nm0827: now today we're going to talk about [0.2] fatigue [1.1] and that 
doesn't mean that i'm going to [0.3] pack the lecture in half way through 
because i'm worn out [0.9] although with you lot [1.0] the ability to feel 
knackered after a lecture is very easy [0.2] i will say that [1.0] er [0.6] 
you've all got i hope this piece of [0.3] paper these notes come on [1.2] which 
i've given out [0.2] take this please [2.8] we're not going to get on to this 
yet [0.2] but we will in a moment [0.9] now [0.4] fatigue [0.4] is a strange [0.
6] phenomenon [0.8] and it's [0.2] to do [0.2] with [1.1] loading [1.8] which 
varies [6.8] it varies [1.8] so in other words it's oscillating [0.4] well 
here's some good words [0.3] oscillating [0.3] or fluctuating [3.8] loads [1.2] 
so a classic example of this would be a car going over a bumpy road what's [0.
2] er [0.2] does the er [0.2] suspension experience [0.6] what about an out of 
balance piece of machinery [0.5] some pieces of machinery of course are 
deliberately out of balance [0.6] er [0.3] if you want to crush things you very 
often will have an out of balance thing to give a 
sort of hammer effect [0.8] and [0.4] things like jackhammers that you use for 
[0.5] er making holes in the road [0.5] these also [0.3] are [0.8] er [0.3] 
they're not out of balance but they're c-, [0.2] controlled by air [0.5] yep [3.
1] we're on air so be on your best behaviour [2.2] so [0.5] [sigh] [0.6] 
rotating machinery [1.1] is [2.0] a very important example of this and we'll 
come on to an example of that at the end [0.3] as a sort of case study which is 
what you've got your [0.5] er notes on [1.3] now [0.9] the [0.5] simplest way 
[0.2] to understand fatigue and indeed to understand the history [0.5] how how 
it came to be [0.5] a [0.2] topic [0.7] is to consider what happens in a spoked 
[0.2] wheel [1.9] so you have [0.2] some sort of wheel it could be a horse and 
cart wheel it could be a bicycle wheel it could be a [0.8] gun wheel i don't 
know anything you wa-, [0.2] name it [0.3] think of what it [0.5] looks like [0.
4] now [0.7] obviously [0.3] if you have a wheel [0.8] er [0.4] let's say [0.2] 
er [2.9] right you'll get shot [2.6] let's say that's the front wheel of your 
bike or something or other [0.4] your weight on the frame [0.4] pushes down [0.
9] on there [0.3] so 
there is a vertical loading or a er [0.3] an inclined loading [0.5] on [0.3] 
the axle [0.2] which is here [1.0] okay [0.2] so you've got that [1.0] now [0.
7] the question then is what prevents the fork of the bike going into the 
ground [0.3] well obviously because the wheel is pushing back on the end of the 
fork [0.4] so that if we take that spoke as an example [0.4] this spoke is 
pushing back [1.5] but because the hub if you like does come down a bit because 
you've got a tyre it's squidgy [0.4] the [0.3] spoke above [0.2] is coming down 
[0.6] so if you think about it the upper spoke is in tension [0.4] and the 
lower [0.2] spoke [0.3] is in [0.2] compression [0.9] at that p-, particular 
instant [0.5] and so if the vehicle is stationary [0.5] that is a stress 
pattern [0.3] which will be there [0.5] er as long as you leave it in that 
condition [1.3] if you consider other spokes at angles well they have [0.3] 
some load in them [0.4] er w-, i'm not going to bother [0.3] to work out [0.6] 
how you [0.4] er [0.3] calculate what [0.5] f-, force is in the spokes [0.4] 
but the general idea is that below [0.5] the middle [0.5] there is compression 
and above [0.5] the [0.2] middle [0.2] there is tension [1.7] now the 
next question is what happens when this thing starts to move [1.1] so that [0.
