What are the factors that determine tire wear over a race?

[Ciro Pabón]

I'll always remember the soil mechanichs class that our teacher, Otoniel Fernandez, gave us once upon a time.

He started to explain that you could have to deal with elastic materials. While he spoke, he was all the time bouncing from the class floor a little ball that he had in his hand. He asked us what kind of material the little ball was made of. We all answered "It's an elastic material!". After all, the thing was bouncing from the floor (and with a lot of energy...).

Then he explained us what a plastic material was. To our amazement, he took the little ball, stretched it, and it behaved like a chewing gum: the thing stretched and kept its new form. He asked again what was that thing. Some of us answered "plastic", some others, including me, said "elasto-plastic".

Finally, he started to explain what a viscous material was. When he finished his explanation, he called to our attention the little ball: he had left it on top of his desk, and the thing had "flowed": after a few minutes it looked like a pool of goo. He asked us again what kind of material that was. We said "visco-elasto-plastic". He explained then, what a thixotropic material was: like mike_s says, it's a material that changes his stress-strain modulus depending on the not only on the speed of the load but also on its duration. The longer you sustain the load, the less viscous is the fluid. When you shake it, the thing flows (like ketchup, for example). Most real world materials behave this way, even if minutely or at high stress. I've seen paints that stick to the brush but distribute evenly when applied: they are thixotropic, like many gels and colloids.

We asked him if the little ball was made of a thixotropic material. He smiled. He never wanted to tell us what that thing was, but he told us that soil (mainly clays, whose internal forces are entirely electric) and asphalt behave like that.

Many years later, my best guess is that it was silly putty (the clay used as a toy). I'm still not totally sure, but what I understood instantly in this class, is that the best teachers don't give you answers: they give you questions that may take you years to understand and a whole life to "feel in your guts".

[Mikey_s]

Great anecdote Ciro!

I spent several years of my early career playing around with a rheometer looking at flow properties (mainly of bitumen and polymer blends, but also some other materials). Silly putty is a fascinating material and is a rather extreme example of a visco-elastic material - but I think it it is not too different from some of the tyre compounds used in F1. I once attended a training course on rheology and there were peole from all sorts of industries there, including a girl from Heinz who was using a rheometer to look at flow properties of tomato paste for ketchup. Since then I think about it every time I see some ketchup. They design in a yield stress so that you have to hit the bottom of the bottle to get the material to flow out onto your plate, then it is supposed to stop in a neat blob! There were loads of other applications that are not immediately obvious; 3M were looking at magnetic slurries for spreading onto video tapes, Glaxo Wellcome were looking at ointments to get the right "feel" as the ointment was rubbed in, and a veterinary hospital was looking at vaginal mucus from cows (yuck!) to determine the right time to breed! A colleague of mine was looking at non-linear behaviour in brain tissue for the Ministry of Defence (to see whether ejector seats would damage the pilots brain!). It's a fascinating field...

Persovik,

the squash ball analogy may not be the best one for tyre performance, but it does illustrate some of the aspects if the discussion rather well (I'm a keen squash player btw). As ReubenG points out the mathematical models used for analysing flow prperties are approximations (as with any model), but for the most part they do describe performance rather well. When the squash ball is cold it doesnt bounce at all well. The viscous component is dominant, so when you drop or hit the ball the energy is dissipated and the ball does not bounce; the energy is dissipated as heat, so the ball starts to heat up. As it heats up the viscous modulus reduces in magnitude, to a point at which the elastic component becomes the dominant component of the ball stiffness. The air inside the ball also heats up, increasing the pressure and pumps the ball up a bit too.

The key point is to remember that if heat is generated there is a dissipative process occuring and energy is being lost - such processes are not elastic; elasticity is, by definition, recoverable.

Lots of things are changing as the tyre is used; temperature, stress, chemical changes to the rubber. As ReubenG said, there are linear and non-linear effects to take into account too. All of these make tyre selection and formulation something of an art (with a HUGE dose of science behind it). It is very complex and too difficult to describe concisely in a short forum response... but the underlying principles are quite simple... if there is heat being generated then there are dissipative forces at work... not elastic!

