2015 paper (structural)

Question 1

Compare and contrast the characteristic appearance of ‘fatigue’ and ‘stress corrosion cracking

Answer 1

Fatigue failure

• Produced by oscillating stress and at values less than short term fracture stress.
• Cracks initiate at surface defects etc, and grow initially down slip bands before turning perpendicular to major tensile stress.
• Sub critical crack growth proceeds, leaving smooth surface showing possibly ‘beach markings before crack accelerates when it reaches critical size, giving a more brittle appearance.

Stress Corrosion

• Static load or internal stress
• Susceptible material and environmental agent
• Inter-granular cracks usually evident, with fairly brittle failure, etc

Question 2

Compare and contrast the characteristic appearance of ‘fast fracture’ in metals with those of ‘fatigue failure’

Answer 2

Fast fracture

• crack propagates rapidly
• at macro level, bright appearance, facetted due to cleavage or inter-granular fracture
• generally rougher than fatigue, possible more evidence of ridges

Fatigue fracture

• at macro level, two zones visible, slow sub-critical crack growth region and fast crack growth region
• “beach markings” may be visible and radiate from crack origin
• at micro level, striations may be seen, indicating successive jumps,of crack size in slow growth region, which is generally smooth, while the fast growth region is as above

Question 3

What is meant by the term “plane strain”

Answer 3

• Plane strain exists at the tip of a crack in a loaded thick specimen
• The high stress at the crack tip in the ‘x’ direction causes Poisson’s contraction in the ‘y’ and ‘z’ direction, but this is restricted by the lower stressed region further from the crack- thus inducing a triaxial stress with stresses σx, σy, and σz-,the only strains in the yz plane.

Question 4

Define the terms of the Griffith formula

refer to book

Answer 4

• Gc= toughness (energy in J/m^2)
• E=Modulus (N/m^2)
• c= crack length (m)
• d= Poisson’s ratio
• For ductile metals ,Gc is high
• For ductile polymers, Gc is mediocre
• For ceramics (or metals + polymers in cold worked state), Gc is low

Question 5

Define or explain, using sketches if necessary:

-Anelasticity and mechanical hysteresis

Answer 5

• Where strain strain lags behind stress but is still elastic and recoverable.
• Cycling the stress produces a hysteresis loop, with energy lost on each cycle equal to area in loop or (show diagram of stress/strain loop)

Question 6

Define or explain, using sketches if necessary:

-Thermo-elastic effect

Answer 6

-rapid tensile straining, adiabatic so temperature of material falls, compression raises temperature.

Question 7

Define or explain, using sketches if necessary:

-Relaxation modulus

Answer 7

-E(R) = stress applied/ strain after given time

Question 8

Define or explain, using sketches if necessary:

-Specific damping capacity

Answer 8

• Specific damping capacity = ΔW/W i.e energy absorbed per cycle divided by total strain energy input.
• W=1/2 σmax •εmax

Question 9

Compare relative damping capacities of cast

Answer 9

-Damping capacity important in minimising machinery noise or vibration, and therefore less danger of fatigue
=in rubber, absorbs energy and increases friction

• Cast iron has superior damping capacity to mild steel due to large graphite flakes absorbing vibration.
• In rubber ,damping is even higher due to molecular structure

Question 10

Distinguish the difference between the terms ‘atactic’, ‘isotactic’ and ‘syndiotactic’ as applied to polymers such as polystyrene. The relaxation modulus of isotactic polystyrene is higher than that of atactic polystyrene of the same molecular weight. Explain this in terms of different structures that may result from different tacticities.
Sketch graph of the variation of relaxation modulus with temperature from 20 to 250 degrees celsius for atactic polystyrene given that the glass transition temp is 100 degrees and the melting point is 240 degrees

Answer 10

• Isotatic has benzene side groups all on the same side
• Atactic has random placing of side groups
• Syndiotactic has alternating placing of side groups#
• Isotactic type is easiest to crystallise, closer packing leads to higher bonding forces between molecules- higher modulus
• Atactic, due to random side groups, is non-crystalline, less densely packed, so lowest modulus

Question 11

Hoop stress equation

Answer 11

P(D-2t)/2
where 
P is internal pressure
D is diameter 
t is wall thickness

Question 12

Griffith Equation
When
K>Kc
Where 
K=ασ√(πa)
Kc=√(EGc)

Define terms

Answer 12

K>Kc= stress intensity factor>fracture toughness of material

α= Geometrical factor depending on crack shape, orientation
σ= applied stress
a= crack length
E= Modulus
Gc= material toughness (J/m^2)

Question 13

Paris Equation

(da)/(dN)=A(ΔK)^p

Answer 13

A= constant for type of material
p= constant for type of material
ΔK= range in stress intensity factor
ΔK=Kmax - Kmin=ασmax√(πa) -ασmin√(πa)