A Phenomenological Discrete Brittle Damage-Mechanics Model for Fatigue of MEMS Devices With Application to LIGA Ni

A Numerical Fatigue Damage Model for Life Scatter of MEMS Devices

“…In addition, Table II lists the Weibull slopes and strengths obtained. As expected, the values of both the Weibull slope and strength obtained using the inhomogeneous elastic modulus is lower than the ones calculated using the uniform elastic modulus, which is similar to the results of Slack et al [28]. The Weibull slope of initiation lives of the specimens with inhomogeneous elastic modulus is equal to 8.77 which is significantly lower than the value 20.19 obtained for the uniform elastic properties.…”

“…Considering the initiation lives, the effects of the internal voids are still more noticeable, the Weibull slope is 0.77, and the strength decreases from 9228 cycles to 1732 cycles. As expected, the introduction of the internal voids decreases dramatically the fatigue lives and increases their scatter, as observed by Slack et al [28]. Table II summarizes the results obtained in this section.…”

“…Using the Voronoi FE framework gives the advantage and ability to calculate the deformation and stress distribution of domains with arbitrary microstructural topology. In addition, the current model considers both crack initiation and propagation stages, and concludes that much of the fatigue life is spent in the initiation stage, as described by Slack et al [28]. In this investigation, 31 MEMS specimens with different microstructural distributions are considered under the cycling loading to estimate their fatigue lives and evaluate the scatter existing between the lives due to the different randomness sources.…”

“…Zavattieri [26] and later, Zavattieri and Espinosa [27] showed that Voronoi polygons having random shapes and sizes can be used to simulate the grain structure of polycrystalline materials and its consequent effects on the fatigue life. Recently, using the Voronoi tessellation in a discrete element framework, Slack et al [28] proposed a discrete damage mechanics model to study the fatigue of MEMS devices. They assumed that much of the fatigue life is spent in the initiation stage and therefore only considered this stage.…”

“…For this purpose, damage mechanics approach developed by Kachanov [29], Robotnov [30], Chaboche [31], Memon et al [32], and Slack et al [28] is incorporated into a Voronoi finite element model (VFEM) developed by Jalalahmadi and Sadeghi [33]. The model developed for this investigation relates the fatigue life to a damage parameter D which is a measure of the gradual material degradation under cyclic loading.…”