Continuum Mechanical Investigatious on Microstructures

Schiltges G.

The mechanical characterization of microstructures, i.e. structures whose characteristic dimensions are in the μm-range, is the main topic of this thesis. To achieve this goal, an approach is chosen which might be called downscaling. This means that the microstructures are tested and analysed with the same techniques as known from classical material testing, but adapted to the specific problems and needs of small dimensions.The specimens used during this work consist of two different materials. The silicon samples were produced by anisotropic wet etching. The metallic specimens, either pure Ni or NiFe alloys, were made with the LlGA technique.One of the main problems with mechanical tests on microstructures is the determination of the geometrical dimensions. The accuracy of the results obtained in any structural analysis is mainly dependent on the accuracy in the dimension measurement. A possible way of how fairly accurate measurements can be achieved is shown, and an error analysis is made.Two main characterization techniques are used in the present work, static tou-sional tests and dynamic resonance tests. The dynamic tests allow the determination of the elastic constants by measuring the resonance frequency. This is done for several modes, beam modes as well as plate modes. As some of the materials investigated have a non-isotropic behaviour, an orthotropic model is used. Foul out of nine constants have an influence strong enough to allow their cletermination. To solve the inverse problem, i.e. deduce the elastic constants when knowing the resonance frequencies. an iterative least square procedure is used, involving numerical and experimental data.During the dynamic tests, higher harmonic excitations of the specimens are observed. This behaviour can be traced back to two different sources. The excitation signal is not a purely sinusoiclal sigial, but also contains higher harmonics. This is however not sufficient to explain the behaviour of some modes. It is shown that a non-linear model is quantitatively in good agreement with the experimental results. Possible reasons for the non-linearity in the mechanical system are discussed.The static test is performed using a specially designed torsional setup. The main difficulty consists in the measurement of the tiny torques occurring during the test. This problem is solved with a self-built differential torque-sensor, allowing measurements in the μNm-range, with an accuracy of 3% of the nominal value, and a resolution of less than 0.1 μNm. The working principle of the sensor is based on the fact that the toque acting in the microsample induces a rotation of a rigid part of the sensor, which is connected to a spring. By measuring the displacement of the rigid part at two different points, the torque can be deduced. It is important to notice that no friction9 caused either by torque or longitudinal forces, occurs in the sensor. The torsional setup leads to results in the form of torque-rotation diagrams. By analysing these structural responses, it is possible to calculate the dominating elastic constants, e.g. two shear moduli. This is done with the same mixed numerical experimental technique as applied during the resonance tests. The results obtained by the two different tests are in good ngreement.The knowledge of the elastic constants is a necessary condition for the determination of failure criteria. Due to stress concentrations in the silicon sample, failure always occurs at one of the notches present due to the fabrication process. An energy criterion, based on surface energy considerations, is formulated with the help of numerical simulations. For metallic specimens? both von Mises’ and Tresca’s hypotheses are formulated. The critical equivalent stresses found at the beginning of yielding lie between the equivalent stresses of von Mises and Tresca.