2] this now goes forward [0.2] so that that point there [1.0] er if we move the 
wheel [0.2] along we rotate it through [0.4] er a hundred-and- [0.2] eighty 
degrees [0.6] what happens [1.8] well what we find of course is that that [0.2] 
blobbed point there [0.8] is now down here [0.7] and so here are the spokes [0.
2] et cetera et cetera [1.1] and so what it means is that that spoke [0.2] 
which was above the axis [0.2] is now below [0.9] and what was below [0.2] a 
hundred-and-eighty degrees later is now above [1.2] but the stress state [0.4] 
what the wheel has to do to hold the thing up [0.3] is exactly the same as 
before [0.6] so this bottom thing is in compression [0.4] and [0.2] the top one 
[0.2] is in [0.3] tension still [1.2] but this one [0.3] was up there [1.2] so 
what was in tension [0.5] is now in compression [0.7] and if you roll it 
another a hundred-and-eighty degrees it goes back to where it was [0.6] and [0.
3] so [0.3] the tension has become compression [0.2] has become tension has 
become pompre-, er progression [0.3] [whistle] [0.6] tension [0.2] has become 
compression [0.3] has become tension [1.2] so if you were 
to plot this out [0.5] as [0.7] the force [0.6] experienced [0.4] by the spoke 
force in spoke [0.6] against [0.2] er [0.4] rotation [1.9] revolutions whatever 
you want to call it [1.0] of the wheel [2.2] what you'd have [0.2] is [0.7] a 
[0.4] load up there [0.2] if we consider one spoke [0.3] tension [0.7] it drops 
down to nothing when it's half way [0.8] because the horizontal spokes don't 
have anything in them [0.3] because they're not resisting any [0.3] horizontal 
[0.3] motion [0.2] if [0.3] the [0.8] force is [0.4] truly vertical [0.7] and 
then [0.3] going on a bit more [0.4] it goes below [0.5] and goes to an equal 
value [0.4] but in [0.5] compression and then it does this and so on and so 
forth [2.3] and [0.5] this [0.5] you can show with a bit of trigonometry i'm 
not going to do it today [0.2] but in fact it's a sine curve [3.4] so the 
process of rolling or rotating a wheel or an axle or [0.7] anything like that 
[0.6] produces [0.2] alternating [0.2] tension and compression [1.6] so that 
the [0.4] spoke of the wheel [0.3] is experiencing [0.2] this [0.3] phenomenon 
of [0.5] a varying [0.3] tension compression [0.2] alternating [0.3] 
fluctuating [0.4] oscillating whatever the those words you wish to use [1.3] 
and the question [0.2] is 
well so what [1.6] why should we be worried [0.8] well we have to be worried [0.
2] because it turns out [0.5] that this oscillating loading [0.2] can [0.2] 
break things [0.2] can fail things [0.5] at much [0.3] lower [0.2] stresses [0.
6] than you would [0.6] work out [0.2] on the basis of a simple [0.3] single [0.
3] monotonic [0.3] pull [0.3] or push [1.9] that's why it's important [2.9] who 
first thought about this [0.8] well you might think that people with [0.2] 
horses and carts go up to the Museum of English Rural Life up the top of campus 
[0.4] have a look in there you might have thought that farmers might have been 
interested in this [0.7] and perhaps they were [0.3] but if you think of the 
state of roads before eighteen-thirty forty or fifty or whatever [0.5] they 
were sort of rutted tracks [0.2] even the so-called turnpikes [0.4] and 
therefore if anything broke it was probably because [0.2] there was a big 
pothole in the road [0.4] in the way that we all [0.5] have problems with cars 
and bikes if we [0.5] go over a [0.6] what appears to be a puddle but in fact 
it's a [0.5] like a [0.2] bucket-shaped hole full of water and you damage your 
front 
suspension and so on [1.0] so [0.9] and what you've got [0.4] is the problem [0.
2] of [0.9] er [0.6] rotating [0.2] machinery [0.9] rotating wheels [0.7] in 
the old days there were fractures but they never thought about it [0.7] what [0.
