The mechanical problems in micron and meso-scale underlie the important aspects of research for structural and functional design of advanced materials. One of the examples is to study the finite deformation induced by martensitic transformation, and the formation of the complex microstructures simultaneously. The transformation tensor and its symmetry related martensitic variants are of great importance on the functional fatigue properties. But in-situ experimental mechanics methods to quantitatively characterize the surface reliefs of martensitic materials during the phase transformation are seldomly reported. Another large group of mesoscale mechanics problem is for the micro-electro-mechanical systems. While there are many methods to fabricate various delicate MEMS structures, the qu...[ Read more ]

The mechanical problems in micron and meso-scale underlie the important aspects of research for structural and functional design of advanced materials. One of the examples is to study the finite deformation induced by martensitic transformation, and the formation of the complex microstructures simultaneously. The transformation tensor and its symmetry related martensitic variants are of great importance on the functional fatigue properties. But in-situ experimental mechanics methods to quantitatively characterize the surface reliefs of martensitic materials during the phase transformation are seldomly reported. Another large group of mesoscale mechanics problem is for the micro-electro-mechanical systems. While there are many methods to fabricate various delicate MEMS structures, the quantitative characterization of the structure and deformation of these micro devices is rare. In this thesis, we propose a new experimental mechanics method, optical reflective differential interference microscopy (DInM), designed for quantitative surface topography characterization to study the mechanics problems in micron to meso-scales. In particular, we demonstrate our quantitative optical system to characterize the surface topography of martensitic materials and silicon ribbons on soft substrate quantitatively and dynamically at mesoscale, which is from tens of micron meters to several millimeters. DInM is a contactless real-time characterization method with sub-micron spatial resolution. Compared to other surface topography characterization methods, such as atomic force microscope (AFM) and scanning electronic microscope (SEM), DInM provides a sufficient accuracy for surface topographic characterization with much larger field of view at a much higher frame speed. We theorized that DInM can be applied to characterize the dynamics of deformation at a solid-solid phase transformation, and the buckling process of an elastic thin film on a viscoelastic substrate.

We theorized mathematical models for the single beam-shear DInM and self-developed dual beam-shear DInM. In addition, we designed various subsystems to calibrate the optical components and parameters for the DInM system. Particularly, we employed the localization analysis for charactering the small shear angle of Nomarski prism, which allows for resolving the shear angle beyond the optical diffraction limit. Three different Nomarski prisms are employed to verify our technique and obtain a resolution below 0.5 μrad. Our prism calibration method provides a stand-alone characterization of polarizing prisms with a high accuracy for dual beam-shear DInM. After the calibration and assembling, the DInM method is validated by characterizing the surface topography of a CuAlNi single crystalline martensitic material. The characterized surface topography of the martensitic twins by our system agrees well with the measurement given by the atomic force microscopy. Compared to one dimensional surface height gradient calculated from the height profile measured by the atomic force microscopy, our method directly characterizes the local gradient with 0.005 accuracy.

Our self-developed dual beam-shear DInM can directly measure the time dependent out-of-plane deformation gradient component X_3,I where I = 1, 2. The system quantifies the surface topographic evolution under a sub-millimeter view of field with frame rate of 28 data points per second. Our DInM prototype provides the lateral resolution of 787nm for up to 12% measurable out-of-plane strains. We use our system to characterize the stress-induced phase transformation in NiTi alloy and the dynamic buckling process of silicon ribbon on soft substrate under uniaxial compression. It successfully captures the time evolution of the surface topographies and the full-field deformation gradients during the experiments. In the experiment of NiTi uniaxial loading, our experimental platform quantifies the distortion in elastic transition layer between the austenite and martensite phases. In the experiment of silicon ribbon buckling, several noteworthy dynamic behaviors are revealed and strain rate dependency of two characteristic speeds is reported. The establishment of dual beam-shear DInM opens a new avenue in the field of experimental meso/micromechanics.