High-resolution optical microscopy for characterising microstructural deformation in microtensile testing.

Imaging surface deformation of a coupon specimen in microtensile testing with an optical microscope presents challenges due to the narrow depth of field (DoF) of optical microscopes. Materials being heterogeneous at microscopic length scale, the sample surface deforms into a complex 3D surface texture, evolving continuously as the loading increases. Because of the narrow DoF, the region that is in focus within the field of view (FoV) decreases substantially in size with the increasing out-of-plane heterogeneous deformation. To address this challenge, a method based on image blending and stabilisation of the captured image frames is proposed. Image blending combines the partial regions that are in focus from a set of successive image frames captured at different working distances from the object surface plane to construct a single image that has a large part of the FoV in focus. The blended images are then obtained at different levels of macroscopic strains, that is the global homogeneous strain, in order to characterise the evolution of the heterogeneous deformation. The image stabilisation removes any misalignments of the blended images by spatially realigning them choosing a common feature as a reference point. The validation of the proposed method with conventionally and additively manufactured stainless steel 316L (SS 316L) specimens demonstrates excellent improvement in image quality. Almost 100% of the FoV is maintained in focus regardless of the amount of out-of-plane heterogeneous deformation caused during tensile testing, which is quite remarkable for optical microscopy imaging. Consequently, the blended and stabilised images enhanced the accuracy of digital image correlation (DIC). Time-lapse videos of the deformation generated using these images captured the evolution of the slip bands and their transmission through twinning boundaries in the stainless steel microstructure. Overall, this study demonstrates the feasibility of using image-processing techniques to advance optical microscopy to image complex 3D surfaces evolving with time.

Generalization of the theory of far-field caustics by the catastrophe theory.

To generalize the theory of far-field caustics, three theorems and several corollaries are presented in this paper. Using the law of reflection and catastrophe theory we have established conditions to predict caustic patterns in a 3-D space, which were created from the reflection of a light beam from an analytically known surface. The general theory was readily reduced to the already known cases of diffraction, indicating the validity of the general theory. Experimental evidence in two simple cases of reflectors, consisting of triangular and rectangular membranes, corroborated the results of the theory.