2] made this an important subject [0.2] was the growth of railways [2.5] 
because for the first time you had a smooth [0.2] track [0.9] and you had [0.3] 
wheels [0.3] going along that smooth track [1.7] and of course [0.2] the 
engineers of the day [0.4] although [0.7] they were [0.4] not [0.6] er given 
all the materials that we have today we've done a bit of that a bit of the 
history wrought iron [0.5] malleable iron [0.2] et cetera et cetera Bessemer 
steel [0.4] not coming along until the eighteen-fifties this in fact held up [0.
2] the [0.5] growth of railways because all of the manual methods of making [0.
4] ductile [0.4] er steel before that han-, before that time [0.7] er [0.3] 
nevertheless you had a reasonably smooth [0.5] thing [0.6] system with a 
reasonably smooth wheels and all the rest of it [0.5] and what they discovered 
was that these axles were breaking the axles were breaking not so much the 
wheels [0.5] they might have had spokes but 
they might have been solid wooden blocked wheels it doesn't matter [0.9] why 
were the axles breaking [0.4] well [0.3] let's look [0.2] at [0.2] this picture 
[0.7] but looking at it from the [0.3] end this way [0.3] and let it not be a 
bicycle wheel any more [0.3] let it be [0.4] er [0.2] two wheels on an axle [0.
2] like a railway [0.5] axle so this [0.3] look at it sideways [0.5] and you've 
got this [0.3] sort of [0.6] device [0.8] and there [0.4] is the [0.6] axle [2.
2] and here is the wheel [0.5] er [0.6] and there is the [0.8] the rail [2.0] 
do you know [0.4] by the way some clever [0.9] character [0.2] said there was a 
method of preventing [0.4] trains coming off [0.6] rails [1.3] and what he said 
was [0.5] that when you look end on like this what you actually need [0.6] is a 
[0.3] wheel [1.1] which looks like this [2.0] and the [0.3] you know the rail 
is in there [1.6] and so [0.2] you know [0.2] the wheel wouldn't come off [2.8] 
that a good idea [2.8] well it isn't a good idea [0.4] but you know the 
original explanation for why it wasn't a good idea [1.0] because they said 
that's no good [0.3] you'd have to go to the end of the track to get the 
vehicles on [3.4] [laughter] think of it [1.3] right [0.6] now [0.4] if you 
have this system [0.6] and if you have outside 
bearings [0.3] so it's like a goods wagon with [0.2] springs and so on [0.8] 
there's the [0.3] axle box [0.3] there here's the spring the force is pushing 
down there [1.5] so [0.4] what does that do [0.3] well obviously if you think 
about it [0.3] it must bend the axle [0.4] i'm exaggerating it but that's what 
[0.3] happens the axle gets [0.2] bent [2.7] what happens when you bend a beam 
[0.3] you've had namex's lectures last year [0.5] when you bend a beam that bit 
goes into tension [0.6] the [0.2] underneath goes into compression [1.4] that 
is a hogging beam remember the word hogging from [0.6] pigs [0.8] sagging and 
hogging that's hogging [0.7] tension [0.8] compression [1.9] what happens [0.2] 
a hundred-and-eighty degrees later [0.3] well this bottom bit has gone on the 
top the top's gone on the bottom [0.2] it's exactly the same as this it's the 
top and bottom of the axle now [0.4] not the [0.6] upper and lower spokes [0.4] 
and so [0.4] the [0.3] stress state in that [0.5] axle is exactly the same [0.
