Fractures- Stress Intensity Factors

Question 1

Formula for stress intensity factor, K1

Answer 1

K1=Cσapp x rt(πa)
σapp is applied stress
C is geometrical constant

Question 2

What is the function of θ in the Irwin equation for when ij is yy, xx and xy?

Answer 2

yy: f(θ)=cos(θ/2)(1+sin(θ/2)sin(3θ/2))
xx: f(θ)=cos(θ/2)(1-sin(θ/2)sin(3θ/2))
xy: f(θ)=sin(θ/2)cos(θ/2)cos(3θ/2))

Question 3

Assumptions for the Irwin equation

Answer 3

Material is a continuum (ignores individual atoms)
The crack tip is infinitely sharp and can support infinite stress
The normal stress across the crack surface is 0
The stress field a long way from the crack is unaffected but the crack

Question 4

Where is the solution for the Irwin equation accurate?

Answer 4

Only near the crack tip

Question 5

Modes of crack growth

Answer 5

Mode 1: opening mode (stress normal to edge crack)
Mode 2: plane shear (sliding) mode (stress parallel like drawers)
Mode 3: anti-plane shear (tearing) mode (paper tear)

Question 6

Critical stress intensity factor

Answer 6

The value that K1 has to equal or exceed in order for fracture to occur. K1c.
Is a material constant
Units MPam^1/2 or MNm^-3/2

Question 7

Formula for critical stress intensity factor using Griffith equation

Answer 7

K1c=rt(2E’(γs+γp))

Symbols same as for Griffith equation

Question 8

Where to find formulae for C (geometrical constant) for centre crack and edge crack?

Answer 8

Data pack page 4 with diagrams

Question 9

What does C equal if width of plate is much greater than crack length for centre and edge cracks?

Answer 9

Centre: 1
Edge: 1.12

Question 10

Formula for point force loading on a centre crack in a large plate

Answer 10

K1=P/rt(πa) x rt(a+x/a-x)
P is force per unit thickness
x is distance from centre of crack to line of action of P
This is formula for K1 at edge closer to P
For other edge invert fraction to a-x/a+x
a is half of crack length (longest)

Question 11

If point force acts through centre of centre crack, how does K1 vary with crack length?

Answer 11

K1 decreases as a increases by 1/rt(a)

Question 12

Formula for K1 for uniform pressure inside a centre crack

Answer 12

K1=Prt(πa)
Where P is pressure
Same form as for uniform stress K1=σrt(πa)

Question 13

How do SIFs combine for internal pressure and uniform applied stress?

Answer 13

They K1s for each case on its own add together

Question 14

Formula for SIF for cylinder with internal pressure (not in datapack)

Answer 14

K1=CP(1+R/t)rt(πa)
Where R is radius of pressure vessel
t is thickness of pressure vessel

Question 15

Formula for K1 for double edge cracked finite width plate

Answer 15

K1=Cσrt(πa)

Long formula for C in data pack

Question 16

Where to find formula for embedded elliptical crack in infinite plate

Answer 16

One in data pack but another on page 10 lecture 3

Question 17

What are a, c and φ in formulae for embedded elliptical cracks in finite or infinite plate?

Answer 17

2a is height (shorter). 2c is length (longer)
φ: have largest circle possible that fits in crack, point on edge of crack draw horizontal line to circle, measure angle from radius to this point on circle from horizontal.

Question 18

What are a, c and φ in formulae for semi-elliptical cracks in finite plate?

Answer 18

a is depth of crack, 2c is length of crack

φ: have similar to embedded circle but only semi circle, do same with horizontal line and angle of radius.

Question 19

Where to find formulae for quarter cracks

Answer 19

In data pack