[Ciro Pabón]

Thanks, mikey_s: now you know how you can use a little silly putty to intrigue people in your next class... I've done it.

I am keenly aware of chemical changes in asphalt. Rubber is a polymer of isoprene: is like a train of carbon atoms. Chemical (or mechanical) changes include the breaking of the polymer. This diminishes its elasticity, like when you compare a short spring with a long one. The long spring "gives" you more strain before the "spring" is fully compressed. In the case of asphalt, what happens is that long "asphaltenes" break and convert into shorter "maltenes" (I'm not sure about the english names for that stuff, perhaps Mikey_s knows). This happens mainly because ultraviolet radiation and mechanical action of loads.

To sum up: in Colombia we design the places where the cars go at low speed with a thicker asphalt surface, to allow for the rheological changes, like the ones Mikey_s describes that happens in ketchup. This is notorious in toll plazas, for example, or in parking lots, specially with the high temperatures we have here. We tend to follow "rational" asphalt design methods, like the Shell one, instead of "empirical" methods, like AASHTO, because of that.

Secondly, when we do asphalt recycling we tend to use "rejuvenators", that include long polymer chains, to compensate for the chemical changes in the asphalt mix.

[Mikey_s]

Apologies to the others for a somewhat off-topic response, but...

Ciro, the silly putty was already used! we (European bitumen association - the outfit i am currently working for) ran an international workshop on rheology in 1999 - Silly putty made it into the opening address where one of the speakers walked on stage and bowled a ball to another speaker who played it with a cricket bat. then placed it on the lecturn as he opened the workshop - during the speech it dribbled down the front of the lectern!

In the case of asphalt, what happens is that long "asphaltenes" break and convert into shorter "maltenes" (I'm not sure about the english names for that stuff, perhaps Mikey_s knows). This happens mainly because ultraviolet radiation and mechanical action of loads.

Ciro, the names are the same, but in practice the mechanism of ageing of bitumen (asphalt cement) is not as you describe. In fact under the influence of ageing the asphaltene content tends to increase as resins in the maltene fraction condense (by reaction with oxygen) to form larger molecules - there is a clear increase in molecular weight and polarity of the bitumen over time. In respect of the mechanical properties the stiffness (complex modulus) of the bitumen increases and the material becomes brittle. Both the elastic modulus and viscous modulus increase, with the elastic modulud increasing somewhat faster at long loading times - hence the predominant failure mode for aged pavements is cracking, rather than deformation. Delighted to hear you use the Shell Pavement Design Method! SPDM was one of, if not the first analytical design methods.

Back on topic; chain scission of the polymer probably is probably not a large effect in tyre performance evolution (although it definitely happens in asphalt mixtures) - it tends to occur as a result of oxygen attack on the unsaturated double bonds in the polyisoprene, or polybutadiene section of the copolymers - but my sense is that the crosslinking agents will be working in the opposite direction and leading to an increase in molecular weight (with a resultant increase in complex modulus, and a reduction in viscous component). Nontheless, it is a fascinating and highly complex field to think about (if that's what interests you!)

[Ciro Pabón]

@Mikey_s: I took my "silly putty class" in 1986... I think Mr. Fernández probably took his example from another person, I don't believe he "invented" that "demonstration". He is a brilliant person, anyway: he is one of the few persons that has achieved a perfect A+ engineering grade at mexican UNAM university, one of the largest in the world. I agree with Mikey: tire aging does not include "environmental" aging, of course, as F1 tyres are good for a few hours or days and I doubt very much they are stored longer than a few weeks.

What I've read (and that Mikey_s explained somehow) is that the "liquid" phase of the rubber compound exudes from the tire when heated and that the exhaustion of this "liquid" is what determines the life of the Formula One tire. Of course, this is not true for regular tyres.

I've probably mentioned that to you, however, this is the source of my "knowledge", in the remote case you haven't read it:

http://unisci.com/stories/20022/0612023.htm

I quote from that article:

What do Formula One racing tires have in common with fly's feet? This apparently bizarre question can be answered with the aid of physics: They are both soft and supple and exude a more or less sticky liquid.

