Fracture and delamination of elastic thin films on compliant substrates : modeling and simulations

Mei, Haixia
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Different fracture modes have been observed in thin film structures. One common approach used in fracture analysis is based on the principle of linear elastic fracture mechanics (LEFM), which assumes pre-existing cracks and treats the materials as linear elastic except for the damage zone around the crack tip. Alternatively, a nonlinear cohesive zone model (CZM) can be used to simulate both nucleation and growth of cracks. In this dissertation, the approaches of LEFM and CZM are employed to study fracture and delamination of elastic thin films on compliant substrates under various loading conditions. First, compression-induced buckling of elastic thin films on elastic compliant substrates is studied by analytical and numerical methods. The critical condition for onset of buckling instability without and with a pre-existing delamination crack is predicted. By comparing the critical strains, a map for the initial buckling modes is constructed with respect to the film/substrate stiffness ratio and the interfacial defect size. For an elastic film on a highly compliant substrate, nonlinear post-buckling analysis is conducted to simulate concomitant wrinkling and buckle-delamination, with a long-range interaction between the two buckling modes through the compliant substrate. By using a layer of cohesive elements for the interface, progressive co-evolution of wrinkling and delamination is simulated. In particular, the effects of interfacial properties (strength and toughness) on the initiation and propagation of wrinkle-induced interfacial delamination are examined. Next, using a set of finite element models, the effects of interfacial delamination and substrate penetration on channel cracking of brittle thin films are analyzed. It is found that, depending on the elastic mismatch and the toughness of interface and substrate, a channel crack may grow with interfacial delamination and/or substrate cracking. By comparing the effective energy release rates, the competition between the two fracture modes is discussed. Cohesive zone modeling is then employed to simulate nucleation and growth of delamination and penetration from the root of a channel crack. By comparing the results from the approaches of LEFM and CZM, the characteristic fracture resistance from small-scale bridging to large-scale bridging is identified. Finally, to determine the nonlinear traction-separation relation for cohesive zone modeling of a bimaterial interface, a hybrid approach is developed by combining experimental measurements and finite element simulations. In particular, both analytical and numerical models for wedge-loaded double cantilever beam specimens are developed. A two-step fitting procedure is proposed to determine the interface toughness and strength based on the measurements of the steady-state crack length and the local crack opening displacements.