9] as [0.3] the stress state in the spoke [0.6] and in fact in those wheels if 
they were spoked wheels [0.2] the spokes were being fatigued [0.3] and the 
axles were also [0.3] 
being [0.3] fatigued [1.4] anyway [0.2] these [0.3] axles [0.2] began to break 
[0.4] for no apparent reason [0.8] and [0.6] so [0.6] the [0.4] people in 
charge of the railways [0.5] s-, thought well [0.4] either we're not making the 
wheels very [0.2] well [0.2] or [0.9] there is a problem [0.3] that we don't 
understand [0.7] and it was a problem that they didn't understand and the 
problem was this thing called fatigue [0.9] and the man who [0.5] started all 
this work off [0.5] was an Austrian [0.3] whose name was Wöhler [0.7] that 
name keeps coming up [1.1] W-O-umlaut-H-L-E-R Wöhler [0.9] who was [0.7] not 
sure what he was might be some sort of chief engineer of the Austrian railways 
one of the Austrian railway companies [0.5] anyway he [1.8] started to 
investigate this [0.4] business [1.0] and [0.2] he very cleverly [0.4] came up 
[0.2] with a sort of test [0.6] which [0.2] in many ways is still used as a 
fatigue test even [0.3] today [0.8] and the 
best way for you to think about it is to think of going downstairs into the 
workshop [0.7] and going to one of namex [0.3] namex's lathes [0.5] and saying 
okay here [0.4] is a chuck [0.2] on the lathe [1.1] can't spell [0.2] chuck [0.
9] and what you do [0.2] you have a [0.2] normal round [0.4] tensile [0.3] test 
piece [0.7] which you [0.4] are used to [0.2] so [0.2] here is this round [0.4] 
tensile test piece [0.3] but instead of putting it in one of namex's machines 
and pulling it until it breaks or whatever you're doing [0.6] what you do is 
you stuff one end into the chuck [1.1] so you lock it in the chuck [0.4] and if 
you [0.3] turned the lathe on [0.2] the thing would [0.2] rotate [2.1] but what 
Wöhler then did was to say right [0.3] at this end [0.2] i'm going to put some 
sort of collar [0.5] with [0.5] roller bearings or ball bearings it doesn't 
matter [0.6] so here's looking [0.2] from the end elevation [0.8] there [0.4] 
is the specimen [0.4] here is a sort of collar [0.2] going round it with [0.9] 
ball bearings and things like that [0.4] and from that [0.2] you hang a weight 
you put a mass on it [1.4] and so [0.2] 
obviously [0.6] the weight [0.2] on the end of this thing [0.5] what is it [0.
2] it's a cantilever [0.4] and it's like the things that you solved in part one 
[1.0] so you can work out the deflection you can work out the bending stress 
and you can do everything else [3.7] and what happens well [0.5] the cantilever 
the top is tension the bottom's compression [1.1] hundred-and-eighty degrees 
later [1.3] the [0.4] compression has become tension and the tension has become 
p-, [0.2] compression et cetera et cetera [1.4] and old Wöhler [0.5] very 
clever [0.6] he started to do [0.3] tests [2.1] what sort of tests did he do [1.
