Fracture Mechanics (Simon Hogg)

Question 1

What is meant by periodic shearing force?

Answer 1

When a perfect lattice slips, there is zero stress when lattice rows align, when the top row is pulled past the bottom row by half an atom and when it reaches the rest position again so this force is periodical like a sin wave.

Question 2

What does Tm represent in a lattice slip formula?

Answer 2

Max shear stress (where distance displaced is 1/4 of distance between atom centres)

Question 3

Why do dislocations slip easier than a whole lattice shear?

Answer 3

Only a few atomic bonds need to be broken to move so they glide with lower stress

Question 4

What is Peierls-Nabarro stress?

Answer 4

Minimum external stress required to move a dislocation irreversibly without assistance of lattice vibrations.

Question 5

What is the relationship with closely packed and separation?

Answer 5

InterAtomic spacing (separation) is widthways, interplane spacing (packing) is vertically

As separation increases, packing gets closer

Question 6

What does Peierls-Nabarro stress tell us about d/b relationship?

Answer 6

Big b (atomic spacing) = Small d (interplane spacing)

Question 7

What is the Schmid factor?

Answer 7

Stress x cos(theta) x cos(lambda)

Slip will exist on slip system that has max value of schmid factor

Question 8

What is strength?

Answer 8

Resistance of a material to fracture or to plastic flow (depends on text books)

Question 9

How does temperature affect failure mechanism?

Answer 9

Room temps - usually ductile
Very low temps - usually brittle
Slow strain at high temps - usually some form of creep

Question 10

How does attraction force change as you pull two atoms apart?

Answer 10

Under a tensile load, atomic spacing increases as the strain is greater than the attraction pulling it together, as they separate, this attraction decreases until a peak stress point when the atoms no longer attract each other.

Question 11

How much do stress concentrations differ from the applied stress?

Answer 11

Proportional to the applied stress x sqrt (pi x 1/2 crack length / distance from crack tip)

Question 12

Why is crack tip radius normally approaching zero?

Answer 12

Cracks are sharp

Question 13

Where is maximum cohesive strength achieved in a stress concentration?

Answer 13

Crack tip

Question 14

How do brittle and ductile fractures normally occur?

Answer 14

Brittle - Trans or intergranular fracture, very little energy adsorbed, no plastic deformation and rapid crack propagation

Ductile - Normally by a cavitation mechanism, lots of energy adsorbed due to plastic deformation in ‘plastic zone’ at crack tip, crack propagation is slow and stable

Question 15

With reference to the grains, how does cleavage (transgranular) failure occur?

Answer 15

Crack propagates by breaking atomic bonds on specific planes - normally most densely packed (in BCC - {001})

Crack path will pass through grains

Steps/ridges in a grain are due to small changes in local misorientation which can change cleavage plane

Question 16

How will a polycrystalline grain boundary affect transgranular cracks?

Answer 16

Crack path will divert when crossing a grain boundary

Question 17

When and how does intergranular failure occur?

Answer 17

Usually when detrimental impurities segregate to grain boundaries in polycrystalline materials.

Impurities reduce the cohesion between grains so they separate with little to no plastic deformation.

Question 18

What will happen if a polycrystalline material doesn’t cleave?

Answer 18

Most likely fail in a ductile transgranular manner

Small particles in metals act as stress concentrators which can seperate from matrix or fracture themselves

Results in an internal crack at centre of necked region.

The nucleated voids then grow and join as crack advances until final fracture

Question 19

What is cup and cone failure?

Answer 19

Shape of the two parts that have fractured - most metals fracture by shear at a 45 angle to applied stress.

Question 20

What is ductile dimpling?

Answer 20

Where particles have separated from matrix in ductile fracture

Question 21

Describe the appearance of a fractured brittle polycrystalline metal.

Answer 21

Macroscopic - would look flat as plastic deformation before fracture is negligible

Microscopic - fracture surface may feature a series of steps if cleavaged - steps would correspond to the change in cleavage plane within a grain OR fracture surface may appear granular if failure was intergranular as grain boundaries will have seperated

Question 22

Describe the appearance of a fractured ductile polycrystalline metal.

Answer 22

If material was very pure, completely ductile would mean it reduces to a point before final fracture.

Most metals though would have a cup and cone appearance with a flat central fibrous region and 45 degree shear region at edges.

Microscopically, you’d see dimples or voids from particles which may decohese or fracture if matrix is strong

Question 23

Why is a brittle material more sensitive to cracks?

Answer 23

Yield strength is high so little to no plastic deformation to relieve the stress at the crack tip.

In a ductile material, void formation happens and absorbs energy at the crack tip which blunts it to reduce the stress concentration.

Question 24

Describe the appearance of a fracture surface that has failed due to fatigue.

Answer 24

Macroscopic - steps called ‘beachmarks’ due to the interruption of the stress cycle

Microscopic - striations due to the avg distance the crack front moves per cycle (much tinier)

Question 25

Describe the appearance of a fracture surface due to hydrogen embrittlement.

Answer 25

Varies from microvoids (ductile) to ‘quasi-cleavage’ (brittle) to intergranular

Question 26

What is the square indent picture?

Answer 26

Vickers hardness indent

Annealing twins present

Wavy lines represent slip steps where dislocation emerges

Height of steps = magnitude of Burgers vector

Steps change orientation in different grains - they don’t move randomly in crystal structures