Paper 4 Flashcards
high/low cycle fatigue
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
relationship btw hardness and yield stress. when would this change?
H=3*sigma_y
on work hardening, this wd increase
what is true hardness?
H=F/A where F is const force with which pointed diamond is pressed into surface and A is the projected area
how to minimise chance of catastrophic failure in a vessel?
work harden the material, ppt harden, quench from high temp, make defect free
condition for fast frac
sigma rt(pi*a) > Kc in MPa m^1/2
fast frac
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.
what are cracks often associated with?
welds
what can inhibit crack propagation
adding fibres/fillers
difference in cracking btw metals and glasses
metals: ductile tearing possible
glasses: virtually no plastic deformation possible so crack propagation via cleaving of interatomic bonds
fatigue failure
low cycle and high cycle of uncracked components is controlled by crack initiation
fatigue of cracked structures controlled by crack propagation
creep
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
mechanism for steady state creep
- 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.
- 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
final stage of creep
tertiary creep = onset of creep damage. Internal cavities form => failure
ductile tearing
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
how can you change the toughness of a material?
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
molecular struc and mech behaviour in amorphous polymer
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.
glass transition temp
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
work hardening
deformation of material permanent as plastic deformation occurs. bonds rupture and irreversible elongation of chemical bonds and dislocations can occur
necking
frac becomes imminent, corresponds to a geometric instability, CSA of specimen begins to narrow
inertial FOR
frame which moves at constant velocity (i.e. with no acceleration) relative to the distant stars. It doesn’t rotate
high stress creep
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
low stress creep
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
neutral axis
line of zero stress in a beam subjected to pure bending, i.e. NA is unstressed and unstrained
if a beam is in pure bending
total axial/compressive force is zero
what is 1/ymax called
elastic or section modulus Z in [m]
are marble, brick, concrete and stone weak in tension or compression?
weak in tension
can consider critical level of compression
sigma =My/I - |C|/A
for trapezium rule with n strips, what is the error prop to?
n^-2
what is the error for the trapezium rule with 2n strips?
c/(4n^2)
what is the error in Simpson’s rule prop to?
for n strips, prop to h^4 or n^-4
simp exact for cubic or less
total error of Euler’s method for n strips of width h
error prop to h