7] he put different weights [0.4] on [1.3] these [0.2] test pieces [0.8] so he 
changed [0.2] this [1.2] W [0.5] weight [1.6] and he rotated the lathe [1.3] 
and he found out [0.3] how many rotations it took [0.4] before [0.4] the 
specimen broke [2.3] all right [2.0] and [0.5] he then [0.6] plotted [1.4] the 
load [1.5] against the number of cycles N [0.2] cycles [0.6] to failure [0.8] 
and failure here is breakage [3.3] i say it's breakage because of course [0.6] 
you could define failure [0.3] and [0.5] in [0.4] part three i'll teach you 
plasticity and failure of course could be [0.3] permanently being bent [1.1] 
obviously if 
an axle [0.5] permanently gets bent it's not much good as an axle [1.1] er so 
you always design within the elastic stress range we've already been through 
this in this course [1.1] so he's got load he's got number of cycles to failure 
[0.4] now [0.5] if you have [0.5] no cycles [0.8] it's really just bending 
bending bending bending bending until it breaks [0.9] and that's like a static 
quasi-static test [0.5] and you'd have a a value there [0.5] say [3.1] if you 
then [0.3] increase [0.3] the weight [1.1] and [0.6] start the machine up [0.8] 
and [0.6] wait for something to happen [0.5] you'll find [0.5] that [0.7] the 
[0.7] lifetime or the number of cycles to failure [1.0] is [0.8] lower [2.1] in 
other words [0.8] if you want the thing to last [1.4] a hundred cycles a 
thousand cycles [1.4] it will only take a certain load [0.4] and then it'll 
break [1.5] he puts [1.2] more weights on [0.4] and he finds that he [0.9] can 
[0.6] go out [0.3] there [1.5] more cycles lower [0.2] loads [0.4] so these 
loads are dropping [0.6] all the time [0.9] and he finds [0.2] that sort of 
behaviour [2.1] and that is a [0.2] classic [0.2] sort [0.2] of so-called 
fatigue curve [1.7] and in the literature [0.3] you'll find these things called 
[0.2] 
S- [1.3] N [0.4] curves [1.3] now [0.4] we these days use sigma [0.2] for 
stress [1.1] er [0.2] and h-, originally of course he used load [0.2] but you 
can convert it to stress verily easy [0.2] easily using bending theory [1.6] so 
[0.4] in the books you'll find that [0.2] called very often an S-N curve [0.4] 
and it means a fatigue curve [6.0] now [0.9] because [0.4] these numbers of 
cycles in fact are very high they go into the millions [0.9] you don't normally 
[0.2] plot it on Cartesian coordinates [1.0] you can have load or stress [0.2] 
here [0.4] in [0.3] Cartesian coordinates [0.4] but here [0.2] you have the log 
[0.4] you do it on a semi-log plot [0.4] of log [0.2] numbers of cycles [1.3] 
and what you find [0.6] more or less is that the data follow [0.5] some sort of 
falling line like that [1.0] and maybe [0.3] that's [0.2] ten-to-the-six so 
that's a million cycles [0.5] ten-five ten-four ten-three thousand cycles [0.5] 
hundred cycles [0.3] ten and [1.0] et cetera one remember there's no-, not a 
zero [0.2] on a log scale [0.2] what's the log of zero [2.0] come on what [2.2] 
what is it 
sm0828: [0.4] 
nm0827: log of zero [0.5] no the log of one is zero what's the log of zero 
sm0829: [2.8] 
nm0827: it may be in Dublin dear boy 
but it's minus-infinity in the rest of the world [1.2] [laugh] [laughter] the 
log of zero is [0.4] bloody big it's minus-infinity [0.3] so the zero on a 
scale is [0.5] over [0.3] there somewhere [0.4] so never put a zero on a log 
scale [0.8] now [0.9] old Wöhler f-, was playing around with steel [0.6] and 
he discovered [0.9] that [0.9] after about [1.5] ten-to-the-six after about a 
million cycles [0.5] the thing levelled out [2.4] that was pretty interesting 
really [0.8] and so that was called [0.3] an endurance [1.0] limit [5.1] and 
remember [0.7] he [0.2] was dealing with [0.2] steels [0.2] or [0.6] wrought 
irons or [0.6] some ferrous [0.9] object [0.3] anyway [2.9] and that was for 
simple [0.2] so-called [0.2] reversed bending [0.7] and reversed bending is 
like Wöhler and his cantilever [0.5] where [0.2] you have that so it goes from 
plus- [0.7] T [0.5] to minus-C those are equal magnitudes [0.3] and you go 
through [0.2] zero in the middle [3.0] now [1.5] if you have an endurance limit 
[0.8] that's [0.4] great [1.1] if you think about it [0.9] because what it 
means is [0.5] according to this diagram [0.9] that if you have that sort of 
loading system [0.6] providing you keep 
your stresses below this endurance limit [0.8] then you have an [0.3] infinite 
