Investigations on the fatigue and crack growth behavior in resonating microbeams [thesis]

Andrea Cambruzzi, Jürg Dual, Hans-Jakob Schindler
2010
An increasing number of devices, whose sizes are well below that of the conventional mechanical components, have been fabricated and some of them are already available on the market. In this emerging field of micro-electro-mechanical systems (MEMS) the reduced dimensions have enabled to exploit several new possibilities, but they have also induced the need to face as many new challenges. In this work just one of these challenges has been examined, namely the mechanical reliability of these
more » ... es during service life. Silicon and polysilicon are the most well established materials in the microfabrication processes, but they are intrinsically brittle and may be damaged by an overload or by a mechanical shock. Metals, instead, are known to have a better toughness and they can be processed by a still increasing number of fabrication technologies (LIGA, EFAB, microforging...). On the other hand, fatigue can be a serious issue, when the metallic component is subjected to a large number of loading cycles. The data obtained by testing samples of conventional size may not be applicable to microcomponents due to the difference in the fabrication process and to the potential occurrence of a size effect. Therefore it is important to find a methodology to investigate the fatigue properties in metallic microsamples at their typical size. A scaling approach was employed to characterize the material properties: conventional fatigue and fatigue crack growth experiments were performed on specimens in bending with a decreasing characteristic size. Conventional testing setups may also be scaled down to measure the tiny forces and displacements, but a large effort must be spent in ensuring the accuracy of the measurements. The resonating method described in this work can be quite easily implemented and the accuracy of the velocity signal is guaranteed by a laser Doppler interferometry technique. When the excitation frequency is controlled by a phase locked loop feedback system, the microspecimen can be maintained in resonance condition and its resonance frequency can be determined with very high precision (down to 1ppm). Therefore monitoring the frequency drop during the cyclical loading is an appealing and size-independent method to measure the compliance increase due to the presence of a crack in fatigue crack growth experiments. Firstly, a model describing the dynamic behavior of the control system has been xi Abstract built to understand the effect of the controller parameters on the resulting measurements. Choosing the parameters is a trade off between the noise reduction and the capability of the system to track a sudden frequency change. Moreover it was demonstrated that the presence of a resonator coupled with the control system does not reduce the stability of the system, but, on the contrary, it reduces the overshooting of the phase error during the transients. A phase locked loop based on a phase-frequency detector was implemented to improve the robustness of the system and to decouple it from the amplitude feedback control. Secondly, the microfabrication procedure of the UV-LIGA microbeams based on the SU8 thick photoresist is described. The encountered processing weaknesses and the proposed solutions are discussed. The microstructure of the samples was observed by means of the ion channeling contrast in a dual beam microscope. The grains have a columnar structure oriented in the thickness direction with a diameter of roughly 2 µm. The samples have also been characterized by a tensile test and an attempt has been made to measure the toughness: due to the presumed high toughness value, the samples have failed by plastic shear. A model based on the linear elastic finite element method has been developed to calculate the crack length and the stress intensity factor from the frequency and the amplitude of the sample oscillations. Some corrections accounting for the effects of the crack tip plasticity and the plasticity induced crack closure have been presented. The accuracy in the crack length measurements was found to be in reasonable agreement with the measurements performed in a scanning electron microscope. Further investigations on the dynamic response of the samples have been accomplished to explain their nonlinear behavior, which could affect the accuracy of the model. It has been demonstrated that typical bending-longitudinal geometrical nonlinearity has a negligible influence at the considered oscillation amplitude, but the material nonlinearities in the metallic samples may be relevant. This material nonlinearity has been mathematically explained by a model containing a quadratic hysteresis in the stress-strain relationship. The high cycle fatigue behavior of the microbeams with 120 µm and 60 µm width has been measured. No significant differences were observed between the two types of samples, but the fatigue resistance has been found to be comparable to the hardened bulk nickel values. In the fatigue crack growth experiments on the notched microbeams (width 120, 60, 30 µm) it was found that the loading rate has an influence on the measured experimental data. This phenomenon has been qualitatively explained by the plasticity induced crack closure effect. No net trend has been recognized comparing the different sizes except for a slight increase in the stress intensity factor threshold for the smaller beams. In all the specimens an unusual steep Paris curve has been measured. This effect can be explained by the narrow stress intensity factor range measurable at this scale and its proximity to the threshold region. Despite the high yielding stress of these samples, the small
doi:10.3929/ethz-a-006113270 fatcat:ldce65a53jbzre6fq5tljr3rli