## Analysis of stress singularity of adhered contacts in MEMS

##### Résumé

MEMS devices are usually multimaterial systems where interfaces are formed at the junction of two materials. Failure occurs at adhered contacts because of biomaterial stress singularities at interface comers. Magnitude of the stress field induced due to this singularity is given by the value of the notch stress intensity. Hence it becomes very important to design MEMS devices based on the stress intensity-fracture toughness failure criterion. Inherent uncertainty of design parameters (which includes singularity parameters) in MEMS devices necessitates probabilistic design rather than deterministic design. The probabilistic design of MEMS devices, with a microswitch as our device example, has been performed to find the probability of failure of the switch based on stress intensity-fracture toughness failure criterion.
The two main objectives of this research are to determine the stress field around a bimaterial singularity for a given bimaterial specimen and evaluate the probability of failure based on stress intensity-fracture toughness failure criterion using probabilistic analysis.
The scope of work is fourfold. First, the order of the singularity is determined using two different methods, namely, Complex potential method and Airy stress function method. The equivalence of these methods is verified. Second, the influence coefficients are determined using analytical methods. Third, the stress intensity factor is determined using finite element methods. Fourth, the probabilistic analysis of the microswitch is performed based on stress intensity-fracture toughness failure criterion.
The order of singularity has been determined to be 0.512 and 0.696. The stress intensity factor has been determined to be 0.7708 MPa m0.488 from finite element analysis. The probability that the notch stress intensity exceeds the fracture toughness is found to be 0.612.

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