[0.2] life [3.3] so you can have [0.3] a life forever [0.8] providing [0.4] you 
[0.8] recognize that there is an endurance limit [0.5] or what is sometimes 
called a fatigue [0.2] limit [2.2] i'll explain there is a difference and i'll 
explain that in a minute [0.8] but fatigue limit or endurance limit [0.5] and 
that happens for steels [7.3] now [3.7] if you [3.6] don't [0.6] test it just 
in bending which is what we've [0.2] been doing here [0.7] you might for 
example [0.4] want to test something in axial fatigue so you would have your 
specimen in the usual way [0.6] but you would [0.2] oscillate it [0.2] in the 
axial direction [0.2] this would be like trying to [0.4] estimate what's going 
on with the spokes [1.2] 'cause they're going [0.5] tension compression tension 
compre-, [0.3] but in [0.6] unidirectional loading not in bending [0.5] is 
there a difference [0.9] can you make a machine [0.3] which [0.2] does this 
well of course you can do it on the types of testing machines down in namex's 
lab [0.6] these are screw-driven machines [0.4] and if you think about it you 
just drive 
the screw one way drive the screw the other way and you can do [0.2] this [1.8] 
you might be saying to yourself well [0.5] er [0.5] it's all very well [0.2] 
talking about rotation [0.4] speed [0.2] of oscillation frequency of 
oscillation [0.3] but does [0.3] how fast you do it matter [0.6] is there a 
difference between sort of oscillating very slowly [0.5] and [0.3] oscillating 
[0.3] you know like a [0.9] i don't know [1.0] a er [0.2] bird flaps its wings 
or something else something very very fast [0.4] and the answer is yes there is 
[0.9] and it's particularly important in things like plastics [0.6] where 
because you are [0.3] oscillating the load you're obviously doing work [0.5] 
force point of application [0.6] that work [0.3] becomes heat [0.6] in a metal 
[0.2] the heat tends to be dissipated but in plastics it tends to be localized 
where the thing is happening [0.7] that then alters as we saw the other week [0.
3] the properties [1.0] the strength varies with the temperature and the speed 
at which you're doing it and so on [0.4] so the speed does matter [0.8] but [1.
2] whilst in the lab with the namex type machine [0.2] the oscillation rate is 
[0.6] pretty 
limited [0.3] pretty limited [0.6] you can have very [0.2] fast [0.2] v-, [0.7] 
axial oscillations [0.5] and the firm that [0.2] invented the [1.0] method of 
doing this is a firm called Amsler [0.4] who are in Switzerland [0.6] and what 
they did was really very clever [0.7] because [0.3] they [0.2] attached what 
amounts to a whacking great big [0.2] tuning fork [0.2] to the bottom of the 
specimen [0.8] i mean a big one [0.5] really big [1.1] the biggest Amsler 
machines the tuning fork would be [0.3] about [0.3] the size of [0.3] where i 
am here [1.2] and you can get that resonating [0.6] and of course it puts the 
[0.6] er [0.2] device into [0.3] oscillation [0.9] and you [0.5] by altering 
the amplitude of the tuning fork [0.2] you [0.2] alter the load you can set 
this on the machine [0.8] and [0.2] then you can generate [0.4] er these same 
sort of data [0.9] well what do you get [0.4] what do you get what do you get 
well [0.9] it's like this [0.5] but [0.6] this plot if i say this is bending 
pure bending [1.0] if you have the [0.3] axial thing [0.5] this [0.7] says the 
same sort of thing [0.3] but [0.4] goes to a lower [0.2] value [0.4] before it 
[0.2] levels out [1.4] so this would be axial [1.0] fatigue [2.7] and you might 
also say [0.5] er [0.2] well what about other methods of 
loading [0.6] what about if we [0.2] twist things you've heard of torsional 
suspensions on motor cars [0.5] what happens if you think of having [0.2] a 
tube or a rod [0.3] which itself is [0.4] not [0.2] being twisted monotonically 
but is fluctuating in the twist what happens there [0.7] well [0.4] er the same 
sort of thing [0.3] but this time [0.2] it goes down [0.3] h-, even lower [1.8] 
down to there [0.3] not drawn that very well [2.1] so that this endurance limit 
[0.4] although [0.4] it's very good [2.7] the values that you have depend on 
the mode [0.5] of [0.9] deformation so bending to axial [0.5] er to torsion to 
twist [6.6] now [1.0] er before the days of what's called fracture mechanics 
which is the subject i shall teach you next term [0.6] where we are talking 
about the progression of cracks [0.5] through bodies [0.2] before that time [0.
