Short answer: Speaking of age only (as opposed to physical limits of a tire) If you have a full size spare, it should be replaced after exceeding 10 years past the (in the United States, this is the DOT stamped date on the tire) manufacture date. If you have a donut, the same 10 year recommendation applies but not all tires are equal.
Although there is an accepted answer, that answer adheres to government standards designed with safety in mind, my answer is more to inform so that someone understands why their tire would need to be replaced.
Disclaimer: I don't ever replace the donuts on any of my cars because they have been in good condition even at 15, 20 years.
Second Disclaimer: I always get triggered watching tire salespeople tell someone they need to change their donut and quoting them $400 when the tire is in good condition. This generates mistrust in people and results in them being no longer trusting of professionals.
A tire only needs to be replaced once it has reached the physical limits of the tire or the rubber has begun to degrade and fail.
What does physical limits mean
Physical limits of a tire are when the tire is no longer able to perform upto the specification it was manufactured to.
Common limits are:
- Tire tread depth too low. This is because modern tires are designed as water pumps, with inadequate water pumping capability, the tire will hydroplane.
- Support ply has failed or is damaged.
- Tire belt is damaged beyond repair i.e. puncture causes belt separation or "unzipping".
- Tire rubber has separated from interior components.
What does it mean for rubber to degrade or fail
Rubber has degraded once it's chemical structure has changed to the point that the tensile strength, color, shape, etc of the rubber has changed.
Rubber has failed once the material no longer retains its bonds. The material separates, resulting in a tear, hole, separation, etc causing the rubber to no longer be able to support itself.
Think of degradation as the rubber chemically changing, and a failure as a physical change.
Causes of tire degradation and failure
Broad catergories would be:
- Poor Design (causes a tire to be 'abused' in normal conditions)
- Poor Materials
- Poor Specification (poor understanding of materials causes a tire to be 'abused' in normal conditions)
Root causes would be:
- Chemically assisted degradation (think salts, acids, alkalis)
- Excessive heat
- Fatigue (used to generally describe tires used under normal conditions that were designed for but not that the load expected)
- Abrasion (i.e. hitting a curb, also tread wear is just abrasion slowly wearing away the tire)
- Tearing (tire blowouts and belt separations put excessive load on the rubber causing it to tear)
- Excessive pressure or compression (think inflating a tire until it explodes or a tire having to handle an excessive weight load)
- Ozone/UV assisted degradation
Chemicals and Ozone/UV
The kind of chemicals/processes that destroy rubber are well documented on the Wikipedia for polymer degradation. I have quote paraphrased items from the page for things relevant to tires.
Ozonolysis and Ozone cracking
Ozone cracking in Natural rubber tubing
Cracks can be formed in many different elastomers by ozone attack. Tiny traces of the gas in the air will attack double bonds in rubber chains, with Natural rubber, polybutadiene, Styrene-butadiene rubber and NBR being most sensitive to degradation. Ozone cracks form in products under tension, but the critical strain is very small. The cracks are always oriented at right angles to the strain axis, so will form around the circumference in a rubber tube bent over. The problem of ozone cracking can be prevented by adding anti-ozonants to the rubber before vulcanization. Ozone cracks were commonly seen in automobile tire sidewalls, but are now seen rarely thanks to these additives.
Photo-oxidation of polymers
The polymers are susceptible to attack by atmospheric oxygen, especially at elevated temperatures encountered during processing to shape. Many process methods such as extrusion and injection moulding involve pumping molten polymer into tools, and the high temperatures needed for melting may result in oxidation unless precautions are taken.
The Wikipedia article goes into greater scientific detail but the takeaway is that any oxidation based defect is likely to originate from manufacturer. The only other way for oxidation to affect the tire is for it to be exposed to something else that is oxidizing (like iron oxide aka rust).
In early 1990, it was reported that imide-linked resins in CFRP composites degrade when bare composite is coupled with an active metal in salt water environments. This is because corrosion not only occurs at the aluminum anode, but also at the carbon fiber cathode in the form of a very strong base with a pH of about 13. This strong base reacts with the polymer chain structure degrading the polymer. Polymers affected include bismaleimides (BMI), condensation polyimides, triazines, and blends thereof. Degradation occurs in the form of dissolved resin and loose fibers.
CFRP is commonly used in tires, the tldr is salt can corrode some of the material in a tire. Some is enough to cause material degradation.
Chlorine is a highly reactive gas, which will attack susceptible polymers such as acetal resin and polybutylene pipework. In essence, the gas attacks sensitive parts of the chain molecules (especially secondary, tertiary, or allylic carbon atoms), oxidizing the chains and ultimately causing chain cleavage.
Chlorine effectively dries rubber out and damages molecules by reacting with and changing them.
Heat, Abrasion, Tearing, Excessive Pressure/Compression are somewhat self explanatory. The tie directly to the physical limits of a tire.
Fatigue is caused generally by things like inconsistent inflation (i.e. a leaking valve steam causes the user to just air up the tire before every drive), time-driven, generally diagnosable by micro-cracking or what industry calls "dry-rot" (i.e. google michelin dry rot).
There's also another thing I didn't mention above because its hard to see the uniqueness of it as a failure point. In the rubber industry, there a term, 'set', which refers to tension maintained for a period of time and then released.
A good example of this is measuring the stress on an object as an output of strain. Through this we can measure deformation.
Example: You squeeze a basketball and let go. You do it a second time. If the strain put on the ball was equal each time, the stess is equal. Well, if you squeeze the ball so hard it pops, the stress is no longer the same because the ball is deformed.
This is why my friend who drives over potholes everyday keeps having to buy new tires. It is not that the final pothole caused a failure in his tire, the cause is a previous pothole putting so much strain on the tire it was deformed. The tire slowly deforms more as additional strain is put on it, until it fails.
Why on earth have I gone into so much detail about tire failure
Because none of these things happen in a clean dry trunk. If you have never taken the spare out of your trunk/hatch, and there is no moisture in your trunk/hatch. There's nothing to degrade your tire or make it approach it's physical limits.
Why have I never bought a new donut
Armed with my somewhat useless knowledge of rubber and tires, everytime I have had a flat in one of my many 10+ year old cars. I would pull out my spare that I kept inflated along with the rest of my tires. I would inspect it for cracking or signs of degradation. The tire rubber would still be supple and flexible with no signs of impeding doom.
This is not me endorsing driving on a 10+ year old donut.