Paper 4

Question 1

high/low cycle fatigue

Answer 1

repeated stress cycles => material may fail by fatigue at stresses well below tensile strength and often below yield strength. For uncracked components, failure is crack-initiation controlled.
high cycle:
sigma max < sigma yield, Nf>1000 cycles
cycles occur within elastic deformation region of material e.g. rotational/vibrational systems
low cycle: opposite, plastic strain associated with each cycle e.g. occasionally overloaded components

Question 2

relationship btw hardness and yield stress. when would this change?

Answer 2

H=3*sigma_y

on work hardening, this wd increase

Question 3

what is true hardness?

Answer 3

H=F/A where F is const force with which pointed diamond is pressed into surface and A is the projected area

Question 4

how to minimise chance of catastrophic failure in a vessel?

Answer 4

work harden the material, ppt harden, quench from high temp, make defect free

Question 5

condition for fast frac

Answer 5

sigma rt(pi*a) > Kc in MPa m^1/2

Question 6

fast frac

Answer 6

rapid growth (speed of sound in material) of existing cracks which suddenly become unstable. Frac can occur far below material yield strength and is due to presence of cracks. If stress intensity factor K > fract toughness Kc i.e. if sigma y rt(pi*a) > rt(E*Gc) then fast frac
i.e. if wk done by movement of external forces greater than or equal to change in stored elastic energy and energy absorbed by crack propagation.

Question 7

what are cracks often associated with?

Answer 7

welds

Question 8

what can inhibit crack propagation

Answer 8

adding fibres/fillers

Question 9

difference in cracking btw metals and glasses

Answer 9

metals: ductile tearing possible
glasses: virtually no plastic deformation possible so crack propagation via cleaving of interatomic bonds

Question 10

fatigue failure

Answer 10

low cycle and high cycle of uncracked components is controlled by crack initiation
fatigue of cracked structures controlled by crack propagation

Question 11

creep

Answer 11

time dependent strain behaviour of a material
with const load strain increases with time e.g. sagging pipes
with const displacement stress decreases with time e.g. slackening bolts
important at high temps bc diffusion thermally activated process
for metals/ceramics high temp corresponds to btw 30% and 50% of melt temp and for glasses/polymers a high temp is around the glass transition temp

Question 12

mechanism for steady state creep

Answer 12

1. power-law/dislocation: at high stress results in migration of atoms away from loaded dislocations, helps to remove obstacles which prevent dislocation motion. Once removed, dislocations can climb and glide.
2. Diffusion creep. Governed by mass transfer of atoms, not dislocations. Two main types a) bulk diffusion of atoms through interstices/into vacancies
   b) fast diffusion along channels provided by either gb’s or dislocation cores

Question 13

final stage of creep

Answer 13

tertiary creep = onset of creep damage. Internal cavities form => failure

Question 14

ductile tearing

Answer 14

crack propagation mechanism which dissipates energy by performing plastic work at crack tip. e.g. consider a loaded piece of ductile material (Cu or mild steel at or above RT) which has a crack. At a certain load, frac can occur, originating at crack. frac sface v rough so lots of plastic work occurred.
most metals, including pure ones, have tiny compounds (inclusions) formed by rxn of impurity atoms with the metal. In the plastic zone around the tip, the plastic flow occurs around the inclusions leading to cavities which coalesce as the plastic flow progresses and so the crack propagates. The plastic flow blunts the crack tip, decreasing the local stress. At the crack tip itself, local stress just enough to continue plastically deforming the work hardened metal there. This mechanism is called ductile tearing and consumes lots of energy by plastic flow. so Gc and Kc high

Question 15

how can you change the toughness of a material?

Answer 15

alloying can reduce toughness as resistance to dislocation motion is reduced so yield strength raised and plastic zone shrinks. Heat treating alloys can lead to different crystal structures which are very hard but also brittle. For crystallographic reasons, dislocation mobility greatly reduced at temps much less than 0 deg for bcc and hcp strucs and so metals w these strucs (including steel) become brittle at low temps. Metals with fcc (e.g. Cu, Pb, Al) hardly affected

Question 16

molecular struc and mech behaviour in amorphous polymer

Answer 16

no long range order, formed of long chains of monomer repeating units with vdW’s btw them. polymer held together by H-bonding, mech intertwining of chains

above Tg, polymers particularly susceptible to creep. individual chains randomly oriented and intertwined.

Question 17

glass transition temp

Answer 17

at T > Tg enough energy in the chains of atoms to break free of most of the vdw bonds. When an amorphous polymer is loaded, the chains move more freely.
so it takes less load to displace the material a certain amount when material is above Tg compared to below and a very large drop in E is noticed when T > Tg

Question 18

work hardening

Answer 18

deformation of material permanent as plastic deformation occurs. bonds rupture and irreversible elongation of chemical bonds and dislocations can occur

Question 19

necking

Answer 19

frac becomes imminent, corresponds to a geometric instability, CSA of specimen begins to narrow

Question 20

inertial FOR

Answer 20

frame which moves at constant velocity (i.e. with no acceleration) relative to the distant stars. It doesn’t rotate

Question 21

high stress creep

Answer 21

n approx 3-8
power-law/dislocation creep
obstacles such as dislocations and small ppts impede dislocation movement
diffusion of atoms helps unlock dislocations from these obstacles
climb and glide

Question 22

low stress creep

Answer 22

n approx = 1
diffusion creep - due to tfer of atoms, not dislocation movement.
2 main types: 1. bulk diffusion 2. fast diffusion along gb or dislocation core
grain size can affect creep rate

Question 23

neutral axis

Answer 23

line of zero stress in a beam subjected to pure bending, i.e. NA is unstressed and unstrained

Question 24

if a beam is in pure bending

Answer 24

total axial/compressive force is zero

Question 25

what is 1/ymax called

Answer 25

elastic or section modulus Z in [m]

Question 26

are marble, brick, concrete and stone weak in tension or compression?

Answer 26

weak in tension
can consider critical level of compression
sigma =My/I - |C|/A

Question 27

for trapezium rule with n strips, what is the error prop to?

Answer 27

n^-2

Question 28

what is the error for the trapezium rule with 2n strips?

Answer 28

c/(4n^2)

Question 29

what is the error in Simpson’s rule prop to?

Answer 29

for n strips, prop to h^4 or n^-4

simp exact for cubic or less

Question 30

total error of Euler’s method for n strips of width h

Answer 30

error prop to h