9] people [1.1] were [1.8] limited in a sense as to what they could use for 
data [0.4] and they tended rightly or wrongly [0.5] to reference everything to 
the simple tension test [0.8] so in the simple tension test which you know 
about [0.5] load against extension or stress against strain [0.5] er 
engineering stress and 
strain [1.0] there is your yield [0.9] there is the [0.2] ultimate tensile 
strength we discussed this in the corresponding lectures in part one [0.6] so 
what these [1.1] chaps [0.2] did from about eighteen-fifty up until well up 
until the second war and even now in fact [0.5] for a for an empirical sort of 
corre-, correlation [0.3] they said [0.3] what's that value bend or axial or 
torsion [0.3] as a proportion of something that i can easily measure [0.5] and 
the thing that they could easily measure was the ultimate tensile strength [0.
2] 
maximum load over the starting area [1.6] all right [1.0] so [1.0] when you 
look at these types of diagrams [0.4] you will find labelled on to the diagrams 
[0.4] what these levels are [1.0] so [0.3] if i [1.3] just rub that out [0.4] 
put them in again [2.3] you'll find that the [0.2] bending-only one [0.4] is 
about [0.2] and it's very rough [0.3] about point-five of the U-T-S [0.7] so in 
other words if you had a piece of steel with a U-T-S of about three-hundred 
megapascals [0.4] er that value for pure bending [0.4] pure reverse bending 
Wöhler bending would be about [0.4] er three-hundred-over-two [0.2] which is a 
hundred-and-fifty [1.8] if you have the [0.3] axial fatigue [0.5] that value is 
about [0.2] point-four-three of U-T-S [0.7] i don't know that i believe the 
point-three [0.6] i suppose i believe the point-four [0.2] but it's that sort 
of thing [1.2] and if you go down to torsion [0.6] the [0.8] lowest one there 
[0.3] it's about point-three of the U-T-S [0.7] so again a three-hundred 
megapascal very weak [0.3] low carbon steel in torsion [0.5] would not [0.2] 
take [0.7] more [0.3] than [0.4] three-hundred-over-three [1.0] er [0.2] about 
[0.2] a hundred megapa-, pascals [0.3] reversed [0.2] twist [0.5] so you need 
to 
think about that if you're designing a torsional suspension for a motor car [2.
4] now then [2.4] this is all very well [1.6] but [1.7] is it true for all 
materials [0.5] and unfortunately the answer it is not true [0.4] for all 
materials [1.7] what i've drawn there [0.2] with these endurance limits [0.5] 
are true [0.6] only [0.3] of [0.2] irons and steels [0.3] as [0.2] for 
practical purposes [0.7] titanium and one or two other funny things perhaps [0.
5] er [0.3] er [0.4] have these sort of features [0.6] but [0.5] the important 
thing [0.3] is and in particularly in terms of normal engineering [0.4] is that 
aluminium alloys [4.0] do not have [0.9] there's no fatigue limit [3.2] so if 
you were to plot these types of things for aluminium alloys [0.5] you would 
have this just going down and down and down and down and down [2.5] and [1.2] 
so [0.3] if [0.2] ten-to-the-six a million cycles [0.5] is the endurance limit 
for [0.5] er steels [0.6] then [0.7] it doesn't level out for [0.2] most [0.3] 
aluminium [0.2] alloys [2.5] you check [0.2] in the books [0.6] which 
particular metals obey [0.5] the endurance limit idea [0.3] and which don't [1.
