Rate-dependent fracture of a silicon/epoxy interface under mixed-mode loading conditions




Yang, Tianhao

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Rate-dependent fracture has been observed for many polymer-based interfaces, where both the interfacial strength and adhesion energy (or fracture toughness) often increase with increasing separation rates, while the opposite trend typically defines the behavior of the bulk polymer. This dissertation mainly addresses the following two aspects: the characterization of the rate-dependent fracture for a silicon/epoxy interface under mixed-mode loading conditions, and the development of a multiscale, mechanism-based model for simulating rate-dependent fracture at interfaces. First, nominally mode-I fracture experiments were conducted with double cantilever beam (DCB) specimens. Symmetric displacement control was enforced at the loading point, while the separation rate was varied in order to examine the rate dependence. A beam on elastic foundation (BEF) analysis was adopted for estimating the crack length and J-integral. An iterative approach was used to extract the interfacial traction-separation relations (TSR), which exhibited a noticeable rate dependence as both the interfacial strength and fracture toughness increased with increasing separation rates. Motivated by this observation, a rate dependent cohesive zone model was developed, where the damage evolution within the cohesive zone is determined by a thermally activated bond rupture process. The rate-dependent cohesive zone model was implemented via a finite difference method to solve the DCB problem numerically. The model parameters were extracted by comparing the numerical results with measurements. Next, to improve the modeling of the rate-dependent fracture, a multiscale mechanism-based approach was proposed to include the entropic effects of polymer chains and a nonlinear energy barrier for bond rupture. A rate-dependent cohesive zone model was developed from the bottom up at four levels: the bond level, the chain level, the interface level, and the specimen level. Bonds are described by a potential energy function (e.g., Lennard-Jones potential) with an equilibrium bond length and a bond energy. A series of bonds form a molecular chain, which is modeled as a freely jointed chain (FJC) with stretchable bonds. Then, with a large number of molecular chains at the interface level, the chain survival probability follows the thermally activated bond rupture kinetics with a microscopic time scale, leading to a rate-dependent damage process for the interface. Here, an interface with statistically distributed chain lengths is also considered. To compare with the fracture experiments at the specimen level, the interface model was implemented via a user-defined surface interaction subroutine (UINTER) in the finite element package ABAQUS for numerical simulations. With a few parameters extracted for the molecular structures of the interface, the model was able to reproduce the rate-dependent fracture of the silicon/epoxy interface under mode-I conditions. Finally, the rate-dependent fracture for the same interface was examined under mixed-mode loading conditions. A dual-actuator loading device was designed and developed to achieve a full range of the mode-mix with DCB specimens, where the two displacements at the loading end can be controlled independently. For each mode mix, the ratio of the end displacements between the upper and lower beams was kept a constant, while the rate effect was examined by varying the displacement rates proportionally. The nominal phase angle of mode mix at the initial crack tip was correlated to the displacement ratio based on the linear elastic fracture mechanics (LEFM) analysis. The balance condition was naturally satisfied via the symmetry of the specimen configuration (silicon/epoxy/silicon), so that the direct extraction of the crack-tip TSRs was made possible by a decoupled beam interaction analysis using only the far-field measurements including forces, displacements and rotations at the loading end of the specimen. The mixed-mode interfacial fracture was found to be rate dependent as both normal and shear components of the interfacial strength and toughness increased with increasing displacement rates. A BEF analysis with an extension for shear interactions was used to estimate the crack growth and the local separation rates in both the normal and tangential directions. It turned out that the local separation rates varied as damage evolved across the interface, thus leading to a locally history dependent fracture behavior. These findings underline the importance of the local separation rate and history on the interfacial properties and provide insights for further model developments.


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