Browsing by Author "Schänzel, Lisa-Marie"

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Phase field modeling of fracture in rubbery and glassy polymers at finite thermo-viscoelastic deformations
(2015) Schänzel, Lisa-Marie; Miehe, Christian (Prof. Dr.-Ing.)
The goal of this work is to provide a theoretical and computer based model for brittle and ductile fracture mechanics, which enables the modeling of complex fracture phenomena with large deformations. A central aspect of this work is to provide a comprehensive theoretical study of a phase field model of fracture and its application towards the modeling of crack initiation and growth in rubbery and glassy polymers at finite thermo-viscoelastic deformations. The other main aspects are the development of new algorithms for crack propagation and investigations towards the predictive quality of these new methods. Fracture is the partial or full separation of an object or material into two or more pieces under the influence of stress. In 1920, Griffith introduced the so-called energy release rate for brittle elastic materials which is the energy required for crack propagation and thus, created the energetic fracture criterion. Fracture mechanic models exist for the description of both sharp and diffusive crack discontinuities. Models describing sharp crack discontinuities include cohesive-zone models or configurational-force-driven models. These, however, suffer in situations with complex crack evolution. In contrast, phase field type diffusive crack approaches are smooth continuum formulations. These avoid the modeling of discontinuities and thus allow a straightforward computation of complex curved crack and fracture phenomena such as crack initiation, crack branching or crack arrest. This work presents the application of a fracture phase field model towards the modeling of crack initiation and growth in rubbery and glassy polymers at finite thermo-viscoelastic deformations. Due to their molecular structure, polymeric materials show a wide range of both, mechanical material behavior as well as fracture behavior. Rubbery polymers show highly nonlinear elasticity, characterized by the typical S-shaped uniaxial nominal stress-stretch relation. The origin of the characteristic of rubber to undergo large elastic deformations, is the ability of the coiled and entangled polymer chains to elongate and disentangle under tensile stress, such that the macromolecules align in the direction of the applied force. The complex three-dimensional structure of rubbery polymers consists of chemically crosslinked and entangled macromolecules. These take up compact, random configurations, which lead to complex viscoelastic material behavior. Thermoelastic polymers and elastomers show rate dependent material behavior. During slow deformation, the molecular segments can easily rotate and realign. Thus, the entanglements contribute little to the stiffness and the material deforms almost completely elastically. However, with increasing deformation rate, the transformations of the molecular segments can no longer keep up with the rate of defomation. Hence, the stiffness of the material increases. Macroscopic fracture of rubbery polymers is a result of the failure of the molecular network. Crack propagation takes place when molecular chains whose crosslinks lie on opposite sides of the crack plane are broken. These considerations resulted in the definition of a micromechanically motivated energy release rate, necessary for crack propagation. Crack growth in rubbery polymers is rarely brittle, but mostly a gradual tearing of the material under constant energy consumption, which strongly depends on the velocity of the crack tip. Reasons for this are dissipative effects in both the bulk material and the process zone. An increase in temperature results in an increasing polymer molecule mobility, a decrease of dissipative effects and thus a decrease of energy release rate. Amorphous glassy polymers exhibit a small range of linear elastic deformation. The strength is limited by brittle fracture, cold drawing, shear yielding or crazing. Cold drawing is characterized by a small range of linear elastic strains up to the yield point, followed by a large amount of plastic deformation during which, the stress remains almost constant. Macroscopically a stable neck spreads over the object in question within which the molecules are stretched and align in the direction of the applied force. Crazing is also termed dilatational normal stress yielding and is a plastic deformation mechanism. Crazes consist of dense arrays of fibrils separated by voids. They can grow in width and length until the fibrils break down, which eventually leads to structural failure. Shear yielding and crazing are not completely independent, nor do they exclude each other. Changing the temperature or the rate of deformation and thus modifying the mobility and reaction of the molecules, causes a change of yield stress and brittle fracture stress. Thus a transition from ductile to brittle material response can take place.