2] the [0.5] important ones [0.4] 
as i say are the ferrous [0.2] and [0.4] aluminium [0.2] alloys [1.2] but what 
does that mean [1.0] what does that mean if you want to design an aeroplane [0.
6] which is made [0.2] mostly [0.2] out [0.2] of [0.6] aluminium [0.4] alloys 
[2.7] 
sm0830: has to be scrapped after ten years 
nm0827: [laughter] [0.5] ten years [0.5] no well good idea [0.5] well [0.2] the 
implication of this is that of course you cannot design for infinite life [0.5] 
that is very true [1.3] and what it does say is that you have to be very very 
careful about inspections [1.1] you have to look for cracks it's cracks that 
we're dealing round to and i'll be showing you some pictures of fatigues in a 
minute [0.9] you have to look [0.2] for [0.5] er cracks [0.6] now [1.0] of 
course [0.2] if you have [0.4] a piece of steel [0.6] and you [1.1] are [0.2] 
in an application where [0.7] you don't want it to last [0.3] more than a 
million cycles [0.8] then you don't have to limit yourself to working below 
here you can work up here [1.3] and a typical example of that would be a gun 
barrel [0.5] think of the old naval guns [0.2] you know twelve inch shells 
whatever [0.7] i'm reading a book at the moment by Edmund Blunden called 
Undertones of War 
about all the ghastly things in the trenches in the First World War and he goes 
on about these [0.4] whizz-bangs that go over [0.5] and [0.3] you know these 
are [0.2] ten inch shells which just plop in the mud [0.2] and they're duds 
they don't go off [1.3] if they do go off [0.3] he wouldn't have been around to 
[0.6] write the book [0.8] anyway these big gun barrels you're not going to 
fire that barrel [0.3] a million times [0.2] naval guns [0.4] if you read 
Jane's Ships and things like that naval guns [1.0] those big guns were not even 
after things like Jutland were not fired that many times [0.6] so you might 
argue [0.4] that you could be in a thousand cycles [0.2] and so you could 
design [0.4] at the higher stress level [1.2] if you design at the higher 
stress level of course you want less material [0.8] so it's this weight [0.2] 
business that comes into this [1.4] and this is important in relation to 
aluminium because of you know [0.4] space vehicles aerospace [0.5] light [0.3] 
weight [0.5] materials [0.3] very high specific strengths toughnesses and so on 
and so forth [0.5] so [0.9] you don't have to go 
below there but if you want the thing to last for a long time and you don't 
want your customers coming back and saying oi i you know bought something from 
you and it's broken [0.5] you don't want to have the reputation of being the 
Arthur Daley of er engineering design or whatever it is [0.5] then you have to 
[0.2] think about these things and of course there are standards which say [0.
4] you [0.2] must [0.2] design below these stresses if it satisfies this 
particular standard [0.7] but you don't have to and in some circumstances you 
needn't [0.6] but the problem is [0.4] that [0.3] although this part of the 
diagram is called the [0.3] finite [0.3] life [1.2] region and of course this 
is the infinite [0.2] life [0.5] region [0.9] you have a problem with the 
aluminium alloys 'cause you don't know where you are [0.7] because it's all [0.
3] finite [0.2] life [5.3] there is not an infinite life with those things [1.
8] you've still got a design [0.2] you still have to tell people how good or 
how bad [0.3] aluminium alloys are [0.5] so what happens is you still quote [0.
3] this value here [0.6] in the same way that you quote this value here [0.3] 
even though it [0.2] doesn't [0.2] plateau [0.2] out [1.8] and you don't call 
it the endurance limit [0.6] you call it the fatigue limit which was the other 
word you see [1.7] er those of us like me who tend to be a bit sloppy we use 
the things in-, [0.2] interchangeably [0.8] but strictly endurance limit is the 
ferrous thing and fatigue limit is a chosen value [0.7] at a given number of 
cycles