent to modified Griffith equation using stress based approach

Answer 10

σij=(σrt(πa)/rt(2πr))fij(θ)
KI=Cσrt(πa)
For failure KI>=KIc

Question 11

For the Irwin equation with stress intensity factor, what do the subscript i and j mean for σ?

Answer 11

They indicate the direction of stress
If they are yy, stress is normal to crack length
If xx, stress parallel to crack length
If xy, shear stress