To predict remaining useful life of battery what kind of data is required to have, for calculation of the battery life?
This is a very interesting question! I am sure some of the experts in this field will join the discussion. My thoughts on this....
For remaining life calculation of structural materials, first we need to know the critical crack length of the material that promotes unstable crack growth. Such a parameter of batteries is not relevant.
For primary batteries, the lifetime is given by the capacity in terms of mAh by the manufacturer's specification. For example, Duracell AA battery capacity is about 2200 mAh. If you know the circuit load in terms of mA and number of hours the battery has been in use, then it is a simple math to find out the remaining life.
On the other hand, estimation of the remaining useful lifetime of a rechargeable battery is not that straight forward....
For estimating the remaining life of a secondary or rechargeable battery, the required parameter is cycle life of the battery - similar to 'S-N curve' for describing the fatigue life of a material. The cycle life of a battery depends on the discharge condition (0.1 C, 1 C , 10 C etc) assuming that charging rate is a constant. There are several additional parameters that affect the cycle life which is a green area of research!
This paper may give an idea: Energies 2014, 7, 4895-4909; doi:10.3390/en7084895
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