The original article (it's not free):

http://prola.aps.org/abstract/PRL/v87/i11/e116101

In certain modes of vibration and at certain frequencies, the modulus of elasticity can increase a thousandfold (not free, also), with the consequences you can imagine for heat dissipation:

http://scitation.aip.org/getabs/servlet ... s&gifs=yes

So, if you believe the theory F1 tires are "sucked dry" instead of being simply "weared away" like regular tires. How is this influenced by more downforce, I don't know.

[persovik]

What I've read (and that Mikey_s explained somehow) is that the "liquid" phase of the rubber compound exudes from the tire when heated and that the exhaustion of this "liquid" is what determines the life of the Formula One tire. Of course, this is not true for regular tyres.

Hmmm, I find that quite hard to believe.......and it goes against everything I ever learned about tyres (bearing in mind that I obviously don't know too much about rubber)
The tyre goes harder and less grippy from 'normal' chemical hardening when heated (vulcanisation) It also goes harder from the rather quick changes that occur in styrene at temperature, which can leave the surface of an worn tyre almost plastic-like when cold.

Back to what I don't understand; viscousity in rubber. Can one assume that the elastic property of a rubber (if you ignore aging) is more or less unchanged within normal operating temperatures, and any changes is due to viscousity changes? Will a bouncy rubber be less likely to change behaviour because the viscous element is smaller?

Final question, since you all seem to be bitumen experts: Is mixing recycled rubber into the bitumen a complicated and expensive process, og can anybody do it, assuming they have got the standard roadpaving equipment?

I'll try to answer the original question:
Factors like track temperature and track abrasity (age of the tarmac, what sort of rock has been used as filler, surface structure) are obviously important. A track that has been well rubbered in is kinder on the tyres than a 'green' track. A dusty track causes more wear than a clean track.
Long corners are hard on tyres, you enter with slightly cold tyres, have optimum temperature mid corner and exit the corner with tyres that are slightly overheated. A track of unifirm character is kinder than a track that can be divided into two or more parts of different character. Low speed corners are often quite bad because the driving style will often be more agressive with turn in understeer and wheelspin at the exits.
Traditionally, very stiff diff-settings are tyre killers, a stiff diff causes turn in understeer and high wear on the inside rear, but todays very advanced 'magic' diffs are a lot kinder.
The setting of the traction-control has a big influence as well: Increasing the speed-difference between front and rear wheels by as little as 1 km/h in a front-rear difference monitor or allowing as little as a single degree extra wind up in a shaft speed oscillation monitor can easily increase wear by 50%.
Getting wheel angles slightly wrong or having the wrong tyre-pressure are big factors, often the wrong settings are forced upon the team as a compromise to solve a handling problem or more often a problem with getting heat into the tyres.
Having the wrong nut behind the steering wheel also causes a lot - or very little tyre wear, depending on what is wrong with that particular nut.

[Mikey_s]

Persovik,

rheological models (like most models, and as has already been said) are used to describe behaviour. The flow properties of viscoelastic materials are also very complex and sometimes it is easier to describe using examples and also going back to some basic principles;

Let's start with water, a nice newtonian liquid; it has viscous properties, i.e. it will flow under an applied stress in a rate determined by the magnitude of the stress, but it gets stiffer when you change the loading frequency because the molecules simply cannot get out of the way of each other, so water is nice and soft if you gently press (long loading time) your finger into it, but if you hit it hard (short loading time) it feels quite hard. So the properties are loading time dependent and the "stiffness" (complex modulus) increases as the loading time decreases and this will go on more or less indefinitely so that if you were to fall into water at high speed it would be just as fatal as falling onto a concrete floor. Take another viscous material; syrup. as you heat it up the viscosity reduces (it gets runnier), and as you cool it down the viscosity increases (it gets thicker).

Elastic materials tend to have a stiffness (complex modulus) which is relatively independent of loading time, but can be affected by temperature (i.e. the spring can be less stiff at higher temperature). The stiffness of viscoeslastic materials is described by the complex modulus, G*, which is the square root of the elastic modulus squared plus the viscous modulus squared. Depending upon the loading conditions and the temperature either the viscous component, or the elastic component will dominate the complex modulus. As the temperature of a tyre increases the viscous component will a) reduce in viscosity (allowing the elastic components to become more apparent), but also b) loading time will determine whether the modulus is viscous, elastic, or viscoelastic. Short loading times tend to lead to elastic behaviour, but also the viscous component increases in stiffness, pushing the modulus up (think of the water analogy again).

