|Reflective structures such as space mirrors, silicon wafers, solar reflectors, microelectronic devices to name a few, are made of stiff and brittle materials. They often suffer deformations and catastrophic failure when subjected to thermo-mechanical stresses. In these situations, accurate quantification of mechanical stresses and deformations is essential for safety and structural integrity. Non-contacting methods to perform such measurements at relatively high sensitivities and low cost are important when small deflections are to be detected and quantified.
Motivated by these, a full-field optical technique called reflection-mode Digital Gradient Sensing (r-DGS) has been extended in this thesis to the measurement of small angular deflections of light rays (~10x10-6 radians) reflected off a specularly reflective surface when subjected to non-uniform quasi-static or dynamic stress fields. The working principle of the method along with its governing equations relating angular deflections of light rays to surface slopes is explained.
The feasibility of the method to study deformations in thin plates is first demonstrated under quasi-static conditions by quantifying out-of-plane deflections of a thin silicon wafer subjected to controlled loading and boundary conditions. The measurements performed on a clamped circular plate subjected to a central deflection are successfully compared with the theoretical solutions. The curvatures are also evaluated from the measured surface slopes and compared to their theoretical counterparts. From the measured slope data, surface topography is successfully deduced through numerical integration. Following these baseline experiments, the method is extended to the measurement of surface slopes during stress wave propagation in a thin plate by coupling r-DGS methodology with high-speed photography. Time-resolved measurements for the problem of a thin ‘free-free’ PMMA disk subjected to projectile impact by a steel ball is selected for this demonstration. The surface slopes in two orthogonal planes have been successfully measured during the transient event and used to evaluate topographical informa-
tion. The topographic measurements are successfully complemented using 3D elasto-dynamic finite element computations.
Next, the feasibility of r-DGS method to detect disbond and damage in layered plates is demonstrated. First a disbond detection study is carried out on an adhesively bonded bi-layered PMMA plate with an embedded defect. Subsequently its applicability is extended to detect delamination caused by the mechanical impact on glass fiber reinforced epoxy composite sheets. Thermal excitation of the damaged plates is used in these experiments to induce deformations and detect the resulting manifestations of the defect or damage by examining aberrations in the surface slope fields. The methodology is also employed to demonstrate the method’s feasibility to map thermo-mechanical deformations of flip-chip silicon-die attachments to a ceramic substrate.
The r-DGS method is finally extended to study fracture mechanics problems by mapping surface slopes in the close vicinity of a deformed crack tip in edge cracked specimens under mode-I and mixed-mode (mode-I/II) loading conditions. Both quasi-static and dynamic loading configurations involving inertially loaded stationary crack and growing crack are studied and the corresponding stress intensity factor histories are evaluated. The stress intensity factors measured in these cases are in agreement with the analytical or finite element results demonstrating the feasibility of r-DGS to experimental fracture mechanics.