Measure the cranking current (you may need a shunt resistor) and divide the battery capacity by that current.
That will be the upper bound for the cranking duration - actual 'real-world' values will depend on the voltage discharge curve of the battery and will require experimentation to see what types of battery have a given behaviour.
I am not certain what you mean by an accelerated charge cycle,
Do you mean that you want to fully discharge the battery and then find some way of re-charging it super-quickly? Much faster than a normal battery charger would?
If so, there are commercial battery chargers that can place a full charge on a battery in a few seconds but these are quite expensive - around £1500UK. Many battery sales units use them in the UK.
Because it is possible to destroy a lead-acid battery explosively, these units have controls built into them to prevent this - hence the price.
It is possible to simply add a similar battery in parallel that will recharge the first using current dumping. But this will have no safety controls preventing damage to both batteries.
I have seen experimental super-capacitor arrays that can replace lead acid and can be charged in around 30 seconds and they perform much better than the lead acid when cranking engines.
Assuming that a good car starter battery can last for about 2 years in the car before dying, I wanted to know how I can get a new battery and use it in the laboratory to simulate this degradation in a short time, say a month.
The two factors that affect lead acid battery cycle life (number of cycles) are depth of discharge and heat. Both of these accelerate the sulfation of the lead plates.
Discharging a battery to 20% or less sustained charge can reduce the cycle count by 80%. Draining the battery to fully flat each time could reduce the number of cycles down to 100 or so.
Similarly operating in high temperatures (up to 60C) can reduce the cycle count quickly.
To recharge the battery, if you cannot obtain a rapid charger as previously described, then most modern vehicles have excellent rapid charging circuits. Simply connect your test battery in parallel to the vehicle battery using jump leads (as they are known in the UK) - heavy duty cables with 'crocodile' connectors - and run the engine for 20 to 30 minutes. Your battery should be fully charged by then.