Using far-field measurements for determining mixed-mode interactions at interfaces
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Traction–separation relations (TSR) can be used to represent the interactions at a bimaterial interface during fracture and adhesion. The goal of this work is to develop a direct method to extract mixed-mode TSRs using only the far-field measurements. The first topic of the dissertation deals with extracting mixed-mode TSRs based on a combination of global and local measurements including load-displacement, crack extension, crack tip opening displacement, and fracture resistance curves. Mixed-mode interfacial fracture experiments were conducted using the end loaded split (ELS) configuration for a silicon-epoxy interface, where the epoxy thickness was used to control the phase angle of the fracture mode-mix. Infra-red crack opening interferometry (IR-COI) was used to measure the normal crack opening displacements. For the resistance curves, an approximate value of the J-integral was calculated based on a beam-on-elastic-foundation model that referenced the measured load-displacement data. A damage-based cohesive zone model with mixed-mode TSRs was then adopted in finite element analyses, with the interfacial properties determined directly from the experiments. With the mode-I fracture toughness from a previous study, the model was used to predict mixed-mode fracture of a silicon/epoxy interface for phase angles ranging from -42˚ to 0˚. Additional measurements would be necessary to further extend the reach of the model to mode-II dominant conditions. The second topic of the dissertation addresses characterization of interfacial interactions between copper through-silicon vias (TSV) and silicon substrates. A suitable choice of via length allowed a direct method to be implemented for determining the mode-II traction-separation relation between silicon and copper TSVs. This interface was loaded in a nano-indentation experiment on specimens with pre cracks that were fabricated using focused-ion-beam (FIB) milling. The elastic and plastic properties of the copper vias were characterized from micro-pillar compression experiments and associated finite element analyses. Analytical and numerical models were developed for extracting the parameters of traction-separation relation. The third topic of the dissertation explores a more general approach to directly extract the mixed-mode traction-separation relations using only far-field measurements from laminated beam specimens. Balanced laminated beam configurations were used to conduct the mixed-mode fracture experiment on a silicon-epoxy interface. The far-field measurements included the displacement at the middle of the bottom adherend at a point behind of the crack front, the force-displacement response, and the angle of rotation at the end of the top adherend. With these far-field measurements, the J integrals in mode-I and mode-II could be calculated separately when the ratio between the thickness and the bending stiffness is the same for both the top and bottom adherends. The local separations at the crack tip are also calculated using these far-field measurements. The traction-separation relations are then obtained directly through numerical differentiation of the obtained J integral with respect to the local separations. This method was validated by comparing to the local measurements of normal separation using IR-COI technique. The extracted normal and shear TSR showed decoupled behavior in damage initiation and evolution which indicate that it is impossible to model using potential-based TSRs. A promising attempt was made to subtract out the elastic deformations of the epoxy that was used in this work. This was achieved by conducting a cohesive zone analysis using an extracted pair of normal and shear traction-separation relations for a particular mode-mix without the epoxy between the adherends.