. Can one assume that the elastic property of a rubber (if you ignore aging) is more or less unchanged within normal operating temperatures

With the caveat that I know more than a litttle about rheology, but not so much about tyres... The magnitude of the elastic component (normally) remains unchanged at a given temperature within the linear range of the tyre (it's a bit motre complicated than described above because some polymers have a delayed elastic component which can be temperature dependent) - in other words provided that the rubber is not subjected to very large strains (deformations). But the viscous component will change it's magnitude depending upon loading time and, depending upon the relative contribution of the viscous component, that can influence the overall stiffness considerably.

Will a bouncy rubber be less likely to change behaviour because the viscous element is smaller?

It is probably helpful to try and think conceptually about the tyre construction; There are elastic polymers which behave elastically. There are viscous extender oils and there are fillers which will lead to plastic deformations. Then there are reactive chemicals which will start to react as the temperature increases and crosslink the elastic molecules increasing the stiffness of the elastic component. So in a mostly elastic material (e.g. polybutadiene) there is a very small viscous component) and the complex modulus will be relatively constant over a range of loading times. The complex modulus is dominated by the elastic modulus.

It also goes harder from the rather quick changes that occur in styrene at temperature, which can leave the surface of an worn tyre almost plastic-like when cold.

you are partly correct; Polystyrene is a hard, plastic polymer, but the polymers used in tyres are generally co-polymers, i.e. there are blocks of polystyrene grafted onto blocks of polybutadiene (or polyisoprene, or chloroprene, or etc...) which tend to be soft, stretchy polymers. Of course tehy do change stiffness with temperature, but tyres do not generally see temperatures that would take them to the glassy state (perhaps in northern Canada in winter!!).

Is mixing recycled rubber into the bitumen a complicated and expensive process, or can anybody do it, assuming they have got the standard road paving equipment?

In principle recycled polymers can be (and in practice are) used in road construction. However, even though most people (Ciro and myself excepted!!) consider roads to be fairly low tech, they are, in fact, engineering structures which are designed to accomodate a range of loads and operate over a range of temperatures. Care is required when adding in waste streams as these are (almost by definition) poorly controlled products and variable in composition (the tread and thre carcass of the tyre are made of different polymers, truck tyres are different chemically from car tyres, etc). However, whilst the actual incorporation is not too complex, the chemical composition of the tyre and the bitumen is very complex and there are highly complex mechanical properties which depend on the chemistry. So everything needs to be tightly controlled if it is to be done... finally roads are expensive and inconvenient to maintain, so the entire life cycle needs to be considered when deciding whether it is beneficial to "dispose" of a waste into a highway... happy to discuss in a pm if you are really interested!

[Ciro Pabón]

Is mixing recycled rubber into the bitumen a complicated and expensive process, og can anybody do it, assuming they have got the standard roadpaving equipment?

Short answer: no, it isn't complicated. And, yes, it is expensive. Of course, believe what Mikey_s tells us, in case he corrects me later: he is the scientist, I'm just an engineer.

First, to clarify a little the following, asphalt-rubber mixes (A-R) are defined as mixtures that incorporate at least 15% rubber (from recycled tyres, normally), according to ASTM specification D8-88. Another condition is that the rubber "has reacted with the hot asphalt mix to swell the rubber particles".

The only piece of "extra" machinery you need is the rubber plant. This is a portable machine you incorporate into the asphalt plant to mix rubber and asphalt.

You also need to use widened tips on the "sprayers" in case you spray the material, which is fairly rare in my country. You can spray asphalt only if your country regulations are relatively lax about asphalt seals and you are allowed (and don't care) to contaminate wide areas. The contamination caused by asphalt rubber is said to be similar to asphalt-only mixes, which is (in technical terms ) A LOT. Next time you walk around hot asphalt, remember that the stuff is carcinogenic. I wonder if adding rubber, sulphur and whatnots contributes to make it healthier...

