Study of fracture and stress-induced morphological instabilities in polymeric materials

We study the phenomena of fracture in polymers at the molecular and continuum level. At a molecular level, we study the failure of polymer/polymer interfaces. Our main focus is on a specific mode of failure known as chain pull-out fracture, which is common to weak adhesive junctions, and polymer blends and mixtures. In the case of the interface between incompatible polymers, reinforcement is achieved by adding a block copolymer to the interface. We introduce a microscopic model based on Brownian dynamics to investigate the effect of the polymerization index N, of the block connector chain, on fracture toughness of such reinforced polymeric junctions. We consider the mushroom regime, where connector chains are grafted with low surface density, for the case of large pulling velocity. We find that for short chains the interface fracture toughness depends linearly on the polymerization index N of the connector chains, while for longer chains the dependence becomes N 3/2. We propose a scaling argument, based on the geometry of the initial configuration, that accounts for both short and long chains and the crossover between them.; At the continuum level, we study the pattern selection mechanism of finger-like crack growth phenomena in gradient driven growth problems in general, and the structure of stress-induced morphological instabilities in crazing of polymer glasses in particular. We simulate solidification in a narrow channel through the use of a phase-field model with an adaptive grid. By tuning a dimensionless parameter, the Péclet number, we show a continuous crossover from a free dendrite at high Péclet numbers to anisotropic viscous fingering at low Péclet numbers. At low Péclet numbers we find good agreement between our results, theoretical predictions, and experiment, providing the first quantitative test of solvability theory for anisotropic viscous fingers. For high undercoolings, we find new phenomena, a solid forger which satisfies stability and thermodynamic criterion. We further provide an analytical form for the shape of these fingers, based on local models of solidification, which fits our numerical results from simulation. Later we study the growth of crazes in polymer glasses by deriving the equations of motion of plastic flow at the craze tip, and the steady-state velocity profile of this flow. By developing a phenomenological model, we solve the full time-dependent equations of motion of this highly non-linear phenomena. Our simulation produces the steady-state cellular pattern observed in experiments. We further show that polymer glasses with lower yield stress produce cellular patterns with sharper tips and more cells, indicating instabilities with smaller wavelengths.