|Shape and surface topography evaluation from measured slopes is of considerable engineering significance in optical metrology and experimental mechanics. These kinematic quantities are often used for metrology of optical and electronic elements, wave front reconstruction and rectification, deformation and damage quantification of structural members, to name a few. In this context, a full-field optical method called reflection-mode Digital Gradient Sensing (r-DGS) based on random speckle correlation principle capable of measuring extremely small angular deflections of light rays (~10-4 degree) is advanced in the first part of this dissertation to quantify surface slopes of thin structures. The measured quantities from r-DGS upon integration can accurately quantify surface topography. Accordingly, a Higher-order Finite-difference-based Least-squares Integration (HFLI) scheme is developed. By combining these tools, high-fidelity quantification of surface topography is demonstrated, and the measurement accuracy is assessed. It is found that the accuracy is influenced by the temporal frequency of the recording device. Ultrahigh-speed digital photography at 106 frames per second resulted in nanoscale (10-20 nm) out-of-plane deformation measurement accuracy over relatively large (75×75 mm2) region-of-interest (ROI) whereas slower recording speeds of 101 frames per second decreased the accuracy to sub-micron values emphasizing the role random vibrations play in this methodology.
Quantitative visualization of both surface slopes and out-of-plane deformations of thin carbon fiber reinforced plates (CFRP) of different layups subjected to dynamic out-of-plane impact loading at microsecond intervals are made next. Again, challenges of measuring extremely small surface slopes simultaneously in two orthogonal directions with microsecond resolution over relatively large ROI are overcome. Furthermore, the surface slopes, differentiated numerically to determine curvatures, allow estimation of in-plane stresses when used in conjunction with the elastic plate theory.
The loading-rate effects on fracture mechanics of unidirectional CFRP are explored in the next part of this dissertation using r-DGS. Fracture responses of single-edge notched multi-layer unidirectional CFRP subjected to symmetric static and dynamic loadings are studied. Effect of different fiber orientations relative to the notch direction is explored. Nominally mode-I fracture occurs when the fiber orientation is 0° whereas mixed-mode (mode-I and -II) fracture ensues in all other fiber orientations (15°-60°) studied. An over-deterministic least-squares methodology for extracting stress intensity factors (SIFs) for propagating cracks is developed by exploiting orthogonal surface slopes measured from r-DGS. Results show that crack-face fiber-bridges offer significant resistance to growth under quasi-static loading conditions; however, the same is found largely absent under dynamic conditions emphasizing the loading rate effects.
In the next part of this dissertation, two modified Digital Gradient Sensing (DGS) methods of even higher measurement sensitivity suitable for studying ultralow-toughness and high-stiffness transparent solids such as soda-lime glass are proposed. These methods are devised by combining r-DGS with the transmission-mode DGS (or, t-DGS). These methods involve an additional reflective surface behind the transparent substrate, either as a standalone reflector or as a rear face reflective film deposition. The former approach, designated as t2-DGS method, offers measurement sensitivity twice that of t-DGS whereas the latter called transmission-reflection DGS or tr-DGS results in more than three-fold sensitivity. The governing equations of tr-DGS are developed and demonstrated for measuring angular deflection fields in the crack-tip region during static and fracture events.
Lastly, tr-DGS and t2-DGS methods are extended to examine the fracture mechanics of soda-lime glass, a high stiffness and low toughness material. Extremely high crack speeds (in excess of 1500 m/s), ultralow failure strain (εf < 0.1%) and highly localized sub-micron scale deformations are among the challenges overcome in this material. These two new methods are applied to map stress gradients around dynamically growing cracks in glass plates subjected to dynamic impact loading and extract fracture parameters. The r-DGS method is also implemented to show the need for higher measurement sensitivity to study such challenging materials.