The cost of asphalt-rubber is almost twice the cost of regular asphalt. Promoters underplay this fact, explaining that you can use less thick asphalt layers. Duration of asphalt increases and noise diminishes. You get rid of some tires, that sometimes are a headache at waste disposal sites. Another advantage is that you can use them on top of old portland concrete layers, usually to avoid the "reflection" of the cracks on the asphalt layer, because the stuff is more elastic. One thing I don't like about the asphalt-rubber is that the asphalt plant stinks more than usual: it smells like burned rubber...

Patents expired in 1992 (the process to control the temperature while rubber is added was developed in the 60's by a guy from Phoenix, Charles McDonald). The ASTM specification was published only in 1998.

Back on thread: if you don't believe that F1 tyres (and other racing tyres) get their grip from the exuded "liquid phase", then you are not going to believe the explanation given by Mr. Persson about the "coefficient of friction", but speaking in technical terms, it is "extremely cool". Have you noticed how quick is the class about friction in the university? Until this guy wrote his seminal article, I'd say we hadn't improved our knowledge of friction since the XVII century.

Anyway, let me tell you that his research and equations are used by major tire manufacturers and that his is the first explanation I've seen on how friction works: the larger the downforce, the larger the contact surface "developed" at the microscopic level. The first link I provided explains how the viscosity component is extremely important for Formula One tires.

I don't know for sure if he's right, but I haven't heard competing explanations. Besides, if his explanation is wrong, I wish to know why Formula One tires are so dependent on temperature to develop grip. Anyway, I share your sane skepticism: sometimes I don't believe what I see with my own eyes, much less what I heard from others... What I know is that his equations allow manufacturers to deduce the properties of tyres, just testing a piece of rubber.

So, going away from the "normal" explanations on tire wear for "regular" tyres, and with the caveat about believing things said by others, I'd say that more downforce means you have to use harder tyres, unless you want to "squeeze" their viscous properties faster.

[persovik]

......
Back on thread: if you don't believe that F1 tyres (and other racing tyres) get their grip from the exuded "liquid phase", then you are not going to believe the explanation given by Mr. Persson about the "coefficient of friction", but speaking in technical terms, it is "extremely cool". Have you noticed how quick is the class about friction in the university? Until this guy wrote his seminal article, I'd say we hadn't improved our knowledge of friction since the XVII century.

Anyway, let me tell you that his research and equations are used by major tire manufacturers and that his is the first explanation I've seen on how friction works: the larger the downforce, the larger the contact surface "developed" at the microscopic level. The first link I provided explains how the viscosity component is extremely important for Formula One tires.

I don't know for sure if he's right, but I haven't heard competing explanations. Besides, if his explanation is wrong, I wish to know why Formula One tires are so dependent on temperature to develop grip. Anyway, I share your sane skepticism: sometimes I don't believe what I see with my own eyes, much less what I heard from others... What I know is that his equations allow manufacturers to deduce the properties of tyres, just testing a piece of rubber.

So, going away from the "normal" explanations on tire wear for "regular" tyres, and with the caveat about believing things said by others, I'd say that more downforce means you have to use harder tyres, unless you want to "squeeze" their viscous properties faster.

It was this part I din't believe:

In contrast to dry-weather tires in Formula One racing, which exude resins and actually even out irregularities in the asphalt, thus considerably improving the area of contact, normal tires do not secrete any fluid since the disadvantage of "Schumi" & Co's good road holding properties is the considerable tire wear. Racing tires are literally sucked dry.

This seem to imply that the rubber contains a liquid component that can be squeezed or sucked out of the tyre, like if you filled a rubber sponge with some sticky gel. Isn't it the case that the liquid or viscous phase is bonded to the structure, and while there is viscousflow, the flow is not able to leave the rubber except for a surface to surface bond transfer when temperature and mechanical conditions allow it, i.e. when the bonds of the structure breaks and some of the bonds are able to attach themselves to a new structure?

I believe the friction model.

Thanks for the asphalt info, I'm thinking of getting a gokart track resurfaced, and would like the track to offer a little more grip.