The quartz plate in the ICP system is cracked.what is the reason behind it. Can it be happened because of the RF power coupled through the quartz plate and it can cause some stress in the quartz plate?
Yes. The relevance of this causation depends on the frequency of the RF applied, as the plate will likely be mechanically resonating at that frequency, a harmonic, or a subharmonic, due to piezoelectric effect, possibly causing the crack.
A secondary and much less likely reason is long-term or sudden heating, again dependent on frequency (quartz is not a good conductor of electricity below its dielectric limit).
If the applied voltage is very high, it could exceed the dielectric strength of the plate, causing physical damage (melting and/or cracking) due to the sudden conducting of a current. The dielectric strength of quartz is about 8 × 10e6 v/m.
See details at https://hypertextbook.com/facts/2008/JeffreyWong.shtml etc.